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
   PHN

Two-port
---------------------

.. autosummary::
   :toctree: generated/

   TwelveTerm
   SOLT
   EightTerm
   UnknownThru
   TRL
   MultilineTRL
   NISTMultilineTRL
   SixteenTerm
   LMR16


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 numpy as npy
from numpy import linalg
from numpy.linalg import det
from numpy import mean, std, angle, real, imag, exp, ones, zeros, poly1d, invert, einsum, sqrt, unwrap,log,log10
import json
from numbers import Number
from collections import OrderedDict
import os
from copy import deepcopy, copy
import itertools
from warnings import warn
import six.moves.cPickle as pickle

from ..mathFunctions import complex_2_db, sqrt_phase_unwrap, \
    find_correct_sign, find_closest,  ALMOST_ZERO, rand_c, cross_ratio
from ..frequency import *
from ..network import *
from ..networkSet import func_on_networks as fon
from ..networkSet import NetworkSet
from .. import util
from ..io.touchstone import read_zipped_touchstones
from .. import __version__ as skrf__version__


## later imports. delayed to solve circular dependencies
#from io.general import write
#from io.general import read_all_networks

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 load 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(object): ''' Base class for all Calibration objects. This class implements the common mechanisms for all calibration algorithms. Specific calibration algorithms should inheret this class and overide 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): ''' 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 sloppy_input == False: warn('dictionary passed, sloppy_input automatically activated') sloppy_input = True if hasattr(ideals, 'keys'): ideals = ideals.values() if sloppy_input == False: warn('dictionary passed, sloppy_input automatically activated') 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 self_calibration == False and len(self.measured) != len(self.ideals): raise(IndexError('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]: print('Warning: Frequency information doesn\'t match on ideals[{}], attempting to interpolate the ideal[{}] Network ..'.format(k,k)) try: # try to resample our ideals network to match # the meaurement frequency self.ideals[k].interpolate_self(\ self.measured[0].frequency) print('Success') except: raise(IndexError('Failed to interpolate. Check frequency of ideals[{}].'.format(k))) # 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 = '%s Calibration: \'%s\', %s'\ %(self.family,name,str(self.frequency)) else: output = '%s Calibration: \'%s\', %s, %i-standards'\ %(self.family,name,str(self.frequency),\ len(self.measured)) return output def __repr__(self): return self.__str__()
[docs] def run(self): ''' Runs 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 of dict of Networks. ''' if hasattr(ntwk_list, 'keys'): return dict([(k, self.apply_cal(ntwk_list[k])) for k in ntwk_list]) else:
return [self.apply_cal(k) for k in ntwk_list]
[docs] def apply_cal_to_all_in_dir(self, *args, **kwargs): ''' ''' from ..io.general import read_all_networks ntwkDict = read_all_networks(*args, **kwargs)
return self.apply_cal_to_list(ntwkDict)
[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): ''' Creates 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): ''' Creates 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') 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 currect dict of error coefficients ''' for k in d: d[k] = d[k].flatten()
self._coefs.update(d) @property def output_from_run(self): ''' Returns 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 dict([(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): ''' the directivity normalized to the reflection tracking ''' try: return self.coefs_ntwks['directivity']/\ self.coefs_ntwks['reflection tracking'] except: pass try: out = {} for direction in ['forward','reverse']: out[direction + ' normalized directvity'] =\ self.coefs_ntwks[direction + ' directivity']/\ self.coefs_ntwks[direction + ' reflection tracking'] return out except: raise ValueError('cant find error coefs') @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 load 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 for k in coefs_list_8term: if k not in d and 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 for k in coefs_list_12term: if k not in d and k in coefs_list_8term: return convert_8term_2_12term(d) return 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): ''' Returns 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): ''' 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 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): ''' 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): ''' 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): ''' 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 untill here because of a circular depency 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]class OnePort(Calibration): ''' Standard algorithm for a one port calibration. Solves the linear set of equations: .. math:: e_{11}\mathbf{i_1m_1}-\Delta