"""
.. module:: skrf.calibration.calibration
================================================================
calibration (:mod:`skrf.calibration.calibration`)
================================================================
This module provides objects for VNA calibration. Specific algorithms
inherit from the common base class :class:`Calibration`.
Base Class
----------
.. autosummary::
:toctree: generated/
Calibration
One-port
--------
.. autosummary::
:toctree: generated/
OnePort
SDDL
SDDLWeikle
PHN
Two-port
--------
.. autosummary::
:toctree: generated/
TwelveTerm
SOLT
EightTerm
UnknownThru
LRM
LRRM
MRC
TRL
MultilineTRL
NISTMultilineTRL
TUGMultilineTRL
SixteenTerm
LMR16
Normalization
Multi-port
--------
.. autosummary::
:toctree: generated/
MultiportCal
MultiportSOLT
Three Receiver (1.5 port)
-------------------------
.. autosummary::
:toctree: generated/
TwoPortOnePath
EnhancedResponse
Generic Methods
---------------
.. autosummary::
:toctree: generated/
terminate
unterminate
determine_line
PNA interaction
---------------
.. autosummary::
:toctree: generated/
convert_skrfcoefs_2_pna
convert_pnacoefs_2_skrf
"""
from __future__ import annotations
import json
import warnings
from collections import OrderedDict, defaultdict
from copy import copy
from itertools import combinations
from numbers import Number
from textwrap import dedent
from typing import Literal
from warnings import warn
import numpy as np
from numpy import angle, einsum, exp, imag, invert, linalg, ones, poly1d, real, sqrt, zeros
from numpy.linalg import det
from scipy.optimize import least_squares
from .. import __version__ as skrf__version__
from .. import util
from ..io.touchstone import read_zipped_touchstones
from ..mathFunctions import ALMOST_ZERO, cross_ratio, find_closest, find_correct_sign, rand_c, sqrt_phase_unwrap
from ..network import (
Network,
average,
connect,
renormalize_s,
s2t,
s2z,
subnetwork,
t2s,
two_port_reflect,
z2s,
zipfile,
)
from ..networkSet import NetworkSet
ComplexArray = np.typing.NDArray[complex]
global coefs_list_12term
coefs_list_12term =[
'forward directivity',
'forward source match',
'forward reflection tracking',
'forward transmission tracking',
'forward load match',
'forward isolation',
'reverse directivity',
'reverse load match',
'reverse reflection tracking',
'reverse transmission tracking',
'reverse source match',
'reverse isolation'
]
global coefs_list_8term
"""
There are various notations used for this same model. Given that all
measurements have been unterminated properly the error box model holds
and the following equalities hold:
k = e10/e23 # in s-param
k = alpha/beta # in mark's notation
beta/alpha *1/Err = 1/(e10e32) # marks -> rytting notation
"""
coefs_list_8term = [
'forward directivity',
'forward source match',
'forward reflection tracking',
'reverse directivity',
'reverse source match',
'reverse reflection tracking',
'forward switch term',
'reverse switch term',
'k',
'forward isolation',
'reverse isolation'
]
global coefs_list_3term
coefs_list_3term = [
'directivity',
'source match',
'reflection tracking',
]
[docs]
class Calibration:
"""
Base class for all Calibration objects.
This class implements the common mechanisms for all calibration
algorithms. Specific calibration algorithms should inherit this
class and override the methods:
* :func:`Calibration.run`
* :func:`Calibration.apply_cal`
* :func:`Calibration.embed` (optional)
The family of properties prefixed `coefs` and
`coefs..ntwks` returns error coefficients. If the property coefs
is accessed and empty, then :func:`Calibration.run` is called.
"""
family = ''
[docs]
def __init__(self, measured, ideals, sloppy_input=False,
is_reciprocal=True,name=None, self_calibration=False,*args, **kwargs):
r"""
Calibration initializer.
Notes
-----
About the order of supplied standards,
If the measured and ideals parameters are lists of Networks and
`sloppy_input=False`, then their elements must align. However,
if the measured and ideals are dictionaries, or
`sloppy_input=True`, then we will try to align them for you
based on the names of the networks (see `func:`align_measured_ideals`).
You do not want to use this `sloppy_input` feature if the
calibration depends on the standard order (like TRL).
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use `sloppy_input`)
sloppy_input : Boolean.
Allows ideals and measured lists to be 'aligned' based on
the network names.
is_reciprocal : Boolean
enables the reciprocity assumption on the calculation of the
error_network, which is only relevant for one-port
calibrations.
name: string
the name of this calibration instance, like 'waveguide cal'
this is just for convenience [None].
self_calibration: Boolean
True if there are less ideals than measurements.
Used in self-calibration such as LMR, LRRM, where some of the
standards can be unknown.
\*args, \*\*kwargs : key-word arguments
stored in self.kwargs, which may be used by sub-classes
most likely in `run`.
"""
# allow them to pass di
# lets make an ideal flush thru for them :
if hasattr(measured, 'keys'):
measured = measured.values()
if not sloppy_input:
warn('dictionary passed, sloppy_input automatically activated', stacklevel=2)
sloppy_input = True
if hasattr(ideals, 'keys'):
ideals = ideals.values()
if not sloppy_input:
warn('dictionary passed, sloppy_input automatically activated', stacklevel=2)
sloppy_input = True
# fill measured and ideals with copied lists of input
self.measured = [ntwk.copy() for ntwk in measured]
self.ideals = [ntwk.copy() for ntwk in ideals]
self.sloppy_input=sloppy_input
if sloppy_input:
self.measured, self.ideals = \
align_measured_ideals(self.measured, self.ideals)
self.self_calibration = self_calibration
if not self_calibration and len(self.measured) != len(self.ideals):
raise(IndexError(dedent(
"""
The length of measured and ideals lists are different.
Number of ideals must equal the number of measured.
If you are using `sloppy_input` ensure the names are uniquely alignable.
"""
)))
# ensure all the measured Networks' frequency's are the same
for measure in self.measured:
if self.measured[0].frequency != measure.frequency:
raise(ValueError("Measured Networks don't have matching frequencies."))
if np.any(self.measured[0].z0 != measure.z0):
raise(ValueError("Measured Networks don't have matching z0."))
if len(self.measured) > 0:
if np.any(self.measured[0].z0 != self.measured[0].z0[0,0]):
warn("Non-constant z0 in measurements. Expect trouble", stacklevel=2)
# ensure that all ideals have same frequency of the measured
# if not, then attempt to interpolate
for k in list(range(len(self.ideals))):
if self.ideals[k].frequency != self.measured[0].frequency:
print(dedent(
f"""Warning: Frequency information doesn't match on ideals[{k}],
attempting to interpolate the ideal[{k}] Network .."""))
try:
# try to resample our ideals network to match
# the measurement frequency
self.ideals[k].interpolate_self(\
self.measured[0].frequency)
print('Success')
except Exception as err:
raise(IndexError(f'Failed to interpolate. Check frequency of ideals[{k}].')) from err
if np.any(self.ideals[k].z0 != self.measured[0].z0):
raise ValueError("Measured and ideals z0 are different.")
# passed to calibration algorithm in run()
self.kwargs = kwargs
self.name = name
self.is_reciprocal = is_reciprocal
# initialized internal properties to None
self._residual_ntwks = None
self._caled_ntwks =None
self._caled_ntwk_sets = None
def __str__(self):
if self.name is None:
name = ''
else:
name = self.name
if 'fromcoefs' in self.family.lower():
output = f"{self.family} Calibration: '{name}', {self.frequency}"
else:
output = f"{self.family} Calibration: '{name}', {self.frequency}, {len(self.measured)}-standards"
return output
def __repr__(self):
return self.__str__()
[docs]
def run(self):
"""
Run the calibration algorithm.
"""
raise NotImplementedError('The Subclass must implement this')
[docs]
def apply_cal(self, ntwk):
"""
Apply correction to a Network.
"""
raise NotImplementedError('The Subclass must implement this')
[docs]
def apply_cal_to_list(self, ntwk_list):
"""
Apply correction to list or dict of Networks.
"""
if hasattr(ntwk_list, 'keys'):
return {k: self.apply_cal(nw) for k, nw in ntwk_list.items()}
else:
return [self.apply_cal(k) for k in ntwk_list]
[docs]
def apply_cal_to_all_in_dir(self, *args, **kwargs):
"""
Apply correction to all touchstone files in a given directory.
See `skrf.io.general.read_all_networks`.
"""
from ..io.general import read_all_networks
ntwkDict = read_all_networks(*args, **kwargs)
return self.apply_cal_to_list(ntwkDict)
[docs]
def apply_cal_to_network_set(self, ntwk_set):
"""
Apply correction to a NetworkSet.
"""
cal_ns = NetworkSet([self.apply_cal(ntwk) for ntwk in ntwk_set])
if hasattr(ntwk_set, 'name'):
cal_ns.name = ntwk_set.name
return cal_ns
[docs]
def embed(self,ntwk):
"""
Embed an ideal response in the estimated error network[s]
"""
raise NotImplementedError('The Subclass must implement this')
[docs]
def pop(self,std=-1):
"""
Remove and return tuple of (ideal, measured) at index.
Parameters
----------
std : int or str
the integer of calibration standard to remove, or the name
of the ideal or measured calibration standard to remove.
Returns
-------
ideal,measured : tuple of skrf.Networks
the ideal and measured networks which were popped out of the
calibration
"""
if isinstance(std, str):
for idx,ideal in enumerate(self.ideals):
if std == ideal.name:
std = idx
if isinstance(std, str):
for idx,measured in enumerate(self.measured):
if std == measured.name:
std = idx
if isinstance(std, str):
raise (ValueError(f'standard {std} not found in ideals'))
return (self.ideals.pop(std), self.measured.pop(std))
[docs]
def remove_and_cal(self, std):
"""
Remove a cal standard and correct it, returning correct and ideal.
This requires requires overdetermination. Useful in
troubleshooting a calibration in which one standard is junk, but
you dont know which.
Parameters
----------
std : int or str
the integer of calibration standard to remove, or the name
of the ideal or measured calibration standard to remove.
Returns
-------
ideal,corrected : tuple of skrf.Networks
the ideal and corrected networks which were removed out of the
calibration
"""
measured, ideals = copy(self.measured), copy(self.ideals)
i,m = self.pop(std)
self.run()
c = self.apply_cal(m)
self.measured = measured
self.ideals = ideals
self.run()
return c,i
[docs]
@classmethod
def from_coefs_ntwks(cls, coefs_ntwks, **kwargs):
"""
Create a calibration from its error coefficients.
Parameters
----------
coefs_ntwks : dict of Networks objects
error coefficients for the calibration
See Also
--------
Calibration.from_coefs
"""
# assigning this measured network is a hack so that
# * `calibration.frequency` property evaluates correctly
# * TRL.__init__() will not throw an error
if not hasattr(coefs_ntwks,'keys'):
# maybe they passed a list? lets try and make a dict from it
coefs_ntwks = NetworkSet(coefs_ntwks).to_dict()
coefs = NetworkSet(coefs_ntwks).to_s_dict()
frequency = list(coefs_ntwks.values())[0].frequency
cal= cls.from_coefs(frequency=frequency, coefs=coefs, **kwargs)
return cal
[docs]
@classmethod
def from_coefs(cls, frequency, coefs, **kwargs):
"""
Create a calibration from its error coefficients.
Parameters
----------
frequency : :class:`~skrf.frequency.Frequency`
frequency info, (duh)
coefs : dict of numpy arrays
error coefficients for the calibration
See Also
--------
Calibration.from_coefs_ntwks
"""
# assigning this measured network is a hack so that
# * `calibration.frequency` property evaluates correctly
# * TRL.__init__() will not throw an error
n = Network(frequency = frequency,
s = rand_c(frequency.npoints,2,2))
measured = [n,n,n]
if 'forward switch term' in coefs:
switch_terms = (Network(frequency = frequency,
s=coefs['forward switch term']),
Network(frequency = frequency,
s=coefs['reverse switch term']))
kwargs['switch_terms'] = switch_terms
cal = cls(measured, measured, **kwargs)
cal.coefs = coefs
cal.family += '(fromCoefs)'
return cal
@property
def frequency(self):
"""
:class:`~skrf.frequency.Frequency` object of the calibration.
"""
return self.measured[0].frequency.copy()
@property
def nstandards(self):
"""
Number of ideal/measurement pairs in calibration.
"""
if len(self.ideals) != len(self.measured):
warn("number of ideals and measured don't agree", stacklevel=2)
return len(self.ideals)
@property
def coefs(self):
"""
Dictionary or error coefficients in form of numpy arrays.
The keys of this will be different depending on the
Calibration Model. This dictionary should be populated
when the `run()` function is called.
Notes
-----
when setting this, property, the numpy arrays are flattened.
this makes accessing the coefs more concise in the code.
See Also
--------
coefs_3term
coefs_8term
coefs_12term
coefs_ntwks
"""
try:
return self._coefs
except(AttributeError):
self.run()
return self._coefs
@coefs.setter
def coefs(self,d):
"""
"""
for k in d:
d[k] = d[k].flatten()
self._coefs = d
[docs]
def update_coefs(self, d):
"""
Update current dict of error coefficients.
"""
for k in d:
d[k] = d[k].flatten()
self._coefs.update(d)
@property
def output_from_run(self):
"""
Return any output from the :func:`run`.
This just returns whats in _output_from_run, and calls
:func:`run` if that attribute is non-existent.
finally, returns None if run() is called, and nothing is in
_output_from_run.
