Source code for skrf.calibration.calibration

"""
.. module:: skrf.calibration.calibration

================================================================
calibration (:mod:`skrf.calibration.calibration`)
================================================================


This module  provides objects for VNA calibration. Specific algorithms
inherit from the common base class  :class:`Calibration`.

Base Class
----------

.. autosummary::
   :toctree: generated/

   Calibration

One-port
--------

.. autosummary::
   :toctree: generated/

   OnePort
   SDDL
   SDDLWeikle
   PHN

Two-port
--------

.. autosummary::
   :toctree: generated/

   TwelveTerm
   SOLT
   EightTerm
   UnknownThru
   LRM
   LRRM
   MRC
   TRL
   MultilineTRL
   NISTMultilineTRL
   TUGMultilineTRL
   SixteenTerm
   LMR16
   Normalization

Multi-port
--------

.. autosummary::
   :toctree: generated/

   MultiportCal
   MultiportSOLT

Three Receiver (1.5 port)
-------------------------

.. autosummary::
   :toctree: generated/

   TwoPortOnePath
   EnhancedResponse


Generic Methods
---------------
.. autosummary::
   :toctree: generated/

   terminate
   unterminate
   determine_line

PNA interaction
---------------
.. autosummary::
   :toctree: generated/

   convert_skrfcoefs_2_pna
   convert_pnacoefs_2_skrf

"""

import json
import warnings
from collections import OrderedDict, defaultdict
from copy import copy
from itertools import combinations
from numbers import Number
from textwrap import dedent
from warnings import warn

import numpy as npy
from numpy import angle, einsum, exp, imag, invert, linalg, ones, poly1d, real, sqrt, zeros
from numpy.linalg import det
from scipy.optimize import least_squares

from .. import __version__ as skrf__version__
from .. import util
from ..io.touchstone import read_zipped_touchstones
from ..mathFunctions import ALMOST_ZERO, cross_ratio, find_closest, find_correct_sign, rand_c, sqrt_phase_unwrap
from ..network import (
    Network,
    average,
    connect,
    renormalize_s,
    s2t,
    s2z,
    subnetwork,
    t2s,
    two_port_reflect,
    z2s,
    zipfile,
)
from ..networkSet import NetworkSet

ComplexArray = npy.typing.NDArray[complex]

global coefs_list_12term
coefs_list_12term =[
    'forward directivity',
    'forward source match',
    'forward reflection tracking',
    'forward transmission tracking',
    'forward load match',
    'forward isolation',
    'reverse directivity',
    'reverse load match',
    'reverse reflection tracking',
    'reverse transmission tracking',
    'reverse source match',
    'reverse isolation'
    ]



global coefs_list_8term
"""
There are various notations used for this same model. Given that all
measurements have been unterminated properly the error box model holds
and the following equalities hold:

k = e10/e23    # in s-param
k = alpha/beta # in mark's notation
beta/alpha *1/Err = 1/(e10e32)  # marks -> rytting notation
"""
coefs_list_8term = [
    'forward directivity',
    'forward source match',
    'forward reflection tracking',
    'reverse directivity',
    'reverse source match',
    'reverse reflection tracking',
    'forward switch term',
    'reverse switch term',
    'k',
    'forward isolation',
    'reverse isolation'
    ]
global coefs_list_3term
coefs_list_3term = [
    'directivity',
    'source match',
    'reflection tracking',
    ]