e\,\mathbf{m_1}+e_{00}=\mathbf{i_1} e_{11}\mathbf{i_2m_2}-\Delta e\,\mathbf{m_2}+e_{00}=\mathbf{i_2} e_{11}\mathbf{i_3m_3}-\Delta e\,\mathbf{m_3}+e_{00}=\mathbf{i_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): ''' ''' numStds = self.nstandards numCoefs=3 mList = [self.measured[k].s.reshape((-1,1)) for k in list(range(numStds))] iList = [self.ideals[k].s.reshape((-1,1)) for k in list(range(numStds))] # 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 list(range(numStds))]).reshape(-1,1)# m-vector at f i = npy.array([ iList[k][f] for k in list(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)[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): raise(ValueError('matrix has singular values. ensure standards are far enough away on smith chart')) # 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 = npy.sqrt(tracking) s11 = self.coefs['directivity'] s22 = self.coefs['source match'] er_ntwk.s = npy.array([[s11, s21],[s12,s22]]).transpose().reshape(-1,2,2)
return er_ntwk.inv**ntwk
[docs] def embed(self,ntwk): embedded = ntwk.copy() embedded = self.error_ntwk**embedded embedded.name = ntwk.name
return embedded 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' 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, *args, **kwargs) def run(self): #meaured 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, *args, **kwargs)
[docs] def run(self): #meaured 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, *args, **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 # meaured (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 |s21| and |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 transmissve 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 neccesary Calibration.__init__(self, *args, **kwargs) # if they didnt tell us the number of thrus, then lets # hueristcally determine it trans_thres_mag = 10 ** (trans_thres / 20) if n_thrus is None: warn('n_thrus is None, guessing which stds are transmissive') 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 transimssive 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 is True: 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 indecies 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(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs])) coefs.update(dict([('reverse %s'%k, p2_coefs[k]) for k in p2_coefs])) eight_term_coefs = convert_12term_2_8term(coefs) coefs.update(dict([(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. If your `thru` is not flush you need to use `TwelveTerm` instead of SOLT. Redundant flush 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 flush thru standard. If the ideal element for the thru is set to None, a flush thru is assumed. If your `thru` is not flush you need to use `TwelveTerm` instead of SOLT. Use 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 measurments 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('Cant 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] 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]] thru = NetworkSet(self.measured[-n_thrus:]).mean_s # 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 = port1_cal.coefs p2_coefs = 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(thru), dtype=complex) p2_coefs['isolation'] = npy.zeros(len(thru), dtype=complex) p1_coefs['load match'] = port1_cal.apply_cal(thru.s11).s.flatten() p2_coefs['load match'] = port2_cal.apply_cal(thru.s22).s.flatten() p1_coefs['transmission tracking'] = \ (thru.s21.s.flatten() - p1_coefs.get('isolation',0))*\ (1. - p1_coefs['source match']*p1_coefs['load match']) p2_coefs['transmission tracking'] = \ (thru.s12.s.flatten() - p2_coefs.get('isolation',0))*\ (1. - p2_coefs['source match']*p2_coefs['load match']) coefs = {} coefs.update(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs])) coefs.update(dict([('reverse %s'%k, p2_coefs[k]) for k in p2_coefs])) eight_term_coefs = convert_12term_2_8term(coefs) coefs.update(dict([(l, eight_term_coefs[l]) for l in \ ['forward switch term','reverse switch term','k'] ]))
self._coefs = coefs
[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): ''' 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 |s21| and |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 measurments source_port : [1,2] The port on which the source is active. should be 1 or 2 See Also ------------ TwelveTerm.__init__ ''' self.sp = source_port-1 self.rp = 1 if self.sp == 0 else 0 kwargs.update({'measured':measured, 'ideals':ideals, 'n_thrus':n_thrus})
TwelveTerm.__init__(self,*args, **kwargs)
[docs] def run(self): ''' if self.sp !=0: raise NotImplementedError('not implemented yet. you can just flip() all your data though. ') n_thrus = self.n_thrus p1_m = [k.s11 for k in self.measured[:-n_thrus]] p1_i = [k.s11 for k in self.ideals[:-n_thrus]] thru = NetworkSet(self.measured[-n_thrus:]).mean_s # create one port calibration for reflective standards port1_cal = OnePort(measured = p1_m, ideals = p1_i) # cal coefficient pdictionaries p1_coefs = port1_cal.coefs if self.kwargs.get('isolation',None) is not None: raise NotImplementedError() p1_coefs['isolation'] = isolation.s21.s.flatten() else: p1_coefs['isolation'] = npy.zeros(len(thru), dtype=complex) p1_coefs['load match'] = port1_cal.apply_cal(thru.s11).s.flatten() p1_coefs['transmission tracking'] = \ (thru.s21.s.flatten() - p1_coefs.get('isolation',0))*\ (1. - p1_coefs['source match']*p1_coefs['load match']) coefs = {}''' # 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('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(dict([(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') 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') 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,