"""
try:
return self._output_from_run
except(AttributeError):
# maybe i havent run yet
self.run()
try:
return self._output_from_run
except(AttributeError):
# i did run and there is no output_from_run
return None
@property
def coefs_ntwks(self):
"""
Dictionary of error coefficients in form of Network objects.
See Also
--------
coefs_3term_ntwks
coefs_12term_ntwks
coefs_8term_ntwks
"""
ns = NetworkSet.from_s_dict(d=self.coefs,
frequency=self.frequency)
return ns.to_dict()
@property
def coefs_3term(self):
"""
Dictionary of error coefficients for One-port Error model.
Contains the keys:
* directivity
* source match
* reflection tracking'
"""
return {k: self.coefs.get(k) for k in [\
'directivity',
'source match',
'reflection tracking',
]}
@property
def coefs_3term_ntwks(self):
"""
Dictionary of error coefficients in form of Network objects.
"""
ns = NetworkSet.from_s_dict(d=self.coefs_3term,
frequency=self.frequency)
return ns.to_dict()
@property
def normalized_directivity(self):
"""
Directivity normalized to the reflection tracking.
"""
try:
return self.coefs_ntwks['directivity']/\
self.coefs_ntwks['reflection tracking']
except Exception:
pass
try:
out = {}
for direction in ['forward','reverse']:
out[direction + ' normalized directivity'] =\
self.coefs_ntwks[direction + ' directivity']/\
self.coefs_ntwks[direction + ' reflection tracking']
return out
except Exception as err:
raise ValueError('cant find error coefs') from err
@property
def coefs_8term(self):
"""
Dictionary of error coefficients for 8-term (Error-box) Model.
Contains the keys:
* forward directivity
* forward source match
* forward reflection tracking
* reverse directivity
* reverse source match
* reverse reflection tracking
* forward switch term
* reverse switch term
* k
* forward isolation
* reverse isolation
Notes
-----
If this calibration uses the 12-term model, then
:func:`convert_12term_2_8term` is called. See [1]_
References
----------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
"""
d = self.coefs
if all([k in d.keys() for k in coefs_list_3term]):
raise ValueError("Can't convert one port error terms to two port error terms")
# Check if we have all 12-term keys and convert to 8-term if we do.
if all([k in d.keys() for k in coefs_list_12term]):
return convert_12term_2_8term(d)
return d
@property
def coefs_8term_ntwks(self):
"""
Dictionary of error coefficients in form of Network objects.
"""
ns = NetworkSet.from_s_dict(d=self.coefs_8term,
frequency=self.frequency)
return ns.to_dict()
@property
def coefs_12term(self):
"""
Dictionary of error coefficients for 12-term Model.
Contains the keys:
* forward directivity
* forward source match
* forward reflection tracking
* forward transmission tracking
* forward load match
* forward isolation
* reverse directivity
* reverse load match
* reverse reflection tracking
* reverse transmission tracking
* reverse source match
* reverse isolation
Notes
-----
If this calibration uses the 8-term model, then
:func:`convert_8term_2_12term` is called. See [1]_
References
----------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
"""
d = self.coefs
if all([k in d.keys() for k in coefs_list_3term]):
raise ValueError("Can't convert one port error terms to two port error terms")
# Check if we have all 12-term keys and return the coefs if we do
if all([k in d.keys() for k in coefs_list_12term]):
return d
return convert_8term_2_12term(d)
@property
def coefs_12term_ntwks(self):
"""
Dictionary or error coefficients in form of Network objects.
"""
ns = NetworkSet.from_s_dict(d=self.coefs_12term,
frequency=self.frequency)
return ns.to_dict()
@property
def verify_12term(self):
"""
"""
Edf = self.coefs_12term['forward directivity']
Esf = self.coefs_12term['forward source match']
Erf = self.coefs_12term['forward reflection tracking']
Etf = self.coefs_12term['forward transmission tracking']
Elf = self.coefs_12term['forward load match']
Edr = self.coefs_12term['reverse directivity']
Elr = self.coefs_12term['reverse load match']
Err = self.coefs_12term['reverse reflection tracking']
Etr = self.coefs_12term['reverse transmission tracking']
Esr = self.coefs_12term['reverse source match']
return Etf*Etr - (Err + Edr*(Elf - Esr))*(Erf + Edf *(Elr - Esf))
@property
def verify_12term_ntwk(self):
return Network(s= self.verify_12term, frequency = self.frequency)
@property
def residual_ntwks(self):
"""
Dictionary of residual Networks.
These residuals are complex differences between the ideal
standards and their corresponding corrected measurements.
"""
return [caled - ideal for (ideal, caled) in zip(self.ideals, self.caled_ntwks)]
@property
def residual_ntwk_sets(self):
"""
Returns a NetworkSet for each `residual_ntwk`, grouped by their names.
"""
residual_sets={}
std_names = list(set([k.name for k in self.ideals]))
for std_name in std_names:
residual_sets[std_name] = NetworkSet(
[k for k in self.residual_ntwks if k.name.startswith(std_name)])
return residual_sets
@property
def caled_ntwks(self):
"""
List of the corrected calibration standards.
"""
return self.apply_cal_to_list(self.measured)
@property
def caled_ntwk_sets(self):
"""
Return a NetworkSet for each `caled_ntwk`, grouped by their names.
"""
caled_sets={}
std_names = list(set([k.name for k in self.ideals ]))
for std_name in std_names:
caled_sets[std_name] = NetworkSet(
[k for k in self.caled_ntwks if k.name.startswith(std_name)])
return caled_sets
@property
def biased_error(self) -> NetworkSet:
"""
Estimate of biased error for overdetermined calibration with
multiple connections of each standard.
Returns
-------
biased_error : skrf.Network
Network with s_mag is proportional to the biased error
Notes
-----
Mathematically, this is
.. math::
mean_s(|mean_c(r)|)
Where:
* r: complex residual errors
* mean_c: complex mean taken across connection
* mean_s: complex mean taken across standard
See Also
--------
biased_error
unbiased_error
total_error
"""
rns = self.residual_ntwk_sets
out = NetworkSet([rns[k].mean_s for k in rns]).mean_s_mag
out.name = 'Biased Error'
return out
@property
def unbiased_error(self) -> NetworkSet:
"""
Estimate of unbiased error for overdetermined calibration with
multiple connections of each standard.
Returns
-------
unbiased_error : skrf.Network
Network with s_mag is proportional to the unbiased error
Notes
-----
Mathematically, this is
mean_s(std_c(r))
where:
* r : complex residual errors
* std_c : standard deviation taken across connections
* mean_s : complex mean taken across standards
See Also
--------
biased_error
unbiased_error
total_error
"""
rns = self.residual_ntwk_sets
out = NetworkSet([rns[k].std_s for k in rns]).mean_s_mag
out.name = 'Unbiased Error'
return out
@property
def total_error(self) -> NetworkSet:
"""
Estimate of total error for overdetermined calibration with
multiple connections of each standard.This is the combined
effects of both biased and un-biased errors.
Returns
-------
total_error : skrf.Network
Network with s_mag is proportional to the total error
Notes
-----
Mathematically, this is
std_cs(r)
where:
* r : complex residual errors
* std_cs : standard deviation taken across connections and standards
See Also
--------
biased_error
unbiased_error
total_error
"""
out = NetworkSet(self.residual_ntwks).mean_s_mag
out.name = 'Total Error'
return out
@property
def error_ntwk(self):
"""
The calculated error Network or Network[s].
This will return a single two-port network for a one-port cal.
For a 2-port calibration this will return networks
for forward and reverse excitation. However, these are not
sufficient to use for embedding, see the :func:`embed` function
for that.
"""
return error_dict_2_network(
self.coefs,
frequency = self.frequency,
is_reciprocal= self.is_reciprocal)
[docs]
def write(self, file=None, *args, **kwargs):
r"""
Write the Calibration to disk using :func:`~skrf.io.general.write`.
Parameters
----------
file : str or file-object
filename or a file-object. If left as None then the
filename will be set to Calibration.name, if its not None.
If both are None, ValueError is raised.
\*args, \*\*kwargs : arguments and keyword arguments
passed through to :func:`~skrf.io.general.write`
Notes
-----
If the self.name is not None and file is can left as None
and the resultant file will have the `.ntwk` extension appended
to the filename.
Examples
--------
>>> cal.name = 'my_cal'
>>> cal.write()
See Also
--------
skrf.io.general.write
skrf.io.general.read
"""
# this import is delayed until here because of a circular dependency
from ..io.general import write
if file is None:
if self.name is None:
raise (ValueError('No filename given. You must provide a filename, or set the name attribute'))
file = self.name
write(file,self, *args, **kwargs)
[docs]
@util.axes_kwarg
def plot_calibration_errors(self, *args, ax: util.Axes = None, **kwargs):
"""
Plot biased, unbiased and total error in dB scaled.
See Also
--------
biased_error
unbiased_error
total_error
"""
port_list = self.biased_error.port_tuples
for m,n in port_list:
ax.set_title(f"S{self.biased_error.ntwk_set[0]._fmt_trace_name(m,n)}")
self.unbiased_error.plot_s_db(m,n,**kwargs)
self.biased_error.plot_s_db(m,n,**kwargs)
self.total_error.plot_s_db(m,n,**kwargs)
ax.set_ylim(-100,0)
[docs]
def plot_caled_ntwks(self, attr: str = 's_smith', show_legend: bool = False, **kwargs):
r"""
Plot corrected calibration standards.
Given that the calibration is overdetermined, this may be used
as a heuristic verification of calibration quality.
Parameters
----------
attr : str
Network property to plot, ie 's_db', 's_smith', etc.
Default is 's_smith'
show_legend : bool, optional
draw a legend or not. Default is False.
\*\*kwargs : kwargs
passed to the plot method of Network
"""
ns = NetworkSet(self.caled_ntwks)
fig, axes = util.subplots(figsize=(8,8))
kwargs.update({'show_legend':show_legend})
for ax ,(m, n) in zip(axes, ns[0].port_tuples):
ax.set_title(f"S{ns.ntwk_set[0]._fmt_trace_name(m, n)}")
ns.__getattribute__('plot_'+attr)(m, n, **kwargs)
fig.tight_layout()
[docs]
def plot_residuals(self, attr: str = 's_db', **kwargs):
r"""
Plot residual networks.
Given that the calibration is overdetermined, this may be used
as a metric of the calibration's *goodness of fit*
Parameters
----------
attr : str, optional.
Network property to plot, ie 's_db', 's_smith', etc.
Default is 's_db'
\*\*kwargs : kwargs
passed to the plot method of Network
See Also
--------
Calibration.residual_networks
"""
NetworkSet(self.residual_ntwks).__getattribute__('plot_'+attr)(**kwargs)
[docs]
class OnePort(Calibration):
r"""
Standard algorithm for a one port calibration.
Solves the linear set of equations:
.. math::
e_{11}\mathbf{i_1m_1}-\Delta e\,\mathbf{i_1}+e_{00}=\mathbf{m_1}
e_{11}\mathbf{i_2m_2}-\Delta e\,\mathbf{i_2}+e_{00}=\mathbf{m_2}
e_{11}\mathbf{i_3m_3}-\Delta e\,\mathbf{i_3}+e_{00}=\mathbf{m_3}
...
Where **m**'s and **i**'s are the measured and ideal reflection coefficients,
respectively.
If more than three standards are supplied, then a least square
algorithm is applied.
See [1]_ and [2]_
References
----------
.. [1] http://na.tm.agilent.com/vnahelp/tip20.html
.. [2] Bauer, R.F., Jr.; Penfield, Paul, "De-Embedding and Unterminating,"
Microwave Theory and Techniques, IEEE Transactions on , vol.22, no.3, pp.282,288, Mar 1974
doi: 10.1109/TMTT.1974.1128212
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1128212&isnumber=25001
"""
family = 'OnePort'
[docs]
def __init__(self, measured, ideals,*args, **kwargs):
"""
One Port initializer.
If more than three standards are supplied then a least square
algorithm is applied.
Notes
-----
See func:`Calibration.__init__` for details about
automatic standards alignment (aka `sloppy_input`)
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use `sloppy_input`)
args, kwargs :
passed to func:`Calibration.__init__`
Notes
-----
This uses numpy.linalg.lstsq() for least squares calculation
See Also
--------
Calibration.__init__
"""
Calibration.__init__(self, measured, ideals,
*args, **kwargs)
[docs]
def run(self):
""" Run the calibration algorithm.