[docs] class Calibration: """ Base class for all Calibration objects. This class implements the common mechanisms for all calibration algorithms. Specific calibration algorithms should inherit this class and override the methods: * :func:`Calibration.run` * :func:`Calibration.apply_cal` * :func:`Calibration.embed` (optional) The family of properties prefixed `coefs` and `coefs..ntwks` returns error coefficients. If the property coefs is accessed and empty, then :func:`Calibration.run` is called. """ family = ''
[docs] def __init__(self, measured, ideals, sloppy_input=False, is_reciprocal=True,name=None, self_calibration=False,*args, **kwargs): r""" Calibration initializer. Notes ----- About the order of supplied standards, If the measured and ideals parameters are lists of Networks and `sloppy_input=False`, then their elements must align. However, if the measured and ideals are dictionaries, or `sloppy_input=True`, then we will try to align them for you based on the names of the networks (see `func:`align_measured_ideals`). You do not want to use this `sloppy_input` feature if the calibration depends on the standard order (like TRL). Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use `sloppy_input`) sloppy_input : Boolean. Allows ideals and measured lists to be 'aligned' based on the network names. is_reciprocal : Boolean enables the reciprocity assumption on the calculation of the error_network, which is only relevant for one-port calibrations. name: string the name of this calibration instance, like 'waveguide cal' this is just for convenience [None]. self_calibration: Boolean True if there are less ideals than measurements. Used in self-calibration such as LMR, LRRM, where some of the standards can be unknown. \*args, \*\*kwargs : key-word arguments stored in self.kwargs, which may be used by sub-classes most likely in `run`. """ # allow them to pass di # lets make an ideal flush thru for them : if hasattr(measured, 'keys'): measured = measured.values() if not sloppy_input: warn('dictionary passed, sloppy_input automatically activated', stacklevel=2) sloppy_input = True if hasattr(ideals, 'keys'): ideals = ideals.values() if not sloppy_input: warn('dictionary passed, sloppy_input automatically activated', stacklevel=2) sloppy_input = True # fill measured and ideals with copied lists of input self.measured = [ntwk.copy() for ntwk in measured] self.ideals = [ntwk.copy() for ntwk in ideals] self.sloppy_input=sloppy_input if sloppy_input: self.measured, self.ideals = \ align_measured_ideals(self.measured, self.ideals) self.self_calibration = self_calibration if not self_calibration and len(self.measured) != len(self.ideals): raise(IndexError(dedent( """ The length of measured and ideals lists are different. Number of ideals must equal the number of measured. If you are using `sloppy_input` ensure the names are uniquely alignable. """ ))) # ensure all the measured Networks' frequency's are the same for measure in self.measured: if self.measured[0].frequency != measure.frequency: raise(ValueError('measured Networks dont have matching frequencies.')) # ensure that all ideals have same frequency of the measured # if not, then attempt to interpolate for k in list(range(len(self.ideals))): if self.ideals[k].frequency != self.measured[0].frequency: print(dedent( f"""Warning: Frequency information doesn't match on ideals[{k}], attempting to interpolate the ideal[{k}] Network ..""")) try: # try to resample our ideals network to match # the measurement frequency self.ideals[k].interpolate_self(\ self.measured[0].frequency) print('Success') except Exception as err: raise(IndexError(f'Failed to interpolate. Check frequency of ideals[{k}].')) from err # passed to calibration algorithm in run() self.kwargs = kwargs self.name = name self.is_reciprocal = is_reciprocal # initialized internal properties to None self._residual_ntwks = None self._caled_ntwks =None self._caled_ntwk_sets = None
def __str__(self): if self.name is None: name = '' else: name = self.name if 'fromcoefs' in self.family.lower(): output = f"{self.family} Calibration: '{name}', {self.frequency}" else: output = f"{self.family} Calibration: '{name}', {self.frequency}, {len(self.measured)}-standards" return output def __repr__(self): return self.__str__()
[docs] def run(self): """ Run the calibration algorithm. """ raise NotImplementedError('The Subclass must implement this')
[docs] def apply_cal(self, ntwk): """ Apply correction to a Network. """ raise NotImplementedError('The Subclass must implement this')
[docs] def apply_cal_to_list(self, ntwk_list): """ Apply correction to list or dict of Networks. """ if hasattr(ntwk_list, 'keys'): return {k: self.apply_cal(nw) for k, nw in ntwk_list.items()} else: return [self.apply_cal(k) for k in ntwk_list]
[docs] def apply_cal_to_all_in_dir(self, *args, **kwargs): """ Apply correction to all touchstone files in a given directory. See `skrf.io.general.read_all_networks`. """ from ..io.general import read_all_networks ntwkDict = read_all_networks(*args, **kwargs) return self.apply_cal_to_list(ntwkDict)
[docs] def apply_cal_to_network_set(self, ntwk_set): """ Apply correction to a NetworkSet. """ cal_ns = NetworkSet([self.apply_cal(ntwk) for ntwk in ntwk_set]) if hasattr(ntwk_set, 'name'): cal_ns.name = ntwk_set.name return cal_ns
[docs] def embed(self,ntwk): """ Embed an ideal response in the estimated error network[s] """ raise NotImplementedError('The Subclass must implement this')
[docs] def pop(self,std=-1): """ Remove and return tuple of (ideal, measured) at index. Parameters ---------- std : int or str the integer of calibration standard to remove, or the name of the ideal or measured calibration standard to remove. Returns ------- ideal,measured : tuple of skrf.Networks the ideal and measured networks which were popped out of the calibration """ if isinstance(std, str): for idx,ideal in enumerate(self.ideals): if std == ideal.name: std = idx if isinstance(std, str): for idx,measured in enumerate(self.measured): if std == measured.name: std = idx if isinstance(std, str): raise (ValueError('standard %s not found in ideals'%std)) return (self.ideals.pop(std), self.measured.pop(std))
[docs] def remove_and_cal(self, std): """ Remove a cal standard and correct it, returning correct and ideal. This requires requires overdetermination. Useful in troubleshooting a calibration in which one standard is junk, but you dont know which. Parameters ---------- std : int or str the integer of calibration standard to remove, or the name of the ideal or measured calibration standard to remove. Returns ------- ideal,corrected : tuple of skrf.Networks the ideal and corrected networks which were removed out of the calibration """ measured, ideals = copy(self.measured), copy(self.ideals) i,m = self.pop(std) self.run() c = self.apply_cal(m) self.measured = measured self.ideals = ideals self.run() return c,i
[docs] @classmethod def from_coefs_ntwks(cls, coefs_ntwks, **kwargs): """ Create a calibration from its error coefficients. Parameters ---------- coefs_ntwks : dict of Networks objects error coefficients for the calibration See Also -------- Calibration.from_coefs """ # assigning this measured network is a hack so that # * `calibration.frequency` property evaluates correctly # * TRL.__init__() will not throw an error if not hasattr(coefs_ntwks,'keys'): # maybe they passed a list? lets try and make a dict from it coefs_ntwks = NetworkSet(coefs_ntwks).to_dict() coefs = NetworkSet(coefs_ntwks).to_s_dict() frequency = list(coefs_ntwks.values())[0].frequency cal= cls.from_coefs(frequency=frequency, coefs=coefs, **kwargs) return cal
[docs] @classmethod def from_coefs(cls, frequency, coefs, **kwargs): """ Create a calibration from its error coefficients. Parameters ---------- frequency : :class:`~skrf.frequency.Frequency` frequency info, (duh) coefs : dict of numpy arrays error coefficients for the calibration See Also -------- Calibration.from_coefs_ntwks """ # assigning this measured network is a hack so that # * `calibration.frequency` property evaluates correctly # * TRL.__init__() will not throw an error n = Network(frequency = frequency, s = rand_c(frequency.npoints,2,2)) measured = [n,n,n] if 'forward switch term' in coefs: switch_terms = (Network(frequency = frequency, s=coefs['forward switch term']), Network(frequency = frequency, s=coefs['reverse switch term'])) kwargs['switch_terms'] = switch_terms cal = cls(measured, measured, **kwargs) cal.coefs = coefs cal.family += '(fromCoefs)' return cal
@property def frequency(self): """ :class:`~skrf.frequency.Frequency` object of the calibration. """ return self.measured[0].frequency.copy() @property def nstandards(self): """ Number of ideal/measurement pairs in calibration. """ if len(self.ideals) != len(self.measured): warn("number of ideals and measured don't agree", stacklevel=2) return len(self.ideals) @property def coefs(self): """ Dictionary or error coefficients in form of numpy arrays. The keys of this will be different depending on the Calibration Model. This dictionary should be populated when the `run()` function is called. Notes ----- when setting this, property, the numpy arrays are flattened. this makes accessing the coefs more concise in the code. See Also -------- coefs_3term coefs_8term coefs_12term coefs_ntwks """ try: return self._coefs except(AttributeError): self.run() return self._coefs @coefs.setter def coefs(self,d): """ """ for k in d: d[k] = d[k].flatten() self._coefs = d
[docs] def update_coefs(self, d): """ Update current dict of error coefficients. """ for k in d: d[k] = d[k].flatten() self._coefs.update(d)
@property def output_from_run(self): """ Return any output from the :func:`run`. This just returns whats in _output_from_run, and calls :func:`run` if that attribute is non-existent. finally, returns None if run() is called, and nothing is in _output_from_run. """ try: return self._output_from_run except(AttributeError): # maybe i havent run yet self.run() try: return self._output_from_run except(AttributeError): # i did run and there is no output_from_run return None @property def coefs_ntwks(self): """ Dictionary of error coefficients in form of Network objects. See Also -------- coefs_3term_ntwks coefs_12term_ntwks coefs_8term_ntwks """ ns = NetworkSet.from_s_dict(d=self.coefs, frequency=self.frequency) return ns.to_dict() @property def coefs_3term(self): """ Dictionary of error coefficients for One-port Error model. Contains the keys: * directivity * source match * reflection tracking' """ return {k: self.coefs.get(k) for k in [\ 'directivity', 'source match', 'reflection tracking', ]} @property def coefs_3term_ntwks(self): """ Dictionary of error coefficients in form of Network objects. """ ns = NetworkSet.from_s_dict(d=self.coefs_3term, frequency=self.frequency) return ns.to_dict() @property def normalized_directivity(self): """ Directivity normalized to the reflection tracking. """ try: return self.coefs_ntwks['directivity']/\ self.coefs_ntwks['reflection tracking'] except Exception: pass try: out = {} for direction in ['forward','reverse']: out[direction + ' normalized directivity'] =\ self.coefs_ntwks[direction + ' directivity']/\ self.coefs_ntwks[direction + ' reflection tracking'] return out except Exception as err: raise ValueError('cant find error coefs') from err @property def coefs_8term(self): """ Dictionary of error coefficients for 8-term (Error-box) Model. Contains the keys: * forward directivity * forward source match * forward reflection tracking * reverse directivity * reverse source match * reverse reflection tracking * forward switch term * reverse switch term * k * forward isolation * reverse isolation Notes ----- If this calibration uses the 12-term model, then :func:`convert_12term_2_8term` is called. See [1]_ References ---------- .. [1] "Formulations of the Basic Vector Network Analyzer Error Model including Switch Terms" by Roger B. Marks """ d = self.coefs if all([k in d.keys() for k in coefs_list_3term]): raise ValueError("Can't convert one port error terms to two port error terms") # Check if we have all 12-term keys and convert to 8-term if we do. if all([k in d.keys() for k in coefs_list_12term]): return convert_12term_2_8term(d) return d @property def coefs_8term_ntwks(self): """ Dictionary of error coefficients in form of Network objects. """ ns = NetworkSet.from_s_dict(d=self.coefs_8term, frequency=self.frequency) return ns.to_dict() @property def coefs_12term(self): """ Dictionary of error coefficients for 12-term Model. Contains the keys: * forward directivity * forward source match * forward reflection tracking * forward transmission tracking * forward load match * forward isolation * reverse directivity * reverse load match * reverse reflection tracking * reverse transmission tracking * reverse source match * reverse isolation Notes ----- If this calibration uses the 8-term model, then :func:`convert_8term_2_12term` is called. See [1]_ References ---------- .. [1] "Formulations of the Basic Vector Network Analyzer Error Model including Switch Terms" by Roger B. Marks """ d = self.coefs if all([k in d.keys() for k in coefs_list_3term]): raise ValueError("Can't convert one port error terms to two port error terms") # Check if we have all 12-term keys and return the coefs if we do if all([k in d.keys() for k in coefs_list_12term]): return d return convert_8term_2_12term(d) @property def coefs_12term_ntwks(self): """ Dictionary or error coefficients in form of Network objects. """ ns = NetworkSet.from_s_dict(d=self.coefs_12term, frequency=self.frequency) return ns.to_dict() @property def verify_12term(self): """ """ Edf = self.coefs_12term['forward directivity'] Esf = self.coefs_12term['forward source match'] Erf = self.coefs_12term['forward reflection tracking'] Etf = self.coefs_12term['forward transmission tracking'] Elf = self.coefs_12term['forward load match'] Edr = self.coefs_12term['reverse directivity'] Elr = self.coefs_12term['reverse load match'] Err = self.coefs_12term['reverse reflection tracking'] Etr = self.coefs_12term['reverse transmission tracking'] Esr = self.coefs_12term['reverse source match'] return Etf*Etr - (Err + Edr*(Elf - Esr))*(Erf + Edf *(Elr - Esf)) @property def verify_12term_ntwk(self): return Network(s= self.verify_12term, frequency = self.frequency) @property def residual_ntwks(self): """ Dictionary of residual Networks. These residuals are complex differences between the ideal standards and their corresponding corrected measurements. """ return [caled - ideal for (ideal, caled) in zip(self.ideals, self.caled_ntwks)] @property def residual_ntwk_sets(self): """ Returns a NetworkSet for each `residual_ntwk`, grouped by their names. """ residual_sets={} std_names = list(set([k.name for k in self.ideals])) for std_name in std_names: residual_sets[std_name] = NetworkSet( [k for k in self.residual_ntwks if k.name.startswith(std_name)]) return residual_sets @property def caled_ntwks(self): """ List of the corrected calibration standards. """ return self.apply_cal_to_list(self.measured) @property def caled_ntwk_sets(self): """ Return a NetworkSet for each `caled_ntwk`, grouped by their names. """ caled_sets={} std_names = list(set([k.name for k in self.ideals ])) for std_name in std_names: caled_sets[std_name] = NetworkSet( [k for k in self.caled_ntwks if k.name.startswith(std_name)]) return caled_sets @property def biased_error(self) -> NetworkSet: """ Estimate of biased error for overdetermined calibration with multiple connections of each standard. Returns ------- biased_error : skrf.Network Network with s_mag is proportional to the biased error Notes ----- Mathematically, this is .. math:: mean_s(|mean_c(r)|) Where: * r: complex residual errors * mean_c: complex mean taken across connection * mean_s: complex mean taken across standard See Also -------- biased_error unbiased_error total_error """ rns = self.residual_ntwk_sets out = NetworkSet([rns[k].mean_s for k in rns]).mean_s_mag out.name = 'Biased Error' return out @property def unbiased_error(self) -> NetworkSet: """ Estimate of unbiased error for overdetermined calibration with multiple connections of each standard. Returns ------- unbiased_error : skrf.Network Network with s_mag is proportional to the unbiased error Notes ----- Mathematically, this is mean_s(std_c(r)) where: * r : complex residual errors * std_c : standard deviation taken across connections * mean_s : complex mean taken across standards See Also -------- biased_error unbiased_error total_error """ rns = self.residual_ntwk_sets out = NetworkSet([rns[k].std_s for k in rns]).mean_s_mag out.name = 'Unbiased Error' return out @property def total_error(self) -> NetworkSet: """ Estimate of total error for overdetermined calibration with multiple connections of each standard.This is the combined effects of both biased and un-biased errors. Returns ------- total_error : skrf.Network Network with s_mag is proportional to the total error Notes ----- Mathematically, this is std_cs(r) where: * r : complex residual errors * std_cs : standard deviation taken across connections and standards See Also -------- biased_error unbiased_error total_error """ out = NetworkSet(self.residual_ntwks).mean_s_mag out.name = 'Total Error' return out @property def error_ntwk(self): """ The calculated error Network or Network[s]. This will return a single two-port network for a one-port cal. For a 2-port calibration this will return networks for forward and reverse excitation. However, these are not sufficient to use for embedding, see the :func:`embed` function for that. """ return error_dict_2_network( self.coefs, frequency = self.frequency, is_reciprocal= self.is_reciprocal)
[docs] def write(self, file=None, *args, **kwargs): r""" Write the Calibration to disk using :func:`~skrf.io.general.write`. Parameters ---------- file : str or file-object filename or a file-object. If left as None then the filename will be set to Calibration.name, if its not None. If both are None, ValueError is raised. \*args, \*\*kwargs : arguments and keyword arguments passed through to :func:`~skrf.io.general.write` Notes ----- If the self.name is not None and file is can left as None and the resultant file will have the `.ntwk` extension appended to the filename. Examples -------- >>> cal.name = 'my_cal' >>> cal.write() See Also -------- skrf.io.general.write skrf.io.general.read """ # this import is delayed until here because of a circular dependency from ..io.general import write if file is None: if self.name is None: raise (ValueError('No filename given. You must provide a filename, or set the name attribute')) file = self.name write(file,self, *args, **kwargs)
[docs] @util.axes_kwarg def plot_calibration_errors(self, *args, ax: util.Axes = None, **kwargs): """ Plot biased, unbiased and total error in dB scaled. See Also -------- biased_error unbiased_error total_error """ port_list = self.biased_error.port_tuples for m,n in port_list: ax.set_title(f"S{self.biased_error.ntwk_set[0]._fmt_trace_name(m,n)}") self.unbiased_error.plot_s_db(m,n,**kwargs) self.biased_error.plot_s_db(m,n,**kwargs) self.total_error.plot_s_db(m,n,**kwargs) ax.set_ylim(-100,0)
[docs] def plot_caled_ntwks(self, attr: str = 's_smith', show_legend: bool = False, **kwargs): r""" Plot corrected calibration standards. Given that the calibration is overdetermined, this may be used as a heuristic verification of calibration quality. Parameters ---------- attr : str Network property to plot, ie 's_db', 's_smith', etc. Default is 's_smith' show_legend : bool, optional draw a legend or not. Default is False. \*\*kwargs : kwargs passed to the plot method of Network """ ns = NetworkSet(self.caled_ntwks) fig, axes = util.subplots(figsize=(8,8)) kwargs.update({'show_legend':show_legend}) for ax ,(m, n) in zip(axes, ns[0].port_tuples): ax.set_title(f"S{ns.ntwk_set[0]._fmt_trace_name(m, n)}") ns.__getattribute__('plot_'+attr)(m, n, **kwargs) fig.tight_layout()
[docs] def plot_residuals(self, attr: str = 's_db', **kwargs): r""" Plot residual networks. Given that the calibration is overdetermined, this may be used as a metric of the calibration's *goodness of fit* Parameters ---------- attr : str, optional. Network property to plot, ie 's_db', 's_smith', etc. Default is 's_db' \*\*kwargs : kwargs passed to the plot method of Network See Also -------- Calibration.residual_networks """ NetworkSet(self.residual_ntwks).__getattribute__('plot_'+attr)(**kwargs)
[docs] class OnePort(Calibration): r""" Standard algorithm for a one port calibration. Solves the linear set of equations: .. math:: e_{11}\mathbf{i_1m_1}-\Delta e\,\mathbf{i_1}+e_{00}=\mathbf{m_1} e_{11}\mathbf{i_2m_2}-\Delta e\,\mathbf{i_2}+e_{00}=\mathbf{m_2} e_{11}\mathbf{i_3m_3}-\Delta e\,\mathbf{i_3}+e_{00}=\mathbf{m_3} ... Where **m**'s and **i**'s are the measured and ideal reflection coefficients, respectively. If more than three standards are supplied, then a least square algorithm is applied. See [1]_ and [2]_ References ---------- .. [1] http://na.tm.agilent.com/vnahelp/tip20.html .. [2] Bauer, R.F., Jr.; Penfield, Paul, "De-Embedding and Unterminating," Microwave Theory and Techniques, IEEE Transactions on , vol.22, no.3, pp.282,288, Mar 1974 doi: 10.1109/TMTT.1974.1128212 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1128212&isnumber=25001 """ family = 'OnePort'
[docs] def __init__(self, measured, ideals,*args, **kwargs): """ One Port initializer. If more than three standards are supplied then a least square algorithm is applied. Notes ----- See func:`Calibration.__init__` for details about automatic standards alignment (aka `sloppy_input`) Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use `sloppy_input`) args, kwargs : passed to func:`Calibration.__init__` Notes ----- This uses numpy.linalg.lstsq() for least squares calculation See Also -------- Calibration.__init__ """ Calibration.__init__(self, measured, ideals, *args, **kwargs)
[docs] def run(self): """ Run the calibration algorithm. """ numStds = self.nstandards numCoefs=3 mList = [self.measured[k].s.reshape((-1,1)) for k in range(numStds)] iList = [self.ideals[k].s.reshape((-1,1)) for k in range(numStds)] if not all([n.number_of_ports==1 for n in self.ideals]): raise RuntimeError(f'ideals for {self.family} should be 1-port Networks') if not all([n.number_of_ports==1 for n in self.measured]): raise RuntimeError(f'measured networks for {self.family} should be 1-port Networks') # ASSERT: mList and aList are now kx1x1 matrices, where k in frequency fLength = len(mList[0]) #initialize outputs abc = npy.zeros((fLength,numCoefs),dtype=complex) residuals = npy.zeros((fLength,\ npy.sign(numStds-numCoefs)),dtype=complex) parameter_variance = npy.zeros((fLength, 3,3),dtype=complex) measurement_variance = npy.zeros((fLength, 1),dtype=complex) # loop through frequencies and form m, a vectors and # the matrix M. where M = i1, 1, i1*m1 # i2, 1, i2*m2 # ...etc for f in list(range(fLength)): #create m, i, and 1 vectors one = npy.ones(shape=(numStds,1)) m = npy.array([ mList[k][f] for k in range(numStds)]).reshape(-1,1)# m-vector at f i = npy.array([ iList[k][f] for k in range(numStds)]).reshape(-1,1)# i-vector at f # construct the matrix Q = npy.hstack([i, one, i*m]) # calculate least squares abcTmp, residualsTmp = npy.linalg.lstsq(Q,m,rcond=None)[0:2] if numStds > 3: measurement_variance[f,:]= residualsTmp/(numStds-numCoefs) parameter_variance[f,:] = \ abs(measurement_variance[f,:])*\ npy.linalg.inv(npy.dot(Q.T,Q)) abc[f,:] = abcTmp.flatten() try: residuals[f,:] = residualsTmp except ValueError as err: raise(ValueError('matrix has singular values. ensure standards are far enough away on smith chart'))\ from err # convert the abc vector to standard error coefficients a,b,c = abc[:,0], abc[:,1],abc[:,2] e01e10 = a+b*c e00 = b e11 = c self._coefs = {\ 'directivity':e00,\ 'reflection tracking':e01e10, \ 'source match':e11\ } # output is a dictionary of information self._output_from_run = { 'residuals':residuals, 'parameter variance':parameter_variance } return None
[docs] def apply_cal(self, ntwk): er_ntwk = Network(frequency = self.frequency, name=ntwk.name) tracking = self.coefs['reflection tracking'] s12 = npy.sqrt(tracking) s21 = s12 s11 = self.coefs['directivity'] s22 = self.coefs['source match'] er_ntwk.s = npy.array([[s11, s12],[s21,s22]]).transpose(2,0,1) return er_ntwk.inv**ntwk
[docs] def embed(self,ntwk): embedded = self.error_ntwk ** ntwk embedded.name = ntwk.name return embedded
[docs] class SDDLWeikle(OnePort): """ Short-Delay-Delay-Load (Oneport Calibration). One-port self-calibration, which contains a short, a load, and two delays shorts of unity magnitude but unknown phase. Originally designed to be resistant to flange misalignment, see [1]_. References ---------- .. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment," Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006. """ family = 'SDDL'