*args, **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)[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): caled = ntwk.copy() inv = linalg.inv T1,T2,T3,T4 = self.T_matrices ntwk.s[:,1,0] -= self.coefs['forward isolation'] ntwk.s[:,0,1] -= self.coefs['reverse isolation'] ntwk = self.unterminate(ntwk) for f in list(range(len(ntwk.s))): t1,t2,t3,t4,m = T1[f,:,:],T2[f,:,:],T3[f,:,:],\ T4[f,:,:],ntwk.s[f,:,:] caled.s[f,:,:] = inv(-1*m.dot(t3)+t1).dot(m.dot(t4)-t2)
return caled
[docs] def embed(self, ntwk): ''' ''' embedded = ntwk.copy() inv = linalg.inv T1,T2,T3,T4 = self.T_matrices for f in list(range(len(ntwk.s))): t1,t2,t3,t4,a = T1[f,:,:],T2[f,:,:],T3[f,:,:],\ T4[f,:,:],ntwk.s[f,:,:] embedded.s[f,:,:] = (t1.dot(a)+t2).dot(inv(t3.dot(a)+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([\ [ -1*detX, zero ],\ [ zero, -1*k*detY]])\ .transpose().reshape(-1,2,2) T2 = npy.array([\ [ Edf, zero ],\ [ zero, k*Edr]])\ .transpose().reshape(-1,2,2) T3 = npy.array([\ [ -1*Esf, zero ],\ [ zero, -1*k*Esr]])\ .transpose().reshape(-1,2,2) T4 = npy.array([\ [ one, zero ],\ [ zero, k ]])\ .transpose().reshape(-1,2,2) 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, k ],\ [ Erf/k, Esf ]])\ .transpose().reshape(-1,2,2) S2 = npy.array([\ [ Edr, Err ],\ [ one, Esr ]])\ .transpose().reshape(-1,2,2) #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_pw(S1, z, z0_new) S2 = renormalize_s_pw(S2, z, z0_new) else: S1 = renormalize_s(S1, z, z0_new) S2 = renormalize_s(S2, z, z0_new) 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 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): ''' 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 indivdually 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 : and approximaitly 90deg matched line (can be lossy) The reflect ideals can also be given as a +-1. 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 macthed (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 ''' #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 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 EightTerm.__init__(self, measured = measured, ideals = ideals,
*args, **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. 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='estimate', k_method='multical', c0=None, z0_ref=50, z0_line=None, *args, **kwargs): ''' NISTMultilineTRL initializer Note that the order of `measured` is strict. It must be [Thru, Reflect, Line]. Multiple reflects can also be used, see `n_reflects` argument. 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, Reflect, Line] 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. 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 center of the through. 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` == 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` == None and `z0_line` == None. If `z0_ref` == 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` == 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 ''' self.refl_offset = refl_offset self.ref_plane = ref_plane self.er_est = er_est self.l = l 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 try: self.Grefls[0] except TypeError: self.Grefls = [self.Grefls] if self.refl_offset == None: self.refl_offset = [0]*len(self.Grefls) try: self.refl_offset[0] except TypeError: self.refl_offset = [self.refl_offset] if len(measured) != len(self.Grefls) + len(l): raise ValueError("Amount of measurements doesn't match amount of line lengths and reflection coefficients") #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, *args, **kwargs) m_sw = [k for k in self.measured_unterminated] n_reflects = len(self.Grefls) self.measured_reflects = m_sw[1:1+n_reflects] self.measured_lines = [m_sw[0]] self.measured_lines.extend(m_sw[1+n_reflects:]) 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 det = linalg.det 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=npy.complex) z0 = npy.zeros(fpoints, dtype=npy.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=npy.complex) Tmat1 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex) Tmat2 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex) Smat1 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex) Smat2 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex) e = npy.zeros(shape=(fpoints, 7), dtype=npy.complex) nstd = npy.zeros(shape=(fpoints), dtype=npy.