"""
numStds = self.nstandards
numCoefs=3
mList = [self.measured[k].s.reshape((-1,1)) for k in range(numStds)]
iList = [self.ideals[k].s.reshape((-1,1)) for k in range(numStds)]
if not all([n.number_of_ports==1 for n in self.ideals]):
raise RuntimeError(f'ideals for {self.family} should be 1-port Networks')
if not all([n.number_of_ports==1 for n in self.measured]):
raise RuntimeError(f'measured networks for {self.family} should be 1-port Networks')
# ASSERT: mList and aList are now kx1x1 matrices, where k in frequency
fLength = len(mList[0])
#initialize outputs
abc = np.zeros((fLength,numCoefs),dtype=complex)
residuals = np.zeros((fLength,\
np.sign(numStds-numCoefs)),dtype=complex)
parameter_variance = np.zeros((fLength, 3,3),dtype=complex)
measurement_variance = np.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 = np.ones(shape=(numStds,1))
m = np.array([ mList[k][f] for k in range(numStds)]).reshape(-1,1)# m-vector at f
i = np.array([ iList[k][f] for k in range(numStds)]).reshape(-1,1)# i-vector at f
# construct the matrix
Q = np.hstack([i, one, i*m])
# calculate least squares
abcTmp, residualsTmp = np.linalg.lstsq(Q,m,rcond=None)[0:2]
if numStds > 3:
measurement_variance[f,:]= residualsTmp/(numStds-numCoefs)
parameter_variance[f,:] = \
abs(measurement_variance[f,:])*\
np.linalg.inv(np.dot(Q.T,Q))
abc[f,:] = abcTmp.flatten()
try:
residuals[f,:] = residualsTmp
except ValueError as err:
raise(ValueError('matrix has singular values. ensure standards are far enough away on smith chart'))\
from err
# convert the abc vector to standard error coefficients
a,b,c = abc[:,0], abc[:,1],abc[:,2]
e01e10 = a+b*c
e00 = b
e11 = c
self._coefs = {\
'directivity':e00,\
'reflection tracking':e01e10, \
'source match':e11\
}
# output is a dictionary of information
self._output_from_run = {
'residuals':residuals,
'parameter variance':parameter_variance
}
return None
[docs]
def apply_cal(self, ntwk):
er_ntwk = Network(frequency = self.frequency, name=ntwk.name)
tracking = self.coefs['reflection tracking']
s12 = np.sqrt(tracking)
s21 = s12
s11 = self.coefs['directivity']
s22 = self.coefs['source match']
er_ntwk.s = np.array([[s11, s12],[s21,s22]]).transpose(2,0,1)
return er_ntwk.inv**ntwk
[docs]
def embed(self,ntwk):
embedded = self.error_ntwk ** ntwk
embedded.name = ntwk.name
return embedded
[docs]
class SDDLWeikle(OnePort):
"""
Short-Delay-Delay-Load (Oneport Calibration).
One-port self-calibration, which contains a short, a load, and
two delays shorts of unity magnitude but unknown phase. Originally
designed to be resistant to flange misalignment, see [1]_.
References
----------
.. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment,"
Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006.
"""
family = 'SDDL'
[docs]
def __init__(self, measured, ideals, *args, **kwargs):
"""
Short-Delay-Delay-Load initializer.
Measured and ideal networks must be in the order:
* short
* delay short1
* delay short2
* load
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
args, kwargs :
passed to func:`Calibration.__init__`
See Also
--------
Calibration.__init__
"""
if (len(measured) != 4) or (len(ideals)) != 4:
raise IndexError('Incorrect number of standards.')
Calibration.__init__(self, measured = measured,
ideals =ideals, **kwargs)
[docs]
def run(self):
#measured reflection coefficients
w_s = self.measured[0].s.flatten() # short
w_1 = self.measured[1].s.flatten() # delay short 1
w_2 = self.measured[2].s.flatten() # delay short 2
w_l = self.measured[3].s.flatten() # load
# ideal response of reflection coefficients
G_l = self.ideals[3].s.flatten() # gamma_load
# handle singularities
G_l[G_l ==0] = ALMOST_ZERO
w_1p = w_1 - w_s # between (9) and (10)
w_2p = w_2 - w_s
w_lp = w_l - w_s
## NOTE: the published equation has an incorrect sign on this argument
## perhaps because they assume arg to measure clockwise angle??
alpha = exp(1j*2*angle(1./w_2p - 1./w_1p)) # (17)
p = alpha/( 1./w_1p - alpha/w_1p.conj() - (1.+G_l)/(G_l*w_lp )) # (22)
q = p/(alpha* G_l) #(23) (put in terms of p)
Bp_re = -1*((1 + (imag(p+q)/real(q-p)) * (imag(q-p)/real(p+q)))/\
(1 + (imag(p+q)/real(q-p))**2)) * real(p+q) # (25)
Bp_im = imag(q+p)/real(q-p) * Bp_re #(24)
Bp = Bp_re + Bp_im*1j
B = Bp + w_s #(10)
C = Bp * (1./w_1p - alpha/w_1p.conj()) + alpha * Bp/Bp.conj() #(20)
A = B - w_s + w_s*C #(6)
# convert the abc vector to standard error coefficients
e00 = B
e11 = -C
e01e10 = A + e00*e11
self._coefs = {\
'directivity':e00,\
'reflection tracking':e01e10, \
'source match':e11\
}
[docs]
class SDDL(OnePort):
"""
Short-Delay-Delay-Load (Oneport Calibration).
One-port self-calibration, which contains a short, a load, and
two delays shorts of unity magnitude but unknown phase. Originally
designed to be resistant to flange misalignment, see [1]_.
References
----------
.. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment,"
Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006.
"""
family = 'SDDL'
[docs]
def __init__(self, measured, ideals, *args, **kwargs):
"""
Short-Delay-Delay-Load initializer.
Measured and ideal networks must be in the order:
[ Short, Delay short1, Delay short2, Load]
The ideal delay shorts can be set to `None`, as they are
determined during the calibration.
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
args, kwargs :
passed to func:`Calibration.__init__`
See Also
--------
Calibration.__init__
"""
# if they pass None for the ideal responses for delay shorts
# then we will copy the short standard in their place. this is
# only to avoid throwing an error when initializing the cal, the
# values are not used.
if ideals[1] is None:
ideals[1] = ideals[0].copy()
if ideals[2] is None:
ideals[2] = ideals[0].copy()
if (len(measured) != 4) or (len(ideals)) != 4:
raise IndexError('Incorrect number of standards.')
Calibration.__init__(self, measured = measured,
ideals =ideals, **kwargs)
[docs]
def run(self):
#measured impedances
d = s2z(self.measured[0].s,1) # short
a = s2z(self.measured[1].s,1) # delay short 1
b = s2z(self.measured[2].s,1) # delay short 2
c = s2z(self.measured[3].s,1) # load
l = s2z(self.ideals[-1].s,1) # ideal def of load
cr_alpha = cross_ratio(b,a,c,d)
cr_beta = cross_ratio(a,b,c,d)
alpha = imag(cr_alpha)/real(cr_alpha/l)
beta = imag(cr_beta)/real(cr_beta/l)
self.ideals[1].s = z2s(alpha*1j,1)
self.ideals[2].s = z2s(beta*1j,1)
OnePort.run(self)
[docs]
class PHN(OnePort):
"""
Pair of Half Knowns (One Port self-calibration).
"""
family = 'PHN'
[docs]
def __init__(self, measured, ideals, *args, **kwargs):
"""
"""
if (len(measured) != 4) or (len(ideals)) != 4:
raise IndexError('Incorrect number of standards.')
Calibration.__init__(self, measured = measured,
ideals =ideals, **kwargs)
[docs]
def run(self):
# ideals (in impedance)
a = s2z(self.ideals[0].s,1).flatten() # half known
b = s2z(self.ideals[1].s,1).flatten() # half known
c = s2z(self.ideals[2].s,1).flatten() # fully known
d = s2z(self.ideals[3].s,1).flatten() # fully known
# measured (in impedances)
a_ = s2z(self.measured[0].s,1).flatten() # half known
b_ = s2z(self.measured[1].s,1).flatten() # half known
c_ = s2z(self.measured[2].s,1).flatten() # fully known
d_ = s2z(self.measured[3].s,1).flatten() # fully known
z = cross_ratio(a_,b_,c_,d_)
# intermediate variables
e = c-d-c*z
f = d-c-d*z
g = c*d*z
A = -real(f*z.conj())
B = 1j*imag( f*e.conj() + g.conj()*z)
C = real( g*e.conj())
npts = len(A)
b1,b2 = zeros(npts, dtype=complex), zeros(npts, dtype=complex)
for k in range(npts):
p = poly1d([A[k],B[k],C[k]])
b1[k],b2[k] = p.r
a1 = -(f*b1 + g)/(z*b1 + e)
a2 = -(f*b2 + g)/(z*b2 + e)
# temporarily translate into s-parameters so make the root-choice
# choosing a root in impedance doesnt generally work for typical
# calibration standards
b1_s = z2s(b1.reshape(-1,1,1),1)
b2_s = z2s(b2.reshape(-1,1,1),1)
a1_s = z2s(a1.reshape(-1,1,1),1)
a2_s = z2s(a2.reshape(-1,1,1),1)
b_guess = z2s(b.reshape(-1,1,1),1)
a_guess = z2s(a.reshape(-1,1,1),1)
distance1 = abs(a1_s - a_guess) + abs(b1_s - b_guess)
distance2 = abs(a2_s - a_guess) + abs(b2_s - b_guess)
b_found = np.where(distance1<distance2, b1, b2)
a_found = np.where(distance1<distance2, a1, a2)
self.ideals[0].s = z2s(a_found.reshape(-1,1,1),1)
self.ideals[1].s = z2s(b_found.reshape(-1,1,1),1)
OnePort.run(self)
## Two Ports
[docs]
class TwelveTerm(Calibration):
"""
12-term, full two-port calibration.
`TwelveTerm` is the traditional, fully determined, two-port calibration
originally developed in [1]_.
`TwelveTerm` can accept any number of reflect and transmissive standards,
as well as arbitrary (non-flush) transmissive standards.
* If more than 3 reflect standards are provided, a least-squares
solution is implemented for the one-port stage of the calibration.
* If more than 1 transmissive standard is given the `load match`,
and `transmission tracking` terms are calculated multiple times
and averaged.
References
------------
.. [1] "Calibration Process of Automatic Network Analyzer Systems" by Stig Rehnmark
"""
family = 'TwelveTerm'
[docs]
def __init__(self, measured, ideals, n_thrus=None, trans_thres=-40,
*args, **kwargs):
"""
TwelveTerm initializer.
Use the `n_thrus` argument to explicitly define the number of
transmissive standards. Otherwise, if `n_thrus=None`, then we
will try and guess which are transmissive, by comparing the mean
:math:`|s21|` and :math:`|s12|` responses (in dB) to `trans_thres`.
Notes
------
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
-------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
n_thrus : int
Number of transmissive standards. If None, we will try and
guess for you by comparing measure transmission to trans_thres,
trans_thres: float
The minimum transmission magnitude (in dB) that is
the threshold for categorizing a transmissive standard.
Compared to the measured s21,s12 meaned over frequency
Only use if n_thrus=None.
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports with a perfect isolation
between the ports. Used for determining the isolation error terms.
If no measurement is given leakage is assumed to be zero.
Loads don't need to be same as the one used as a match standard or
even have similar reflection coefficients. Reflects can be also used,
but accuracy might not be as good.