[docs] def __init__(self, measured, ideals, *args, **kwargs): """ Short-Delay-Delay-Load initializer. Measured and ideal networks must be in the order: * short * delay short1 * delay short2 * load Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use sloppy_input args, kwargs : passed to func:`Calibration.__init__` See Also -------- Calibration.__init__ """ if (len(measured) != 4) or (len(ideals)) != 4: raise IndexError('Incorrect number of standards.') Calibration.__init__(self, measured = measured, ideals =ideals, **kwargs)
[docs] def run(self): #measured reflection coefficients w_s = self.measured[0].s.flatten() # short w_1 = self.measured[1].s.flatten() # delay short 1 w_2 = self.measured[2].s.flatten() # delay short 2 w_l = self.measured[3].s.flatten() # load # ideal response of reflection coefficients G_l = self.ideals[3].s.flatten() # gamma_load # handle singularities G_l[G_l ==0] = ALMOST_ZERO w_1p = w_1 - w_s # between (9) and (10) w_2p = w_2 - w_s w_lp = w_l - w_s ## NOTE: the published equation has an incorrect sign on this argument ## perhaps because they assume arg to measure clockwise angle?? alpha = exp(1j*2*angle(1./w_2p - 1./w_1p)) # (17) p = alpha/( 1./w_1p - alpha/w_1p.conj() - (1.+G_l)/(G_l*w_lp )) # (22) q = p/(alpha* G_l) #(23) (put in terms of p) Bp_re = -1*((1 + (imag(p+q)/real(q-p)) * (imag(q-p)/real(p+q)))/\ (1 + (imag(p+q)/real(q-p))**2)) * real(p+q) # (25) Bp_im = imag(q+p)/real(q-p) * Bp_re #(24) Bp = Bp_re + Bp_im*1j B = Bp + w_s #(10) C = Bp * (1./w_1p - alpha/w_1p.conj()) + alpha * Bp/Bp.conj() #(20) A = B - w_s + w_s*C #(6) # convert the abc vector to standard error coefficients e00 = B e11 = -C e01e10 = A + e00*e11 self._coefs = {\ 'directivity':e00,\ 'reflection tracking':e01e10, \ 'source match':e11\ }
[docs] class SDDL(OnePort): """ Short-Delay-Delay-Load (Oneport Calibration). One-port self-calibration, which contains a short, a load, and two delays shorts of unity magnitude but unknown phase. Originally designed to be resistant to flange misalignment, see [1]_. References ---------- .. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment," Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006. """ family = 'SDDL'
[docs] def __init__(self, measured, ideals, *args, **kwargs): """ Short-Delay-Delay-Load initializer. Measured and ideal networks must be in the order: [ Short, Delay short1, Delay short2, Load] The ideal delay shorts can be set to `None`, as they are determined during the calibration. Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use sloppy_input args, kwargs : passed to func:`Calibration.__init__` See Also -------- Calibration.__init__ """ # if they pass None for the ideal responses for delay shorts # then we will copy the short standard in their place. this is # only to avoid throwing an error when initializing the cal, the # values are not used. if ideals[1] is None: ideals[1] = ideals[0].copy() if ideals[2] is None: ideals[2] = ideals[0].copy() if (len(measured) != 4) or (len(ideals)) != 4: raise IndexError('Incorrect number of standards.') Calibration.__init__(self, measured = measured, ideals =ideals, **kwargs)
[docs] def run(self): #measured impedances d = s2z(self.measured[0].s,1) # short a = s2z(self.measured[1].s,1) # delay short 1 b = s2z(self.measured[2].s,1) # delay short 2 c = s2z(self.measured[3].s,1) # load l = s2z(self.ideals[-1].s,1) # ideal def of load cr_alpha = cross_ratio(b,a,c,d) cr_beta = cross_ratio(a,b,c,d) alpha = imag(cr_alpha)/real(cr_alpha/l) beta = imag(cr_beta)/real(cr_beta/l) self.ideals[1].s = z2s(alpha*1j,1) self.ideals[2].s = z2s(beta*1j,1) OnePort.run(self)
[docs] class PHN(OnePort): """ Pair of Half Knowns (One Port self-calibration). """ family = 'PHN'
[docs] def __init__(self, measured, ideals, *args, **kwargs): """ """ if (len(measured) != 4) or (len(ideals)) != 4: raise IndexError('Incorrect number of standards.') Calibration.__init__(self, measured = measured, ideals =ideals, **kwargs)
[docs] def run(self): # ideals (in impedance) a = s2z(self.ideals[0].s,1).flatten() # half known b = s2z(self.ideals[1].s,1).flatten() # half known c = s2z(self.ideals[2].s,1).flatten() # fully known d = s2z(self.ideals[3].s,1).flatten() # fully known # measured (in impedances) a_ = s2z(self.measured[0].s,1).flatten() # half known b_ = s2z(self.measured[1].s,1).flatten() # half known c_ = s2z(self.measured[2].s,1).flatten() # fully known d_ = s2z(self.measured[3].s,1).flatten() # fully known z = cross_ratio(a_,b_,c_,d_) # intermediate variables e = c-d-c*z f = d-c-d*z g = c*d*z A = -real(f*z.conj()) B = 1j*imag( f*e.conj() + g.conj()*z) C = real( g*e.conj()) npts = len(A) b1,b2 = zeros(npts, dtype=complex), zeros(npts, dtype=complex) for k in range(npts): p = poly1d([A[k],B[k],C[k]]) b1[k],b2[k] = p.r a1 = -(f*b1 + g)/(z*b1 + e) a2 = -(f*b2 + g)/(z*b2 + e) # temporarily translate into s-parameters so make the root-choice # choosing a root in impedance doesnt generally work for typical # calibration standards b1_s = z2s(b1.reshape(-1,1,1),1) b2_s = z2s(b2.reshape(-1,1,1),1) a1_s = z2s(a1.reshape(-1,1,1),1) a2_s = z2s(a2.reshape(-1,1,1),1) b_guess = z2s(b.reshape(-1,1,1),1) a_guess = z2s(a.reshape(-1,1,1),1) distance1 = abs(a1_s - a_guess) + abs(b1_s - b_guess) distance2 = abs(a2_s - a_guess) + abs(b2_s - b_guess) b_found = npy.where(distance1<distance2, b1, b2) a_found = npy.where(distance1<distance2, a1, a2) self.ideals[0].s = z2s(a_found.reshape(-1,1,1),1) self.ideals[1].s = z2s(b_found.reshape(-1,1,1),1) OnePort.run(self)
## Two Ports
[docs] class TwelveTerm(Calibration): """ 12-term, full two-port calibration. `TwelveTerm` is the traditional, fully determined, two-port calibration originally developed in [1]_. `TwelveTerm` can accept any number of reflect and transmissive standards, as well as arbitrary (non-flush) transmissive standards. * If more than 3 reflect standards are provided, a least-squares solution is implemented for the one-port stage of the calibration. * If more than 1 transmissive standard is given the `load match`, and `transmission tracking` terms are calculated multiple times and averaged. References ------------ .. [1] "Calibration Process of Automatic Network Analyzer Systems" by Stig Rehnmark """ family = 'TwelveTerm'
[docs] def __init__(self, measured, ideals, n_thrus=None, trans_thres=-40, *args, **kwargs): """ TwelveTerm initializer. Use the `n_thrus` argument to explicitly define the number of transmissive standards. Otherwise, if `n_thrus=None`, then we will try and guess which are transmissive, by comparing the mean :math:`|s21|` and :math:`|s12|` responses (in dB) to `trans_thres`. Notes ------ See func:`Calibration.__init__` for details about automatic standards alignment (aka `sloppy_input`). Parameters ------------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use sloppy_input n_thrus : int Number of transmissive standards. If None, we will try and guess for you by comparing measure transmission to trans_thres, trans_thres: float The minimum transmission magnitude (in dB) that is the threshold for categorizing a transmissive standard. Compared to the measured s21,s12 meaned over frequency Only use if n_thrus=None. isolation : :class:`~skrf.network.Network` object Measurement with loads on both ports with a perfect isolation between the ports. Used for determining the isolation error terms. If no measurement is given leakage is assumed to be zero. Loads don't need to be same as the one used as a match standard or even have similar reflection coefficients. Reflects can be also used, but accuracy might not be as good. See Also ----------- Calibration.__init__ """ kwargs.update({'measured':measured, 'ideals':ideals}) # note: this will enable sloppy_input and align stds if necessary Calibration.__init__(self, *args, **kwargs) # if they didnt tell us the number of thrus, then lets # heuristically determine it trans_thres_mag = 10 ** (trans_thres / 20) if n_thrus is None: warn('n_thrus is None, guessing which stds are transmissive', stacklevel=2) n_thrus=0 for k in self.ideals: mean_trans = NetworkSet([k.s21, k.s12]).mean_s_mag trans_mag = npy.mean(mean_trans.s_mag.flatten()) # this number is arbitrary but reasonable if trans_mag > trans_thres_mag: n_thrus +=1 if n_thrus ==0: raise ValueError( 'couldnt find a transmissive standard. check your data, or explicitly use `n_thrus` argument' ) self.n_thrus = n_thrus # if they didntly give explicit order, lets try and put the # more transmissive standards last, by sorted measured/ideals # based on mean s21 if self.sloppy_input: trans = [npy.mean(k.s21.s_mag) for k in self.ideals] # see http://stackoverflow.com/questions/6618515/sorting-list-based-on-values-from-another-list # get order of indices of sorted means s21 order = [x for (y,x) in sorted(zip(trans, range(len(trans))),\ key=lambda pair: pair[0])] self.measured = [self.measured[k] for k in order] self.ideals = [self.ideals[k] for k in order]
[docs] def run(self): """ """ n_thrus = self.n_thrus p1_m = [k.s11 for k in self.measured[:-n_thrus]] p2_m = [k.s22 for k in self.measured[:-n_thrus]] p1_i = [k.s11 for k in self.ideals[:-n_thrus]] p2_i = [k.s22 for k in self.ideals[:-n_thrus]] thrus = self.measured[-n_thrus:] ideal_thrus = self.ideals[-n_thrus:] # create one port calibration for reflective standards port1_cal = OnePort(measured = p1_m, ideals = p1_i) port2_cal = OnePort(measured = p2_m, ideals = p2_i) # cal coefficient dictionaries p1_coefs = dict(port1_cal.coefs) p2_coefs = dict(port2_cal.coefs) if self.kwargs.get('isolation',None) is not None: p1_coefs['isolation'] = self.kwargs['isolation'].s21.s.flatten() p2_coefs['isolation'] = self.kwargs['isolation'].s12.s.flatten() else: p1_coefs['isolation'] = npy.zeros(len(self.frequency), dtype=complex) p2_coefs['isolation'] = npy.zeros(len(self.frequency), dtype=complex) # loop thru thrus, and calculate error terms for each one # load match and transmission tracking for ports 1 and 2 lm1, lm2,tt1, tt2 = [],[],[],[] for thru, thru_i in zip(thrus, ideal_thrus): lm1.append(thru_i.inv**port1_cal.apply_cal(thru.s11)) lm2.append(thru_i.flipped().inv**port2_cal.apply_cal(thru.s22)) # forward transmission tracking g = lm1[-1].s d = p1_coefs['source match'].reshape(-1,1,1) e,f,b,h = thru_i.s11.s, thru_i.s22.s,thru_i.s21.s,thru_i.s12.s m = thru.s21.s - p1_coefs['isolation'].reshape(-1,1,1) ac = m*1./b * (1 - (d*e + f*g + b*g*h*d) + (d*e*f*g) ) tt1.append(ac[:]) # reverse transmission tracking thru.flip(),thru_i.flip() # flip thrus to keep same ports as above g = lm2[-1].s d = p2_coefs['source match'].reshape(-1,1,1) e,f,b,h = thru_i.s11.s, thru_i.s22.s,thru_i.s21.s,thru_i.s12.s m = thru.s21.s - p2_coefs['isolation'].reshape(-1,1,1) ac = m*1./b * (1 - (d*e+f*g+b*g*h*d) + d*e*f*g) tt2.append(ac[:]) thru.flip(), thru_i.flip() # flip em back p1_coefs['transmission tracking'] = npy.mean(npy.array(tt1),axis=0).flatten() p2_coefs['transmission tracking'] = npy.mean(npy.array(tt2),axis=0).flatten() p1_coefs['load match'] = NetworkSet(lm1).mean_s.s.flatten() p2_coefs['load match'] = NetworkSet(lm2).mean_s.s.flatten() # update coefs coefs = {} coefs.update({'forward %s'%k: p1_coefs[k] for k in p1_coefs}) coefs.update({'reverse %s'%k: p2_coefs[k] for k in p2_coefs}) eight_term_coefs = convert_12term_2_8term(coefs) coefs.update({l: eight_term_coefs[l] for l in \ ['forward switch term','reverse switch term','k'] }) self._coefs = coefs
[docs] def apply_cal(self,ntwk): """ """ caled = ntwk.copy() s11 = ntwk.s[:,0,0] s12 = ntwk.s[:,0,1] s21 = ntwk.s[:,1,0] s22 = ntwk.s[:,1,1] Edf = self.coefs['forward directivity'] Esf = self.coefs['forward source match'] Erf = self.coefs['forward reflection tracking'] Etf = self.coefs['forward transmission tracking'] Elf = self.coefs['forward load match'] Eif = self.coefs.get('forward isolation',0) Edr = self.coefs['reverse directivity'] Elr = self.coefs['reverse load match'] Err = self.coefs['reverse reflection tracking'] Etr = self.coefs['reverse transmission tracking'] Esr = self.coefs['reverse source match'] Eir = self.coefs.get('reverse isolation',0) D = (1+(s11-Edf)/(Erf)*Esf)*(1+(s22-Edr)/(Err)*Esr) -\ ((s21-Eif)/(Etf))*((s12-Eir)/(Etr))*Elf*Elr caled.s[:,0,0] = \ (((s11-Edf)/(Erf))*(1+(s22-Edr)/(Err)*Esr)-\ Elf*((s21-Eif)/(Etf))*(s12-Eir)/(Etr)) /D caled.s[:,1,1] = \ (((s22-Edr)/(Err))*(1+(s11-Edf)/(Erf)*Esf)-\ Elr*((s21-Eif)/(Etf))*(s12-Eir)/(Etr)) /D caled.s[:,1,0] = \ ( ((s21 -Eif)/(Etf))*(1+((s22-Edr)/(Err))*(Esr-Elf)) )/D caled.s[:,0,1] = \ ( ((s12 -Eir)/(Etr))*(1+((s11-Edf)/(Erf))*(Esf-Elr)) )/D return caled
[docs] def embed(self, ntwk): measured = ntwk.copy() s11 = ntwk.s[:,0,0] s12 = ntwk.s[:,0,1] s21 = ntwk.s[:,1,0] s22 = ntwk.s[:,1,1] det = s11*s22 - s12*s21 Edf = self.coefs['forward directivity'] Esf = self.coefs['forward source match'] Erf = self.coefs['forward reflection tracking'] Etf = self.coefs['forward transmission tracking'] Elf = self.coefs['forward load match'] Eif = self.coefs.get('forward isolation',0) Edr = self.coefs['reverse directivity'] Elr = self.coefs['reverse load match'] Err = self.coefs['reverse reflection tracking'] Etr = self.coefs['reverse transmission tracking'] Esr = self.coefs['reverse source match'] Eir = self.coefs.get('reverse isolation',0) measured = ntwk.copy() D1 = (1 - Esf*s11 - Elf*s22 + Esf*Elf*det) D2 = (1 - Elr*s11 - Esr*s22 + Esr*Elr*det) measured.s[:,0,0] = Edf + Erf * (s11 - Elf*det)/D1 measured.s[:,1,0] = Eif + Etf * s21/D1 measured.s[:,1,1] = Edr + Err * (s22 - Elr*det)/D2 measured.s[:,0,1] = Eir + Etr * s12/D2 return measured
[docs] class SOLT(TwelveTerm): """ Short-Open-Load-Thru, Full two-port calibration. SOLT is the traditional, fully determined, two-port calibration originally developed in [1]_. Although the acronym SOLT implies the use of 4 standards, skrf's algorithm can accept any number of reflect standards, If more than 3 reflect standards are provided a least-squares solution is implemented for the one-port stage of the calibration. Redundant thru measurements can also be used, through the `n_thrus` parameter. See :func:`__init__` References ------------ .. [1] W. Kruppa and K. F. Sodomsky, "An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence)," IEEE Transactions on Microwave Theory and Techniques, vol. 19, no. 1, pp. 122-123, Jan. 1971. See Also --------- TwelveTerm """ family = 'SOLT'
[docs] def __init__(self, measured, ideals, n_thrus=1, *args, **kwargs): """ SOLT initializer. If you arent using `sloppy_input`, then the order of the standards must align. If `n_thrus!=None`, then the thru standard[s] must be last in the list. The `n_thrus` argument can be used to allow multiple measurements of the thru standard. If the ideal element for the thru is set to None, a flush thru is assumed. Notes ----- See func:`Calibration.__init__` for details about automatic standards alignment (aka `sloppy_input`). Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use `sloppy_input`) The thru standard can be None n_thrus : int number of thru measurements isolation : :class:`~skrf.network.Network` object Measurement with loads on both ports. Used for determining the isolation error terms. If no measurement is given isolation is assumed to be zero. See Also -------- TwelveTerm.__init__ """ # see if they passed a None for the thru, and if so lets # make an ideal flush thru for them for k in range(-n_thrus,len(ideals)): if ideals[k] is None: if (n_thrus is None) or (hasattr(ideals, 'keys')) or \ (hasattr(measured, 'keys')): raise ValueError(dedent( """Can't use sloppy_input and have the ideal thru be None. Measured and ideals must be lists, or dont use None for the thru ideal.""")) ideal_thru = measured[0].copy() ideal_thru.s[:,0,0] = 0 ideal_thru.s[:,1,1] = 0 ideal_thru.s[:,1,0] = 1 ideal_thru.s[:,0,1] = 1 ideals[k] = ideal_thru kwargs.update({'measured':measured, 'ideals':ideals, 'n_thrus':n_thrus}) TwelveTerm.__init__(self,*args, **kwargs)
[docs] class TwoPortOnePath(TwelveTerm): """ Two Port One Path Calibration (aka poor man's TwelveTerm). Provides full error correction on a switchless three receiver system, i.e. you can only measure the waves a1,b1,and b2. Given this architecture, the DUT must be flipped and measured twice to be fully corrected. To allow for this, the `apply_cal` method takes a tuple of measurements in the order (forward,reverse), and creates a composite measurement that is correctable. """ family = 'TwoPortOnePath'
[docs] def __init__(self, measured, ideals, n_thrus=None, source_port=1, *args, **kwargs): """ Two Port One Path Calibration initializer. Use the `n_thrus` argument to explicitly define the number of transmissive standards. Otherwise, if `n_thrus=None`, then we will try and guess which are transmissive, by comparing the mean :math: `|s21|` and :math: `|s12|` responses (in dB) to `trans_thres`. Notes ----- See func:`Calibration.__init__` for details about automatic standards alignment (aka `sloppy_input`). Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use sloppy_input n_thrus : int number of thru measurements source_port : [1,2] The port on which the source is active. should be 1 or 2 See Also -------- TwelveTerm.__init__ """ if source_port not in [1, 2]: raise ValueError("Invalid source_port value. Expected 1 or 2.") self.sp = source_port-1 self.rp = 1 if self.sp == 0 else 0 # Make S12 = S21 and S22 = S11 for numerical reasons measured_sym = [m.copy() for m in measured] for m in measured_sym: m.s[:,self.sp, self.rp] = m.s[:,self.rp, self.sp] m.s[:,self.rp, self.rp] = m.s[:,self.sp, self.sp] kwargs.update({'measured':measured_sym, 'ideals':ideals, 'n_thrus':n_thrus}) TwelveTerm.__init__(self,*args, **kwargs)
[docs] def run(self): """ """ # run a full twelve term then just copy all forward error terms # over reverse error terms TwelveTerm.run(self) out_coefs = self.coefs.copy() if self.sp ==0: forward = 'forward' reverse = 'reverse' elif self.sp ==1: forward = 'reverse' reverse = 'forward' else: raise ValueError('source_port is out of range. should be 1 or 2.') for k in self.coefs: if k.startswith(forward): k_out = k.replace(forward,reverse) out_coefs[k_out] = self.coefs[k] eight_term_coefs = convert_12term_2_8term(out_coefs) out_coefs.update({l: eight_term_coefs[l] for l in \ ['forward switch term','reverse switch term','k'] }) self._coefs = out_coefs
[docs] def apply_cal(self, ntwk_tuple): """ apply the calibration to a measurement. Notes ----- Full correction is possible given you have measured your DUT in both orientations. Meaning, you have measured the device, then physically flipped the device and made a second measurement. This tuple of 2-port Networks is what is meant by (forward,reverse), in the docstring below If you pass a single 2-port Network, then the measurement will only be partially corrected using what is known as the `EnhancedResponse` calibration. Parameters ---------- network_tuple: tuple, or Network tuple of 2-port Networks in order (forward, reverse) OR a single 2-port Network. """ if isinstance(ntwk_tuple,tuple) or isinstance(ntwk_tuple,list): f,r = ntwk_tuple[0].copy(), ntwk_tuple[1].copy() sp,rp = self.sp,self.rp ntwk = f.copy() ntwk.s[:,sp,sp] = f.s[:,sp,sp] ntwk.s[:,rp,sp] = f.s[:,rp,sp] ntwk.s[:,rp,rp] = r.s[:,sp,sp] ntwk.s[:,sp,rp] = r.s[:,rp,sp] out = TwelveTerm.apply_cal(self, ntwk) return out else: warnings.warn('only gave a single measurement orientation, error correction is partial without a tuple', stacklevel=2) ntwk = ntwk_tuple.copy() sp,rp = self.sp,self.rp ntwk.s[:,rp,rp] = 0 ntwk.s[:,sp,rp] = 0 out = TwelveTerm.apply_cal(self, ntwk) out.s[:,rp,rp] = 0 out.s[:,sp,rp] = 0 return out
[docs] class EnhancedResponse(TwoPortOnePath): """ Enhanced Response Partial Calibration. Why are you using this? For full error you correction, you can measure the DUT in both orientations and instead use TwoPortOnePath Accuracy of correct measurements will rely on having a good match at the passive side of the DUT. For code-structuring reasons, this is a dummy placeholder class. Its just TwoPortOnePath, which defaults to enhancedresponse correction when you apply the calibration to a single network, and not a tuple of networks. """ family = 'EnhancedResponse'
[docs] class EightTerm(Calibration): """ General EightTerm (aka Error-box) Two-port calibration. This is basically an extension of the one-port algorithm to two-port measurements, A least squares estimator is used to determine the error coefficients. No self-calibration takes place. The concept is presented in [1]_ , but implementation follows that of [2]_ . See :func:`__init__` Notes ----- An important detail of implementing the error-box model is that the internal switch must be correctly accounted for. This is done through the measurement of :term:`switch terms`. References ---------- .. [1] Speciale, R.A.; , "A Generalization of the TSD Network-Analyzer Calibration Procedure, Covering n-Port Scattering-Parameter Measurements, Affected by Leakage Errors," Microwave Theory and Techniques, IEEE Transactions on, vol.25, no.12, pp. 1100- 1115, Dec 1977. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1129282&isnumber=25047 .. [2] Rytting, D. (1996) Network Analyzer Error Models and Calibration Methods. RF 8: Microwave Measurements for Wireless Applications (ARFTG/NIST Short Course Notes) """ family = 'EightTerm'
[docs] def __init__(self, measured, ideals, switch_terms=None, isolation=None, ut_hook=None,*args, **kwargs): """ EightTerm Initializer. Notes ----- See func:`Calibration.__init__` for details about automatic standards alignment (aka `sloppy_input`). Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list switch_terms : tuple of :class:`~skrf.network.Network` objects the pair of switch terms in the order (forward, reverse) isolation : :class:`~skrf.network.Network` object Measurement with loads on both ports with a perfect isolation between the ports. Used for determining the isolation error terms. If no measurement is given leakage is assumed to be zero. Loads don't need to be same as the one used as a match standard or even have similar reflection coefficients. Reflects can be also used, but accuracy might not be as good. """ self.switch_terms = switch_terms if switch_terms is None: warn('No switch terms provided', stacklevel=2) if isolation is None: self.isolation = measured[0].copy() self.isolation.s[:,:,:] = 0 else: self.isolation = isolation.copy() #Zero port matching so that networks can be simply subtracted self.isolation.s[:,0,0] = 0 self.isolation.s[:,1,1] = 0 self.ut_hook=ut_hook Calibration.__init__(self, measured = measured, ideals = ideals, **kwargs)
[docs] def unterminate(self,ntwk): """ Unterminates switch terms from a raw measurement. See Also -------- calibration.unterminate """ if self.ut_hook is not None: return self.ut_hook(self,ntwk) if self.switch_terms is not None: gamma_f, gamma_r = self.switch_terms return unterminate(ntwk, gamma_f, gamma_r) else: return ntwk
[docs] def terminate(self, ntwk): """ Terminate a network with switch terms. See Also -------- calibration.terminate """ if self.switch_terms is not None: gamma_f, gamma_r = self.switch_terms return terminate(ntwk, gamma_f, gamma_r) else: return ntwk
@property def measured_unisolated(self): return [k-self.isolation for k in self.measured] @property def measured_unterminated(self): return [self.unterminate(k) for k in self.measured_unisolated]
[docs] def run(self): numStds = self.nstandards numCoefs = 7 mList = [k.s for k in self.measured_unterminated] iList = [k.s for k in self.ideals] fLength = len(mList[0]) #initialize outputs error_vector = npy.zeros(shape=(fLength,numCoefs),dtype=complex) residuals = npy.zeros(shape=(fLength,4*numStds-numCoefs),dtype=complex) Q = npy.zeros((numStds*4, 7),dtype=complex) M = npy.zeros((numStds*4, 1),dtype=complex) # loop through frequencies and form m, a vectors and # the matrix M. where M = e00 + S11i # i2, 1, i2*m2 # ...etc for f in list(range(fLength)): # loop through standards and fill matrix for k in list(range(numStds)): m,i = mList[k][f,:,:],iList[k][f,:,:] # 2x2 s-matrices Q[k*4:k*4+4,:] = npy.array([\ [ 1, i[0,0]*m[0,0], -i[0,0], 0, i[1,0]*m[0,1], 0, 0 ],\ [ 0, i[0,1]*m[0,0], -i[0,1], 0, i[1,1]*m[0,1], 0, -m[0,1] ],\ [ 0, i[0,0]*m[1,0], 0, 0, i[1,0]*m[1,1], -i[1,0], 0 ],\ [ 0, i[0,1]*m[1,0], 0, 1, i[1,1]*m[1,1], -i[1,1], -m[1,1] ],\ ]) #pdb.set_trace() M[k*4:k*4+4,:] = npy.array([\ [ m[0,0]],\ [ 0 ],\ [ m[1,0]],\ [ 0 ],\ ]) # calculate least squares error_vector_at_f, residuals_at_f = npy.linalg.lstsq(Q,M,rcond=None)[0:2] #if len (residualsTmp )==0: # raise ValueError( 'matrix has singular values, check standards') error_vector[f,:] = error_vector_at_f.flatten() residuals[f,:] = residuals_at_f e = error_vector # put the error vector into human readable dictionary self._coefs = {\ 'forward directivity':e[:,0], 'forward source match':e[:,1], 'forward reflection tracking':(e[:,0]*e[:,1])-e[:,2], 'reverse directivity':e[:,3]/e[:,6], 'reverse source match':e[:,4]/e[:,6], 'reverse reflection tracking':(e[:,4]/e[:,6])*(e[:,3]/e[:,6])- (e[:,5]/e[:,6]), 'k':e[:,6], } self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fLength, dtype=complex), 'reverse switch term': npy.zeros(fLength, dtype=complex), }) # output is a dictionary of information self._output_from_run = { 'error vector':e, 'residuals':residuals } return None