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 Da[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=npy.complex) \ - (1.0/lines)*npy.ones(shape=(lines-1, lines-1), dtype=npy.complex) b1_vec = npy.zeros(lines-1, dtype=npy.complex) b2_vec = npy.zeros(lines-1, dtype=npy.complex) CoA1_vec = npy.zeros(lines-1, dtype=npy.complex) CoA2_vec = npy.zeros(lines-1, dtype=npy.complex) b1_vec2 = npy.zeros(lines-1, dtype=npy.complex) b2_vec2 = npy.zeros(lines-1, dtype=npy.complex) CoA1_vec2 = npy.zeros(lines-1, dtype=npy.complex) CoA2_vec2 = npy.zeros(lines-1, dtype=npy.complex) 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(n-1): 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 = 0 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=npy.complex) dl_vec = npy.zeros(lines-1, dtype=npy.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 heurestics 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=npy.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=npy.complex) Vc = npy.zeros(shape=(lines-1,lines-1), dtype=npy.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_factor2*exp_factor.conjugate() + \ (abs(exp(-gamma[m]*l[line_c[m]])))**2 * \ exp(-gamma[m]*len_b)*(exp(-gamma[m]*len_a)).conjugate() n = (exp_factor - 1/exp_factor).conjugate()* \ (exp_factor2-1/exp_factor2) Vb[a,b] /= n Vb[b,a] = Vb[a,b].conjugate() Vc[a,b] = 1/(exp_factor2*exp_factor.conjugate()) + \ 1/( (abs(exp(-gamma[m]*l[line_c[m]])))**2 * \ exp(-gamma[m]*len_b)*(exp(-gamma[m]*len_a)).conjugate() ) Vc[a,b] /= n Vc[b,a] = Vc[a,b].conjugate() def solve_A(B1, B2, CoA1, CoA2): #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=npy.complex) A2_vals = npy.zeros(len(measured_reflects), dtype=npy.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_r[0,0] - B1)/(npy.sqrt(Ap*Arr)*(1 - S_r[0,0]*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 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 inv_Vb = inv(Vb) inv_Vc = inv(Vc) sum_inv_Vb = npy.sum(inv_Vb) sum_inv_Vc = npy.sum(inv_Vc) 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) 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) 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 == 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) 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') 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('Unknown k_method: {}'.format(self.k_method)) #Reference plane shift if self.ref_plane != 0: try: shift1 = exp(-2*gamma[m]*self.ref_plane[0]) shift2 = exp(-2*gamma[m]*self.ref_plane[1]) except TypeError: shift1 = exp(-2*gamma[m]*self.ref_plane) shift2 = exp(-2*gamma[m]*self.ref_plane) 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 if self.z0_line is not None: raise ValueError('Only one of c0 or z0_line can be given.') try: c0m = self.c0[m] except TypeError: c0m = self.c0 z0[m] = gamma[m]/(1j*2*npy.pi*freqs[m]*c0m) else: #Set the known line characteristic impedance if self.z0_line is not None: try: z0[m] = self.z0_line[m] except TypeError: z0[m] = self.z0_line else: try: z0[m] = self.z0_ref[m] except TypeError: z0[m] = self.z0_ref #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) if npy.shape(self.z0_ref) != (fpoints,): z0_ref = self.z0_ref*npy.ones(fpoints, dtype=npy.complex)
self.renormalize(z0, z0_ref, powerwave=powerwave)
[docs] @classmethod def from_coefs(cls, frequency, coefs, **kwargs): ''' Creates 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): ''' Effective permittivity of the solved line. Currently, this only works for TEM media. If you are using non-TEM media (ie rectangular waveguide) then you need to compute er yourself from gamma. ''' 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 key, ntwk in self.coefs_ntwks.items(): 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 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): ''' 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,
*args, **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] thru_approx = self.ideals[-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'] X = port1_cal.error_ntwk Y = port2_cal.error_ntwk # 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(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs])) coefs.update(dict([('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') 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 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' def __init__(self, measured, ideals, *args, **kwargs): ''' 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, *args, **kwargs) 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] thru_approx = self.ideals[-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'] X = port1_cal.error_ntwk Y = port2_cal.error_ntwk # 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(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs])) coefs.update(dict([('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') 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') Calibration.__init__(self, measured = measured, ideals = ideals,
*args, **kwargs)