See Also
-----------
Calibration.__init__
"""
kwargs.update({'measured':measured,
'ideals':ideals})
# note: this will enable sloppy_input and align stds if necessary
Calibration.__init__(self, *args, **kwargs)
# if they didnt tell us the number of thrus, then lets
# heuristically determine it
trans_thres_mag = 10 ** (trans_thres / 20)
if n_thrus is None:
warn('n_thrus is None, guessing which stds are transmissive', stacklevel=2)
n_thrus=0
for k in self.ideals:
mean_trans = NetworkSet([k.s21, k.s12]).mean_s_mag
trans_mag = np.mean(mean_trans.s_mag.flatten())
# this number is arbitrary but reasonable
if trans_mag > trans_thres_mag:
n_thrus +=1
if n_thrus ==0:
raise ValueError(
'couldnt find a transmissive standard. check your data, or explicitly use `n_thrus` argument'
)
self.n_thrus = n_thrus
# if they didntly give explicit order, lets try and put the
# more transmissive standards last, by sorted measured/ideals
# based on mean s21
if self.sloppy_input:
trans = [np.mean(k.s21.s_mag) for k in self.ideals]
# see http://stackoverflow.com/questions/6618515/sorting-list-based-on-values-from-another-list
# get order of indices of sorted means s21
order = [x for (y,x) in sorted(zip(trans, range(len(trans))),\
key=lambda pair: pair[0])]
self.measured = [self.measured[k] for k in order]
self.ideals = [self.ideals[k] for k in order]
[docs]
def run(self):
"""
"""
n_thrus = self.n_thrus
p1_m = [k.s11 for k in self.measured[:-n_thrus]]
p2_m = [k.s22 for k in self.measured[:-n_thrus]]
p1_i = [k.s11 for k in self.ideals[:-n_thrus]]
p2_i = [k.s22 for k in self.ideals[:-n_thrus]]
thrus = self.measured[-n_thrus:]
ideal_thrus = self.ideals[-n_thrus:]
# create one port calibration for reflective standards
port1_cal = OnePort(measured = p1_m, ideals = p1_i)
port2_cal = OnePort(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = dict(port1_cal.coefs)
p2_coefs = dict(port2_cal.coefs)
if self.kwargs.get('isolation',None) is not None:
p1_coefs['isolation'] = self.kwargs['isolation'].s21.s.flatten()
p2_coefs['isolation'] = self.kwargs['isolation'].s12.s.flatten()
else:
p1_coefs['isolation'] = np.zeros(len(self.frequency), dtype=complex)
p2_coefs['isolation'] = np.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'] = np.mean(np.array(tt1),axis=0).flatten()
p2_coefs['transmission tracking'] = np.mean(np.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({f'forward {k}': p1_coefs[k] for k in p1_coefs})
coefs.update({f'reverse {k}': p2_coefs[k] for k in p2_coefs})
eight_term_coefs = convert_12term_2_8term(coefs)
coefs.update({l: eight_term_coefs[l] for l in \
['forward switch term','reverse switch term','k'] })
self._coefs = coefs
[docs]
def apply_cal(self,ntwk):
"""
"""
caled = ntwk.copy()
s11 = ntwk.s[:,0,0]
s12 = ntwk.s[:,0,1]
s21 = ntwk.s[:,1,0]
s22 = ntwk.s[:,1,1]
Edf = self.coefs['forward directivity']
Esf = self.coefs['forward source match']
Erf = self.coefs['forward reflection tracking']
Etf = self.coefs['forward transmission tracking']
Elf = self.coefs['forward load match']
Eif = self.coefs.get('forward isolation',0)
Edr = self.coefs['reverse directivity']
Elr = self.coefs['reverse load match']
Err = self.coefs['reverse reflection tracking']
Etr = self.coefs['reverse transmission tracking']
Esr = self.coefs['reverse source match']
Eir = self.coefs.get('reverse isolation',0)
D = (1+(s11-Edf)/(Erf)*Esf)*(1+(s22-Edr)/(Err)*Esr) -\
((s21-Eif)/(Etf))*((s12-Eir)/(Etr))*Elf*Elr
caled.s[:,0,0] = \
(((s11-Edf)/(Erf))*(1+(s22-Edr)/(Err)*Esr)-\
Elf*((s21-Eif)/(Etf))*(s12-Eir)/(Etr)) /D
caled.s[:,1,1] = \
(((s22-Edr)/(Err))*(1+(s11-Edf)/(Erf)*Esf)-\
Elr*((s21-Eif)/(Etf))*(s12-Eir)/(Etr)) /D
caled.s[:,1,0] = \
( ((s21 -Eif)/(Etf))*(1+((s22-Edr)/(Err))*(Esr-Elf)) )/D
caled.s[:,0,1] = \
( ((s12 -Eir)/(Etr))*(1+((s11-Edf)/(Erf))*(Esf-Elr)) )/D
return caled
[docs]
def embed(self, ntwk):
measured = ntwk.copy()
s11 = ntwk.s[:,0,0]
s12 = ntwk.s[:,0,1]
s21 = ntwk.s[:,1,0]
s22 = ntwk.s[:,1,1]
det = s11*s22 - s12*s21
Edf = self.coefs['forward directivity']
Esf = self.coefs['forward source match']
Erf = self.coefs['forward reflection tracking']
Etf = self.coefs['forward transmission tracking']
Elf = self.coefs['forward load match']
Eif = self.coefs.get('forward isolation',0)
Edr = self.coefs['reverse directivity']
Elr = self.coefs['reverse load match']
Err = self.coefs['reverse reflection tracking']
Etr = self.coefs['reverse transmission tracking']
Esr = self.coefs['reverse source match']
Eir = self.coefs.get('reverse isolation',0)
measured = ntwk.copy()
D1 = (1 - Esf*s11 - Elf*s22 + Esf*Elf*det)
D2 = (1 - Elr*s11 - Esr*s22 + Esr*Elr*det)
measured.s[:,0,0] = Edf + Erf * (s11 - Elf*det)/D1
measured.s[:,1,0] = Eif + Etf * s21/D1
measured.s[:,1,1] = Edr + Err * (s22 - Elr*det)/D2
measured.s[:,0,1] = Eir + Etr * s12/D2
return measured
[docs]
class SOLT(TwelveTerm):
"""
Short-Open-Load-Thru, Full two-port calibration.
SOLT is the traditional, fully determined, two-port calibration
originally developed in [1]_.
Although the acronym SOLT implies the use of 4 standards, skrf's
algorithm can accept any number of reflect standards, If
more than 3 reflect standards are provided a least-squares solution
is implemented for the one-port stage of the calibration.
Redundant thru measurements can also be used, through the `n_thrus`
parameter. See :func:`__init__`
References
------------
.. [1] W. Kruppa and K. F. Sodomsky, "An Explicit Solution for the Scattering Parameters of a Linear Two-Port
Measured with an Imperfect Test Set (Correspondence)," IEEE Transactions on Microwave Theory and Techniques,
vol. 19, no. 1, pp. 122-123, Jan. 1971.
See Also
---------
TwelveTerm
"""
family = 'SOLT'
[docs]
def __init__(self, measured, ideals, n_thrus=1, *args, **kwargs):
"""
SOLT initializer.
If you arent using `sloppy_input`, then the order of the
standards must align.
If `n_thrus!=None`, then the thru standard[s] must be last in
the list. The `n_thrus` argument can be used to allow multiple
measurements of the thru standard.
If the ideal element for the thru is set to None, a flush thru
is assumed.
Notes
-----
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use `sloppy_input`)
The thru standard can be None
n_thrus : int
number of thru measurements
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports. Used for determining the
isolation error terms. If no measurement is given isolation is
assumed to be zero.
See Also
--------
TwelveTerm.__init__
"""
# see if they passed a None for the thru, and if so lets
# make an ideal flush thru for them
for k in range(-n_thrus,len(ideals)):
if ideals[k] is None:
if (n_thrus is None) or (hasattr(ideals, 'keys')) or \
(hasattr(measured, 'keys')):
raise ValueError(dedent(
"""Can't use sloppy_input and have the ideal thru be None.
Measured and ideals must be lists, or dont use None for the thru ideal."""))
ideal_thru = measured[0].copy()
ideal_thru.s[:,0,0] = 0
ideal_thru.s[:,1,1] = 0
ideal_thru.s[:,1,0] = 1
ideal_thru.s[:,0,1] = 1
ideals[k] = ideal_thru
kwargs.update({'measured':measured,
'ideals':ideals,
'n_thrus':n_thrus})
TwelveTerm.__init__(self,*args, **kwargs)
[docs]
class TwoPortOnePath(TwelveTerm):
"""
Two Port One Path Calibration (aka poor man's TwelveTerm).
Provides full error correction on a switchless three receiver
system, i.e. you can only measure the waves a1,b1,and b2.
Given this architecture, the DUT must be flipped and measured
twice to be fully corrected.
To allow for this, the `apply_cal` method takes a tuple of
measurements in the order (forward,reverse), and creates a composite
measurement that is correctable.
"""
family = 'TwoPortOnePath'
[docs]
def __init__(self, measured, ideals, n_thrus=None, source_port=1,
*args, **kwargs):
"""
Two Port One Path Calibration initializer.
Use the `n_thrus` argument to explicitly define the number of
transmissive standards. Otherwise, if `n_thrus=None`, then we
will try and guess which are transmissive, by comparing the mean
:math: `|s21|` and :math: `|s12|` responses (in dB) to `trans_thres`.
Notes
-----
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
n_thrus : int
number of thru measurements
source_port : [1,2]
The port on which the source is active. should be 1 or 2
See Also
--------
TwelveTerm.__init__
"""
if source_port not in [1, 2]:
raise ValueError("Invalid source_port value. Expected 1 or 2.")
self.sp = source_port-1
self.rp = 1 if self.sp == 0 else 0
# Make S12 = S21 and S22 = S11 for numerical reasons
measured_sym = [m.copy() for m in measured]
for m in measured_sym:
m.s[:,self.sp, self.rp] = m.s[:,self.rp, self.sp]
m.s[:,self.rp, self.rp] = m.s[:,self.sp, self.sp]
kwargs.update({'measured':measured_sym,
'ideals':ideals,
'n_thrus':n_thrus})
TwelveTerm.__init__(self,*args, **kwargs)
[docs]
def run(self):
"""
"""
# run a full twelve term then just copy all forward error terms
# over reverse error terms
TwelveTerm.run(self)
out_coefs = self.coefs.copy()
if self.sp ==0:
forward = 'forward'
reverse = 'reverse'
elif self.sp ==1:
forward = 'reverse'
reverse = 'forward'
else:
raise ValueError('source_port is out of range. should be 1 or 2.')
for k in self.coefs:
if k.startswith(forward):
k_out = k.replace(forward,reverse)
out_coefs[k_out] = self.coefs[k]
eight_term_coefs = convert_12term_2_8term(out_coefs)
out_coefs.update({l: eight_term_coefs[l] for l in \
['forward switch term','reverse switch term','k'] })
self._coefs = out_coefs
[docs]
def apply_cal(self, ntwk_tuple):
"""
apply the calibration to a measurement.
Notes
-----
Full correction is possible given you have measured your DUT
in both orientations. Meaning, you have measured the device,
then physically flipped the device and made a second measurement.
This tuple of 2-port Networks is what is meant by
(forward,reverse), in the docstring below
If you pass a single 2-port Network, then the measurement will
only be partially corrected using what is known as the
`EnhancedResponse` calibration.
Parameters
----------
network_tuple: tuple, or Network
tuple of 2-port Networks in order (forward, reverse) OR
a single 2-port Network.
"""
if isinstance(ntwk_tuple,tuple) or isinstance(ntwk_tuple,list):
f,r = ntwk_tuple[0].copy(), ntwk_tuple[1].copy()
sp,rp = self.sp,self.rp
ntwk = f.copy()
ntwk.s[:,sp,sp] = f.s[:,sp,sp]
ntwk.s[:,rp,sp] = f.s[:,rp,sp]
ntwk.s[:,rp,rp] = r.s[:,sp,sp]
ntwk.s[:,sp,rp] = r.s[:,rp,sp]
out = TwelveTerm.apply_cal(self, ntwk)
return out
else:
warnings.warn('only gave a single measurement orientation, error correction is partial without a tuple',
stacklevel=2)
ntwk = ntwk_tuple.copy()
sp,rp = self.sp,self.rp
ntwk.s[:,rp,rp] = 0
ntwk.s[:,sp,rp] = 0
out = TwelveTerm.apply_cal(self, ntwk)
out.s[:,rp,rp] = 0
out.s[:,sp,rp] = 0
return out
[docs]
class EnhancedResponse(TwoPortOnePath):
"""
Enhanced Response Partial Calibration.
Why are you using this?
For full error you correction, you can measure the DUT in both
orientations and instead use TwoPortOnePath
Accuracy of correct measurements will rely on having a good match
at the passive side of the DUT.
For code-structuring reasons, this is a dummy placeholder class.
Its just TwoPortOnePath, which defaults to enhancedresponse correction
when you apply the calibration to a single network, and not a tuple
of networks.
"""
family = 'EnhancedResponse'
[docs]
class EightTerm(Calibration):
"""
General EightTerm (aka Error-box) Two-port calibration.
This is basically an extension of the one-port algorithm to two-port
measurements, A least squares estimator is used to determine the
error coefficients. No self-calibration takes place.
The concept is presented in [1]_ , but implementation follows that
of [2]_ .
See :func:`__init__`
Notes
-----
An important detail of implementing the error-box
model is that the internal switch must be correctly accounted for.
This is done through the measurement of :term:`switch terms`.
References
----------
.. [1] Speciale, R.A.; , "A Generalization of the TSD Network-Analyzer Calibration Procedure,
Covering n-Port Scattering-Parameter Measurements, Affected by Leakage Errors,"
Microwave Theory and Techniques, IEEE Transactions on,
vol.25, no.12, pp. 1100- 1115, Dec 1977.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1129282&isnumber=25047
.. [2] Rytting, D. (1996) Network Analyzer Error Models and Calibration Methods.
RF 8: Microwave Measurements for Wireless Applications (ARFTG/NIST Short Course Notes)
"""
family = 'EightTerm'
[docs]
def __init__(self, measured, ideals, switch_terms=None,
isolation=None, ut_hook=None,*args, **kwargs):
"""
EightTerm Initializer.
Notes
-----
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports with a perfect isolation
between the ports. Used for determining the isolation error terms.
If no measurement is given leakage is assumed to be zero.
Loads don't need to be same as the one used as a match standard or
even have similar reflection coefficients. Reflects can be also used,
but accuracy might not be as good.
"""
self.switch_terms = switch_terms
if switch_terms is None:
warn('No switch terms provided', stacklevel=2)
if isolation is None:
self.isolation = measured[0].copy()
self.isolation.s[:,:,:] = 0
else:
self.isolation = isolation.copy()
#Zero port matching so that networks can be simply subtracted
self.isolation.s[:,0,0] = 0
self.isolation.s[:,1,1] = 0
self.ut_hook=ut_hook
Calibration.__init__(self,
measured = measured,
ideals = ideals,
**kwargs)
[docs]
def unterminate(self,ntwk):
"""
Unterminates switch terms from a raw measurement.
See Also
--------
calibration.unterminate
"""
if self.ut_hook is not None:
return self.ut_hook(self,ntwk)
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return unterminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
[docs]
def terminate(self, ntwk):
"""
Terminate a network with switch terms.
See Also
--------
calibration.terminate
"""
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return terminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
@property
def measured_unisolated(self):
return [k-self.isolation for k in self.measured]
@property
def measured_unterminated(self):
return [self.unterminate(k) for k in self.measured_unisolated]
[docs]
def run(self):
numStds = self.nstandards
numCoefs = 7
mList = [k.s for k in self.measured_unterminated]
iList = [k.s for k in self.ideals]
fLength = len(mList[0])
#initialize outputs
error_vector = np.zeros(shape=(fLength,numCoefs),dtype=complex)
residuals = np.zeros(shape=(fLength,4*numStds-numCoefs),dtype=complex)
Q = np.zeros((numStds*4, 7),dtype=complex)
M = np.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,:] = np.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,:] = np.array([\
[ m[0,0]],\
[ 0 ],\
[ m[1,0]],\
[ 0 ],\
])
# calculate least squares
error_vector_at_f, residuals_at_f = np.linalg.lstsq(Q,M,rcond=None)[0:2]
#if len (residualsTmp )==0:
# raise ValueError( 'matrix has singular values, check standards')
error_vector[f,:] = error_vector_at_f.flatten()
residuals[f,:] = residuals_at_f
e = error_vector
# put the error vector into human readable dictionary
self._coefs = {\
'forward directivity':e[:,0],
'forward source match':e[:,1],
'forward reflection tracking':(e[:,0]*e[:,1])-e[:,2],
'reverse directivity':e[:,3]/e[:,6],
'reverse source match':e[:,4]/e[:,6],
'reverse reflection tracking':(e[:,4]/e[:,6])*(e[:,3]/e[:,6])- (e[:,5]/e[:,6]),
'k':e[:,6],
}
self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': np.zeros(fLength, dtype=complex),
'reverse switch term': np.zeros(fLength, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e,
'residuals':residuals
}
return None
[docs]
def apply_cal(self, ntwk):
"""Applies the calibration to the input network.