[docs] def apply_cal(self, ntwk): """Applies the calibration to the input network. Inverse of `embed`. Parameters ---------- ntwk : :class:`~skrf.network.Network` Uncalibrated input network. Returns ------- caled : :class:`~skrf.network.Network` Calibrated network. """ caled = ntwk.copy() T1,T2,T3,T4 = self.T_matrices caled.s[:,1,0] -= self.coefs['forward isolation'] caled.s[:,0,1] -= self.coefs['reverse isolation'] caled = self.unterminate(caled) caled.s = linalg.inv(-caled.s @ T3 + T1) @ (caled.s @ T4 - T2) return caled
[docs] def embed(self, ntwk): """Applies the error boxes to the calibrated input network. Inverse of `apply_cal`. Parameters ---------- ntwk : :class:`~skrf.network.Network` Calibrated input network. Returns ------- embedded : :class:`~skrf.network.Network` Network with error boxes applied. """ embedded = ntwk.copy() T1,T2,T3,T4 = self.T_matrices embedded.s = (T1 @ ntwk.s + T2) @ linalg.inv(T3 @ ntwk.s + T4) embedded = self.terminate(embedded) embedded.s[:,1,0] += self.coefs['forward isolation'] embedded.s[:,0,1] += self.coefs['reverse isolation'] return embedded
@property def T_matrices(self): """ Intermediate matrices used for embedding and de-embedding. Returns ------- T1,T2,T3,T4 : numpy ndarray """ ec = self.coefs npoints = len(ec['k']) one = npy.ones(npoints,dtype=complex) zero = npy.zeros(npoints,dtype=complex) Edf = self.coefs['forward directivity'] Esf = self.coefs['forward source match'] Erf = self.coefs['forward reflection tracking'] Edr = self.coefs['reverse directivity'] Esr = self.coefs['reverse source match'] Err = self.coefs['reverse reflection tracking'] k = self.coefs['k'] detX = Edf*Esf-Erf detY = Edr*Esr-Err T1 = npy.array([ [ -detX, zero ], [ zero, -k*detY ] ]).transpose(2,0,1) T2 = npy.array([ [ Edf, zero ], [ zero, k*Edr ] ]).transpose(2,0,1) T3 = npy.array([ [ -Esf, zero ], [ zero, -k*Esr ] ]).transpose(2,0,1) T4 = npy.array([ [ one, zero ], [ zero, k ] ]).transpose(2,0,1) return T1,T2,T3,T4
[docs] def renormalize(self, z0_old, z0_new, powerwave=False): """Renormalizes the calibration error boxes to a new reference impedance. Useful for example after doing a TRL calibration with non-50 ohm transmission lines. After the TRL calibration reference impedance is the line characteristic impedance. If the transmission line characteristic impedance is known this function can be used to renormalize the reference impedance to 50 ohms or any other impedance. """ ec = self.coefs npoints = len(ec['k']) one = npy.ones(npoints,dtype=complex) Edf = self.coefs['forward directivity'] Esf = self.coefs['forward source match'] Erf = self.coefs['forward reflection tracking'] Edr = self.coefs['reverse directivity'] Esr = self.coefs['reverse source match'] Err = self.coefs['reverse reflection tracking'] k = self.coefs['k'] S1 = npy.array([ [ Edf, Erf/k ], [ k, Esf ] ]).transpose(2,0,1) S2 = npy.array([ [ Edr, one ], [ Err, Esr ] ]).transpose(2,0,1) #Port impedances before renormalization. #Only the DUT side (port 2) is renormalized. #VNA side (port 1) stays unchanged. z = npy.array([z0_new, z0_old]).transpose() if powerwave: S1 = renormalize_s(S1, z, z0_new, s_def='power') S2 = renormalize_s(S2, z, z0_new, s_def='power') else: S1 = renormalize_s(S1, z, z0_new, s_def='traveling') S2 = renormalize_s(S2, z, z0_new, s_def='traveling') self.coefs['forward directivity'] = S1[:,0,0] self.coefs['forward source match'] = S1[:,1,1] self.coefs['forward reflection tracking'] = S1[:,0,1]*S1[:,1,0] self.coefs['reverse directivity'] = S2[:,0,0] self.coefs['reverse source match'] = S2[:,1,1] self.coefs['reverse reflection tracking'] = S2[:,1,0]*S2[:,0,1] self.coefs['k'] = S1[:,1,0]/S2[:,0,1] return None
[docs] class TRL(EightTerm): """ Thru-Reflect-Line (also called LRL for Line-Reflect-Line). A Similar self-calibration algorithm as developed by Engen and Hoer [1]_, more closely following into a more matrix form in [2]_. Reference impedance of the calibration is characteristic impedance of the transmission lines. If the characteristic impedance is known, reference impedance can be renormalized using `EightTerm.renormalize` function. See Also -------- determine_line function which actually determines the line s-parameters References ---------- .. [1] G. F. Engen and C. A. Hoer, "Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer," IEEE Transactions on Microwave Theory and Techniques, vol. 27, no. 12, pp. 987-993, 1979. .. [2] H.-J. Eul and B. Schiek, "A generalized theory and new calibration procedures for network analyzer self-calibration," IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 4, pp. 724-731, 1991. """ family = 'TRL'
[docs] def __init__(self, measured, ideals=None, estimate_line=False, n_reflects=1,solve_reflect=True, *args,**kwargs): r""" Initialize a TRL calibration. Note that the order of `measured` and `ideals` is strict. It must be [Thru, Reflect, Line]. A multiline algorithms is used if more than one line is passed. A multi-reflect algorithm is used if multiple reflects are passed, see `n_reflects` argument. All of the `ideals` can be individually set to `None`, or the entire list set to `None` (`ideals=None`). For each ideal set to `None`, the following assumptions are made: * thru : flush thru * reflect : flush shorts * line : an approximately 90deg matched line (can be lossy) The reflect ideals can also be given as a +-1. If thru is non-zero length, the calibration is done with zero length thru and the ideal thru length is subtracted from the ideal lines. The resulting calibration reference plane is at the center of the thru. Ideal reflect standard reference plane is at the center of the thru even if the ideal thru length is non-zero. Note you can also use the `estimate_line` option to automatically estimate the initial guess for the line length from measurements . This is sensible if you have no idea what the line length is, but your **error networks** are well matched (E_ij >>E_ii). Notes ----- This implementation inherits from :class:`EightTerm`. dont forget to pass switch_terms. Parameters ---------- measured : list of :class:`~skrf.network.Network` must be in order [Thru, Reflect[s], Line[s]]. if the number of reflects is >1 then use `n_reflects` argument. ideals : list of :class:`~skrf.network.Network`, [+1,-1] , None must be in order [Thru, Reflect, Line]. Each element in the list may be None, or equivalently, the list may be None. Also the reflects can be simply given as +1 or -1. estimate_line : bool should we estimates the length of the line standard from raw measurements, if not we assume its about 90 deg. solve_reflect : bool Solve for the reflect or not. n_reflects : 1 number of reflective standards \*args, \*\*kwargs : passed to EightTerm.__init__ dont forget the `switch_terms` argument is important Examples -------- >>> thru = rf.Network('thru.s2p') >>> reflect = rf.Network('reflect.s2p') >>> line = rf.Network('line.s2p') Ideals is None, so we assume it's close to a flush short: >>> trl = TRL(measured=[thru,reflect,line], ideals=None) Reflect is given as close to a flush short: >>> trl = TRL(measured=[thru,reflect,line], ideals=[None,-1,None]) Reflect is given as close to a flush open: >>> trl = TRL(measured=[thru,reflect,line], ideals=[None,+1,None]) See Also -------- determine_line determine_reflect NISTMultilineTRL TUGMultilineTRL """ #warn('Value of Reflect is not solved for yet.') self.n_stds = n_stds = len(measured) self.n_reflects = n_reflects self.estimate_line = estimate_line self.solve_reflect = solve_reflect ## generate ideals, given various inputs if ideals is None: ideals = [None]*len(measured) if ideals[0] is None: # lets make an ideal flush thru for them ideal_thru = measured[0].copy() ideal_thru.s[:,0,0] = 0 ideal_thru.s[:,1,1] = 0 ideal_thru.s[:,1,0] = 1 ideal_thru.s[:,0,1] = 1 ideals[0] = ideal_thru orig_ideal_thru = None if npy.any(ideals[0].s[:,1,0] != 1) or npy.any(ideals[0].s[:,0,1] != 1): orig_ideal_thru = ideals[0] ideals[0] = ideals[0].copy() ideals[0].s[:,0,0] = 0 ideals[0].s[:,1,1] = 0 ideals[0].s[:,0,1] = 1 ideals[0].s[:,1,0] = 1 for k in range(1,n_reflects+1): if ideals[k] is None: # default assume they are using flushshorts ideals[k] = -1 if isinstance(ideals[k], Number): ideal_reflect = measured[k].copy() ideal_reflect.s[:,0,0] = ideals[k] ideal_reflect.s[:,1,1] = ideals[k] ideal_reflect.s[:,1,0] = 0 ideal_reflect.s[:,0,1] = 0 ideals[k] = ideal_reflect for k in range(n_reflects+1,n_stds): if ideals[k] is None: # lets make an 90deg line for them ideal_line = measured[k].copy() ideal_line.s[:,0,0] = 0 ideal_line.s[:,1,1] = 0 ideal_line.s[:,1,0] = -1j ideal_line.s[:,0,1] = -1j ideals[k] = ideal_line if orig_ideal_thru is not None: ideals[k] = ideals[k].copy() # De-embed original thru ideals[k].s[:,0,1] /= orig_ideal_thru.s[:,0,1] ideals[k].s[:,1,0] /= orig_ideal_thru.s[:,1,0] EightTerm.__init__(self, measured = measured, ideals = ideals, **kwargs)
[docs] def run(self): m_ut = self.measured_unterminated n_reflects = self.n_reflects n_stds = self.n_stds estimate_line = self.estimate_line solve_reflect = self.solve_reflect ideals = self.ideals ## Solve for the line[s] for k in range(n_reflects+1,n_stds): if estimate_line: # setting line_approx to None causes determine_line() to # estimate the line length from raw measurements line_approx = None else: line_approx = ideals[k] self.ideals[k] = determine_line(m_ut[0], m_ut[k], line_approx) # find line ## Solve for the reflect[s] if solve_reflect: for k in range(1,n_reflects+1): # solve for reflect using the last line if they pass >1 r = determine_reflect(m_ut[0],m_ut[k],m_ut[-1],reflect_approx=ideals[k], line_approx=self.ideals[-1]) self.ideals[k] = two_port_reflect(r,r) return EightTerm.run(self)
MultilineTRL = TRL
[docs] class NISTMultilineTRL(EightTerm): """ NIST Multiline TRL calibration. Multiline TRL can use multiple lines to extend bandwidth and accuracy of the calibration. Different line measurements are combined in a way that minimizes the error in calibration. Calibration reference plane is at the edges of the lines. At every frequency point there should be at least one line pair that has phase difference that is not 0 degrees or a multiple of 180 degrees otherwise calibration equations are singular and accuracy is very poor. By default the reference impedance of the calibration is the characteristic impedance of the transmission lines. If the characteristic impedance is known reference impedance can be renormalized by giving `z0_ref` and `z0_line`. Alternatively if capacitance/length of the transmission line is given with `c0` argument, characteristic impedance can be solved assuming that conductance/length is zero. Algorithm is the one published in [0]_, but implementation is based on [1]_. References ---------- .. [0] D. C. DeGroot, J. A. Jargon and R. B. Marks, "Multiline TRL revealed," 60th ARFTG Conference Digest, Fall 2002., Washington, DC, USA, 2002, pp. 131-155. .. [1] K. Yau "On the metrology of nanoscale Silicon transistors above 100 GHz" Ph.D. dissertation, Dept. Elec. Eng. and Comp. Eng., University of Toronto, Toronto, Canada, 2011. """ family = 'TRL'
[docs] def __init__(self, measured, Grefls, l, er_est=1, refl_offset=None, ref_plane=0, gamma_root_choice='auto', k_method='multical', c0=None, z0_ref=50, z0_line=None, *args, **kwargs): r""" NISTMultilineTRL initializer. Note that the order of `measured` is strict. It must be [Thru, Reflects, Lines]. Multiple reflects can also be used. Notes ------- This implementation inherits from :class:`EightTerm`. Don't forget to pass switch_terms. Parameters -------------- measured : list of :class:`~skrf.network.Network` must be in order [Thru, Reflects, Lines] Grefls : complex or list of complex Estimated reflection coefficients of reflect standards. Usually -1 for short or +1 for open. l : list of float Lengths of through and lines. If through is non-zero length its length is subtracted from the line lengths for the calibration and afterwards the calibration reference planes are shifted back by half thru on both ports using the solved propagation constant. er_est : complex Estimated effective permittivity of the lines. Imaginary part is the loss at 1 GHz. Negative imaginary part indicates losses. refl_offset : float or list of float Estimated offsets of the reflect standards from the reference plane at the end of the lines. Negative length is towards the VNA. Units are in meters. ref_plane : float or list of float Reference plane shift after the calibration. Negative length is towards the VNA. Units are in meters. Different shifts can be given to different ports by giving a two element list. First element is shift of port 1 and second is shift of port 2. gamma_root_choice : string Method to use for choosing the correct eigenvalue for propagation constant. 'estimate' : Choose the root that is closer to the estimated propagation constant. Best choice when data is of good quality. To improve the performance in phatological cases it's possible to give estimate of the propagation constant as a keyword argument with 'gamma_est'. 'real' : Force the real part of the gamma to be positive corresponding to a lossy line. Imaginary part can be negative. This is the suggested method when lines have moderate loss and the measurement noise is low. This is the default method. 'auto' : Use heuristics to choose the eigenvalue. 'imag' : Force the imaginary part of the gamma to be positive, corresponding to a positive length line. Real part can be positive. May choose incorrectly when the line is long due to phase wrapping. k_method : string Method to use for determining the 'k' error coefficient. Currently valid choices are 'marks' or 'multical'. The default method is 'multical'. c0 : None, float or list of float Capacitance/length of the transmission line in units F/m used for reference impedance renormalization. Characteristic impedance of the transmission lines can be determined from the solved propagation constant if capacitance per length is known. After the characteristic impedance is solved reference impedance of the calibration is changed to `z0_ref`. Solved characteristic impedance can be accessed with `cal.z0`. Assumes TEM mode and conductance/length to be zero. If `c0` == `z0_line` is None, the characteristic impedance is not renormalized. In this case reference impedance of the calibration is characteristic impedance of the transmission lines. z0_ref : None, complex or list of complex New reference impedance for the characteristic impedance renormalizarion. No effect if `c0` is None and `z0_line` is None. If `z0_ref` is None, no renormalization is done. z0_line : None, complex or list of complex Characteristic impedance of the transmission lines. Used for reference impedance renormalization. If `z0` == `z0_line` is None, the characteristic impedance is not renormalized. In this case reference impedance of the calibration is characteristic impedance of the transmission lines. \*args, \*\*kwargs : passed to EightTerm.__init__ dont forget the `switch_terms` argument is important See Also -------- TUGMultilineTRL """ self.refl_offset = refl_offset if npy.isscalar(ref_plane): ref_plane = [ref_plane, ref_plane] self.ref_plane = ref_plane self.er_est = er_est self.l = [float(v) for v in l] # cast to float, see gh-895 self.Grefls = Grefls self.gamma_root_choice = gamma_root_choice self.k_method = k_method self.z0_ref = z0_ref self.c0 = c0 self.z0_line = z0_line fpoints = len(measured[0].frequency) if npy.isscalar(self.z0_ref): self.z0_ref = [self.z0_ref] * fpoints if npy.isscalar(self.z0_line): self.z0_line = [self.z0_line] * fpoints if npy.isscalar(self.z0_ref): self.c0 = [self.c0] * fpoints if npy.isscalar(self.Grefls): # assume a single reflect self.Grefls = [self.Grefls] n_reflects = len(self.Grefls) if self.refl_offset is None: self.refl_offset = [0] * len(self.Grefls) if npy.isscalar(self.refl_offset): self.refl_offset = [self.refl_offset] * n_reflects if len(measured) != len(self.Grefls) + len(l): raise ValueError(dedent( f"""Amount of measurements {len(measured)} doesn't match amount of line lengths {len(l)} and reflection coefficients {len(self.Grefls)}""")) #Not used, but needed for Calibration class init ideals = measured #EightTerm applies the switch correction EightTerm.__init__(self, measured = measured, ideals = ideals, self_calibration=True, **kwargs) m_sw = [k for k in self.measured_unterminated] self.measured_reflects = m_sw[1:1+n_reflects] self.measured_lines = [m_sw[0]] self.measured_lines.extend(m_sw[1+n_reflects:]) self.ref_plane[0] -= l[0]/2 self.ref_plane[1] -= l[0]/2 self.refl_offset = [r - l[0]/2 for r in self.refl_offset] # The first line is thru self.l = [i - self.l[0] for i in self.l] if len(l) != len(self.measured_lines): raise ValueError("Different amount of lines and line lengths found")
[docs] def run(self): c = 299792458.0 pi = npy.pi inv = linalg.inv exp = npy.exp log = npy.log abs = npy.abs gamma_est_user = self.kwargs.get('gamma_est', None) measured_reflects = self.measured_reflects measured_lines = self.measured_lines measured_lines_t = list(map(lambda x: s2t(x.s), self.measured_lines)) l = self.l er_est = self.er_est freqs = measured_lines[0].f fpoints = len(freqs) lines = len(l) gamma = npy.zeros(fpoints, dtype=complex) z0 = npy.zeros(fpoints, dtype=complex) gamma_est = (1j*2*pi*freqs[0]/c)*npy.sqrt(er_est.real + 1j*er_est.imag/(freqs[0]*1e-9)) line_c = npy.zeros(fpoints, dtype=int) er_eff = npy.zeros(fpoints, dtype=complex) Tmat1 = npy.ones(shape=(fpoints, 2, 2), dtype=complex) Tmat2 = npy.ones(shape=(fpoints, 2, 2), dtype=complex) Smat1 = npy.ones(shape=(fpoints, 2, 2), dtype=complex) Smat2 = npy.ones(shape=(fpoints, 2, 2), dtype=complex) e = npy.zeros(shape=(fpoints, 7), dtype=complex) nstd = npy.zeros(shape=(fpoints), dtype=float) def t2s_single(t): return t2s(t[npy.newaxis,:,:])[0] def s2t_single(s): return s2t(s[npy.newaxis,:,:])[0] def root_choice(Mij, dl, gamma_est): e_val = linalg.eigvals(Mij) Da = [0,0] Db = [0,0] ga = [0,0] gb = [0,0] for i in [0,1]: if i == 0: eij1 = e_val[0] eij2 = e_val[1] else: eij1 = e_val[1] eij2 = e_val[0] ea = (eij1 + 1/eij2)/2 periods = npy.round(((gamma_est*dl).imag - (-log(ea)).imag)/(2*pi)) ga[i] = (-log(ea) + 1j*2*pi*periods)/dl Da[i] = abs(ga[i]*dl - gamma_est*dl)/abs(gamma_est*dl) eb = (eij2 + 1/eij1)/2 periods = npy.round(-((gamma_est*dl).imag + (-log(eb)).imag)/(2*pi)) gb[i] = (-log(eb) + 1j*2*pi*periods)/dl Db[i] = abs(gb[i]*dl + gamma_est*dl)/abs(-gamma_est*dl) if Da[0] + Db[0] < 0.1*(Da[1] + Db[1]): return e_val if Da[1] + Db[1] < 0.1*(Da[0] + Db[0]): return e_val[::-1] if npy.sign((ga[0]).real) != npy.sign((gb[0]).real): if Da[0] + Db[0] < Da[1] + Db[1]: return e_val else: return e_val[::-1] else: if abs((ga[0]-gb[0]).real) < 0.1*abs((ga[1] + gb[1]).real) \ and abs(ga[0].real/ga[0].imag) > 0.001 \ and ga[0].real > 0: if Da[0] + Db[0] < 0.2: return e_val else: return e_val[::-1] else: if Da[0] + Db[0] < Da[1] + Db[1]: return e_val else: return e_val[::-1] #Unreachable return e_val V_inv = npy.eye(lines-1, dtype=complex) \ - (1.0/lines)*npy.ones(shape=(lines-1, lines-1), dtype=complex) b1_vec = npy.zeros(lines-1, dtype=complex) b2_vec = npy.zeros(lines-1, dtype=complex) CoA1_vec = npy.zeros(lines-1, dtype=complex) CoA2_vec = npy.zeros(lines-1, dtype=complex) b1_vec2 = npy.zeros(lines-1, dtype=complex) b2_vec2 = npy.zeros(lines-1, dtype=complex) CoA1_vec2 = npy.zeros(lines-1, dtype=complex) CoA2_vec2 = npy.zeros(lines-1, dtype=complex) if self.z0_line is not None and self.c0 is not None: raise ValueError('Only one of c0 or z0_line can be given.') for m in range(fpoints): min_phi_eff = pi*npy.ones(lines) #Find the best common line to use for n in range(lines): for k in range(lines): if n == k: continue dl = l[k] - l[n] pd = abs(exp(-gamma_est*dl) - exp(gamma_est*dl))/2 if -1 <= pd <= 1: phi_eff = npy.arcsin( pd ) else: phi_eff = npy.pi/2 min_phi_eff[n] = min(min_phi_eff[n], phi_eff) #Common line is selected to be one with the largest phase difference line_c[m] = npy.argmax(min_phi_eff) #Pre-calculate inverse T-matrix of the common line inv_line_c = inv(measured_lines_t[line_c[m]][m]) #Propagation constant extraction #Compute eigenvalues of each line pair g_dl = npy.zeros(lines-1, dtype=complex) dl_vec = npy.zeros(lines-1, dtype=complex) k = 0 for n in range(lines): #Skip the common line if n == line_c[m]: continue dl = l[n] - l[line_c[m]] Mij = (measured_lines_t[n][m]).dot(inv_line_c) if 'estimate' in self.gamma_root_choice: #Choose the correct root later e_val = linalg.eigvals(Mij) else: #Choose the correct root using heuristics e_val = root_choice(Mij, dl, gamma_est) g_dl1 = -log(0.5*(e_val[0] + 1.0/e_val[1])) g_dl2 = -log(0.5*(e_val[1] + 1.0/e_val[0])) g_dl[k] = g_dl1 if 'real' in self.gamma_root_choice and (g_dl1/dl).real < 0: #Choose root that has bigger real part (more lossier) g_dl[k] = g_dl2 if 'imag' in self.gamma_root_choice and (g_dl1/dl).imag < 0: #Choose root that has larger imaginary part #Only works for short lines g_dl[k] = g_dl2 if 'estimate' in self.gamma_root_choice: #Choose root that is closer to the estimate if gamma_est_user is not None: g_est = gamma_est_user[m] else: #Use estimate from earlier iterations g_est = gamma_est periods1 = npy.round( ((gamma_est*dl).imag - g_dl1.imag)/(2*pi)) periods2 = npy.round( ((gamma_est*dl).imag - g_dl2.imag)/(2*pi)) g_dl1 += 1j*2*pi*periods1 g_dl2 += 1j*2*pi*periods2 if abs(g_dl1 - g_est*dl) < abs(g_dl2 - g_est*dl): g_dl[k] = g_dl1 else: g_dl[k] = g_dl2 else: periods = npy.round(((gamma_est*dl).imag - (g_dl[k].imag))/(2*pi)) g_dl[k] += 1j*2*pi*periods dl_vec[k] = dl k = k + 1 gamma[m] = (dl_vec.transpose().dot(V_inv).dot(g_dl))/(dl_vec.transpose().dot(V_inv).dot(dl_vec)) if m != fpoints-1: gamma_est = gamma[m].real + 1j*gamma[m].imag*freqs[m+1]/freqs[m] er_eff[m] = -(gamma[m]/(2*pi*freqs[m]/c))**2 root1 = [] root2 = [] d1 = [0,0] d2 = [0,0] S_thru = measured_lines[0].s[m] p = 0 for n in range(lines): if n == line_c[m]: continue #Port 1 T = measured_lines_t[n][m].dot(inv_line_c) T = measured_lines[n].s[m,1,0]*measured_lines[line_c[m]].s[m,0,1]*T e_val = linalg.eigvals(T) B1 = npy.array([\ [T[0,1]/(e_val[0]-T[0,0]), T[0,1]/(e_val[1]-T[0,0])], [(e_val[0]-T[1,1])/T[1,0], (e_val[1]-T[1,1])/T[1,0]]]) CoA1 = npy.array([\ [T[1,0]/(e_val[1]-T[1,1]), T[1,0]/(e_val[0]-T[1,1])], [(e_val[1]-T[0,0])/T[0,1], (e_val[0]-T[0,0])/T[0,1]]]) B_est1 = T[0,1]/(exp(gamma[m]*(l[n]-l[line_c[m]]) - T[0,0])) CoA_est1 = T[1,0]/(exp(-gamma[m]*(l[n]-l[line_c[m]]) - T[1,1])) dB1 = abs(B1 - B_est1)/abs(B_est1) dCoA1 = abs(CoA1 - CoA_est1)/abs(CoA_est1) if abs(B1[0,1] - B_est1) < abs(B1[1,1] - B_est1): b1_vec[p] = B1[0,1] b1_vec2[p] = B1[0,0] root1.append([0,1]) else: b1_vec[p] = B1[1,1] b1_vec2[p] = B1[1,0] root1.append([1,1]) if abs(CoA1[0,1] - CoA_est1) < abs(CoA1[1,1] - CoA_est1): CoA1_vec[p] = CoA1[0,1] CoA1_vec2[p] = CoA1[0,0] else: CoA1_vec[p] = CoA1[1,1] CoA1_vec2[p] = CoA1[1,0] d1[0] += npy.sum(dB1[:,root1[-1][1]]) + npy.sum(dCoA1[:,root1[-1][1]]) d1[1] += npy.sum(dB1[:,int(not root1[-1][1])]) + npy.sum(dCoA1[:,int(not root1[-1][1])]) #Port 2 k = npy.array([[0,1],[1,0]], dtype=complex) T = s2t_single(k.dot(measured_lines[n].s[m]).dot(k)).dot(\ inv(s2t_single(k.dot(measured_lines[line_c[m]].s[m]).dot(k)))) T = measured_lines[n].s[m][0,1]*measured_lines[line_c[m]].s[m][1,0]*T e_val = linalg.eigvals(T) B2 = npy.array([\ [T[0,1]/(e_val[0]-T[0,0]), T[0,1]/(e_val[1]-T[0,0])], [(e_val[0]-T[1,1])/T[1,0], (e_val[1]-T[1,1])/T[1,0]]]) CoA2 = npy.array([\ [T[1,0]/(e_val[1]-T[1,1]), T[1,0]/(e_val[0]-T[1,1])], [(e_val[1]-T[0,0])/T[0,1], (e_val[0]-T[0,0])/T[0,1]]]) B_est2 = T[0,1]/(exp(gamma[m]*(l[n]-l[line_c[m]]) - T[0,0])) CoA_est2 = T[1,0]/(exp(-gamma[m]*(l[n]-l[line_c[m]]) - T[1,1])) dB2 = abs(B2 - B_est2)/abs(B_est2) dCoA2 = abs(CoA2 - CoA_est2)/abs(CoA_est2) if abs(B2[0,1] - B_est2) < abs(B2[1,1] - B_est2): b2_vec[p] = B2[0,1] b2_vec2[p] = B2[0,0] root2.append([0,1]) else: b2_vec[p] = B2[1,1] b2_vec2[p] = B2[1,0] root2.append([1,1]) if abs(CoA2[0,1] - CoA_est2) < abs(CoA2[1,1] - CoA_est2): CoA2_vec[p] = CoA2[0,1] CoA2_vec2[p] = CoA2[0,0] else: CoA2_vec[p] = CoA2[1,1] CoA2_vec2[p] = CoA2[1,0] d2[0] += npy.sum(dB2[:,root2[-1][1]]) + npy.sum(dCoA2[:,root2[-1][1]]) d2[1] += npy.sum(dB2[:,int(not root2[-1][1])]) + npy.sum(dCoA2[:,int(not root2[-1][1])]) p += 1 Vb = npy.zeros(shape=(lines-1,lines-1), dtype=complex) Vc = npy.zeros(shape=(lines-1,lines-1), dtype=complex) #Fill in upper triangular matrix l_not_common = [i for i in l if i != l[line_c[m]]] for b in range(len(l_not_common)): for a in range(b+1): if a == b: #Diagonal len_l = l_not_common[a] exp_factor = exp(-gamma[m]*(len_l - l[line_c[m]])) Vb[a,b] = abs(exp_factor)**2 + 1/abs(exp_factor)**2 + \ 2*( abs(exp(-gamma[m]*len_l))*\ abs(exp(-gamma[m]*l[line_c[m]])) )**2 n = abs(exp_factor - 1/exp_factor)**2 Vb[a,b] /= n Vc[a,b] = abs(exp_factor)**2 + 1/(abs(exp_factor))**2 + \ 2/( abs(exp(-gamma[m]*l[line_c[m]]))*\ abs(exp(-gamma[m]*len_l)) )**2 Vc[a,b] /= n