[docs] def unterminate(self,ntwk): ''' Unterminates 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] ],\ [ 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 ],\ [ 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] ],\ [ 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 ],\ ]) #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)[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=npy.complex) T2 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.complex) T3 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.complex) T4 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.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): caled = ntwk.copy() inv = linalg.inv T1,T2,T3,T4 = self.T_matrices ntwk = self.unterminate(ntwk) for f in list(range(len(ntwk.s))): t1,t2,t3,t4,m = T1[f,:,:],T2[f,:,:],T3[f,:,:],\ T4[f,:,:],ntwk.s[f,:,:] caled.s[f,:,:] = inv(-1*m.dot(t3)+t1).dot(m.dot(t4)-t2)
return caled
[docs] def embed(self, ntwk): ''' ''' embedded = ntwk.copy() inv = linalg.inv T1,T2,T3,T4 = self.T_matrices for f in list(range(len(ntwk.s))): t1,t2,t3,t4,a = T1[f,:,:],T2[f,:,:],T3[f,:,:],\ T4[f,:,:],ntwk.s[f,:,:] embedded.s[f,:,:] = (t1.dot(a)+t2).dot(inv(t3.dot(a)+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']) inv = linalg.inv 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 , e110], \ [ e101 , e111]])\ .transpose().reshape(-1,2,2) E2 = npy.array([\ [ e200 , e210], \ [ e201 , e211]])\ .transpose().reshape(-1,2,2) E3 = npy.array([\ [ e300 , e310], \ [ e301 , e311]])\ .transpose().reshape(-1,2,2) E4 = npy.array([\ [ e400 , e410], \ [ e401 , e411]])\ .transpose().reshape(-1,2,2) T1 = npy.zeros(E1.shape, dtype=npy.complex) T2 = T1.copy() T3 = T1.copy() T4 = T1.copy() invE3 = inv(E3) for i in range(npoints): T1[i] = E2[i] - E1[i].dot(invE3[i]).dot(E4[i]) T2[i] = E1[i].dot(invE3[i]) T3[i] = -invE3[i].dot(E4[i]) T4[i] = invE3[i] return T1, T2, T3, T4
[docs] def E_matrices(self, T1, T2, T3, T4): ''' Convert solved calibration T matrices to S-parameters. ''' inv = linalg.inv E1 = npy.zeros(T1.shape, dtype=npy.complex) E2 = npy.zeros(T2.shape, dtype=npy.complex) E3 = npy.zeros(T3.shape, dtype=npy.complex) E4 = npy.zeros(T4.shape, dtype=npy.complex) invT4 = inv(npy.array(T4)) for i in range(len(T1)): E1[i] = T2[i].dot(invT4[i]) E2[i] = T1[i] - T2[i].dot(invT4[i]).dot(T3[i]) E3[i] = invT4[i] E4[i] = -invT4[i].dot(T3[i])
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): """ 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') if type(ideals) == Network: ideals = [ideals] if len(ideals) != 1: raise ValueError("One ideal must be given: Through or reflect definition.") if ideal_is_reflect == False: 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,
*args, **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 == 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 == 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): ''' Creates 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 class Normalization(Calibration): ''' Simple Thru Normalization ''' def run(self): pass def apply_cal(self, input_ntwk): return input_ntwk/average(self.measured) ## 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): ''' Unterminates 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() ntwk_flip = ntwk.copy() ntwk_flip.flip() m.s[:,0,0] = (ntwk**gamma_f).s[:,0,0] m.s[:,1,1] = (ntwk_flip**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
[docs]def determine_line(thru_m, line_m, line_approx=None): ''' 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 attentuators. 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 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 assumeing error networks are well # matched line_approx = line_m/thru_m 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.s[:,1,0]) found_line = line_m.copy() found_line.s = npy.array([[zero, s12],[s12,zero]]).transpose().reshape(-1,2,2)
return found_line 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 measurments 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 line_m : :class:`~skrf.network.Network` raw measurement of a matched transmissive standard reflect_m: :class:`~skrf.network.Network` raw measurement of a reflect 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 relfect, one for each root-choice. useful for troublshooting. Returns ------- reflect : :class:`~skrf.network.Network` a One-port network for the found reflect. ''' #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 = einsum('ijk,ikl -> ijl', rd, inv(rt)) a = tt[:,1,0] b = tt[:,1,1]-tt[:,0,0] c = -tt[:,0,1] sol1 = (-b-sqrt(b*b-4*a*c))/(2*a) sol2 = (-b+sqrt(b*b-4*a*c))/(2*a) e2 = line.s[:,0,1]**2 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]) rootChoice = [abs(x1[i] - e2[i]) < abs(x2[i] - e2[i]) for i in range(len(x1))] 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) b_A = (e-y)/(d-b*f) w1 = reflect_m.s[:,0,0] w2 = reflect_m.s[:,1,1] a = sqrt(((w1-y)*(1+w2*b_A)*(d-y*f))/\ ((w2+gam)*(1-w1/x)*(1-e/x))) out = [] for rootChoice2 in [1,-1] : a= a*rootChoice2 unknownReflectS = (w1-y)/(a*(1-w1/x)) out.append(unknownReflectS) 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) 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) # 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 #npy.sqrt(k_second*k_first)# (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'] # 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 Etr = ((Elr - Esf )/gamma_r) * 1./k 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)