Inverse of `embed`.
Parameters
----------
ntwk : :class:`~skrf.network.Network`
Uncalibrated input network.
Returns
-------
caled : :class:`~skrf.network.Network`
Calibrated network.
"""
caled = ntwk.copy()
T1,T2,T3,T4 = self.T_matrices
caled.s[:,1,0] -= self.coefs['forward isolation']
caled.s[:,0,1] -= self.coefs['reverse isolation']
caled = self.unterminate(caled)
caled.s = linalg.inv(-caled.s @ T3 + T1) @ (caled.s @ T4 - T2)
return caled
[docs]
def embed(self, ntwk):
"""Applies the error boxes to the calibrated input network.
Inverse of `apply_cal`.
Parameters
----------
ntwk : :class:`~skrf.network.Network`
Calibrated input network.
Returns
-------
embedded : :class:`~skrf.network.Network`
Network with error boxes applied.
"""
embedded = ntwk.copy()
T1,T2,T3,T4 = self.T_matrices
embedded.s = (T1 @ ntwk.s + T2) @ linalg.inv(T3 @ ntwk.s + T4)
embedded = self.terminate(embedded)
embedded.s[:,1,0] += self.coefs['forward isolation']
embedded.s[:,0,1] += self.coefs['reverse isolation']
return embedded
@property
def T_matrices(self):
"""
Intermediate matrices used for embedding and de-embedding.
Returns
-------
T1,T2,T3,T4 : numpy ndarray
"""
ec = self.coefs
npoints = len(ec['k'])
one = np.ones(npoints,dtype=complex)
zero = np.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 = np.array([
[ -detX, zero ],
[ zero, -k*detY ]
]).transpose(2,0,1)
T2 = np.array([
[ Edf, zero ],
[ zero, k*Edr ]
]).transpose(2,0,1)
T3 = np.array([
[ -Esf, zero ],
[ zero, -k*Esr ]
]).transpose(2,0,1)
T4 = np.array([
[ one, zero ],
[ zero, k ]
]).transpose(2,0,1)
return T1,T2,T3,T4
[docs]
def renormalize(self, z0_old, z0_new, powerwave=False):
"""Renormalizes the calibration error boxes to a new reference impedance.
Useful for example after doing a TRL calibration with non-50 ohm
transmission lines. After the TRL calibration reference impedance is the
line characteristic impedance. If the transmission line characteristic
impedance is known this function can be used to renormalize the
reference impedance to 50 ohms or any other impedance.
"""
ec = self.coefs
npoints = len(ec['k'])
one = np.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 = np.array([
[ Edf, Erf/k ],
[ k, Esf ]
]).transpose(2,0,1)
S2 = np.array([
[ Edr, one ],
[ Err, Esr ]
]).transpose(2,0,1)
#Port impedances before renormalization.
#Only the DUT side (port 2) is renormalized.
#VNA side (port 1) stays unchanged.
z = np.array([z0_new, z0_old]).transpose()
if powerwave:
S1 = renormalize_s(S1, z, z0_new, s_def='power')
S2 = renormalize_s(S2, z, z0_new, s_def='power')
else:
S1 = renormalize_s(S1, z, z0_new, s_def='traveling')
S2 = renormalize_s(S2, z, z0_new, s_def='traveling')
self.coefs['forward directivity'] = S1[:,0,0]
self.coefs['forward source match'] = S1[:,1,1]
self.coefs['forward reflection tracking'] = S1[:,0,1]*S1[:,1,0]
self.coefs['reverse directivity'] = S2[:,0,0]
self.coefs['reverse source match'] = S2[:,1,1]
self.coefs['reverse reflection tracking'] = S2[:,1,0]*S2[:,0,1]
self.coefs['k'] = S1[:,1,0]/S2[:,0,1]
return None
[docs]
class TRL(EightTerm):
"""
Thru-Reflect-Line (also called LRL for Line-Reflect-Line).
A Similar self-calibration algorithm as developed by Engen and
Hoer [1]_, more closely following into a more matrix form in [2]_.
Reference impedance of the calibration is characteristic impedance of the
transmission lines. If the characteristic impedance is known, reference
impedance can be renormalized using `EightTerm.renormalize` function.
See Also
--------
determine_line function which actually determines the line s-parameters
References
----------
.. [1] G. F. Engen and C. A. Hoer, "Thru-Reflect-Line: An Improved Technique for Calibrating the Dual
Six-Port Automatic Network Analyzer,"
IEEE Transactions on Microwave Theory and Techniques, vol. 27, no. 12, pp. 987-993, 1979.
.. [2] H.-J. Eul and B. Schiek, "A generalized theory and new calibration procedures for network analyzer
self-calibration,"
IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 4, pp. 724-731, 1991.
"""
family = 'TRL'
[docs]
def __init__(self, measured, ideals=None, estimate_line=False,
n_reflects=1,solve_reflect=True, *args,**kwargs):
r"""
Initialize a TRL calibration.
Note that the order of `measured` and `ideals` is strict.
It must be [Thru, Reflect, Line]. A multiline algorithms is
used if more than one line is passed. A multi-reflect algorithm
is used if multiple reflects are passed, see `n_reflects` argument.
All of the `ideals` can be individually set to `None`, or the entire
list set to `None` (`ideals=None`). For each ideal set to `None`,
the following assumptions are made:
* thru : flush thru
* reflect : flush shorts
* line : an approximately 90deg matched line (can be lossy)
The reflect ideals can also be given as a +-1.
If thru is non-zero length, the calibration is done with zero length
thru and the ideal thru length is subtracted from the ideal lines. The
resulting calibration reference plane is at the center of the thru.
Ideal reflect standard reference plane is at the center of the thru even
if the ideal thru length is non-zero.
Note you can also use the `estimate_line` option to
automatically estimate the initial guess for the line length
from measurements . This is sensible
if you have no idea what the line length is, but your **error
networks** are well matched (E_ij >>E_ii).
Notes
-----
This implementation inherits from :class:`EightTerm`. dont
forget to pass switch_terms.
Parameters
----------
measured : list of :class:`~skrf.network.Network`
must be in order [Thru, Reflect[s], Line[s]]. if the number
of reflects is >1 then use `n_reflects` argument.
ideals : list of :class:`~skrf.network.Network`, [+1,-1] , None
must be in order [Thru, Reflect, Line]. Each element in the
list may be None, or equivalently, the list may be None.
Also the reflects can be simply given as +1 or -1.
estimate_line : bool
should we estimates the length of the line standard from
raw measurements, if not we assume its about 90 deg.
solve_reflect : bool
Solve for the reflect or not.
n_reflects : 1
number of reflective standards
\*args, \*\*kwargs : passed to EightTerm.__init__
dont forget the `switch_terms` argument is important
Examples
--------
>>> thru = rf.Network('thru.s2p')
>>> reflect = rf.Network('reflect.s2p')
>>> line = rf.Network('line.s2p')
Ideals is None, so we assume it's close to a flush short:
>>> trl = TRL(measured=[thru,reflect,line], ideals=None)
Reflect is given as close to a flush short:
>>> trl = TRL(measured=[thru,reflect,line], ideals=[None,-1,None])
Reflect is given as close to a flush open:
>>> trl = TRL(measured=[thru,reflect,line], ideals=[None,+1,None])
See Also
--------
determine_line
determine_reflect
NISTMultilineTRL
TUGMultilineTRL
"""
#warn('Value of Reflect is not solved for yet.')
self.n_stds = n_stds = len(measured)
self.n_reflects = n_reflects
self.estimate_line = estimate_line
self.solve_reflect = solve_reflect
## generate ideals, given various inputs
if ideals is None:
ideals = [None]*len(measured)
if ideals[0] is None:
# lets make an ideal flush thru for them
ideal_thru = measured[0].copy()
ideal_thru.s[:,0,0] = 0
ideal_thru.s[:,1,1] = 0
ideal_thru.s[:,1,0] = 1
ideal_thru.s[:,0,1] = 1
ideals[0] = ideal_thru
orig_ideal_thru = None
if np.any(ideals[0].s[:,1,0] != 1) or np.any(ideals[0].s[:,0,1] != 1):
orig_ideal_thru = ideals[0]
ideals[0] = ideals[0].copy()
ideals[0].s[:,0,0] = 0
ideals[0].s[:,1,1] = 0
ideals[0].s[:,0,1] = 1
ideals[0].s[:,1,0] = 1
for k in range(1,n_reflects+1):
if ideals[k] is None:
# default assume they are using flushshorts
ideals[k] = -1
if isinstance(ideals[k], Number):
ideal_reflect = measured[k].copy()
ideal_reflect.s[:,0,0] = ideals[k]
ideal_reflect.s[:,1,1] = ideals[k]
ideal_reflect.s[:,1,0] = 0
ideal_reflect.s[:,0,1] = 0
ideals[k] = ideal_reflect
for k in range(n_reflects+1,n_stds):
if ideals[k] is None:
# lets make an 90deg line for them
ideal_line = measured[k].copy()
ideal_line.s[:,0,0] = 0
ideal_line.s[:,1,1] = 0
ideal_line.s[:,1,0] = -1j
ideal_line.s[:,0,1] = -1j
ideals[k] = ideal_line
if orig_ideal_thru is not None:
ideals[k] = ideals[k].copy()
# De-embed original thru
ideals[k].s[:,0,1] /= orig_ideal_thru.s[:,0,1]
ideals[k].s[:,1,0] /= orig_ideal_thru.s[:,1,0]
EightTerm.__init__(self,
measured = measured,
ideals = ideals,
**kwargs)
[docs]
def run(self):
m_ut = self.measured_unterminated
n_reflects = self.n_reflects
n_stds = self.n_stds
estimate_line = self.estimate_line
solve_reflect = self.solve_reflect
ideals = self.ideals
## Solve for the line[s]
for k in range(n_reflects+1,n_stds):
if estimate_line:
# setting line_approx to None causes determine_line() to
# estimate the line length from raw measurements
line_approx = None
else:
line_approx = ideals[k]
self.ideals[k] = determine_line(m_ut[0], m_ut[k], line_approx) # find line
## Solve for the reflect[s]
if solve_reflect:
for k in range(1,n_reflects+1):
# solve for reflect using the last line if they pass >1
r = determine_reflect(m_ut[0],m_ut[k],m_ut[-1],reflect_approx=ideals[k], line_approx=self.ideals[-1])
self.ideals[k] = two_port_reflect(r,r)
return EightTerm.run(self)
MultilineTRL = TRL
[docs]
class NISTMultilineTRL(EightTerm):
"""
NIST Multiline TRL calibration.
Multiline TRL can use multiple lines to extend bandwidth and accuracy of the
calibration. Different line measurements are combined in a way that minimizes
the error in calibration.
Calibration reference plane is at the edges of the lines.
At every frequency point there should be at least one line pair that has phase
difference that is not 0 degrees or a multiple of 180 degrees otherwise
calibration equations are singular and accuracy is very poor.
By default the reference impedance of the calibration is the characteristic
impedance of the transmission lines. If the characteristic impedance is
known reference impedance can be renormalized by giving `z0_ref` and
`z0_line`. Alternatively if capacitance/length of the transmission line is
given with `c0` argument, characteristic impedance can be solved assuming
that conductance/length is zero.
Algorithm is the one published in [0]_, but implementation is based on [1]_.
References
----------
.. [0] D. C. DeGroot, J. A. Jargon and R. B. Marks, "Multiline TRL revealed,"
60th ARFTG Conference Digest, Fall 2002., Washington, DC, USA, 2002, pp. 131-155.
.. [1] K. Yau "On the metrology of nanoscale Silicon transistors above 100 GHz"
Ph.D. dissertation, Dept. Elec. Eng. and Comp. Eng., University of Toronto, Toronto, Canada, 2011.
"""
family = 'TRL'
[docs]
def __init__(self, measured, Grefls, l,
er_est=1, refl_offset=None, ref_plane=0,
gamma_root_choice='auto', k_method='multical', c0=None,
z0_ref=50, z0_line=None, *args, **kwargs):
r"""
NISTMultilineTRL initializer.
Note that the order of `measured` is strict.
It must be [Thru, Reflects, Lines]. Multiple reflects can
also be used.
Notes
-------
This implementation inherits from :class:`EightTerm`. Don't
forget to pass switch_terms.
Parameters
--------------
measured : list of :class:`~skrf.network.Network`
must be in order [Thru, Reflects, Lines]
Grefls : complex or list of complex
Estimated reflection coefficients of reflect standards.