elif a < b: len_a = l_not_common[a] len_b = l_not_common[b] exp_factor = exp(-gamma[m]*(len_a -l[line_c[m]])) exp_factor2 = exp(-gamma[m]*(len_b -l[line_c[m]])) Vb[a,b] = exp_factor*exp_factor2.conjugate() + \ (abs(exp(-gamma[m]*l[line_c[m]])))**2 * \ exp(-gamma[m]*len_a)*(exp(-gamma[m]*len_b)).conjugate() n = (exp_factor - 1/exp_factor)* \ (exp_factor2-1/exp_factor2).conjugate() Vb[a,b] /= n Vb[b,a] = Vb[a,b].conjugate() Vc[a,b] = 1/(exp_factor*exp_factor2.conjugate()) + \ 1/( (abs(exp(-gamma[m]*l[line_c[m]])))**2 * \ exp(-gamma[m]*len_a)*(exp(-gamma[m]*len_b)).conjugate() ) Vc[a,b] /= n Vc[b,a] = Vc[a,b].conjugate() def solve_A(B1, B2, CoA1, CoA2, S_thru, m): #Determine A using unknown reflect Ap = B1*B2 - B1*S_thru[1,1] - B2*S_thru[0,0] + linalg.det(S_thru) Ap = -Ap/(1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*linalg.det(S_thru)) A1_vals = npy.zeros(len(measured_reflects), dtype=complex) A2_vals = npy.zeros(len(measured_reflects), dtype=complex) for n in range(len(measured_reflects)): S_r = measured_reflects[n].s[m] S_r11 = S_r[0,0] S_r22 = S_r[1,1] Arr = (S_r11 - B1)/(1 - S_r11*CoA1)* \ (1 - S_r22*CoA2)/(S_r22 - B2) Gr_est = self.Grefls[n]*exp(-2*gamma[m]*(self.refl_offset[n] - l[0]/2.)) G_trial = (S_r11 - B1)/(npy.sqrt(Ap*Arr)*(1 - S_r11*CoA1)) if abs( Gr_est/abs(Gr_est) - G_trial/abs(G_trial) ) > npy.sqrt(2): A1_vals[n] = -npy.sqrt(Ap*Arr) else: A1_vals[n] = npy.sqrt(Ap*Arr) A2_vals[n] = A1_vals[n]/Arr A1 = npy.mean(A1_vals) A2 = npy.mean(A2_vals) return A1, A2 inv_Vb = inv(Vb) inv_Vc = inv(Vc) sum_inv_Vb = npy.sum(inv_Vb) sum_inv_Vc = npy.sum(inv_Vc) values = [] #List possible root choices for B and CoA for i in [(0,0), (0,1), (1,0), (1,1)]: if i[0] == 0: b1 = b1_vec coa1 = CoA1_vec else: b1 = b1_vec2 coa1 = CoA1_vec2 if i[1] == 0: b2 = b2_vec coa2 = CoA2_vec else: b2 = b2_vec2 coa2 = CoA2_vec2 B1 = npy.sum(inv_Vb.dot(b1))/sum_inv_Vb B2 = npy.sum(inv_Vb.dot(b2))/sum_inv_Vb CoA1 = npy.sum(inv_Vc.dot(coa1))/sum_inv_Vc CoA2 = npy.sum(inv_Vc.dot(coa2))/sum_inv_Vc denom = 1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*\ (S_thru[0,0]*S_thru[1,1] - S_thru[0,1]*S_thru[1,0]) values.append( (abs(denom), B1, B2, CoA1, CoA2) ) if abs(values[0][0]) > 1e-9 and d1[1]/d1[0] > 10 and d2[1]/d2[0] > 10: #Estimate seems to be correct B1, B2, CoA1, CoA2 = values[0][1:] A1, A2 = solve_A(B1, B2, CoA1, CoA2, S_thru, m) else: #Estimation is incorrect or the accuracy is bad #Choose the root that minimizes error to measurements best_error = None best_values = [] for v in values: if abs(v[0]) < 1e-9: continue B1, B2, CoA1, CoA2 = v[1:] A1, A2 = solve_A(B1, B2, CoA1, CoA2, S_thru, m) C1 = CoA1*A1 C2 = CoA2*A2 R = S_thru[0,1]*(1 - C1*C2)/(A1 - B1*C1) T1 = R*npy.array([[A1, B1],[C1, 1]]) g = npy.array([[0,1],[1,0]]) T2 = npy.array([[A2, B2],[C2, 1]]) error = 0 for n in range(lines): meas = measured_lines[n].s[m] ideal = npy.array([[exp(-gamma[m]*l[n]), 0],[0,exp(gamma[m]*l[n])]]) embedded = t2s_single(T1.dot(ideal).dot(g.dot(inv(T2).dot(g)))) error += npy.sum(abs(embedded - meas)) if best_error is None or error < best_error: best_error = error best_values = v B1, B2, CoA1, CoA2 = best_values[1:] A1, A2 = solve_A(B1, B2, CoA1, CoA2, S_thru, m) sigmab = npy.sqrt(1/(npy.sum(inv_Vb).real)) sigmac = npy.sqrt(1/(npy.sum(inv_Vc).real)) nstd[m] = (sigmab + sigmac)/2 C1 = CoA1*A1 C2 = CoA2*A2 #Determine R1, R2 if self.k_method == 'marks': p1_len_est = self.kwargs.get('p1_len_est', 0) p2_len_est = self.kwargs.get('p2_len_est', 0) z0_phase = npy.angle( npy.sqrt(er_eff[m]) ) Qox = ( 1 - 1j*z0_phase) Qoy = ( 1 - 1j*z0_phase) R1R2 = (S_thru[1,0]*(1 - C1*C2))**-1 gam = A2 - B2*C2 de = (A1-B1*C1)*(R1R2*(A2-B2*C2))**2 beta_sqr = (abs(de)**2 + abs(gam)**2)/\ (de.conjugate()*Qox + de.conjugate()*Qoy) s21y = npy.sqrt( beta_sqr ) R2 = ((A2 -B2*C2)/s21y)**-1 R2_est = exp(gamma[m]*p2_len_est) if abs( R2_est/abs(R2_est) -R2/abs(R2) ) > npy.sqrt(2): R2 = -R2 R1 = R1R2/R2 R1_est = exp(gamma[m]*p1_len_est) if abs( R1_est/abs(R1_est) - R1/abs(R1) ) > npy.sqrt(2): warn('Inconsistencies detected', stacklevel=2) elif self.k_method == 'multical': denom = 1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*\ (S_thru[0,0]*S_thru[1,1] - S_thru[0,1]*S_thru[1,0]) R1 = S_thru[0,1]/denom R2 = S_thru[1,0]/denom else: raise ValueError(f'Unknown k_method: {self.k_method}') #Reference plane shift if npy.any(self.ref_plane): shift1 = exp(-2*gamma[m]*self.ref_plane[0]) shift2 = exp(-2*gamma[m]*self.ref_plane[1]) A1 *= shift1 A2 *= shift2 C1 *= shift1 C2 *= shift2 R1 *= shift1 R2 *= shift2 if self.c0 is not None: #Estimate the line characteristic impedance #using known capacitance/length z0[m] = gamma[m]/(1j*2*npy.pi*freqs[m]*self.c0[m]) else: #Set the known line characteristic impedance if self.z0_line is not None: z0[m] = self.z0_line[m] else: z0[m] = self.z0_ref[m] #Error matrices Tmat1[m,:,:] = R1*npy.array([[A1, B1],[C1, 1]]) Tmat2[m,:,:] = R2*npy.array([[A2, B2],[C2, 1]]) Smat1[m,:,:] = t2s_single(Tmat1[m,:,:]) Smat2[m,:,:] = t2s_single(Tmat2[m,:,:]) #Convert the error coefficients to #definitions used by the EightTerm class. dx = linalg.det(Smat1[m,:,:]) dy = linalg.det(Smat2[m,:,:]) if self.k_method == 'marks': k = Smat1[m,1,0]/Smat2[m,0,1] else: k = dx*dy*Smat1[m,1,0]/(Smat2[m,0,1]*Smat2[m,1,0]) #Error coefficients e[m] = [Smat1[m,0,0], Smat1[m,1,1], dx, Smat2[m,0,0], Smat2[m,1,1], dy, k] self._z0 = z0 self._gamma = gamma self._er_eff = er_eff self._nstd = nstd self._coefs = {\ 'forward directivity':e[:,0], 'forward source match':e[:,1], 'forward reflection tracking':e[:,0]*e[:,1]-e[:,2], 'reverse directivity':e[:,3], 'reverse source match':e[:,4], 'reverse reflection tracking':e[:,4]*e[:,3]- e[:,5], 'k':e[:,6], } self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fpoints, dtype=complex), 'reverse switch term': npy.zeros(fpoints, dtype=complex), }) # output is a dictionary of information self._output_from_run = { 'error vector':e } #Reference impedance renormalization if self.z0_ref is not None and npy.any(z0 != self.z0_ref): powerwave = self.kwargs.get('powerwave', False) self.renormalize(z0, self.z0_ref, powerwave=powerwave)
[docs] @classmethod def from_coefs(cls, frequency, coefs, **kwargs): """ Create a calibration from its error coefficients. Parameters ---------- frequency : :class:`~skrf.frequency.Frequency` frequency info, (duh) coefs : dict of numpy arrays error coefficients for the calibration See Also -------- Calibration.from_coefs_ntwks """ # assigning this measured network is a hack so that # * `calibration.frequency` property evaluates correctly # * __init__() will not throw an error n = Network(frequency = frequency, s = rand_c(frequency.npoints,2,2)) measured = [n,n,n] if 'forward switch term' in coefs: switch_terms = (Network(frequency = frequency, s=coefs['forward switch term']), Network(frequency = frequency, s=coefs['reverse switch term'])) kwargs['switch_terms'] = switch_terms #Fill the required __init__ fields with garbage #and assign the coefficients manually cal = cls(measured, [-1], [0,1], **kwargs) cal.coefs = coefs cal.family += '(fromCoefs)' return cal
@property def gamma(self): """ Propagation constant of the solved line. """ try: return self._gamma except(AttributeError): self.run() return self._gamma @property def er_eff(self): r""" Effective permittivity of the solved line. Defined in terms of the propagation constant: .. math:: \gamma = \alpha + j \beta = \frac{2\pi f}{c} \sqrt{\epsilon_{r,eff}} """ try: return self._er_eff except(AttributeError): self.run() return self._er_eff @property def z0(self): """ Solved characteristic impedance of the transmission lines. This is only solved if C0 parameter (Capacitance/length in units F/m) is given. Solved Z0 assumes that conductance/length is zero and line supports TEM mode. """ try: return self._z0 except(AttributeError): self.run() return self._z0 @property def nstd(self): """ Normalized standard deviation of the calibration error. Normalization is done such that 90 degree long single line gives a standard deviation of 1. """ try: return self._nstd except(AttributeError): self.run() return self._nstd
[docs] def save_calibration(self, filename): """ save calibration as an archive containing the standards, parameters and calibration results Parameters ---------- filename : str the path of the zip archive to save """ parameters = OrderedDict() parameters["file type"] = "skrf calibration" parameters["calibration class"] = self.__class__.__name__ parameters["skrf version"] = skrf__version__ parameters["measured"] = ntwk_names = [ntwk.name for ntwk in self.measured] for i, name in enumerate(ntwk_names): ntwk_names[i] = util.unique_name(name, ntwk_names, i) parameters["ideals"] = None if self.switch_terms: fswitch, rswitch = self.switch_terms # type: Network fswitch.name = "forward switch terms" rswitch.name = "reverse switch terms" parameters["switch terms"] = fswitch.name, rswitch.name else: parameters["switch terms"] = None parameters["kwargs"] = { "Grefls": self.Grefls, "l": self.l, "er_est": self.er_est, "refl_offset": self.refl_offset, "ref_plane": self.ref_plane, "gamma_root_choice": self.gamma_root_choice, "k_method": self.k_method } with zipfile.ZipFile(filename, 'w', compression=zipfile.ZIP_DEFLATED) as archive: archive.writestr("parameters.json", json.dumps(parameters, indent=2)) if self.switch_terms: fswitch.write_touchstone(dir="switch terms", to_archive=archive) rswitch.write_touchstone(dir="switch terms", to_archive=archive) for i, ntwk in enumerate(self.measured): # type: int, Network ntwk.write_touchstone(ntwk_names[i] + ".s2p", dir="measured", to_archive=archive) for ntwk in self.coefs_ntwks.values(): ntwk.write_touchstone(dir="coefs", to_archive=archive) gamma_ntwk = Network(f=self.measured[0].f, s=self.gamma, z0=50., comments="propagation constant") gamma_ntwk.write_touchstone("gamma.s1p", to_archive=archive)
[docs] @classmethod def load_calibration_archive(cls, filename): with zipfile.ZipFile(filename) as archive: parameters = json.loads(archive.open("parameters.json").read().decode("ascii")) measured_dict = read_zipped_touchstones(archive, "measured") switch_terms_dict = read_zipped_touchstones(archive, "switch terms") coefs_dict = read_zipped_touchstones(archive, "coefs") # not used currently gamma_ntwk = Network.zipped_touchstone("gamma.s1p", archive) measured = list() for name in parameters["measured"]: measured.append(measured_dict[name]) if parameters["switch terms"] is None: switch_terms = None else: switch_terms = [ switch_terms_dict[parameters["switch terms"][0]], switch_terms_dict[parameters["switch terms"][1]] ] kwargs = parameters["kwargs"] cal = cls(measured, switch_terms=switch_terms, **kwargs) cal.coefs = NetworkSet(coefs_dict).to_s_dict() cal._gamma = gamma_ntwk.s.flatten() return cal
[docs] class TUGMultilineTRL(EightTerm): """ TUG Multiline TRL calibration. An improved multiline TRL calibration procedure that generalizes the calibration process by solving a single 4x4 weighted eigenvalue problem. The overall algorithm is based on [1]_, but the weighting matrix calculation is based on [2]_. You can read the mathematical details online at [3]_. The calibration reference plane is at the edges of the first line. By default, the reference impedance of the calibration is the characteristic impedance of the transmission lines. If the characteristic impedance is known, the reference impedance can be renormalized afterwards by running the method `renormalize()`. Examples -------- >>> line1 = rf.Network('line1.s2p') >>> line2 = rf.Network('line2.s2p') >>> line3 = rf.Network('line3.s2p') >>> short = rf.Network('short.s2p') >>> dut = rf.Network('dut.s2p') Normal multiline TRL calibration: >>> cal = rf.TUGMultilineTRL(line_meas=[line1,line2,line3], line_lengths=[0, 1e-3, 5e-3], er_est=4-.0j, >>> reflect_meas=short, reflect_est=-1, reflect_offset=0) >>> dut_cal = cal.apply_cal(dut) Case of not using reflect measurements: >>> cal = rf.TUGMultilineTRL(line_meas=[line1,line2,line3], line_lengths=[0, 1e-3, 5e-3], er_est=4-.0j) >>> dut_cal = cal.apply_cal(dut) # only S21 and S12 are correct References ---------- .. [1] Z. Hatab, M. Gadringer and W. Bösch, "Improving The Reliability of The Multiline TRL Calibration Algorithm," _2022 98th ARFTG Microwave Measurement Conference (ARFTG)_, Las Vegas, NV, USA, 2022, pp. 1-5, doi: https://doi.org/10.1109/ARFTG52954.2022.9844064 .. [2] Z. Hatab, M. Gadringer and W. Bösch, "Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration," 2023, e-print: https://arxiv.org/abs/2301.09126 .. [3] https://ziadhatab.github.io/posts/multiline-trl-calibration/ See Also -------- NISTMultilineTRL """ family = 'TRL'
[docs] def __init__(self, line_meas, line_lengths, er_est=1-.0j, reflect_meas=None, reflect_est=None, reflect_offset=0, ref_plane=0, *args, **kwargs): r""" TUGMultilineTRL initializer. The order of the lines in `line_meas` and `line_lengths` should be the same. Also, the first line is defined as thru. If non-zero, the calibration plane is shifted by half of its length using the extracted propagation constant. You can perform calibration without reflect measurements, but this will only provide you with the propagation constant and relative effective permittivity. Without reflect measurements, you can accurately calibrate S21 and S12 of a DUT. However, calibrating S11 and S22 requires a symmetric reflect as part of the calibration process. Notes ------- This implementation inherits from :class:`EightTerm`. Don't forget to pass switch_terms. Parameters -------------- line_meas : list of two-port :class:`~skrf.network.Network` measurement of the lines. First line is defined as thru. line_lengths : list of float Lengths of the lines. If thru is non-zero length, the calibration plane is shifted by half of its length using the solved propagation constant. Units are in meters. er_est : complex Estimated permittivity of the lines at first frequency point of the measurement. Negative imaginary part indicates losses. reflect_meas : a two-port :class:`~skrf.network.Network` or a list of two-port :class:`~skrf.network.Network` measurement of symmetric reflect. Multiple symmetric reflect can be passed in a list, which is used to compute to average solution of the error terms. reflect_est : complex or list of complex Estimated reflection coefficients of reflect standards at first frequency point of the measurement. Usually -1 for short or +1 for open. reflect_offset : float or list of float Offset of the reflect standards from the reference plane. Units are in meters. ref_plane : float or list of float Reference plane shift after the calibration. Negative length is towards the VNA. Units are in meters. Different shifts can be given to different ports by giving a two element list. First element is shift of port 1 and second is shift of port 2. \*args, \*\*kwargs : passed to EightTerm.__init__ dont forget the `switch_terms` argument is important """ self.line_meas = line_meas self.line_lengths = line_lengths self.er_est = er_est*(1+0j) # make complex if len(self.line_lengths) != len(self.line_meas): raise ValueError("Different amount of measured lines and line lengths found.") if len(self.line_lengths) < 2: raise ValueError("Less than two lines have been found.") self.freq = self.line_meas[0].frequency s_nan = npy.array([ npy.eye(2)*npy.nan for f in self.freq.f]) self.reflect_meas = ( [Network(s=s_nan, frequency=self.freq)] if reflect_meas is None else (reflect_meas if isinstance(reflect_meas, list) else [reflect_meas]) ) self.reflect_est = npy.atleast_1d(reflect_est) self.reflect_offset = npy.atleast_1d(reflect_offset)*npy.ones(len(self.reflect_est)) if len(self.reflect_meas) != len(self.reflect_est): raise ValueError("Different amount of measured reflects and estimated reflects found.") # EightTerm applies the switch correction measured = self.line_meas if reflect_meas is None else self.line_meas + self.reflect_meas EightTerm.__init__(self, measured = measured, ideals = measured, # not actually used. Just to initiate the class self_calibration=True, **kwargs) n_lines = len(self.line_lengths) # switch term corrected self.line_meas = self.measured_unterminated[:n_lines] self.reflect_meas = self.reflect_meas if reflect_meas is None else self.measured_unterminated[n_lines:] self.ref_plane = npy.atleast_1d(ref_plane)*npy.ones(2)
[docs] def run(self): # Constants c0 = 299792458 # speed of light in vacuum (m/s) Q = npy.array([[0,0,0,1], [0,-1,0,0], [0,0,-1,0], [1,0,0,0]]) P = npy.array([[1,0,0,0], [0, 0,1,0], [0,1, 0,0], [0,0,0,1]]) # Functions used throughout the calibration def gamma2ereff(x, f): return -(c0 / 2 / npy.pi / f * x) ** 2 def ereff2gamma(x, f): return 2 * npy.pi * f / c0 * npy.sqrt(-x) def s2t_single(S, pseudo=False): T = S.copy() T[0,0] = -(S[0,0]*S[1,1]-S[0,1]*S[1,0]) T[0,1] = S[0,0] T[1,0] = -S[1,1] T[1,1] = 1 return T if pseudo else T/S[1,0] def t2s_single(T, pseudo=False): S = T.copy() S[0,0] = T[0,1] S[0,1] = T[0,0]*T[1,1]-T[0,1]*T[1,0] S[1,0] = 1 S[1,1] = -T[1,0] return S if pseudo else S/T[1,1] def compute_G_with_takagi(A): ''' Implementation of Takagi decomposition to compute the matrix G used to determine the weighting matrix. Takagi decomposition is based on the paper below: Alexander M. Chebotarev, Alexander E. Teretenkov, "Singular value decomposition for the Takagi factorization of symmetric matrices," Applied Mathematics and Computation, Volume 234, 2014, Pages 380-384, https://doi.org/10.1016/j.amc.2014.01.170. ''' u,s,vh = npy.linalg.svd(A) u,s,vh = u[:,:2],s[:2],vh[:2,:] # low-rank truncated (Eckart-Young theorem) phi = npy.sqrt( s*npy.diag(vh@u.conj()) ) G = u@npy.diag(phi) # this is the eigenvalue of the weighted eigenvalue problem (1/2 squared Frobenius norm of W) lambd = s[0]*s[1] return G, lambd def WLS(x,y,w=1): # Weighted least-squares for a single parameter estimation x = x*(1+0j) # force x to be complex type return (x.conj().dot(w).dot(y))/(x.conj().dot(w).dot(x)) def Vgl(N): # inverse covariance matrix for propagation constant computation return npy.eye(N-1, dtype=complex) - (1/N)*npy.ones(shape=(N-1, N-1), dtype=complex) def compute_gamma(X_inv, M, lengths, gamma_est, inx=0): # gamma = alpha + 1j*beta is determined through linear weighted least-squares # with inx you can choose the refrence line. doesn't make any difference. lengths = lengths - lengths[inx] EX = (X_inv@M)[[0,-1],:] # extract z and y columns EX = npy.diag(1/EX[:,inx])@EX # normalize to a reference line based on index `inx` (can be any) del_inx = npy.arange(len(lengths)) != inx # get rid of the reference line # solve for alpha l = -2*lengths[del_inx] gamma_l = npy.log(EX[0,:]/EX[-1,:])[del_inx] alpha = WLS(l, gamma_l.real, Vgl(len(l)+1)) # solve for beta l = -lengths[del_inx] gamma_l = npy.log((EX[0,:] + 1/EX[-1,:])/2)[del_inx] n = npy.round( (gamma_l - gamma_est*l).imag/npy.pi/2 ) gamma_l = gamma_l - 1j*2*npy.pi*n # unwrap beta = WLS(l, gamma_l.imag, Vgl(len(l)+1)) return alpha + 1j*beta def solve_quadratic(v1, v2, inx, x_est): # This is realted to solving the normalized error terms using nullspace approach. # The variable `inx` allowes to reuse the function to shuffel the coeffiecient to get other error terms. v12,v13 = v1[inx] v22,v23 = v2[inx] mask = npy.ones(v1.shape, bool) mask[inx] = False v11,v14 = v1[mask] v21,v24 = v2[mask] if abs(v12) > abs(v22): # to avoid dividing by small numbers k2 = -v11*v22*v24/v12 + v11*v14*v22**2/v12**2 + v21*v24 - v14*v21*v22/v12 k1 = v11*v24/v12 - 2*v11*v14*v22/v12**2 - v23 + v13*v22/v12 + v14*v21/v12 k0 = v11*v14/v12**2 - v13/v12 c2 = npy.array([(-k1 - npy.sqrt(-4*k0*k2 + k1**2))/(2*k2), (-k1 + npy.sqrt(-4*k0*k2 + k1**2))/(2*k2)]) c1 = (1 - c2*v22)/v12 else: k2 = -v11*v12*v24/v22 + v11*v14 + v12**2*v21*v24/v22**2 - v12*v14*v21/v22 k1 = v11*v24/v22 - 2*v12*v21*v24/v22**2 + v12*v23/v22 - v13 + v14*v21/v22 k0 = v21*v24/v22**2 - v23/v22 c1 = npy.array([(-k1 - npy.sqrt(-4*k0*k2 + k1**2))/(2*k2), (-k1 + npy.sqrt(-4*k0*k2 + k1**2))/(2*k2)]) c2 = (1 - c1*v12)/v22 x = npy.array( [v1*x + v2*y for x,y in zip(c1,c2)] ) # 2 solutions mininx = npy.argmin( abs(x - x_est).sum(axis=1) ) return x[mininx] line_meas_S = npy.array([x.s for x in self.line_meas]) # get the S-parameters reflect_meas_S = npy.array([x.s for x in self.reflect_meas]) # get the S-parameters lengths = npy.atleast_1d( self.line_lengths ) # make numpy array er_est = self.er_est reflect_est = self.reflect_est reflect_offset = self.reflect_offset fpoints = len(self.freq.f) Xs = npy.zeros(shape=(fpoints, 4, 4), dtype=complex) # to store the combined error boxes (6 error terms) ks = npy.zeros(shape=(fpoints,), dtype=complex) # to store the 7th transmission error terms er_effs = npy.zeros(shape=(fpoints,), dtype=complex) gammas = npy.zeros(shape=(fpoints,), dtype=complex) lambds = npy.zeros(shape=(fpoints,), dtype=float) # to store the eigenvalue of the weighted eigendecomposition # compute the calibration at each frequency point for m, f in enumerate(self.freq.f): # measurements Mi = npy.array([s2t_single(x) for x in line_meas_S[:,m,:,:]]) # convert to T-parameters M = npy.array([x.flatten('F') for x in Mi]).T Dinv = npy.diag([1/npy.linalg.det(x) for x in Mi]) ## Compute W via Takagi decomposition (also the eigenvalue lambda) G, lambd = compute_G_with_takagi(Dinv@M.T@P@Q@M) W = (G@npy.array([[0,1j],[-1j,0]])@G.T).conj() gamma_est = ereff2gamma(er_est, f) gamma_est = abs(gamma_est.real) + 1j*abs(gamma_est.imag) # this to avoid sign inconsistencies z_est = npy.exp(-gamma_est*lengths) y_est = 1/z_est W_est = (npy.outer(y_est,z_est) - npy.outer(z_est,y_est)).conj() W = -W if abs(W-W_est).sum() > abs(W+W_est).sum() else W # resolve the sign ambiguity ## weighted eigenvalue problem F = M@W@Dinv@M.T@P@Q eigval, eigvec = npy.linalg.eig(F+lambd*npy.eye(4)) inx = npy.argsort(abs(eigval)) v1 = eigvec[:,inx[0]] v2 = eigvec[:,inx[1]] v3 = eigvec[:,inx[2]] v4 = eigvec[:,inx[3]] x1__est = v1/v1[0] x1__est[-1] = x1__est[1]*x1__est[2] x4_est = v4/v4[-1] x4_est[0] = x4_est[1]*x4_est[2] x2__est = npy.array([x4_est[2], 1, x4_est[2]*x1__est[2], x1__est[2]]) x3__est = npy.array([x4_est[1], x4_est[1]*x1__est[1], 1, x1__est[1]]) # solve quadratic equation for each column x1_ = solve_quadratic(v1, v4, [0,3], x1__est) # range x2_ = solve_quadratic(v2, v3, [1,2], x2__est) # nullspace x3_ = solve_quadratic(v2, v3, [2,1], x3__est) # nullspace x4 = solve_quadratic(v1, v4, [3,0], x4_est) # range # build the normalized error terms (average the answers from range and nullspaces) a12 = (x2_[0] + x4[2])/2 b21 = (x3_[0] + x4[1])/2 a21_a11 = (x1_[1] + x3_[3])/2 b12_b11 = (x1_[2] + x2_[3])/2 X_ = npy.kron([[1,b21],[b12_b11,1]], [[1,a12],[a21_a11,1]]) # normalized cal coefficients X_inv = npy.linalg.inv(X_) ## compute propagation constant gamma = compute_gamma(X_inv, M, lengths, gamma_est) er_eff = gamma2ereff(gamma, f) # new estimate of er_eff er_est = er_eff ## solve a11b11 and k from thru measurement (first line in the list) ka11b11,_,_,k = X_inv@M[:,0] a11b11 = ka11b11/k # shift plane to edges of the thru standard plus defined reference plane a11b11 = a11b11*npy.exp(2*gamma*(lengths[0] - self.ref_plane.sum())) k = k*npy.exp(-gamma*(lengths[0] - self.ref_plane.sum())) if npy.isnan(reflect_meas_S[0,m,0,0]): # no reflect measurement available. a11 = npy.sqrt(a11b11) b11 = a11 else: # solve for a11/b11, a11 and b11 (use redundant reflect measurement, if available) reflect_est_offset = reflect_est*npy.exp(-2*gamma*reflect_offset) # shift estimated reflect Mr = npy.array([s2t_single(x, pseudo=True).flatten('F') for x in reflect_meas_S[:,m,:,:]]).T T = X_inv@Mr a11_b11 = -T[2,:]/T[1,:] a11 = npy.sqrt(a11_b11*a11b11) b11 = a11b11/a11 G_cal = ( (reflect_meas_S[:,m,0,0] - a12) / (1 - reflect_meas_S[:,m,0,0]*a21_a11)/a11 + (reflect_meas_S[:,m,1,1] + b21)/(1 + reflect_meas_S[:,m,1,1]*b12_b11)/b11 )/2 # average for inx,(Gcal,Gest) in enumerate(zip(G_cal, reflect_est_offset)): if abs(Gcal - Gest) > abs(Gcal + Gest): a11[inx] = -a11[inx] b11[inx] = -b11[inx] G_cal[inx] = -G_cal[inx] a11 = a11.mean() b11 = b11.mean() X = X_@npy.diag([a11b11, b11, a11, 1]) # build the calibration matrix (de-normalize) Xs[m] = X ks[m] = k gammas[m] = gamma er_effs[m] = er_eff lambds[m] = lambd self._er_eff = er_effs self._gamma = gammas self._lambd = lambds e = npy.zeros(shape=(len(self.freq.f), 7), dtype=complex) e[:,0] = Xs[:,2,3] e[:,1] = -Xs[:,3,2] e[:,2] = -Xs[:,2,2] e[:,3] = -Xs[:,1,3] e[:,4] = Xs[:,3,1] e[:,5] = -Xs[:,1,1] e[:,6] = 1/ks/(e[:,4]*e[:,3]-e[:,5]) self._coefs = {\ 'forward directivity':e[:,0], 'forward source match':e[:,1], 'forward reflection tracking':e[:,0]*e[:,1]-e[:,2], 'reverse directivity':e[:,3], 'reverse source match':e[:,4], 'reverse reflection tracking':e[:,4]*e[:,3]-e[:,5], 'k':e[:,6], } self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fpoints, dtype=complex), 'reverse switch term': npy.zeros(fpoints, dtype=complex), }) # output is a dictionary of information self._output_from_run = { 'error vector':e }
@property def gamma(self): """ Propagation constant of the solved line. """ try: return self._gamma except(AttributeError): self.run() return self._gamma @property def er_eff(self): """ Relative effective permittivity of the solved line. """ try: return self._er_eff except(AttributeError): self.run() return self._er_eff @property def lambd(self): """ Eigenvalue of the weighted eigendecomposition. The closer the eigenvalue to zero, the more sensitive the calibration to error. Similar to the normalized standard deviation of NIST multiline TRL, but reversed. """ try: return self._lambd except(AttributeError): self.run() return self._lambd
[docs] class UnknownThru(EightTerm): """ Two-Port Self-Calibration allowing the *thru* standard to be unknown. This algorithm was originally developed in [1]_, and is based on the 8-term error model (:class:`EightTerm`). It allows the *thru* to be unknown, other than it must be reciprocal. This is useful when when a well-known thru is not realizable. References ---------- .. [1] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru,`" IEEE Microwave and Guided Wave Letters, vol. 2, no. 12, pp. 505-507, 1992. """ family = 'UnknownThru'
[docs] def __init__(self, measured, ideals, *args, **kwargs): r""" UnknownThru Initializer. Note that the *thru* standard must be last in both measured, and ideal lists. The ideal for the *thru* is only used to choose the sign of a square root. Thus, it only has to be have s21, s12 known within :math:`\pi` phase. Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ( or use `sloppy_input`) ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list ( or use `sloppy_input`) switch_terms : tuple of :class:`~skrf.network.Network` objects the pair of switch terms in the order (forward, reverse) """ EightTerm.__init__(self, measured = measured, ideals = ideals, **kwargs)
[docs] def run(self): p1_m = [k.s11 for k in self.measured_unterminated[:-1]] p2_m = [k.s22 for k in self.measured_unterminated[:-1]] p1_i = [k.s11 for k in self.ideals[:-1]] p2_i = [k.s22 for k in self.ideals[:-1]] thru_m = self.measured_unterminated[-1] # create one port calibration for all reflective standards port1_cal = OnePort(measured = p1_m, ideals = p1_i) port2_cal = OnePort(measured = p2_m, ideals = p2_i) # cal coefficient dictionaries p1_coefs = port1_cal.coefs.copy() p2_coefs = port2_cal.coefs.copy() e_rf = port1_cal.coefs_ntwks['reflection tracking'] e_rr = port2_cal.coefs_ntwks['reflection tracking'] # create a fully-determined 8-term cal just get estimate on k's sign # this is really inefficient, i need to work out the math on the # closed form solution et = EightTerm( measured = self.measured, ideals = self.ideals, switch_terms= self.switch_terms) k_approx = et.coefs['k'].flatten() # this is equivalent to sqrt(detX*detY/detM) e10e32 = npy.sqrt((e_rf*e_rr*thru_m.s21/thru_m.s12).s.flatten()) k_ = e10e32/e_rr.s.flatten() k_ = find_closest(k_, -1*k_, k_approx) #import pylab as plb #plot(abs(k_-k_approx)) #plb.show() # create single dictionary for all error terms coefs = {} coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() coefs.update({'forward %s'%k: p1_coefs[k] for k in p1_coefs}) coefs.update({'reverse %s'%k: p2_coefs[k] for k in p2_coefs}) if self.switch_terms is not None: coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: warn('No switch terms provided', stacklevel=2) coefs.update({ 'forward switch term': npy.zeros(len(self.frequency), dtype=complex), 'reverse switch term': npy.zeros(len(self.frequency), dtype=complex), }) coefs.update({'k':k_}) self.coefs = coefs
[docs] class LRM(EightTerm): """ Line-Reflect-Match self-calibration. The required calibration standards are: * Line: Fully known. * Reflect: Unknown reflect, phase needs to be known within 90 degrees. * Match: Fully known. Reflect and match are assumed to be identical on both ports. The measured and ideals lists must be given in LRM order. Implementation is based on [1]_. References ---------- .. [1] Zhao, W.; Liu, S.; Wang, H.; Liu, Y.; Zhang, S.; Cheng, C.; Feng, K.; Ocket, I.; Schreurs, D.; Nauwelaers, B.; Qin, H.; Yang, X. A Unified Approach for Reformulations of LRM/LRMM/LRRM Calibration Algorithms Based on the T-Matrix Representation. Appl. Sci. 2017, 7, 866. """ family = 'LRM'
[docs] def __init__(self, measured, ideals, switch_terms=None, isolation=None, *args, **kwargs): """ LRM Initializer. Parameters ---------- measured : list of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ideals : list of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `measured` list switch_terms : tuple of :class:`~skrf.network.Network` objects the pair of switch terms in the order (forward, reverse) isolation : :class:`~skrf.network.Network` object Measurement with loads on both ports with a perfect isolation between the ports. Used for determining the isolation error terms. If no measurement is given leakage is assumed to be zero. """ super().__init__( measured = measured, ideals = ideals, switch_terms = switch_terms, isolation = isolation, **kwargs)
[docs] def run(self): mList = [k for k in self.measured_unterminated] lm = mList[0] rm = mList[1] mm = mList[2] gm = self.ideals[2].s[:,0,0] if self.ideals[2].nports > 1: if any(gm != self.ideals[2].s[:,1,1]): warnings.warn('Match ideal port 1 and port 2 are different. Using port 1 match also for port 2.', stacklevel=2) if self.ideals[1].nports > 1: if any(self.ideals[1].s[:,0,0] != self.ideals[1].s[:,1,1]): warnings.warn('Reflect ideal port 1 and port 2 are different. Using port 1 reflect also for port 2.', stacklevel=2) inv = npy.linalg.inv tl = self.ideals[0].t fpoints = len(mList[0]) r1 = rm.s[:,0,0] r2 = rm.s[:,1,1] m1 = mm.s[:,0,0] m2 = mm.s[:,1,1] lm11 = lm.s[:,0,0] lm12 = lm.s[:,0,1] lm21 = lm.s[:,1,0] lm22 = lm.s[:,1,1] ones = npy.ones(fpoints, dtype=complex) zeros = npy.zeros(fpoints, dtype=complex) wlr1 = npy.transpose(npy.array([[ones, ones], [r1, m1]]), [2,0,1]) wll1 = npy.transpose(npy.array([[ones, zeros], [lm11, lm12]]), [2,0,1]) wll2 = npy.transpose(npy.array([[zeros, ones], [lm21, lm22]]), [2,0,1]) wlr2 = npy.transpose(npy.array([[ones, ones], [r2, m2]]), [2,0,1]) wl = inv(wlr1) @ wll1 @ inv(wll2) @ wlr2 # xyz2 == (x/y)*z**2 xyz2 = -npy.linalg.det(tl) / npy.linalg.det(wl) c2 = wl[:, 0, 0] c1 = -tl[:, 1, 0] - tl[:, 0, 1] c0 = wl[:, 1, 1] * xyz2 z0 = -c1 + npy.sqrt(c1**2 - 4*c2*c0)/(2*c2) z1 = -c1 - npy.sqrt(c1**2 - 4*c2*c0)/(2*c2) zs = npy.stack([z0, z1]) grs = npy.zeros((2, fpoints), dtype=complex) xs = npy.zeros((2, fpoints), dtype=complex) er = npy.zeros((2, fpoints), dtype=complex) for root in [0, 1]: z = zs[root] xyz = xyz2 / z w11 = wl[:, 0, 0] * z w21 = wl[:, 1, 0] * z w12 = wl[:, 0, 1] * xyz w22 = wl[:, 1, 1] * xyz x = w12 / (tl[:, 1, 0] + tl[:, 1, 1]*gm - w22) gr = (w11 - tl[:, 1, 0] + w21*x) / tl[:, 1, 1] er[root] = npy.abs(gr - self.ideals[1].s[:,0,0]) grs[root] = gr xs[root] = x root = er[0] < er[1] gr = npy.where(root, grs[0], grs[1]) x = npy.where(root, xs[0], xs[1]) z = npy.where(root, zs[0], zs[1]) y = x * z**2 / xyz2 self._solved_r = Network(s=gr, frequency=self.measured[0].frequency) # Calculate error matrices t10 = npy.transpose(npy.array([[ones, x], [gr, gm*x]]), [2,0,1]) \ @ inv(npy.transpose(npy.array([[ones,ones],[r1, m1]]), [2,0,1])) t23 = npy.transpose((1/z)*npy.array([[ones, y], [gr, gm*y]]), [2,0,1]) \ @ inv(npy.transpose(npy.array([[ones,ones],[r2, m2]]), [2,0,1])) Smat1 = t2s(t10) Smat2 = t2s(t23) # Convert the error coefficients to # definitions used by the EightTerm class. dx = linalg.det(Smat1) dy = linalg.det(Smat2) k = Smat1[:,0,1]/Smat2[:,0,1] # Error coefficients e = [Smat1[:,0,0], Smat1[:,1,1], dx, Smat2[:,0,0], Smat2[:,1,1], dy, k] self._coefs = {\ 'forward directivity':e[1], 'forward source match':e[0], 'forward reflection tracking':e[0]*e[1]-e[2], 'reverse directivity':e[4], 'reverse source match':e[3], 'reverse reflection tracking':e[4]*e[3]- e[5], 'k':e[6], } self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fpoints, dtype=complex), 'reverse switch term': npy.zeros(fpoints, dtype=complex), }) # output is a dictionary of information self._output_from_run = { 'error vector':e }
@property def solved_r(self): """ Solved reflect """ try: return self._solved_r except(AttributeError): self.run() return self._solved_r
[docs] class LRRM(EightTerm): """ Line-Reflect-Reflect-Match self-calibration. The required calibration standards are: * Line: Fully known. * Reflect: Unknown reflect, phase needs to be known within 90 degrees. * Reflect: Reflect with known absolute value of the reflection coefficient, \ phase needs to be known within 90 degrees. \ Different from the other reflect. * Match: Match with known resistance in series with unknown inductance. Reflects are assumed to be identical on both ports. Note that the first reflect's magnitude of the reflection coefficient can be unknown, but the second reflect's magnitude of the reflection coefficient needs to be known. Match needs to be only measured on the first port, the second port of match measurement is not used during the calibration. If match_fit == 'lc' then the second reflect is assumed to be a lossless capacitor. Measurements should then include low frequencies for accurate open capacitance determination. 'lc_fit_c_freq' argument can be given to specify the maximum frequency in Hz where open looks like an ideal capacitor, above this frequency open is assumed to only have known absolute value similar to 'l' fit. Default is infinity. Implementation is based on papers [1]_ and [2]_. 'lc' match_fit based on [3]_. References ---------- .. [1] Zhao, W.; Liu, S.; Wang, H.; Liu, Y.; Zhang, S.; Cheng, C.; Feng, K.; Ocket, I.; Schreurs, D.; Nauwelaers, B.; Qin, H.; Yang, X. A Unified Approach for Reformulations of LRM/LRMM/LRRM Calibration Algorithms Based on the T-Matrix Representation. Appl. Sci. 2017, 7, 866. .. [2] F. Purroy and L. Pradell, "New theoretical analysis of the LRRM calibration technique for vector network analyzers," in IEEE Transactions on Instrumentation and Measurement, vol. 50, no. 5, pp. 1307-1314, Oct. 2001. .. [3] S. Liu, I. Ocket, A. Lewandowski, D. Schreurs and B. Nauwelaers, "An Improved Line-Reflect-Reflect-Match Calibration With an Enhanced Load Model," in IEEE Microwave and Wireless Components Letters, vol. 27, no. 1, pp. 97-99, Jan. 2017. """ family = 'LRRM'
[docs] def __init__(self, measured, ideals, switch_terms=None, isolation=None, z0=50, match_fit='l', *args, **kwargs): """ LRRM Initializer. Parameters ---------- measured : list of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must be line, reflect, reflect, match and must align with the `ideals` parameter ideals : list of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `measured` list switch_terms : tuple of :class:`~skrf.network.Network` objects the pair of switch terms in the order (forward, reverse) isolation : :class:`~skrf.network.Network` object Measurement with loads on both ports with a perfect isolation between the ports. Used for determining the isolation error terms. If no measurement is given leakage is assumed to be zero. z0 : int Calibration reference impedance. Only affects the solved match inductance. Has no effect on the solved calibration parameters. match_fit : string or None Match model. Valid choices are: 'l' to fit a single inductance over all frequencies. 'lc' to fit match with series inductor and parallel capacitor and assuming that the second reflect is open with unknown capacitance. 'none' to not fit inductance and let it be different for each frequency point. 'l' or 'lc' is recommended for normal use. """ self.z0 = z0 # TODO: Second port not implemented. self.match_port = 0 # Maximum frequency to assume that open behaves like ideal capacitor when # using match_fit == 'lc'. self.lc_fit_c_freq = kwargs.get('lc_fit_c_freq', float('inf')) self.match_fit = match_fit if self.match_port not in [0, 1]: raise ValueError('match_port must be either 0 or 1.') super().__init__( measured = measured, ideals = ideals, switch_terms = switch_terms, isolation = isolation, **kwargs)
[docs] def run(self): mList = [k for k in self.measured_unterminated] lm = mList[0] r1m = mList[1] r2m = mList[2] mm = mList[3] inv = npy.linalg.inv tl = self.ideals[0].t w = 2*npy.pi*self.measured[0].f fpoints = len(mList[0]) r11 = r1m.s[:,0,0] r12 = r1m.s[:,1,1] r21 = r2m.s[:,0,0] r22 = r2m.s[:,1,1] lm11 = lm.s[:,0,0] lm12 = lm.s[:,0,1] lm21 = lm.s[:,1,0] lm22 = lm.s[:,1,1] mm1 = mm.s[:,0,0] thru_s21 = self.ideals[0].s[:,1,0] ones = npy.ones(fpoints, dtype=complex) zeros = npy.zeros(fpoints, dtype=complex) wlr1 = npy.transpose(npy.array([[ones, ones], [r11, r21]]), [2,0,1]) wll1 = npy.transpose(npy.array([[ones, zeros], [lm11, lm12]]), [2,0,1]) wll2 = npy.transpose(npy.array([[zeros, ones], [lm21, lm22]]), [2,0,1]) wlr2 = npy.transpose(npy.array([[ones, ones], [r12, r22]]), [2,0,1]) wl = inv(wlr1) @ wll1 @ inv(wll2) @ wlr2 # xyz2 == (x/y)*z**2 xyz2 = -npy.linalg.det(tl) / npy.linalg.det(wl) c2 = wl[:, 0, 0] c1 = -tl[:, 1, 0] - tl[:, 0, 1] c0 = wl[:, 1, 1] * xyz2 z0 = (-c1 + npy.sqrt(c1**2 - 4*c2*c0))/(2*c2) z1 = (-c1 - npy.sqrt(c1**2 - 4*c2*c0))/(2*c2) zs = npy.stack([z0, z1]) # wm and solve_gr equations are different if match is on the second port. assert self.match_port == 0 wm_t1 = inv(npy.transpose(npy.array([[ones, ones],[r11, r21]]), [2,0,1])) wm_t2 = npy.transpose(npy.array([[ones], [mm1]]), [2,0,1]) wm = wm_t1 @ wm_t2 wm1 = wm[:, 0, 0] wm2 = wm[:, 1, 0] def solve_gr(gm): gr1s = npy.zeros((2, fpoints), dtype=complex) gr2s = npy.zeros((2, fpoints), dtype=complex) xs = npy.zeros((2, fpoints), dtype=complex) er = npy.zeros((2, fpoints), dtype=complex) efs = npy.zeros((2, 4, fpoints), dtype=complex) for root in [0, 1]: z = zs[root] xyz = xyz2 / z w11 = wl[:, 0, 0] * z w21 = wl[:, 1, 0] * z w12 = wl[:, 0, 1] * xyz w22 = wl[:, 1, 1] * xyz e1 = (tl[:, 1, 1]**2) * wm1 e0 = tl[:, 1, 1] * (tl[:, 1, 0] - w22) * wm1 + tl[:, 1, 1] * wm2 * w12 f1 = tl[:, 1, 1] * (w11 - tl[:, 1, 0]) * wm1 + tl[:, 1, 1] * wm2 * w12 f0 = (w11 - tl[:, 1, 0]) * (tl[:, 1, 0] - w22) * wm1 + wm1 * w21 * w12 gr2 = -(f0 - e0 * gm) / (f1 - e1 * gm) x = w12 / (tl[:, 1, 0] + tl[:, 1, 1]*gr2 - w22) gr1 = ((w11 - tl[:, 1, 0]) * (tl[:, 1, 0] + tl[:, 1, 1] * gr2 - w22) + w21*w12) \ / (tl[:, 1, 1] * (tl[:, 1, 0] + tl[:, 1, 1] * gr2 - w22)) egr1 = npy.abs(gr1 - self.ideals[1].s[:,0,0]) egr2 = npy.abs(gr2 - self.ideals[2].s[:,0,0]) er[root] = egr1 + egr2 gr1s[root] = gr1 gr2s[root] = gr2 efs[root, 0, :] = e1 efs[root, 1, :] = e0 efs[root, 2, :] = f1 efs[root, 3, :] = f0 xs[root] = x root = er[0] < er[1] gr1 = npy.where(root, gr1s[0], gr1s[1]) gr2 = npy.where(root, gr2s[0], gr2s[1]) x = npy.where(root, xs[0], xs[1]) z = npy.where(root, zs[0], zs[1]) efs = npy.where(root, efs[0], efs[1]) y = x * z**2 / xyz2 return gr1, gr2, x, y, z, efs def calc_gm(R, l, c=0): """ Calculates reflection coefficient of resistor R in series with inductance l in parallel with capacitor c. """ return (self.z0 + R*(-1 + 1j*c*w*self.z0) - l*w*(1j + c*w*self.z0)) \ /(-self.z0 + R*(-1 - 1j*c*w*self.z0) + l*w*(-1j + c*w*self.z0)) # First, solve reflects assuming ideal gm gmi = self.ideals[3].s[:, self.match_port, self.match_port] gr1, gr2, x, y, z, efs = solve_gr(gmi) # Next solve for match inductance R = (self.z0 * (1 + gmi)/(1 - gmi)).real # Resistance of the match a = 2*gr2.real + npy.abs(gr2)**2 - \ 2*(gr2*thru_s21**(-2)).real - npy.abs(gr2*thru_s21**(-2))**2 b = 4*R*(gr2.imag + (gr2*thru_s21**(-2)).imag) c = 4*R**2*(npy.abs(gr2)**2 - 1) det = b**2 - 4*a*c if npy.any(det < 0): warnings.warn('Load inductance determination failed. Calibration might be incorrect.', stacklevel=2) det[det < 0] = 0 wL = [None, None] wL[0] = (-b+npy.sqrt(det))/(2*a) wL[1] = (-b-npy.sqrt(det))/(2*a) gm_guess = [None, None] for p in [0,1]: gm_guess[p] = (R + 1j*wL[p] - self.z0)/(R + 1j*wL[p] + self.z0) # Choose the root according to which one is closer to the ideal m_ideal = self.ideals[3].s[:,0,0] root = (npy.abs(gm_guess[0] - m_ideal) > npy.abs(gm_guess[1] - m_ideal)).astype(int) # L from reactance match_l = npy.choose(root, wL)/w match_c = zeros # Weight L estimate by frequency l0 = npy.sum(w * match_l) / npy.sum(w) e1 = efs[0, :] e0 = efs[1, :] f1 = efs[2, :] f0 = efs[3, :] gr2_abs = npy.abs(self.ideals[2].s[:,0,0]) if self.match_fit == 'l': def min_l(l): """ Calculates gr2 absolute value error as a function of the match inductance. """ gm = (R + 1j*w*l - self.z0)/(R + 1j*w*l + self.z0) return gr2_abs - npy.abs((f0 - e0 * gm) / (f1 - e1 * gm)) # Try some alternative initial guesses init_x = npy.linspace(-10, 10, 10) init_l = init_x / (w[-1]) init_guess = [npy.mean(min_l(l)**2) for l in init_l] li = npy.argmin(init_guess) best_guess = init_l[li] # Choose the best guess for the least squares initial value if init_guess[li] < npy.mean(min_l(l0)**2): l0 = best_guess sol = least_squares(min_l, l0, method='lm') match_l = sol.x * npy.ones(match_l.shape) match_c = zeros elif self.match_fit == 'lc': if self.ideals[2].s[0,0,0].real < 0: warnings.warn("2nd reflect assumed to be open, but 2nd ideal ' \ 'doesn't look like open. Calibration is likely incorrect.", stacklevel=2) match_c = -1/(npy.choose(root, wL)*w) c0 = npy.sum(w * match_c) / npy.sum(w) cw = w < 2 * npy.pi * self.lc_fit_c_freq cw = cw.astype(float) def min_lc(x): l, c = x gm = calc_gm(R, l, c) # Calculate open reflection coefficient from gm gr2 = -(f0 - e0 * gm) / (f1 - e1 * gm) # Fit capacitance to gr2 cgr2 = (1j*(-1 + gr2))/((1 + gr2)*w*self.z0) cgr2 = npy.mean(cgr2.real) gr2_c = (1j + cgr2*w*self.z0)/(1j - cgr2*w*self.z0) # Error between fitted open capacitor and calculated open # capacitance e_c = gr2_c + (f0 - e0 * gm) / (f1 - e1 * gm) e_abs = gr2_abs - npy.abs((f0 - e0 * gm) / (f1 - e1 * gm)) e = e_c * cw + (1 - cw) * e_abs return npy.abs(e) # Biggest capacitance value assuming given gm matching. worst_match = 0.4 # -7 dB max_init_c = (2*worst_match)/(npy.sqrt(1 - worst_match**2)*w[-1]*self.z0) # Initial reactance guess, try to find positive L, C. init_x = npy.linspace(0, 20, 10) init_l = init_x / (w[-1]) init_c = npy.linspace(0, max_init_c, 10) init_lc = [(l, c) for l in init_l for c in init_c] if l0 > 0: init_lc.append((l0, 0)) if c0 > 0: init_lc.append((0, c0)) init_guess = [npy.mean(min_lc(x)**2) for x in init_lc] best_guess = init_lc[npy.argmin(init_guess)] l0 = best_guess[0] c0 = best_guess[1] sol = least_squares(min_lc, [l0, c0], method='lm') match_l = sol.x[0] * npy.ones(match_l.shape) match_c = sol.x[1] * npy.ones(match_l.shape) elif self.match_fit == 'none' or self.match_fit is None: pass else: raise ValueError(f'Unknown match_fit {self.match_fit}') gamma_m = calc_gm(R, match_l, match_c) # Solve finally reflects and calibration parameters using the solved match gr1, gr2, x, y, z, _ = solve_gr(gamma_m) freq = self.measured[0].frequency self._solved_l = match_l self._solved_c = match_c self._solved_m = Network(s=gamma_m, frequency=freq, name='LRRM match') self._solved_r1 = Network(s=gr1, frequency=freq, name='LRRM reflect 1') self._solved_r2 = Network(s=gr2, frequency=freq, name='LRRM reflect 2') # Calculate error matrices t10 = npy.transpose(npy.array([[ones, x], [gr1, gr2*x]]), [2,0,1]) \ @ inv(npy.transpose(npy.array([[ones,ones],[r11, r21]]), [2,0,1])) t23 = npy.transpose((1/z)*npy.array([[ones, y], [gr1, gr2*y]]), [2,0,1]) \ @ inv(npy.transpose(npy.array([[ones,ones],[r12, r22]]), [2,0,1])) Smat1 = t2s(t10) Smat2 = t2s(t23) # Convert the error coefficients to # definitions used by the EightTerm class. dx = linalg.det(Smat1) dy = linalg.det(Smat2) k = Smat1[:,0,1]/Smat2[:,0,1] # Error coefficients e = [Smat1[:,0,0], Smat1[:,1,1], dx, Smat2[:,0,0], Smat2[:,1,1], dy, k] self._coefs = {\ 'forward directivity':e[1], 'forward source match':e[0], 'forward reflection tracking':e[0]*e[1]-e[2], 'reverse directivity':e[4], 'reverse source match':e[3], 'reverse reflection tracking':e[4]*e[3]- e[5], 'k':e[6], } self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fpoints, dtype=complex), 'reverse switch term': npy.zeros(fpoints, dtype=complex), }) # output is a dictionary of information self._output_from_run = { 'error vector':e }
@property def solved_l(self): """ Solved inductance of the load """ try: return self._solved_l except(AttributeError): self.run() return self._solved_l @property def solved_c(self): """ Solved capacitance of the load. Zero if match_fit != 'lc'. """ try: return self._solved_c except(AttributeError): self.run() return self._solved_c @property def solved_m(self): """ Solved match """ try: return self._solved_m except(AttributeError): self.run() return self._solved_m @property def solved_r1(self): """ Solved reflect1 """ try: return self._solved_r1 except(AttributeError): self.run() return self._solved_r1 @property def solved_r2(self): """ Solved reflect2 """ try: return self._solved_r2 except(AttributeError): self.run() return self._solved_r2
[docs] class MRC(UnknownThru): """ Misalignment Resistance Calibration. This is an error-box based calibration that is a combination of the SDDL[1]_ and the UnknownThru[2]_, algorithms. The self-calibration aspects of these two algorithms alleviate the need to know the phase of the delay shorts, as well as the exact response of the thru. Thus the calibration is resistant to waveguide flange misalignment. References ---------- .. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment," Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006. .. [2] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru,`" IEEE Microwave and Guided Wave Letters, vol. 2, no. 12, pp. 505-507, 1992. """ family = 'MRC'
[docs] def __init__(self, measured, ideals, *args, **kwargs): r""" MRC Initializer This calibration takes exactly 5 standards, which must be in the order: [Short, DelayShort1, DelayShort1, Load, Thru] The ideals for the delay shorts are not used and the ideal for the *thru* is only used to choose the sign of a square root. Thus, it only has to be have s21, s12 known within :math:`\pi` phase. Parameters -------------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list switch_terms : tuple of :class:`~skrf.network.Network` objects the pair of switch terms in the order (forward, reverse) """ UnknownThru.__init__(self, measured = measured, ideals = ideals, **kwargs)
[docs] def run(self): p1_m = [k.s11 for k in self.measured_unterminated[:-1]] p2_m = [k.s22 for k in self.measured_unterminated[:-1]] p1_i = [k.s11 for k in self.ideals[:-1]] p2_i = [k.s22 for k in self.ideals[:-1]] thru_m = self.measured_unterminated[-1] # create one port calibration for all reflective standards port1_cal = SDDL(measured = p1_m, ideals = p1_i) port2_cal = SDDL(measured = p2_m, ideals = p2_i) # cal coefficient dictionaries p1_coefs = port1_cal.coefs.copy() p2_coefs = port2_cal.coefs.copy() e_rf = port1_cal.coefs_ntwks['reflection tracking'] e_rr = port2_cal.coefs_ntwks['reflection tracking'] # create a fully-determined 8-term cal just get estimate on k's sign # this is really inefficient, i need to work out the math on the # closed form solution et = EightTerm( measured = self.measured, ideals = self.ideals, switch_terms= self.switch_terms) k_approx = et.coefs['k'].flatten() # this is equivalent to sqrt(detX*detY/detM) e10e32 = npy.sqrt((e_rf*e_rr*thru_m.s21/thru_m.s12).s.flatten()) k_ = e10e32/e_rr.s.flatten() k_ = find_closest(k_, -1*k_, k_approx) #import pylab as plb #plot(abs(k_-k_approx)) #plb.show() # create single dictionary for all error terms coefs = {} coefs.update({'forward %s'%k: p1_coefs[k] for k in p1_coefs}) coefs.update({'reverse %s'%k: p2_coefs[k] for k in p2_coefs}) coefs['forward isolation'] = self.isolation.s[:,1,0].flatten() coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten() if self.switch_terms is not None: coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: warn('No switch terms provided', stacklevel=2) coefs.update({ 'forward switch term': npy.zeros(len(self.frequency), dtype=complex), 'reverse switch term': npy.zeros(len(self.frequency), dtype=complex), }) coefs.update({'k':k_}) self.coefs = coefs
[docs] class SixteenTerm(Calibration): """ General SixteenTerm (aka Error-box) Two-port calibration. 16-term error model is a complete error model that can solve for leakages between the different VNA receivers. There are several different combinations of calibration standards that can be used. At least five two port measurements are needed. Using through, open, short, and load standards some combinations result in singular matrix. See [1]_ for list of non-singular combinations. References ----------- .. [1] K. J. Silvonen, "Calibration of 16-term error model (microwave measurement)," in Electronics Letters, vol. 29, no. 17, pp. 1544-1545, 19 Aug. 1993. """ family = 'SixteenTerm'
[docs] def __init__(self, measured, ideals, switch_terms=None, *args, **kwargs): """ SixteenTerm Initializer. Notes ----- Switch terms are already assumed to be corrected since the ordinary correction equations are not valid if the crosstalk is significant. Parameters ---------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. The order must align with the `ideals` parameter ideals : list/dict of :class:`~skrf.network.Network` objects Predicted ideal response of the calibration standards. The order must align with `ideals` list switch_terms : tuple of :class:`~skrf.network.Network` objects the pair of switch terms in the order (forward, reverse) """ self.switch_terms = switch_terms if switch_terms is None: warn('No switch terms provided', stacklevel=2) Calibration.__init__(self, measured = measured, ideals = ideals, **kwargs)