Usually -1 for short or +1 for open.
l : list of float
Lengths of through and lines. If through is non-zero length its
length is subtracted from the line lengths for the calibration and
afterwards the calibration reference planes are shifted back by half
thru on both ports using the solved propagation constant.
er_est : complex
Estimated effective permittivity of the lines.
Imaginary part is the loss at 1 GHz.
Negative imaginary part indicates losses.
refl_offset : float or list of float
Estimated offsets of the reflect standards from the reference plane
at the end of the lines.
Negative length is towards the VNA. Units are in meters.
ref_plane : float or list of float
Reference plane shift after the calibration.
Negative length is towards the VNA. Units are in meters.
Different shifts can be given to different ports by giving a two element list.
First element is shift of port 1 and second is shift of port 2.
gamma_root_choice : string
Method to use for choosing the correct eigenvalue for propagation
constant.
'estimate' : Choose the root that is closer to the estimated propagation
constant. Best choice when data is of good quality. To improve the
performance in phatological cases it's possible to give estimate
of the propagation constant as a keyword argument with 'gamma_est'.
'real' : Force the real part of the gamma to be positive corresponding
to a lossy line. Imaginary part can be negative.
This is the suggested method when lines have moderate loss and the
measurement noise is low. This is the default method.
'auto' : Use heuristics to choose the eigenvalue.
'imag' : Force the imaginary part of the gamma to be positive,
corresponding to a positive length line. Real part can be positive.
May choose incorrectly when the line is long due to phase wrapping.
k_method : string
Method to use for determining the 'k' error coefficient.
Currently valid choices are 'marks' or 'multical'.
The default method is 'multical'.
c0 : None, float or list of float
Capacitance/length of the transmission line in units F/m used for
reference impedance renormalization.
Characteristic impedance of the transmission lines can be determined
from the solved propagation constant if capacitance per length is known.
After the characteristic impedance is solved reference impedance of
the calibration is changed to `z0_ref`.
Solved characteristic impedance can be accessed with `cal.z0`.
Assumes TEM mode and conductance/length to be zero.
If `c0` == `z0_line` is None, the characteristic impedance is not renormalized.
In this case reference impedance of the calibration is characteristic
impedance of the transmission lines.
z0_ref : None, complex or list of complex
New reference impedance for the characteristic impedance renormalizarion.
No effect if `c0` is None and `z0_line` is None.
If `z0_ref` is None, no renormalization is done.
z0_line : None, complex or list of complex
Characteristic impedance of the transmission lines. Used for reference
impedance renormalization.
If `z0` == `z0_line` is None, the characteristic impedance is not renormalized.
In this case reference impedance of the calibration is characteristic
impedance of the transmission lines.
\*args, \*\*kwargs : passed to EightTerm.__init__
dont forget the `switch_terms` argument is important
See Also
--------
TUGMultilineTRL
"""
self.refl_offset = refl_offset
if np.isscalar(ref_plane):
ref_plane = [ref_plane, ref_plane]
self.ref_plane = ref_plane
self.er_est = er_est
self.l = [float(v) for v in l] # cast to float, see gh-895
self.Grefls = Grefls
self.gamma_root_choice = gamma_root_choice
self.k_method = k_method
self.z0_ref = z0_ref
self.c0 = c0
self.z0_line = z0_line
fpoints = len(measured[0].frequency)
if np.isscalar(self.z0_ref):
self.z0_ref = [self.z0_ref] * fpoints
if np.isscalar(self.z0_line):
self.z0_line = [self.z0_line] * fpoints
if np.isscalar(self.c0):
self.c0 = [self.c0] * fpoints
if np.isscalar(self.Grefls):
# assume a single reflect
self.Grefls = [self.Grefls]
n_reflects = len(self.Grefls)
if self.refl_offset is None:
self.refl_offset = [0] * len(self.Grefls)
if np.isscalar(self.refl_offset):
self.refl_offset = [self.refl_offset] * n_reflects
if len(measured) != len(self.Grefls) + len(l):
raise ValueError(dedent(
f"""Amount of measurements {len(measured)} doesn't match amount of line lengths {len(l)}
and reflection coefficients {len(self.Grefls)}"""))
#Not used, but needed for Calibration class init
ideals = measured
#EightTerm applies the switch correction
EightTerm.__init__(self,
measured = measured,
ideals = ideals,
self_calibration=True,
**kwargs)
m_sw = [k for k in self.measured_unterminated]
self.measured_reflects = m_sw[1:1+n_reflects]
self.measured_lines = [m_sw[0]]
self.measured_lines.extend(m_sw[1+n_reflects:])
self.ref_plane[0] -= l[0]/2
self.ref_plane[1] -= l[0]/2
self.refl_offset = [r - l[0]/2 for r in self.refl_offset]
# The first line is thru
self.l = [i - self.l[0] for i in self.l]
if len(l) != len(self.measured_lines):
raise ValueError("Different amount of lines and line lengths found")
[docs]
def run(self):
c = 299792458.0
pi = np.pi
inv = linalg.inv
exp = np.exp
log = np.log
abs = np.abs
gamma_est_user = self.kwargs.get('gamma_est', None)
measured_reflects = self.measured_reflects
measured_lines = self.measured_lines
measured_lines_t = list(map(lambda x: s2t(x.s), self.measured_lines))
l = self.l
er_est = self.er_est
freqs = measured_lines[0].f
fpoints = len(freqs)
lines = len(l)
gamma = np.zeros(fpoints, dtype=complex)
z0 = np.zeros(fpoints, dtype=complex)
gamma_est = (1j*2*pi*freqs[0]/c)*np.sqrt(er_est.real + 1j*er_est.imag/(freqs[0]*1e-9))
line_c = np.zeros(fpoints, dtype=int)
er_eff = np.zeros(fpoints, dtype=complex)
Tmat1 = np.ones(shape=(fpoints, 2, 2), dtype=complex)
Tmat2 = np.ones(shape=(fpoints, 2, 2), dtype=complex)
Smat1 = np.ones(shape=(fpoints, 2, 2), dtype=complex)
Smat2 = np.ones(shape=(fpoints, 2, 2), dtype=complex)
e = np.zeros(shape=(fpoints, 7), dtype=complex)
nstd = np.zeros(shape=(fpoints), dtype=float)
def t2s_single(t):
return t2s(t[np.newaxis,:,:])[0]
def s2t_single(s):
return s2t(s[np.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 = np.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 = np.round(-((gamma_est*dl).imag + (-log(eb)).imag)/(2*pi))
gb[i] = (-log(eb) + 1j*2*pi*periods)/dl
Db[i] = abs(gb[i]*dl + gamma_est*dl)/abs(-gamma_est*dl)
if Da[0] + Db[0] < 0.1*(Da[1] + Db[1]):
return e_val
if Da[1] + Db[1] < 0.1*(Da[0] + Db[0]):
return e_val[::-1]
if np.sign((ga[0]).real) != np.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 = np.eye(lines-1, dtype=complex) \
- (1.0/lines)*np.ones(shape=(lines-1, lines-1), dtype=complex)
b1_vec = np.zeros(lines-1, dtype=complex)
b2_vec = np.zeros(lines-1, dtype=complex)
CoA1_vec = np.zeros(lines-1, dtype=complex)
CoA2_vec = np.zeros(lines-1, dtype=complex)
b1_vec2 = np.zeros(lines-1, dtype=complex)
b2_vec2 = np.zeros(lines-1, dtype=complex)
CoA1_vec2 = np.zeros(lines-1, dtype=complex)
CoA2_vec2 = np.zeros(lines-1, dtype=complex)
if self.z0_line is not None and self.c0 is not None:
raise ValueError('Only one of c0 or z0_line can be given.')
for m in range(fpoints):
min_phi_eff = pi*np.ones(lines)
#Find the best common line to use
for n in range(lines):
for k in range(lines):
if n == k:
continue
dl = l[k] - l[n]
pd = abs(exp(-gamma_est*dl) - exp(gamma_est*dl))/2
if -1 <= pd <= 1:
phi_eff = np.arcsin( pd )
else:
phi_eff = np.pi/2
min_phi_eff[n] = min(min_phi_eff[n], phi_eff)
#Common line is selected to be one with the largest phase difference
line_c[m] = np.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 = np.zeros(lines-1, dtype=complex)
dl_vec = np.zeros(lines-1, dtype=complex)
k = 0
for n in range(lines):
#Skip the common line
if n == line_c[m]:
continue
dl = l[n] - l[line_c[m]]
Mij = (measured_lines_t[n][m]).dot(inv_line_c)
if 'estimate' in self.gamma_root_choice:
#Choose the correct root later
e_val = linalg.eigvals(Mij)
else:
#Choose the correct root using heuristics
e_val = root_choice(Mij, dl, gamma_est)
g_dl1 = -log(0.5*(e_val[0] + 1.0/e_val[1]))
g_dl2 = -log(0.5*(e_val[1] + 1.0/e_val[0]))
g_dl[k] = g_dl1
if 'real' in self.gamma_root_choice and (g_dl1/dl).real < 0:
#Choose root that has bigger real part (more lossier)
g_dl[k] = g_dl2
if 'imag' in self.gamma_root_choice and (g_dl1/dl).imag < 0:
#Choose root that has larger imaginary part
#Only works for short lines
g_dl[k] = g_dl2
if 'estimate' in self.gamma_root_choice:
#Choose root that is closer to the estimate
if gamma_est_user is not None:
g_est = gamma_est_user[m]
else:
#Use estimate from earlier iterations
g_est = gamma_est
periods1 = np.round( ((gamma_est*dl).imag - g_dl1.imag)/(2*pi))
periods2 = np.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 = np.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 = np.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 = np.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] += np.sum(dB1[:,root1[-1][1]]) + np.sum(dCoA1[:,root1[-1][1]])
d1[1] += np.sum(dB1[:,int(not root1[-1][1])]) + np.sum(dCoA1[:,int(not root1[-1][1])])
#Port 2
k = np.array([[0,1],[1,0]], dtype=complex)
T = s2t_single(k.dot(measured_lines[n].s[m]).dot(k)).dot(\
inv(s2t_single(k.dot(measured_lines[line_c[m]].s[m]).dot(k))))
T = measured_lines[n].s[m][0,1]*measured_lines[line_c[m]].s[m][1,0]*T
e_val = linalg.eigvals(T)
B2 = np.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 = np.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] += np.sum(dB2[:,root2[-1][1]]) + np.sum(dCoA2[:,root2[-1][1]])
d2[1] += np.sum(dB2[:,int(not root2[-1][1])]) + np.sum(dCoA2[:,int(not root2[-1][1])])
p += 1
Vb = np.zeros(shape=(lines-1,lines-1), dtype=complex)
Vc = np.zeros(shape=(lines-1,lines-1), dtype=complex)
#Fill in upper triangular matrix
l_not_common = [i for i in l if i != l[line_c[m]]]
for b in range(len(l_not_common)):
for a in range(b+1):
if a == b: #Diagonal
len_l = l_not_common[a]
exp_factor = exp(-gamma[m]*(len_l - l[line_c[m]]))
Vb[a,b] = abs(exp_factor)**2 + 1/abs(exp_factor)**2 + \
2*( abs(exp(-gamma[m]*len_l))*\
abs(exp(-gamma[m]*l[line_c[m]])) )**2
n = abs(exp_factor - 1/exp_factor)**2
Vb[a,b] /= n
Vc[a,b] = abs(exp_factor)**2 + 1/(abs(exp_factor))**2 + \
2/( abs(exp(-gamma[m]*l[line_c[m]]))*\
abs(exp(-gamma[m]*len_l)) )**2
Vc[a,b] /= n
elif a < b:
len_a = l_not_common[a]
len_b = l_not_common[b]
exp_factor = exp(-gamma[m]*(len_a -l[line_c[m]]))
exp_factor2 = exp(-gamma[m]*(len_b -l[line_c[m]]))
Vb[a,b] = exp_factor*exp_factor2.conjugate() + \
(abs(exp(-gamma[m]*l[line_c[m]])))**2 * \
exp(-gamma[m]*len_a)*(exp(-gamma[m]*len_b)).conjugate()
n = (exp_factor - 1/exp_factor)* \
(exp_factor2-1/exp_factor2).conjugate()
Vb[a,b] /= n
Vb[b,a] = Vb[a,b].conjugate()
Vc[a,b] = 1/(exp_factor*exp_factor2.conjugate()) + \
1/( (abs(exp(-gamma[m]*l[line_c[m]])))**2 * \
exp(-gamma[m]*len_a)*(exp(-gamma[m]*len_b)).conjugate() )
Vc[a,b] /= n
Vc[b,a] = Vc[a,b].conjugate()
def solve_A(B1, B2, CoA1, CoA2, S_thru, m):
#Determine A using unknown reflect
Ap = B1*B2 - B1*S_thru[1,1] - B2*S_thru[0,0] + linalg.det(S_thru)
Ap = -Ap/(1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*linalg.det(S_thru))
A1_vals = np.zeros(len(measured_reflects), dtype=complex)
A2_vals = np.zeros(len(measured_reflects), dtype=complex)
for n in range(len(measured_reflects)):
S_r = measured_reflects[n].s[m]
S_r11 = S_r[0,0]
S_r22 = S_r[1,1]
Arr = (S_r11 - B1)/(1 - S_r11*CoA1)* \
(1 - S_r22*CoA2)/(S_r22 - B2)
Gr_est = self.Grefls[n]*exp(-2*gamma[m]*(self.refl_offset[n] - l[0]/2.))