[docs] def unterminate(self,ntwk): """ Unterminate switch terms from a raw measurement. See Also -------- calibration.unterminate """ if self.switch_terms is not None: gamma_f, gamma_r = self.switch_terms return unterminate(ntwk, gamma_f, gamma_r) else: return ntwk
[docs] def terminate(self, ntwk): """ Terminate a network with switch terms. See Also -------- calibration.terminate """ if self.switch_terms is not None: gamma_f, gamma_r = self.switch_terms return terminate(ntwk, gamma_f, gamma_r) else: return ntwk
@property def measured_unterminated(self): return [self.unterminate(k) for k in self.measured]
[docs] def run(self): numStds = self.nstandards numCoefs = 15 mList = [k.s for k in self.measured_unterminated] iList = [k.s for k in self.ideals] fLength = len(mList[0]) #initialize outputs error_vector = npy.zeros(shape=(fLength,numCoefs),dtype=complex) residuals = npy.zeros(shape=(fLength,4*numStds-numCoefs),dtype=complex) Q = npy.zeros((numStds*4, 15),dtype=complex) M = npy.zeros((numStds*4, 1),dtype=complex) # loop through frequencies and form m, a vectors and # the matrix M. #i[j,k] = Actual S-parameters #m[j,k] = Measured S-parameters #t15 is normalized to one for f in list(range(fLength)): # loop through standards and fill matrix for k in list(range(numStds)): m,i = mList[k][f,:,:],iList[k][f,:,:] # 2x2 s-matrices Q[k*4:k*4+4,:] = npy.array([ [ i[0,0], i[1,0], 0 , 0 , 1, 0, 0, 0, -m[0,0]*i[0,0], -m[0,0]*i[1,0], -m[0,1]*i[0,0], -m[0,1]*i[1,0], -m[0,0] , 0 , -m[0,1] ], # noqa: E501 [ i[0,1], i[1,1], 0 , 0 , 0, 1, 0, 0, -m[0,0]*i[0,1], -m[0,0]*i[1,1], -m[0,1]*i[0,1], -m[0,1]*i[1,1], 0 , -m[0,0] , 0 ], # noqa: E501 [ 0 , 0 , i[0,0], i[1,0], 0, 0, 1, 0, -m[1,0]*i[0,0], -m[1,0]*i[1,0], -m[1,1]*i[0,0], -m[1,1]*i[1,0], -m[1,0] , 0 , -m[1,1] ], # noqa: E501 [ 0 , 0 , i[0,1], i[1,1], 0 ,0 ,0, 1, -m[1,0]*i[0,1], -m[1,0]*i[1,1], -m[1,1]*i[0,1], -m[1,1]*i[1,1], 0 , -m[1,0] , 0 ], # noqa: E501 ]) #pdb.set_trace() M[k*4:k*4+4,:] = npy.array([\ [ 0 ],\ [ m[0,1] ],\ [ 0 ],\ [ m[1,1] ],\ ]) ## calculate least squares error_vector_at_f, residuals_at_f = npy.linalg.lstsq(Q,M,rcond=None)[0:2] ##if len (residualsTmp )==0: ## raise ValueError( 'matrix has singular values, check standards') error_vector[f,:] = error_vector_at_f.flatten() residuals[f,:] = residuals_at_f e = error_vector #Normalize e23 = 1 c = e[:,12]/(e[:,12]-e[:,13]*e[:,14]) for i in range(len(e[0])): e[:,i] *= c T1 = npy.zeros(shape=(fLength, 2, 2), dtype=complex) T2 = npy.zeros(shape=(fLength, 2, 2), dtype=complex) T3 = npy.zeros(shape=(fLength, 2, 2), dtype=complex) T4 = npy.zeros(shape=(fLength, 2, 2), dtype=complex) T1[:,0,0] = e[:,0] T1[:,0,1] = e[:,1] T1[:,1,0] = e[:,2] T1[:,1,1] = e[:,3] T2[:,0,0] = e[:,4] T2[:,0,1] = e[:,5] T2[:,1,0] = e[:,6] T2[:,1,1] = e[:,7] T3[:,0,0] = e[:,8] T3[:,0,1] = e[:,9] T3[:,1,0] = e[:,10] T3[:,1,1] = e[:,11] T4[:,0,0] = e[:,12] T4[:,0,1] = e[:,13] T4[:,1,0] = e[:,14] T4[:,1,1] = c # put the error vector into human readable dictionary e1, e2, e3, e4 = self.E_matrices(T1, T2, T3, T4) self._coefs = {\ 'forward directivity':e1[:,0,0], 'reverse directivity':e1[:,1,1], 'forward source match':e4[:,0,0], 'reverse source match':e4[:,1,1], 'forward reflection tracking':e2[:,0,0]*e3[:,0,0], 'reverse reflection tracking':e2[:,1,1], 'k':e3[:,0,0], 'forward isolation':e1[:,1,0], 'reverse isolation':e1[:,0,1], 'forward port 1 isolation':e3[:,1,0], 'reverse port 1 isolation':e2[:,0,1], 'forward port 2 isolation':e2[:,1,0], 'reverse port 2 isolation':e3[:,0,1], 'forward port isolation':e4[:,1,0], 'reverse port isolation':e4[:,0,1], } if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fLength, dtype=complex), 'reverse switch term': npy.zeros(fLength, dtype=complex), }) # output is a dictionary of information self._output_from_run = { 'error vector':e, 'residuals':residuals } return None
[docs] def apply_cal(self, ntwk): """Applies the calibration to the input network. Inverse of `embed`. Parameters ---------- ntwk : :class:`~skrf.network.Network` Uncalibrated input network. Returns ------- caled : :class:`~skrf.network.Network` Calibrated network. """ caled = ntwk.copy() T1,T2,T3,T4 = self.T_matrices caled = self.unterminate(caled) caled.s = linalg.inv(-caled.s @ T3 + T1) @ (caled.s @ T4 - T2) return caled
[docs] def embed(self, ntwk): """Applies the error boxes to the calibrated input network. Inverse of `apply_cal`. Parameters ---------- ntwk : :class:`~skrf.network.Network` Calibrated input network. Returns ------- embedded : :class:`~skrf.network.Network` Network with error boxes applied. """ embedded = ntwk.copy() T1,T2,T3,T4 = self.T_matrices embedded.s = (T1 @ ntwk.s + T2) @ linalg.inv(T3 @ ntwk.s + T4) embedded = self.terminate(embedded) return embedded
@property def T_matrices(self): """ Intermediate matrices used for embedding and de-embedding. Returns ------- T1,T2,T3,T4 : numpy ndarray """ ec = self.coefs npoints = len(ec['forward directivity']) e100 = ec['forward directivity'] e111 = ec['reverse directivity'] e400 = ec['forward source match'] e411 = ec['reverse source match'] e300 = ec['k'] e311 = npy.ones(npoints) e200 = ec['forward reflection tracking']/e300 e211 = ec['reverse reflection tracking'] e110 = ec['forward isolation'] e101 = ec['reverse isolation'] e301 = ec['reverse port 2 isolation'] e310 = ec['forward port 1 isolation'] e201 = ec['reverse port 1 isolation'] e210 = ec['forward port 2 isolation'] e401 = ec['reverse port isolation'] e410 = ec['forward port isolation'] E1 = npy.array([ [ e100 , e101], [ e110 , e111] ]).transpose(2,0,1) E2 = npy.array([ [ e200 , e201], [ e210 , e211] ]).transpose(2,0,1) E3 = npy.array([ [ e300 , e301], [ e310 , e311] ]).transpose(2,0,1) E4 = npy.array([ [ e400 , e401], [ e410 , e411] ]).transpose(2,0,1) invE3 = linalg.inv(E3) T1 = E2 - E1 @ invE3 @ E4 T2 = E1 @ invE3 T3 = -invE3 @ E4 T4 = invE3 return T1, T2, T3, T4
[docs] def E_matrices(self, T1, T2, T3, T4): """ Convert solved calibration T matrices to S-parameters. Returns ------- E1,E2,E3,E4 : numpy ndarray """ invT4 = linalg.inv(npy.array(T4)) E1 = T2 @ invT4 E2 = T1 - T2 @ invT4 @ T3 E3 = invT4 E4 = -invT4 @ T3 return E1, E2, E3, E4
[docs] class LMR16(SixteenTerm): """ SixteenTerm Load-Match-Reflect self-calibration. 16-Term self calibration for leaky VNA. Implementation is based on [1]_. Needs five standards to be measured and given in this order: * Through * Match-match * Reflect-reflect * Reflect-match * Match-reflect Reflect standard needs to be very reflective and same in all measurements. Matching of through and match standards is assumed to be perfect. Loss of the through is assumed to be zero, but its length can be non-zero. Only reflect or through standard needs to be known and the other one will be solved during the calibration. Solved S-parameters of the standards can be accessed with LMR16.solved_through and LMR16.solved_reflect. Switch termination is already assumed to be done either by the previous calibration or during the measurements. Regular switch correction equations used with EightTerm calibration can't be used if leakage is significant. References ------------ .. [1] K. Silvonen, "LMR 16-a self-calibration procedure for a leaky network analyzer," in IEEE Transactions on Microwave Theory and Techniques, vol. 45, no. 7, pp. 1041-1049, Jul 1997 """ family = 'SixteenTerm'
[docs] def __init__(self, measured, ideals, ideal_is_reflect=True, sign=None, switch_terms=None, *args, **kwargs): r""" LMR16 initializer. Due to needing to solve a second order equation during the calibration a choice must be taken on the correct root. Sign argument, +1 or -1, can be given to make the root choice. If sign argument is not given it is tried to be solved automatically by choosing the sign that makes :math:`k = \frac{t_{15}}{t_{12}}` closer to +1, which holds if test fixture is symmetric. Parameters -------------- measured : list/dict of :class:`~skrf.network.Network` objects Raw measurements of the calibration standards. ideals : list/dict of :class:`~skrf.network.Network` objects Estimated response of the reflect or through calibration standard. ideal_is_reflect : Boolean True if given ideal is reflect and False if ideal is through sign : +1,-1 or None Sign to be used for the root choice. """ self.switch_terms = switch_terms if switch_terms is None: warn('No switch terms provided', stacklevel=2) if type(ideals) == Network: ideals = [ideals] if len(ideals) != 1: raise ValueError("One ideal must be given: Through or reflect definition.") if not ideal_is_reflect: self.through = ideals[0].copy() self.reflect = None self._solved_through = self.through self._solved_reflect = Network(s=[0]*len(self.through.f), f=self.through.f, f_unit='Hz') else: self.through = None self.reflect = ideals[0].copy() self._solved_through = Network(s=[[[0,1],[1,0]]]*len(self.reflect.f), f=self.reflect.f, f_unit='Hz') self._solved_reflect = self.reflect if len(measured) != 5: raise ValueError("5 Measurements are needed: T, M-M, R-R, R-M and M-R") self.measured = measured self.sign = sign Calibration.__init__(self, measured = measured, ideals = ideals, sloppy_input=False, self_calibration=True, **kwargs)
[docs] def run(self): mList = [k.s for k in self.measured_unterminated] fLength = len(mList[0]) inv = linalg.inv T1 = [] T2 = [] T3 = [] T4 = [] auto_sign = self.sign is None for f in range(fLength): ma = mList[0][f] #Through mb = mList[1][f] #Match-match mc = mList[2][f] #Reflect-reflect md = mList[3][f] #Reflect-match me = mList[4][f] #Match-reflect nn = inv(me-ma).dot(mb-me) mm = (ma-mc).dot(nn) oo = mb-mc rr = inv(md-ma).dot(mb-md) pp = (ma-mc).dot(rr) m = (pp[1,0] + oo[1,0])*mm[1,1] - (pp[1,1] + oo[1,1])*mm[1,0] n = oo[1,0]*pp[0,1] - oo[1,1]*pp[0,0] o = (mm[0,1]+ oo[0,1])*pp[0,0] - (mm[0,0] + oo[0,0])*pp[0,1] p = oo[0,1]*mm[1,0] - oo[0,0]*mm[1,1] #One of the coefficients is normalized to one t12 = 1.0 auto_sign_abs = [] if auto_sign: self.sign = 1 for sign_tries in [0,1,2]: gt = self.sign*npy.sqrt(m*o/(n*p)) if self.through is None: g = self.reflect.s[f][0,0] t = g/gt self._solved_through.s[f] = npy.array([[0,t],[t,0]]) else: t = self.through.s[f][1,0] g = gt*t self._solved_reflect.s[f] = npy.array([g]) t15 = -(p/o)*(pp[0,0]/mm[1,1])*gt*t12 #If correct sign is not specified try to choose it based #on the fact that with correct sign t15/t12 ~= +1 #Assuming that test fixtures are symmetric if auto_sign: auto_sign_abs.append(npy.abs(1 - t15/t12)) if sign_tries == 0: self.sign = -self.sign if sign_tries == 1: if auto_sign_abs[0] < auto_sign_abs[1]: self.sign = 1 else: self.sign = -1 else: break t13 = -pp[0,1]/pp[0,0]*t15 t14 = -mm[1,0]/mm[1,1]*t12 #Normalize e23 = 1 c = 1/(t15 - t13*t14) t8 = (rr[0,0]*t12 + rr[0,1]*t14)*(1./g) - t13/t t9 = (nn[0,0]*t13 + nn[0,1]*t15)*(1./g) - t12/t t10 = (rr[1,0]*t12 + rr[1,1]*t14)*(1./g) - t15/t t11 = (nn[1,0]*t13 + nn[1,1]*t15)*(1./g) - t14/t t0 = mc[0,0]*t8 + mc[0,1]*t10 - (1./g)*(oo[0,0]*t12+oo[0,1]*t14) t1 = mc[0,0]*t9 + mc[0,1]*t11 - (1./g)*(oo[0,0]*t13+oo[0,1]*t15) t2 = mc[1,0]*t8 + mc[1,1]*t10 - (1./g)*(oo[1,0]*t12+oo[1,1]*t14) t3 = mc[1,0]*t9 + mc[1,1]*t11 - (1./g)*(oo[1,0]*t13+oo[1,1]*t15) t4 = mb[0,0]*t12 + mb[0,1]*t14 t5 = mb[0,0]*t13 + mb[0,1]*t15 t6 = mb[1,0]*t12 + mb[1,1]*t14 t7 = mb[1,0]*t13 + mb[1,1]*t15 T1.append( c*npy.array([[t0,t1],[t2,t3]]) ) T2.append( c*npy.array([[t4,t5],[t6,t7]]) ) T3.append( c*npy.array([[t8,t9],[t10,t11]]) ) T4.append( c*npy.array([[t12,t13],[t14,t15]]) ) T1 = npy.array(T1) T2 = npy.array(T2) T3 = npy.array(T3) T4 = npy.array(T4) #Convert T-matrix to S-parameters #and put error terms in human readable form e1,e2,e3,e4 = self.E_matrices(T1, T2, T3, T4) self._coefs = {\ 'forward directivity':e1[:,0,0], 'reverse directivity':e1[:,1,1], 'forward source match':e4[:,0,0], 'reverse source match':e4[:,1,1], 'forward reflection tracking':e2[:,0,0]*e3[:,0,0], 'reverse reflection tracking':e2[:,1,1], 'k':e3[:,0,0], 'forward isolation':e1[:,1,0], 'reverse isolation':e1[:,0,1], 'forward port 1 isolation':e3[:,1,0], 'reverse port 1 isolation':e2[:,0,1], 'forward port 2 isolation':e2[:,1,0], 'reverse port 2 isolation':e3[:,0,1], 'forward port isolation':e4[:,1,0], 'reverse port isolation':e4[:,0,1], } if self.switch_terms is not None: self._coefs.update({ 'forward switch term': self.switch_terms[0].s.flatten(), 'reverse switch term': self.switch_terms[1].s.flatten(), }) else: self._coefs.update({ 'forward switch term': npy.zeros(fLength, dtype=complex), 'reverse switch term': npy.zeros(fLength, dtype=complex), }) return None
[docs] @classmethod def from_coefs(cls, frequency, coefs, **kwargs): """ Create a calibration from its error coefficients. Parameters ---------- frequency : :class:`~skrf.frequency.Frequency` frequency info, (duh) coefs : dict of numpy arrays error coefficients for the calibration See Also -------- Calibration.from_coefs_ntwks """ n = Network(frequency = frequency, s = rand_c(frequency.npoints,2,2)) measured = [n,n,n,n,n] if 'forward switch term' in coefs: switch_terms = (Network(frequency = frequency, s=coefs['forward switch term']), Network(frequency = frequency, s=coefs['reverse switch term'])) kwargs['switch_terms'] = switch_terms cal = cls(measured, measured[0], **kwargs) cal.coefs = coefs cal.family += '(fromCoefs)' return cal
@property def residual_ntwks(self): """ Dictionary of residual Networks. These residuals are complex differences between the ideal standards and their corresponding corrected measurements. """ #Runs the calibration if needed caled_ntwks = self.caled_ntwks r = self.solved_reflect m = Network(s=[0]*len(self.solved_reflect.f), f=self.solved_reflect.f, f_unit='Hz') mm = two_port_reflect(m, m) mr = two_port_reflect(m, r) rm = two_port_reflect(r, m) rr = two_port_reflect(r, r) ideals = [self.solved_through, mm, rr, rm, mr] return [caled - ideal for (ideal, caled) in zip(ideals, caled_ntwks)] @property def solved_through(self): """ Return the solved through or the ideal through if reflect was solved. """ if not hasattr(self, '_coefs'): self.run() return self._solved_through @property def solved_reflect(self): """ Return the solved reflect or the ideal reflect if through was solved. """ if not hasattr(self, '_coefs'): self.run() return self._solved_reflect
[docs] class Normalization(Calibration): """ Simple Thru Normalization. For calibration the S parameters of the network are divided by average of the measured networks. The ideal networks are not used in the calibration. """
[docs] def run(self): pass
[docs] def apply_cal(self, input_ntwk): return input_ntwk/average(self.measured)
[docs] class MultiportCal: """ Multi-port VNA calibration using two-port calibration method. cal_dict should be a dictionary with key being two-tuples of port numbers, such as (0, 1), (0, 2), ... For each key it should have another dictionary as value. The two required keys are 'method' that should be the two-port calibration class that is used to calibrate that two-port combination (for example SOLT, EightTerm, TRL) and 'measured' which is a list of measured Networks. Other inputs required by the two-port calibration should be given as additional keys (for example 'ideals', 'switch_terms', ...). There should be one common port in all measurements. For example in case of 4-port calibration one possible choice would be to make three measurements between ports: 0-1, 0-2, and 0-3. The list of measured networks can be given as either two-ports, in which case it's assumed that the two ports corresponds to the ports in the key, or multi-ports in which case a subnetwork is taken for calibration according to the key. Example cal_dict for three port measurement: {(0,1): {'method':SOLT, 'measured': [list of measured networks], 'ideals': [list of ideal networks]}, (0,2): {'method':SOLT, 'measured': [list of measured networks], 'ideals': [list of ideal networks]} } `isolation` is optional N-port network of all ports matched for isolation calibration. If None, no isolation calibration is performed. Parameters -------------- cal_dict : dictionary Dictionary of port pair keys as specified above. isolation: :class:`~skrf.network.Network` or None N-port measurement of all matched ports for isolation calibration. None to skip isolation calibration. See Also -------- calibration.MultiportSOLT """ family = 'Multiport'
[docs] def __init__(self, cal_dict, isolation=None): if not isinstance(cal_dict, dict): raise ValueError("cal_dict not dictionary.") nports = None max_key_nports = 0 min_key_nports = float('inf') z0 = None frequency = None for k, c in cal_dict.items(): if len(k) != 2: raise ValueError(f"Invalid cal_dict key {k}. Expected tuple of length two.") if not isinstance(k[0], int) or not isinstance(k[1], int): raise ValueError("cal_dict key should be tuple of ints.") max_key_nports = max(max_key_nports, max(k[0], k[1])) min_key_nports = min(min_key_nports, min(k[0], k[1])) if not isinstance(c, dict): raise ValueError(f"cal_dict[{k}] not dictionary.") if 'method' not in c: raise ValueError(f"cal_dict[{k}] missing key 'method'.") if 'measured' not in c: raise ValueError(f"cal_dict[{k}] missing key 'measured'.") for m in c['measured']: if not isinstance(m, Network): raise ValueError(f"Expected Network in cal_dict[{k}]['measured']") if nports is None: nports = m.nports if m.nports not in [2, nports]: raise ValueError("Measurement have inconsistent number of ports.") if z0 is None: z0 = m.z0[0,0] elif m.z0[0,0] != z0: raise ValueError("Inconsistent z0 in measured.") if frequency is None: frequency = m.frequency elif m.frequency != frequency: raise ValueError("Inconsistent frequency in measured.") self.nports = nports = max_key_nports + 1 if min_key_nports < 0: raise ValueError("Negative port number found. Minimum should be zero.") if min_key_nports != 0: raise ValueError("Missing port 0. Make sure that ports are zero-indexed.") if max_key_nports < 2: raise ValueError("Less than three ports found. Use two-port or one-port calibration directly.") if isolation is not None: # Zero diagonal so that network can be simply subtracted isolation = isolation.copy() if isolation.nports != nports: raise ValueError("Isolation network should have the same number of ports as measurements.") for i in range(nports): isolation.s[:,i,i] = 0 else: s = npy.zeros((len(frequency), nports, nports), dtype=complex) isolation = Network(s=s, z0=z0, frequency=frequency) self.isolation = isolation self.cal_dict = cal_dict self.z0 = z0 self.frequency = frequency self.cals = {}
[docs] def run(self): """ Run the calibration algorithm. """ nports = self.nports p_count = defaultdict(int) self.terminations = [None for i in range(nports)] self._coefs = [{} for i in range(nports)] for p in self.cal_dict.keys(): p_count[p[0]] += 1 p_count[p[1]] += 1 port_multiples = sorted(p_count.values()) if port_multiples[-2] != 1: # It's easy to put `k` in non-repeated ports if one port is always used. # I think this limitation could be removed if the `k` would be # solved to be consistent in repeated ports. raise ValueError("Invalid thru port combinations. One port should be common in all thru measurements.") for p in self.cal_dict.keys(): c = self.cal_dict[p].copy() if 'ideals' in c: ideals = [i if i.nports == 2 else subnetwork(i, p) for i in c['ideals']] c['ideals'] = ideals c['measured'] = [m - subnetwork(self.isolation, p) if m.nports == 2 else subnetwork(m - self.isolation, p) for m in c['measured']] k_side = 0 if p_count[p[0]] > p_count[p[1]]: k_side = 1 method = c.pop('method') self.run_2port(method, p, k_side, **c)
[docs] def run_2port(self, method, p, k_side, **kwargs): r""" Call the two-port calibration algorithm and populate multi-port error coefficients for this port pair. Parameters ---------- method: Two-port calibration class Use to calibrate the port pair. p: tuple of int Length two tuple of port indices in the pair. k_side: int Port to put 'k' coefficient in the pair. \*\*kwargs: Keyword arguments Passed to the calibration method. """ cal = method(**kwargs) cal.run() self.cals[p] = cal coefs = cal.coefs_8term S1, S2 = self.coefs_to_ntwks(coefs, k_side=k_side) one = npy.ones(coefs['k'].shape, dtype=complex) for c in cal.coefs_8term: if 'forward' in c: c2 = c.replace('forward ', '') if 'switch term' in c: self._coefs[p[1]][c2] = coefs[c] else: self._coefs[p[0]][c2] = coefs[c] elif 'reverse' in c: c2 = c.replace('reverse ', '') if 'switch term' in c: self._coefs[p[0]][c2] = coefs[c] else: self._coefs[p[1]][c2] = coefs[c] elif c == 'k': self._coefs[p[k_side]][c] = coefs[c] if 'k' not in self._coefs[p[not k_side]].keys(): self._coefs[p[not k_side]][c] = one else: warn(f'Unknown coefficient in calibration {c}', stacklevel=2) term1 = self.dut_termination(S1, coefs['reverse switch term']) term2 = self.dut_termination(S2, coefs['forward switch term']) f = self.frequency self.terminations[p[0]] = Network(s=term1, z0=self.z0, frequency=f) self.terminations[p[1]] = Network(s=term2, z0=self.z0, frequency=f)
@property def coefs(self): try: return self._coefs except(AttributeError): self.run() return self._coefs @coefs.setter def coefs(self, d): self._coefs = d
[docs] def unterminate_2port(self, ntwk, p1, p2): """ Unterminates switch terms from a raw measurement. See Also -------- calibration.unterminate """ gamma_f = Network(s=self.coefs[p2]['switch term']) gamma_r = Network(s=self.coefs[p1]['switch term']) return unterminate(ntwk, gamma_f, gamma_r)
[docs] def terminate_2port(self, ntwk, p1, p2): """ Terminate a network with switch terms. See Also -------- calibration.terminate """ gamma_f = self.coefs[p2]['switch term'] gamma_r = self.coefs[p1]['switch term'] return terminate(ntwk, gamma_f, gamma_r)
[docs] def T_matrices(self, p1, p2): """ Intermediate matrices used for embedding and de-embedding. Returns ------- T1,T2,T3,T4 : numpy ndarray """ npoints = len(self.coefs[0]['k']) zero = npy.zeros(npoints, dtype=complex) Edf = self.coefs[p1]['directivity'] Esf = self.coefs[p1]['source match'] Erf = self.coefs[p1]['reflection tracking'] Edr = self.coefs[p2]['directivity'] Esr = self.coefs[p2]['source match'] Err = self.coefs[p2]['reflection tracking'] k1 = self.coefs[p1]['k'] k2 = self.coefs[p2]['k'] detX = Edf*Esf-Erf detY = Edr*Esr-Err T1 = npy.array([ [ -k1*detX, zero ], [ zero, -k2*detY ] ]).transpose(2,0,1) T2 = npy.array([ [ k1*Edf, zero ], [ zero, k2*Edr ] ]).transpose(2,0,1) T3 = npy.array([ [ -k1*Esf, zero ], [ zero, -k2*Esr ] ]).transpose(2,0,1) T4 = npy.array([ [ k1, zero ], [ zero, k2 ] ]).transpose(2,0,1) return T1, T2, T3, T4
[docs] def apply_cal(self, ntwk): """ Apply correction to a Network. """ # A new copy of ntwk is created ntwk = ntwk - self.isolation caled = ntwk.copy() # Use traveling definition since it can renormalize to negative real part impedance. s_def = caled.s_def caled.s_def = 'traveling' fpoints = len(ntwk.frequency) ports = npy.arange(self.nports) port_combos = list(combinations(ports, 2)) for p in port_combos: T1, T2, T3, T4 = self.T_matrices(p[0], p[1]) caled_2p = subnetwork(ntwk, p).copy() caled_2p.s_def = 'traveling' caled_2p = self.unterminate_2port(caled_2p, p[0], p[1]) caled_2p.s = linalg.inv(-caled_2p.s @ T3 + T1) @ (caled_2p.s @ T4 - T2) z = npy.zeros((fpoints, 2), dtype=complex) z[:,0] = self.terminations[p[0]].z[:,0,0] z[:,1] = self.terminations[p[1]].z[:,0,0] caled_2p.renormalize(z) for ei, i in enumerate(p): for ej, j in enumerate(p): caled.s[:, i, j] = caled_2p.s[:, ei, ej] for i in range(self.nports): caled.z0[:,i] = self.terminations[i].z[:,0,0] caled.renormalize(ntwk.z0, s_def=s_def) return caled
[docs] def embed(self, ntwk): """ Embed an ideal response in the estimated error network[s] """ fpoints = len(self.coefs[0]['k']) nports = self.nports nout = ntwk.copy() Z = npy.zeros((fpoints, 2*nports, 2*nports), dtype=complex) gammas = [] for e, c in enumerate(self.coefs): gammas.append(Network(s=c['switch term'], frequency=nout.frequency, z0=50)) Z[:, e, e] = c['directivity'] Z[:, nports+e, nports+e] = c['source match'] Z[:, e, nports+e] = c['reflection tracking'] * c['k'] / self.coefs[0]['k'] Z[:, nports+e, e] = self.coefs[0]['k'] / c['k'] # Consistent internal port Z0. nout.z0 = 50 Z = Network(s=Z, frequency=nout.frequency, z0=50) nout = connect(Z, nports, nout, 0, nports) nout = terminate_nport(nout, gammas) nout += self.isolation nout.z0 = ntwk.z0 return nout
[docs] def coefs_to_ntwks(self, coefs, k_side=0): """ Two-port 8-term error coefficients to Networks. Parameters ---------- k_side: int, 0 or 1 Port to put 'k' coefficient. """ npoints = len(coefs['k']) one = npy.ones(npoints, dtype=complex) Edf = coefs['forward directivity'] Esf = coefs['forward source match'] Erf = coefs['forward reflection tracking'] Edr = coefs['reverse directivity'] Esr = coefs['reverse source match'] Err = coefs['reverse reflection tracking'] k = coefs['k'] if k_side == 0: S1 = npy.array([ [ Edf, Erf/k ], [ k, Esf ] ]).transpose(2,0,1) S2 = npy.array([ [ Edr, one ], [ Err, Esr ] ]).transpose(2,0,1) elif k_side == 1: S1 = npy.array([ [ Edf, Erf ], [ one, Esf ] ]).transpose(2,0,1) S2 = npy.array([ [ Edr, one/k ], [ Err*k, Esr ] ]).transpose(2,0,1) else: raise ValueError(f"Invalid k_side {k_side}, expected 0 or 1.") return (S1, S2)
[docs] def dut_termination(self, S, gamma): """Impedance looking from DUT to VNA terminated with switch term.""" term = S[:,1,1] + (S[:,0,1] * S[:,1,0] * gamma) / (1 - S[:,0,0] * gamma) return term
[docs] class MultiportSOLT(MultiportCal): """ Multi-port VNA calibration using two-port calibration method with one transmissive standard for each two-port pair. `method` should be a two-port calibration method such as `EightTerm`, `UnknownThru` or `SOLT`. This class calibrates a multi-port network using the given two-port calibration method. There should be `Nports - 1` thru standards and the number of other standards depending on the number of standards required by the chosen calibration method. Standards should be always given thrus first. Thru standards are used to find the port connections during the calibration and all standards should be N-ports. There should be one common port in all thru measurements. For example in case of 4-port calibration one possible choice would be to make three thru measurements between ports: 0-1, 0-2, and 0-3. If isolation calibration is used it should be not passed as an argument to the two-port calibration and N-port isolation measurement should be instead given as an argument for this class. `switch_terms` should be a list of switch terms with nth entry being the switch term an/bn with source from any other port. Note that in case of two-port this is the reversed order than what two-port calibration would require. If calibration is a 12-term calibration such as `SOLT` or `TwelveTerm` no switch terms are required. `thru_pos` argument can be used to change the order of thru given to the calibration method. `auto` will try to determine it automatically from the calibration method. Other options are `first` and `last`. Other standards are given in the same order they are given to this class. `cal_args` can be used to give addition arguments to the calibration method. If no arguments are given it should be None, otherwise a dictionary of arguments and values. See Also -------- calibration.MultiportCal Lower level multi-port calibration class. This needs to be used for TRL calibration as it has also lines between ports which doesn't fit the interface of this class. """ family = 'Multiport'
[docs] def __init__(self, method, measured, ideals, isolation=None, switch_terms=None, thru_pos='auto', cal_args=None): self.ideals = ideals self.measured = measured self.nports = ideals[0].nports nports = self.nports if nports < 3: raise ValueError("Too few ports in input networks. At least 3 required.") self.switch_terms = switch_terms if thru_pos == 'auto': if method in [LRM, LRRM]: thru_pos = 'first' elif method in [SOLT, EightTerm, UnknownThru, MRC, TwelveTerm]: thru_pos = 'last' else: raise ValueError( "Unable to determine 'thru_pos' automatically. Set it manually to either 'first' or 'last'" ) if thru_pos not in ['last', 'first']: raise ValueError("thru_pos must be either 'first' or 'last'") if cal_args is None: cal_args = {} for i in ideals: if i.nports != self.nports: raise ValueError("Inconsistent number of ports in ideals.") if not issubclass(method, Calibration): raise ValueError("method must be Calibration subclass.") if issubclass(method, SixteenTerm): warn("SixteenTerm calibration is reduced to 8-terms.", stacklevel=2) if len(ideals) < nports - 1: raise ValueError(f"Invalid number of ideals. Expected at least {nports-1} but got {len(ideals)}.") self.thru_ports = [] for thru in ideals[:nports-1]: nonzero = [] for i in range(nports): for j in range(i+1, nports): if thru.s[-1, i, j] != 0: nonzero.append([i, j]) if len(nonzero) != 1: raise ValueError("Invalid thru ideal. Thru should connect exactly two ports.") self.thru_ports.append(tuple(nonzero[0])) #Generate cal_dict in the format required by MultiportCal. nports = self.nports nthrus = nports - 1 cal_dict = {} for e, p in enumerate(self.thru_ports): ideals = [subnetwork(self.ideals[e], p)] ideals_sol = [subnetwork(i, p) for i in self.ideals[nthrus:]] ideals.extend(ideals_sol) measured = [subnetwork(self.measured[e], p)] measured_sol = [subnetwork(i, p) for i in self.measured[nthrus:]] measured.extend(measured_sol) if self.switch_terms is None: sw_terms = None else: sw_terms = [self.switch_terms[i] for i in p][::-1] if thru_pos == 'last': ideals = ideals[1:] + [ideals[0]] measured = measured[1:] + [measured[0]] cal_dict[p] = {} cal_dict[p]['method'] = method cal_dict[p]['ideals'] = ideals cal_dict[p]['measured'] = measured if sw_terms is not None: cal_dict[p]['switch_terms'] = sw_terms for k, v in cal_args.items(): cal_dict[p][k] = v super().__init__(cal_dict=cal_dict, isolation=isolation)
## Functions def ideal_coefs_12term(frequency): """ An ideal set of 12term calibration coefficients. Produces a set of error coefficients, that would result if the error networks were matched thrus """ zero = zeros(len(frequency), dtype='complex') one = ones(len(frequency), dtype='complex') ideal_coefs = {} ideal_coefs.update({k:zero for k in [\ 'forward directivity', 'forward source match', 'forward load match', 'reverse directivity', 'reverse load match', 'reverse source match', ]}) ideal_coefs.update({k:one for k in [\ 'forward reflection tracking', 'forward transmission tracking', 'reverse reflection tracking', 'reverse transmission tracking', ]}) return ideal_coefs
[docs] def unterminate(ntwk, gamma_f, gamma_r): r""" Unterminate switch terms from a raw measurement. In order to use the 8-term error model on a VNA which employs a switched source, the effects of the switch must be accounted for. This is done through `switch terms` as described in [1]_ . The two switch terms are defined as, .. math :: \Gamma_f = \frac{a2}{b2} ,\qquad\text{sourced by port 1}\ \Gamma_r = \frac{a1}{b1} ,\qquad\text{sourced by port 2} These can be measured by four-sampler VNA's by setting up user-defined traces onboard the VNA. If the VNA doesnt have 4-samplers, then you can measure switch terms indirectly by using a two-tier two-port calibration. First do a SOLT, then convert the 12-term error coefs to 8-term, and pull out the switch terms. Parameters ---------- two_port : 2-port Network the raw measurement gamma_f : 1-port Network the measured forward switch term. gamma_f = a2/b2 sourced by port1 gamma_r : 1-port Network the measured reverse switch term gamma_r = a1/b1 sourced by port2 Returns ------- ntwk : Network object References ---------- .. [1] "Formulations of the Basic Vector Network Analyzer Error Model including Switch Terms" by Roger B. Marks """ unterminated = ntwk.copy() # extract scattering matrices m, gamma_r, gamma_f = ntwk.s, gamma_r.s, gamma_f.s u = m.copy() one = npy.ones(ntwk.frequency.npoints) d = one - m[:,0,1]*m[:,1,0]*gamma_r[:,0,0]*gamma_f[:,0,0] u[:,0,0] = (m[:,0,0] - m[:,0,1]*m[:,1,0]*gamma_f[:,0,0])/(d) u[:,0,1] = (m[:,0,1] - m[:,0,0]*m[:,0,1]*gamma_r[:,0,0])/(d) u[:,1,0] = (m[:,1,0] - m[:,1,1]*m[:,1,0]*gamma_f[:,0,0])/(d) u[:,1,1] = (m[:,1,1] - m[:,0,1]*m[:,1,0]*gamma_r[:,0,0])/(d) unterminated.s = u return unterminated
[docs] def terminate(ntwk, gamma_f, gamma_r): """ Terminate a network with switch terms. see [1]_ Parameters ---------- two_port : 2-port Network an unterminated network gamma_f : 1-port Network measured forward switch term. gamma_f = a2/b2 sourced by port1 gamma_r : 1-port Network measured reverse switch term gamma_r = a1/b1 sourced by port2 Returns ------- ntwk : Network object See Also -------- unterminate_switch_terms References ---------- .. [1] "Formulations of the Basic Vector Network Analyzer Error Model including Switch Terms" by Roger B. Marks """ m = ntwk.copy() m.s[:,0,0] = ntwk.s[:,0,0] + ntwk.s[:,1,0]*ntwk.s[:,0,1]*gamma_f.s[:,0,0]/(1-ntwk.s[:,1,1]*gamma_f.s[:,0,0]) m.s[:,1,1] = ntwk.s[:,1,1] + ntwk.s[:,1,0]*ntwk.s[:,0,1]*gamma_r.s[:,0,0]/(1-ntwk.s[:,0,0]*gamma_r.s[:,0,0]) m.s[:,1,0] = ntwk.s[:,1,0]/(1-ntwk.s[:,1,1]*gamma_f.s[:,0,0]) m.s[:,0,1] = ntwk.s[:,0,1]/(1-ntwk.s[:,0,0]*gamma_r.s[:,0,0]) return m
def terminate_nport(ntwk, gammas): """ Terminate N-port network with switch terms. Note that for 2-port the order `gammas` is opposite of terminate. Correct order for 2-port is [gamma_r, gamma_f]. See [1]_ Parameters ---------- two_port : Network an unterminated network. gammas : list of 1-port Network measured switch term. gammas[i] = ai/bi sourced by any other port. Returns ------- ntwk : Network object See Also -------- terminate References ---------- .. [1] "Formulations of the Basic Vector Network Analyzer Error Model including Switch Terms" by Roger B. Marks """ nin = ntwk.copy() # Assign fixed z0 for connections for inner ports. nin.z0 = 50 nout = ntwk.copy() nports = ntwk.nports fpoints = len(ntwk.frequency) if len(gammas) != ntwk.nports: raise ValueError("len(gammas) doesn't match the number of network ports") ones = npy.ones(len(ntwk.s)) for i in range(nports): term = npy.zeros((fpoints, 2*nports, 2*nports), dtype=complex) for j in range(nports): if i == j: term[:,nports+j,j] = ones term[:,j,j+nports] = ones continue term[:,j,j] = gammas[j].s[:,0,0] term[:,nports+j,j] = ones net = Network(s=term, frequency=nin.frequency, z0=50) net = connect(nin, 0, net, 0, nports) for j in range(nports): nout.s[:,j,i] = net.s[:,j,i] nout.z0 = ntwk.z0 return nout def compute_switch_terms(ntwks): """ A method for indirectly computing the switch terms of a VNA using measurements of at least three transmissive reciprocal devices. The VNA does not need to be calibrated, and more than three reciprocal devices can be used. However, the accuracy of the computed switch terms depends on the uniqueness of the measured reciprocal devices. Devices with asymmetric structure and semi-reflective properties can help ensure the conditioning of the system matrix, which solves the switch terms. See [1]_ and [2]_ Parameters ---------- ntwks : List of networks measured reciprocal devices. At least 3 required. Returns ------- Gammas : List of one-port networks of the switch terms. The order is [Gamma21, Gamma12]. Gamma21 is forward and Gamma12 is reverse. References ---------- .. [1] Z. Hatab, M. E. Gadringer, and W. Bösch, "Indirect Measurement of Switch Terms of a Vector Network Analyzer with Reciprocal Devices," 2023, e-print: https://arxiv.org/abs/2306.07066 .. [2] https://ziadhatab.github.io/posts/vna-switch-terms/ See Also -------- terminate unterminate """ if len(ntwks) < 3: raise ValueError("At least three networks are required.") fpoints = len(ntwks[0].frequency) Gamma21_fill = npy.zeros(shape=(fpoints,), dtype=complex) # forward switch term Gamma12_fill = npy.zeros(shape=(fpoints,), dtype=complex) # reverse switch term for inx in range(fpoints): # iterate through all frequency points # create the system matrix H = npy.array([ [-ntwk.s[inx,0,0]*ntwk.s[inx,0,1]/ntwk.s[inx,1,0], -ntwk.s[inx,1,1], 1, ntwk.s[inx,0,1]/ntwk.s[inx,1,0]] for ntwk in ntwks]) _,_,vh = npy.linalg.svd(H) # compute the SVD nullspace = vh[-1,:].conj() # get the nullspace Gamma21_fill[inx] = nullspace[1]/nullspace[2] Gamma12_fill[inx] = nullspace[0]/nullspace[3] Gamma21 = Network(s=Gamma21_fill, frequency=ntwks[0].frequency, name='Gamma21') Gamma12 = Network(s=Gamma12_fill, frequency=ntwks[0].frequency, name='Gamma12') return [Gamma21, Gamma12]
[docs] def determine_line(thru_m, line_m, line_approx=None): r""" Determine S21 of a matched line. Given raw measurements of a `thru` and a matched `line` with unknown s21, this will calculate the response of the line. This works for lossy lines, and attenuators. The `line_approx` is an approximation to line, this used to choose the correct root sign. If left as `None`, it will be estimated from raw measurements, which requires your error networks to be well matched (S_ij >>S_ii). This is possible because two measurements can be combined to create a relationship of similar matrices, as shown below. Equating the eigenvalues between these measurements allows one to solve for S21 of the line. .. math:: M_t = X \cdot A_t \cdot Y \\ M_l = X \cdot A_l \cdot Y\\ M_t \cdot M_{l}^{-1} = X \cdot A_t \cdot A_{l}^{-1} \cdot X^{-1}\\ eig(M_t \cdot M_{l}^{-1}) = eig( A_t \cdot A_{l}^{-1})\\ which can be solved to yield S21 of the line Notes ----- This relies on the 8-term error model, which requires that switch terms are accounted for. specifically, thru and line have their switch terms unterminated. Parameters ---------- thru_m : :class:`~skrf.network.Network` raw measurement of a flush thru line_m : :class:`~skrf.network.Network` raw measurement of a matched transmissive standard line_approx : :class:`~skrf.network.Network` approximate network the ideal line response. if None, then the response is approximated by line_approx = line/thru. This makes the assumption that the error networks have much larger transmission than reflection References ---------- """ npts = len(thru_m) zero = npy.zeros(npts) if line_approx is None: # estimate line length, by assuming error networks are well # matched line_approx_s21 = line_m.s[:,1,0] / thru_m.s[:,1,0] else: line_approx_s21 = line_approx.s[:,1,0] C = thru_m.inv**line_m # the eigen values of the matrix C, are equal to s12,s12^-1) # we need to choose the correct one w,v = linalg.eig(C.t) s12_0, s12_1 = w[:,0], w[:,1] s12 = find_correct_sign(s12_0, s12_1, line_approx_s21) found_line = line_m.copy() found_line.s = npy.array([[zero, s12],[s12,zero]]).transpose(2,0,1) return found_line
def _regularize_inplace(z : ComplexArray, epsilon : float=1e-7) -> ComplexArray: """ Regularize an array inplace around zero """ zero_idx = npy.abs(z)<epsilon z[zero_idx] = .5*(epsilon * npy.exp(npy.angle(z[zero_idx])*1j)+z[zero_idx]) return z def determine_reflect(thru_m, reflect_m, line_m, reflect_approx=None, line_approx=None, return_all=False): """ Determine reflect from a thru, reflect, line measurements. This is used in the TRL algorithm, but is made modular for multi-line, multi-reflect options. Parameters ---------- thru_m : :class:`~skrf.network.Network` raw measurement of a thru reflect_m: :class:`~skrf.network.Network` raw measurement of a reflect standard line_m : :class:`~skrf.network.Network` raw measurement of a matched transmissive standard reflect_approx : :class:`~skrf.network.Network` approximate One-port network for the reflect. if None, then we assume its a flush short (gamma=-1) return_all: bool return all possible values fo reflect, one for each root-choice. useful for troubleshooting. Returns ------- reflect : :class:`~skrf.network.Network` a One-port network for the found reflect. The equations are from "Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer", G.F. Engen et al., 1979 """ # regularize the parameters in case of matched thru and line. see gh-870 thru_m = thru_m.copy() thru_m.s[:, 0, 0] = _regularize_inplace(thru_m.s[:, 0, 0]) thru_m.s[:, 1, 1] = _regularize_inplace(thru_m.s[:, 1, 1]) #Call determine_line first to solve root choice of the propagation constant line = determine_line(thru_m, line_m, line_approx) inv = linalg.inv rt = thru_m.t rd = line_m.t # tt is equal to T from equation (24) in the paper tt = einsum('ijk,ikl -> ijl', rd, inv(rt)) a = tt[:,1,0] b = tt[:,1,1]-tt[:,0,0] c = -tt[:,0,1] sqrtD = sqrt(b*b-4*a*c) # The variables a, b, c define a quadratic equation for which the solutions sol1 and sol2 correspond to the # ratios (r11/r21) and (r12/r22) from equations (30) and (31) in the paper # The quadratic equation has solutions sol1 = (-b-sqrt(b*b-4*a*c))/(2*a), sol2 = (-b+sqrt(b*b-4*a*c))/(2*a) # For a=0 these become degenerate. Also the consequtive equations for x1 and x2 contain singularities for a=0 or c=0 sol1 = (-b-sqrtD)/(2*a) sol2 = (-b+sqrtD)/(2*a) # equation (32) x1 = (tt[:,1,0]*sol1 + tt[:,1,1])/(tt[:,0,1]/sol2 + tt[:,0,0]) x2 = (tt[:,1,0]*sol2 + tt[:,1,1])/(tt[:,0,1]/sol1 + tt[:,0,0]) e2 = line.s[:,0,1]**2 rootChoice = abs(x1 - e2) < abs(x2 - e2) # see gh-870 y = sol1*invert(rootChoice) + sol2*rootChoice x = sol1*rootChoice + sol2*invert(rootChoice) b = y e = thru_m.s[:,0,0] d = -det(thru_m.s) f = -thru_m.s[:,1,1] gam = (f-d/x)/(1-e/x) # equation (40) b_A = (e-b)/(d-b*f) # equation (41): beta/alpha w1 = reflect_m.s[:,0,0] w2 = reflect_m.s[:,1,1] # equation (45) a = sqrt(((w1-b)*(1+w2*b_A)*(d-b*f))/\ ((w2+gam)*(1-w1/x)*(1-e/x))) out = [(w1-b)/(a*(1-w1/x)), (w1-b)/(-a*(1-w1/x))] # equation (47) if return_all: return [Network(frequency=thru_m.frequency, s = k) for k in out] if reflect_approx is None: reflect_approx = reflect_m.copy() reflect_approx.s[:,0,0]=-1 closer = find_closest(out[0], out[1], reflect_approx.s11.s.flatten()) reflect = reflect_approx.copy() reflect.s[:,0,0] = closer return reflect.s11 def convert_12term_2_8term(coefs_12term, redundant_k = False): """ Convert the 12-term and 8-term error coefficients. Derivation of this conversion can be found in [#]_ . References ---------- .. [#] Marks, Roger B.; , "Formulations of the Basic Vector Network Analyzer Error Model including Switch-Terms," ARFTG Conference Digest-Fall, 50th , vol.32, no., pp.115-126, Dec. 1997. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4119948&isnumber=4119931 """ # Nomenclature taken from Roger Marks Edf = coefs_12term['forward directivity'] Esf = coefs_12term['forward source match'] Erf = coefs_12term['forward reflection tracking'] Etf = coefs_12term['forward transmission tracking'] Elf = coefs_12term['forward load match'] Eif = coefs_12term.get('forward isolation',0) # noqa: F841 Edr = coefs_12term['reverse directivity'] Esr = coefs_12term['reverse source match'] Err = coefs_12term['reverse reflection tracking'] Elr = coefs_12term['reverse load match'] Etr = coefs_12term['reverse transmission tracking'] Eir = coefs_12term.get('reverse isolation',0) # noqa: F841 # these are given in eq (30) - (33) in Roger Mark's paper listed in # the docstring # NOTE: k = e10/e23 = alpha/beta # the 'k' nomenclature is from Soares Speciale gamma_f = (Elf - Esr)/(Err + Edr*(Elf - Esr)) gamma_r = (Elr - Esf)/(Erf + Edf*(Elr - Esf)) k_first = Etf/(Err + Edr*(Elf - Esr) ) k_second =1/(Etr/(Erf + Edf *(Elr - Esf))) k = (k_first + k_second)/2. coefs_8term = {} for l in ['forward directivity','forward source match', 'forward reflection tracking','reverse directivity', 'reverse reflection tracking','reverse source match', 'forward isolation', 'reverse isolation']: coefs_8term[l] = coefs_12term[l].copy() coefs_8term['forward switch term'] = gamma_f coefs_8term['reverse switch term'] = gamma_r coefs_8term['k'] = k if redundant_k: coefs_8term['k first'] = k_first coefs_8term['k second'] = k_second return coefs_8term def convert_8term_2_12term(coefs_8term): """ """ Edf = coefs_8term['forward directivity'] Esf = coefs_8term['forward source match'] Erf = coefs_8term['forward reflection tracking'] Edr = coefs_8term['reverse directivity'] Esr = coefs_8term['reverse source match'] Err = coefs_8term['reverse reflection tracking'] gamma_f = coefs_8term['forward switch term'] gamma_r = coefs_8term['reverse switch term'] k = coefs_8term['k'] k_first = coefs_8term.get('k first', k) k_second = coefs_8term.get('k second', k) # taken from eq (36)-(39) in the Roger Marks paper given in the # docstring Elf = Esr + (Err*gamma_f)/(1. - Edr * gamma_f) Elr = Esf + (Erf *gamma_r)/(1. - Edf * gamma_r) Etf = ((Elf - Esr)/gamma_f) * k_first Etr = ((Elr - Esf )/gamma_r) * 1./k_second coefs_12term = {} for l in ['forward directivity','forward source match', 'forward reflection tracking','reverse directivity', 'reverse reflection tracking','reverse source match', 'forward isolation', 'reverse isolation']: coefs_12term[l] = coefs_8term[l].copy() coefs_12term['forward load match'] = Elf coefs_12term['reverse load match'] = Elr coefs_12term['forward transmission tracking'] = Etf coefs_12term['reverse transmission tracking'] = Etr return coefs_12term
[docs] def convert_pnacoefs_2_skrf(coefs): """ Convert PNA error coefficients to skrf error coefficients. Parameters ---------- coefs : dict coefficients as retrieved from PNA ports : tuple port indices. in order (forward, reverse) Returns ------- skrf_coefs : dict same error coefficients but with keys matching skrf's convention """ coefs_map ={'Directivity':'directivity', 'SourceMatch':'source match', 'ReflectionTracking':'reflection tracking', 'LoadMatch':'load match', 'TransmissionTracking':'transmission tracking', 'CrossTalk':'isolation'} skrf_coefs = {} if len(coefs) ==3: for k in coefs: coef= k[:-5] coef_key = coefs_map[coef] skrf_coefs[coef_key] = coefs[k] else: ports = list(set([k[-2] for k in coefs])) ports.sort(key=int) port_map ={ports[0]: 'forward', ports[1]: 'reverse'} for k in coefs: coef,p1,p2 = k[:-5],k[-4],k[-2] # the source port has a different position for reflective # and transmissive standards if coef in ['Directivity','SourceMatch','ReflectionTracking']: coef_key = port_map[p1]+' '+coefs_map[coef] elif coef in ['LoadMatch','TransmissionTracking','CrossTalk']: coef_key = port_map[p2]+' '+coefs_map[coef] skrf_coefs[coef_key] = coefs[k] return skrf_coefs
[docs] def convert_skrfcoefs_2_pna(coefs, ports = (1,2)): """ Convert skrf error coefficients to pna error coefficients Notes ----- The skrf calibration terms can be found in variables * skrf.calibration.coefs_list_3term * skrf.calibration.coefs_list_12term Parameters ---------- coefs : dict complex ndarrays for the cal coefficients as defined by skrf ports : tuple port indices. in order (forward, reverse) Returns ------- pna_coefs : dict same error coefficients but with keys matching skrf's convention """ if not hasattr(ports, '__len__'): ports = ports, coefs_map ={'directivity':'Directivity', 'source match':'SourceMatch', 'reflection tracking':'ReflectionTracking', 'load match':'LoadMatch', 'transmission tracking':'TransmissionTracking', 'isolation':'CrossTalk'} pna_coefs = {} if len(coefs)==3: for k in coefs: coef_key = coefs_map[k] + '(%i,%i)'%(ports[0],ports[0]) pna_coefs[coef_key] = coefs[k] else: port_map_trans ={'forward':ports[1], 'reverse':ports[0]} port_map_refl ={'forward':ports[0], 'reverse':ports[1]} for k in coefs: fr = k.split(' ')[0] # remove 'forward|reverse-ness' eterm = coefs_map[k.lstrip(fr)[1:] ] # the source port has a different position for reflective # and transmissive standards if eterm in ['Directivity','SourceMatch','ReflectionTracking']: coef_key= eterm+'(%i,%i)'%(port_map_refl[fr], port_map_refl[fr]) elif eterm in ['LoadMatch','TransmissionTracking','CrossTalk']: receiver_port = port_map_trans[fr] source_port = port_map_refl[fr] coef_key= eterm+'(%i,%i)'%(receiver_port,source_port) pna_coefs[coef_key] = coefs[k] return pna_coefs
def align_measured_ideals(measured, ideals): """ Aligns two lists of networks based on the intersection of their names. """ measured = [ measure for measure in measured\ for ideal in ideals if ideal.name in measure.name] ideals = [ ideal for measure in measured\ for ideal in ideals if ideal.name in measure.name] return measured, ideals def two_port_error_vector_2_Ts(error_coefficients): ec = error_coefficients npoints = len(ec['k']) one = npy.ones(npoints,dtype=complex) zero = npy.zeros(npoints,dtype=complex) #T_1 = npy.zeros((npoints, 2,2),dtype=complex) #T_1[:,0,0],T_1[:,1,1] = -1*ec['det_X'], -1*ec['k']*ec['det_Y'] #T_1[:,1,1] = -1*ec['k']*ec['det_Y'] T1 = npy.array([\ [ -1*ec['det_X'], zero ],\ [ zero, -1*ec['k']*ec['det_Y']]]).transpose().reshape(-1,2,2) T2 = npy.array([\ [ ec['e00'], zero ],\ [ zero, ec['k']*ec['e33']]]).transpose().reshape(-1,2,2) T3 = npy.array([\ [ -1*ec['e11'], zero ],\ [ zero, -1*ec['k']*ec['e22']]]).transpose().reshape(-1,2,2) T4 = npy.array([\ [ one, zero ],\ [ zero, ec['k']]]).transpose().reshape(-1,2,2) return T1,T2,T3,T4 def error_dict_2_network(coefs, frequency, is_reciprocal=False, **kwargs): """ Create a Network from a dictionary of standard error terms. """ if len (coefs.keys()) == 3: # ASSERT: we have one port data ntwk = Network(**kwargs) if is_reciprocal: #TODO: make this better and maybe have phase continuity # functionality tracking = coefs['reflection tracking'] #s12 = npy.sqrt(tracking) #s21 = npy.sqrt(tracking) s12 = sqrt_phase_unwrap(tracking) s21 = sqrt_phase_unwrap(tracking) else: s21 = coefs['reflection tracking'] s12 = npy.ones(len(s21), dtype=complex) s11 = coefs['directivity'] s22 = coefs['source match'] ntwk.s = npy.array([[s11, s21],[s12,s22]]).transpose().reshape(-1,2,2) ntwk.frequency = frequency return ntwk else: p1,p2 = {},{} for k in ['source match','directivity','reflection tracking']: p1[k] = coefs['forward '+k] p2[k] = coefs['reverse '+k] forward = error_dict_2_network(p1, frequency = frequency, name='forward', is_reciprocal = is_reciprocal,**kwargs) reverse = error_dict_2_network(p2, frequency = frequency, name='reverse', is_reciprocal = is_reciprocal,**kwargs) return (forward, reverse)