G_trial = (S_r11 - B1)/(np.sqrt(Ap*Arr)*(1 - S_r11*CoA1))
if abs( Gr_est/abs(Gr_est) - G_trial/abs(G_trial) ) > np.sqrt(2):
A1_vals[n] = -np.sqrt(Ap*Arr)
else:
A1_vals[n] = np.sqrt(Ap*Arr)
A2_vals[n] = A1_vals[n]/Arr
A1 = np.mean(A1_vals)
A2 = np.mean(A2_vals)
return A1, A2
inv_Vb = inv(Vb)
inv_Vc = inv(Vc)
sum_inv_Vb = np.sum(inv_Vb)
sum_inv_Vc = np.sum(inv_Vc)
values = []
#List possible root choices for B and CoA
for i in [(0,0), (0,1), (1,0), (1,1)]:
if i[0] == 0:
b1 = b1_vec
coa1 = CoA1_vec
else:
b1 = b1_vec2
coa1 = CoA1_vec2
if i[1] == 0:
b2 = b2_vec
coa2 = CoA2_vec
else:
b2 = b2_vec2
coa2 = CoA2_vec2
B1 = np.sum(inv_Vb.dot(b1))/sum_inv_Vb
B2 = np.sum(inv_Vb.dot(b2))/sum_inv_Vb
CoA1 = np.sum(inv_Vc.dot(coa1))/sum_inv_Vc
CoA2 = np.sum(inv_Vc.dot(coa2))/sum_inv_Vc
denom = 1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*\
(S_thru[0,0]*S_thru[1,1] - S_thru[0,1]*S_thru[1,0])
values.append( (abs(denom), B1, B2, CoA1, CoA2) )
if abs(values[0][0]) > 1e-9 and d1[1]/d1[0] > 10 and d2[1]/d2[0] > 10:
#Estimate seems to be correct
B1, B2, CoA1, CoA2 = values[0][1:]
A1, A2 = solve_A(B1, B2, CoA1, CoA2, S_thru, m)
else:
#Estimation is incorrect or the accuracy is bad
#Choose the root that minimizes error to measurements
best_error = None
best_values = []
for v in values:
if abs(v[0]) < 1e-9:
continue
B1, B2, CoA1, CoA2 = v[1:]
A1, A2 = solve_A(B1, B2, CoA1, CoA2, S_thru, m)
C1 = CoA1*A1
C2 = CoA2*A2
R = S_thru[0,1]*(1 - C1*C2)/(A1 - B1*C1)
T1 = R*np.array([[A1, B1],[C1, 1]])
g = np.array([[0,1],[1,0]])
T2 = np.array([[A2, B2],[C2, 1]])
error = 0
for n in range(lines):
meas = measured_lines[n].s[m]
ideal = np.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 += np.sum(abs(embedded - meas))
if best_error is None or error < best_error:
best_error = error
best_values = v
B1, B2, CoA1, CoA2 = best_values[1:]
A1, A2 = solve_A(B1, B2, CoA1, CoA2, S_thru, m)
sigmab = np.sqrt(1/(np.sum(inv_Vb).real))
sigmac = np.sqrt(1/(np.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 = np.angle( np.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 = np.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) ) > np.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) ) > np.sqrt(2):
warn('Inconsistencies detected', stacklevel=2)
elif self.k_method == 'multical':
denom = 1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*\
(S_thru[0,0]*S_thru[1,1] - S_thru[0,1]*S_thru[1,0])
R1 = S_thru[0,1]/denom
R2 = S_thru[1,0]/denom
else:
raise ValueError(f'Unknown k_method: {self.k_method}')
#Reference plane shift
if np.any(self.ref_plane):
shift1 = exp(-2*gamma[m]*self.ref_plane[0])
shift2 = exp(-2*gamma[m]*self.ref_plane[1])
A1 *= shift1
A2 *= shift2
C1 *= shift1
C2 *= shift2
R1 *= shift1
R2 *= shift2
if self.c0 is not None:
#Estimate the line characteristic impedance
#using known capacitance/length
z0[m] = gamma[m]/(1j*2*np.pi*freqs[m]*self.c0[m])
else:
#Set the known line characteristic impedance
if self.z0_line is not None:
z0[m] = self.z0_line[m]
else:
z0[m] = self.z0_ref[m]
#Error matrices
Tmat1[m,:,:] = R1*np.array([[A1, B1],[C1, 1]])
Tmat2[m,:,:] = R2*np.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': np.zeros(fpoints, dtype=complex),
'reverse switch term': np.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 np.any(z0 != self.z0_ref):
powerwave = self.kwargs.get('powerwave', False)
self.renormalize(z0, self.z0_ref, powerwave=powerwave)
[docs]
@classmethod
def from_coefs(cls, frequency, coefs, **kwargs):
"""
Create a calibration from its error coefficients.
Parameters
----------
frequency : :class:`~skrf.frequency.Frequency`
frequency info, (duh)
coefs : dict of numpy arrays
error coefficients for the calibration
See Also
--------
Calibration.from_coefs_ntwks
"""
# assigning this measured network is a hack so that
# * `calibration.frequency` property evaluates correctly
# * __init__() will not throw an error
n = Network(frequency = frequency,
s = rand_c(frequency.npoints,2,2))
measured = [n,n,n]
if 'forward switch term' in coefs:
switch_terms = (Network(frequency = frequency,
s=coefs['forward switch term']),
Network(frequency = frequency,
s=coefs['reverse switch term']))
kwargs['switch_terms'] = switch_terms
#Fill the required __init__ fields with garbage
#and assign the coefficients manually
cal = cls(measured, [-1], [0,1], **kwargs)
cal.coefs = coefs
cal.family += '(fromCoefs)'
return cal
@property
def gamma(self):
"""
Propagation constant of the solved line.
"""
try:
return self._gamma
except(AttributeError):
self.run()
return self._gamma
@property
def er_eff(self):
r"""
Effective permittivity of the solved line.
Defined in terms of the propagation constant:
.. math::
\gamma = \alpha + j \beta = \frac{2\pi f}{c} \sqrt{\epsilon_{r,eff}}
"""
try:
return self._er_eff
except(AttributeError):
self.run()
return self._er_eff
@property
def z0(self):
"""
Solved characteristic impedance of the transmission lines.
This is only solved if C0 parameter (Capacitance/length in units F/m) is given.
Solved Z0 assumes that conductance/length is zero and line supports TEM mode.
"""
try:
return self._z0
except(AttributeError):
self.run()
return self._z0
@property
def nstd(self):
"""
Normalized standard deviation of the calibration error.
Normalization is done such that 90 degree long single line gives
a standard deviation of 1.
"""
try:
return self._nstd
except(AttributeError):
self.run()
return self._nstd
[docs]
def save_calibration(self, filename):
"""
save calibration as an archive containing the standards, parameters and calibration results
Parameters
----------
filename : str
the path of the zip archive to save
"""
parameters = OrderedDict()
parameters["file type"] = "skrf calibration"
parameters["calibration class"] = self.__class__.__name__
parameters["skrf version"] = skrf__version__
parameters["measured"] = ntwk_names = [ntwk.name for ntwk in self.measured]
for i, name in enumerate(ntwk_names):
ntwk_names[i] = util.unique_name(name, ntwk_names, i)
parameters["ideals"] = None
if self.switch_terms:
fswitch, rswitch = self.switch_terms # type: Network
fswitch.name = "forward switch terms"
rswitch.name = "reverse switch terms"
parameters["switch terms"] = fswitch.name, rswitch.name
else:
parameters["switch terms"] = None
parameters["kwargs"] = {
"Grefls": self.Grefls,
"l": self.l,
"er_est": self.er_est,
"refl_offset": self.refl_offset,
"ref_plane": self.ref_plane,
"gamma_root_choice": self.gamma_root_choice,
"k_method": self.k_method
}
with zipfile.ZipFile(filename, 'w', compression=zipfile.ZIP_DEFLATED) as archive:
archive.writestr("parameters.json", json.dumps(parameters, indent=2))
if self.switch_terms:
fswitch.write_touchstone(dir="switch terms", to_archive=archive)
rswitch.write_touchstone(dir="switch terms", to_archive=archive)
for i, ntwk in enumerate(self.measured): # type: int, Network
ntwk.write_touchstone(ntwk_names[i] + ".s2p", dir="measured", to_archive=archive)
for ntwk in self.coefs_ntwks.values():
ntwk.write_touchstone(dir="coefs", to_archive=archive)
gamma_ntwk = Network(f=self.measured[0].f, s=self.gamma, z0=50., comments="propagation constant")
gamma_ntwk.write_touchstone("gamma.s1p", to_archive=archive)
[docs]
@classmethod
def load_calibration_archive(cls, filename):
with zipfile.ZipFile(filename) as archive:
parameters = json.loads(archive.open("parameters.json").read().decode("ascii"))
measured_dict = read_zipped_touchstones(archive, "measured")
switch_terms_dict = read_zipped_touchstones(archive, "switch terms")
coefs_dict = read_zipped_touchstones(archive, "coefs") # not used currently
gamma_ntwk = Network.zipped_touchstone("gamma.s1p", archive)
measured = list()
for name in parameters["measured"]:
measured.append(measured_dict[name])
if parameters["switch terms"] is None:
switch_terms = None
else:
switch_terms = [
switch_terms_dict[parameters["switch terms"][0]],
switch_terms_dict[parameters["switch terms"][1]]
]
kwargs = parameters["kwargs"]
cal = cls(measured, switch_terms=switch_terms, **kwargs)
cal.coefs = NetworkSet(coefs_dict).to_s_dict()
cal._gamma = gamma_ntwk.s.flatten()
return cal
[docs]
class TUGMultilineTRL(EightTerm):
"""
TUG Multiline TRL calibration.
An improved multiline TRL calibration procedure that generalizes the calibration process
by solving a single 4x4 weighted eigenvalue problem.
The overall algorithm is based on [1]_, but the weighting matrix calculation is based on [2]_.
You can read the mathematical details online at [3]_.
The calibration reference plane is at the edges of the first line.
By default, the reference impedance of the calibration is the characteristic impedance
of the transmission lines. If the characteristic impedance is known,
the reference impedance can be renormalized afterwards by running the method `renormalize()`.
Examples
--------
>>> line1 = rf.Network('line1.s2p')
>>> line2 = rf.Network('line2.s2p')
>>> line3 = rf.Network('line3.s2p')
>>> short = rf.Network('short.s2p')
>>> dut = rf.Network('dut.s2p')
Normal multiline TRL calibration:
>>> cal = rf.TUGMultilineTRL(line_meas=[line1,line2,line3], line_lengths=[0, 1e-3, 5e-3], er_est=4-.0j,
>>> reflect_meas=short, reflect_est=-1, reflect_offset=0)
>>> dut_cal = cal.apply_cal(dut)
Case of not using reflect measurements:
>>> cal = rf.TUGMultilineTRL(line_meas=[line1,line2,line3], line_lengths=[0, 1e-3, 5e-3], er_est=4-.0j)
>>> dut_cal = cal.apply_cal(dut) # only S21 and S12 are correct
References
----------
.. [1] Z. Hatab, M. Gadringer and W. Bösch, "Improving The Reliability of The Multiline TRL Calibration Algorithm,"
2022 98th ARFTG Microwave Measurement Conference (ARFTG), Las Vegas, NV, USA, 2022, pp. 1-5,
doi: https://doi.org/10.1109/ARFTG52954.2022.9844064
.. [2] Z. Hatab, M. Gadringer and W. Bösch, "Propagation of Linear Uncertainties Through Multiline
Thru-Reflect-Line Calibration," in IEEE Transactions on Instrumentation and Measurement,
vol. 72, pp. 1-9, 2023, doi: https://doi.org/10.1109/TIM.2023.3296123
.. [3] https://ziadhatab.github.io/posts/multiline-trl-calibration/
See Also
--------
NISTMultilineTRL
"""
family = 'TRL'
[docs]
def __init__(self, line_meas, line_lengths, er_est=1-.0j,
reflect_meas=None, reflect_est=None, reflect_offset=0, ref_plane=0,
*args, **kwargs):
r"""
TUGMultilineTRL initializer.
The order of the lines in `line_meas` and `line_lengths` should be the same.
Also, the first line is defined as thru. If non-zero, the calibration plane is
shifted by half of its length using the extracted propagation constant.
You can perform calibration without reflect measurements, but this will only provide you with the
propagation constant and relative effective permittivity. Without reflect measurements, you can
accurately calibrate S21 and S12 of a DUT. However, calibrating S11 and S22 requires a symmetric
reflect as part of the calibration process.
Notes
-------
This implementation inherits from :class:`EightTerm`. Don't
forget to pass switch_terms.
Parameters
--------------
line_meas : list of two-port :class:`~skrf.network.Network`
measurement of the lines. First line is defined as thru.
line_lengths : list of float
Lengths of the lines. If thru is non-zero length, the calibration plane is
shifted by half of its length using the solved propagation constant.
Units are in meters.
er_est : complex
Estimated permittivity of the lines at first frequency point of the measurement.
Negative imaginary part indicates losses.
reflect_meas : a two-port :class:`~skrf.network.Network` or a list of two-port :class:`~skrf.network.Network`
measurement of symmetric reflect.
Multiple symmetric reflect can be passed in a list, which is used to compute to average solution of the
error terms.
reflect_est : complex or list of complex
Estimated reflection coefficients of reflect standards at first frequency point of the measurement.
Usually -1 for short or +1 for open.
reflect_offset : float or list of float
Offset of the reflect standards from the reference plane.
Units are in meters.
ref_plane : float or list of float
Reference plane shift after the calibration.
Negative length is towards the VNA. Units are in meters.
Different shifts can be given to different ports by giving a two element list.
First element is shift of port 1 and second is shift of port 2.
\*args, \*\*kwargs : passed to EightTerm.__init__
dont forget the `switch_terms` argument is important
"""
self.line_meas = line_meas
self.line_lengths = line_lengths
self.er_est = er_est*(1+0j) # make complex
if len(self.line_lengths) != len(self.line_meas):
raise ValueError("Different amount of measured lines and line lengths found.")
if len(self.line_lengths) < 2:
raise ValueError("Less than two lines have been found.")
self.freq = self.line_meas[0].frequency
s_nan = np.array([ np.eye(2)*np.nan for f in self.freq.f])
self.reflect_meas = (
[Network(s=s_nan, frequency=self.freq)]
if reflect_meas is None
else (reflect_meas if isinstance(reflect_meas, list) else [reflect_meas])
)
self.reflect_est = np.atleast_1d(reflect_est)
self.reflect_offset = np.atleast_1d(reflect_offset)*np.ones(len(self.reflect_est))
if len(self.reflect_meas) != len(self.reflect_est):
raise ValueError("Different amount of measured reflects and estimated reflects found.")
# EightTerm applies the switch correction
measured = self.line_meas if reflect_meas is None else self.line_meas + self.reflect_meas
EightTerm.__init__(self,
measured = measured,
ideals = measured, # not actually used. Just to initiate the class
self_calibration=True,
**kwargs)
n_lines = len(self.line_lengths)
# switch term corrected
self.line_meas = self.measured_unterminated[:n_lines]
self.reflect_meas = self.reflect_meas if reflect_meas is None else self.measured_unterminated[n_lines:]
self.ref_plane = np.atleast_1d(ref_plane)*np.ones(2)
[docs]
def run(self):
# Constants
c0 = 299792458 # speed of light in vacuum (m/s)
Q = np.array([[0,0,0,1], [0,-1,0,0], [0,0,-1,0], [1,0,0,0]])
P = np.array([[1,0,0,0], [0, 0,1,0], [0,1, 0,0], [0,0,0,1]])
# Functions used throughout the calibration
def gamma2ereff(x, f):
return -(c0 / 2 / np.pi / f * x) ** 2
def ereff2gamma(x, f):
return 2 * np.pi * f / c0 * np.sqrt(-x)
def s2t_single(S, pseudo=False):
T = S.copy()
T[0,0] = -(S[0,0]*S[1,1]-S[0,1]*S[1,0])
T[0,1] = S[0,0]
T[1,0] = -S[1,1]
T[1,1] = 1
return T if pseudo else T/S[1,0]
def t2s_single(T, pseudo=False):
S = T.copy()
S[0,0] = T[0,1]
S[0,1] = T[0,0]*T[1,1]-T[0,1]*T[1,0]
S[1,0] = 1
S[1,1] = -T[1,0]
return S if pseudo else S/T[1,1]
def compute_G_with_takagi(A):
'''
Implementation of Takagi decomposition to compute the matrix G used to determine the weighting matrix.
Takagi decomposition is based on the paper below:
Alexander M. Chebotarev, Alexander E. Teretenkov,
"Singular value decomposition for the Takagi factorization of symmetric matrices,"
Applied Mathematics and Computation, Volume 234, 2014, Pages 380-384, https://doi.org/10.1016/j.amc.2014.01.170.
'''
u,s,vh = np.linalg.svd(A)
u,s,vh = u[:,:2],s[:2],vh[:2,:] # low-rank truncated (Eckart-Young theorem)
phi = np.sqrt( s*np.diag(vh@u.conj()) )
G = u@np.diag(phi)
# this is the eigenvalue of the weighted eigenvalue problem (1/2 squared Frobenius norm of W)
lambd = s[0]*s[1]
return G, lambd
def WLS(x,y,w=1):
# Weighted least-squares for a single parameter estimation
x = x*(1+0j) # force x to be complex type
return (x.conj().dot(w).dot(y))/(x.conj().dot(w).dot(x))
def Vgl(N):
# inverse covariance matrix for propagation constant computation
return np.eye(N-1, dtype=complex) - (1/N)*np.ones(shape=(N-1, N-1), dtype=complex)
def compute_gamma(X_inv, M, lengths, gamma_est, inx=0):
# gamma = alpha + 1j*beta is determined through linear weighted least-squares
# with inx you can choose the refrence line. doesn't make any difference.
lengths = lengths - lengths[inx]
EX = (X_inv@M)[[0,-1],:] # extract z and y columns
EX = np.diag(1/EX[:,inx])@EX # normalize to a reference line based on index `inx` (can be any)
del_inx = np.arange(len(lengths)) != inx # get rid of the reference line
# solve for alpha
l = -2*lengths[del_inx]
gamma_l = np.log(EX[0,:]/EX[-1,:])[del_inx]
alpha = WLS(l, gamma_l.real, Vgl(len(l)+1))
# solve for beta
l = -lengths[del_inx]
gamma_l = np.log((EX[0,:] + 1/EX[-1,:])/2)[del_inx]
n = np.round( (gamma_l - gamma_est*l).imag/np.pi/2 )
gamma_l = gamma_l - 1j*2*np.pi*n # unwrap
beta = WLS(l, gamma_l.imag, Vgl(len(l)+1))
return alpha + 1j*beta
def solve_quadratic(v1, v2, inx, x_est):
# This is realted to solving the normalized error terms using nullspace approach.
# The variable `inx` allowes to reuse the function to shuffel the coeffiecient to get other error terms.
v12,v13 = v1[inx]
v22,v23 = v2[inx]
mask = np.ones(v1.shape, bool)
mask[inx] = False
v11,v14 = v1[mask]
v21,v24 = v2[mask]
if abs(v12) > abs(v22): # to avoid dividing by small numbers
k2 = -v11*v22*v24/v12 + v11*v14*v22**2/v12**2 + v21*v24 - v14*v21*v22/v12
k1 = v11*v24/v12 - 2*v11*v14*v22/v12**2 - v23 + v13*v22/v12 + v14*v21/v12
k0 = v11*v14/v12**2 - v13/v12
c2 = np.roots([k2,k1,k0])*np.ones(2)
c1 = (1 - c2*v22)/v12
else:
k2 = -v11*v12*v24/v22 + v11*v14 + v12**2*v21*v24/v22**2 - v12*v14*v21/v22
k1 = v11*v24/v22 - 2*v12*v21*v24/v22**2 + v12*v23/v22 - v13 + v14*v21/v22
k0 = v21*v24/v22**2 - v23/v22
c1 = np.roots([k2,k1,k0])*np.ones(2)
c2 = (1 - c1*v12)/v22
x = np.array( [v1*x + v2*y for x,y in zip(c1,c2)] ) # 2 solutions
mininx = np.argmin( abs(x - x_est).sum(axis=1) )
return x[mininx]
line_meas_S = np.array([x.s for x in self.line_meas]) # get the S-parameters
reflect_meas_S = np.array([x.s for x in self.reflect_meas]) # get the S-parameters
lengths = np.atleast_1d( self.line_lengths ) # make numpy array
er_est = self.er_est
reflect_est = self.reflect_est
reflect_offset = self.reflect_offset
fpoints = len(self.freq.f)
Xs = np.zeros(shape=(fpoints, 4, 4), dtype=complex) # to store the combined error boxes (6 error terms)
ks = np.zeros(shape=(fpoints,), dtype=complex) # to store the 7th transmission error terms
er_effs = np.zeros(shape=(fpoints,), dtype=complex)
gammas = np.zeros(shape=(fpoints,), dtype=complex)
lambds = np.zeros(shape=(fpoints,), dtype=float) # to store the eigenvalue of the weighted eigendecomposition
# compute the calibration at each frequency point
for m, f in enumerate(self.freq.f):
# measurements
Mi = np.array([s2t_single(x) for x in line_meas_S[:,m,:,:]]) # convert to T-parameters
M = np.array([x.flatten('F') for x in Mi]).T
Dinv = np.diag([1/np.linalg.det(x) for x in Mi])
## Compute W via Takagi decomposition (also the eigenvalue lambda)
G, lambd = compute_G_with_takagi(Dinv@M.T@P@Q@M)
W = (G@np.array([[0,1j],[-1j,0]])@G.T).conj()
gamma_est = ereff2gamma(er_est, f)
gamma_est = abs(gamma_est.real) + 1j*abs(gamma_est.imag) # this to avoid sign inconsistencies
z_est = np.exp(-gamma_est*lengths)
y_est = 1/z_est
W_est = (np.outer(y_est,z_est) - np.outer(z_est,y_est)).conj()
W = -W if abs(W-W_est).sum() > abs(W+W_est).sum() else W # resolve the sign ambiguity
## weighted eigenvalue problem
F = M@W@Dinv@M.T@P@Q
eigval, eigvec = np.linalg.eig(F+lambd*np.eye(4))
inx = np.argsort(abs(eigval))
v1 = eigvec[:,inx[0]]
v2 = eigvec[:,inx[1]]
v3 = eigvec[:,inx[2]]
v4 = eigvec[:,inx[3]]
x1__est = v1/v1[0]
x1__est[-1] = x1__est[1]*x1__est[2]
x4_est = v4/v4[-1]
x4_est[0] = x4_est[1]*x4_est[2]
x2__est = np.array([x4_est[2], 1, x4_est[2]*x1__est[2], x1__est[2]])
x3__est = np.array([x4_est[1], x4_est[1]*x1__est[1], 1, x1__est[1]])
# solve quadratic equation for each column
x1_ = solve_quadratic(v1, v4, [0,3], x1__est) # range
x2_ = solve_quadratic(v2, v3, [1,2], x2__est) # nullspace
x3_ = solve_quadratic(v2, v3, [2,1], x3__est) # nullspace
x4 = solve_quadratic(v1, v4, [3,0], x4_est) # range
# build the normalized error terms (average the answers from range and nullspaces)
a12 = (x2_[0] + x4[2])/2
b21 = (x3_[0] + x4[1])/2
a21_a11 = (x1_[1] + x3_[3])/2
b12_b11 = (x1_[2] + x2_[3])/2
X_ = np.kron([[1,b21],[b12_b11,1]], [[1,a12],[a21_a11,1]]) # normalized cal coefficients
X_inv = np.linalg.inv(X_)
## compute propagation constant
gamma = compute_gamma(X_inv, M, lengths, gamma_est)
er_eff = gamma2ereff(gamma, f) # new estimate of er_eff
er_est = er_eff
## solve a11b11 and k from thru measurement (first line in the list)
ka11b11,_,_,k = X_inv@M[:,0]
a11b11 = ka11b11/k
# shift plane to edges of the thru standard plus defined reference plane
a11b11 = a11b11*np.exp(2*gamma*(lengths[0] - self.ref_plane.sum()))
k = k*np.exp(-gamma*(lengths[0] - self.ref_plane.sum()))
if np.isnan(reflect_meas_S[0,m,0,0]):
# no reflect measurement available.
a11 = np.sqrt(a11b11)
b11 = a11
else:
# solve for a11/b11, a11 and b11 (use redundant reflect measurement, if available)
reflect_est_offset = reflect_est*np.exp(-2*gamma*reflect_offset) # shift estimated reflect
Mr = np.array([s2t_single(x, pseudo=True).flatten('F') for x in reflect_meas_S[:,m,:,:]]).T
T = X_inv@Mr
a11_b11 = -T[2,:]/T[1,:]
a11 = np.sqrt(a11_b11*a11b11)
b11 = a11b11/a11
G_cal = (
(reflect_meas_S[:,m,0,0] - a12) / (1 - reflect_meas_S[:,m,0,0]*a21_a11)/a11
+ (reflect_meas_S[:,m,1,1]
+ b21)/(1 + reflect_meas_S[:,m,1,1]*b12_b11)/b11 )/2 # average
for inx,(Gcal,Gest) in enumerate(zip(G_cal, reflect_est_offset)):
if abs(Gcal - Gest) > abs(Gcal + Gest):
a11[inx] = -a11[inx]
b11[inx] = -b11[inx]
G_cal[inx] = -G_cal[inx]
a11 = a11.mean()
b11 = b11.mean()
X = X_@np.diag([a11b11, b11, a11, 1]) # build the calibration matrix (de-normalize)
Xs[m] = X
ks[m] = k
gammas[m] = gamma
er_effs[m] = er_eff
lambds[m] = lambd
self._er_eff = er_effs
self._gamma = gammas
self._lambd = lambds
e = np.zeros(shape=(len(self.freq.f), 7), dtype=complex)
e[:,0] = Xs[:,2,3]
e[:,1] = -Xs[:,3,2]
e[:,2] = -Xs[:,2,2]
e[:,3] = -Xs[:,1,3]
e[:,4] = Xs[:,3,1]
e[:,5] = -Xs[:,1,1]
e[:,6] = 1/ks/(e[:,4]*e[:,3]-e[:,5])
self._coefs = {\
'forward directivity':e[:,0],
'forward source match':e[:,1],
'forward reflection tracking':e[:,0]*e[:,1]-e[:,2],
'reverse directivity':e[:,3],
'reverse source match':e[:,4],
'reverse reflection tracking':e[:,4]*e[:,3]-e[:,5],
'k':e[:,6],
}
self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': np.zeros(fpoints, dtype=complex),
'reverse switch term': np.zeros(fpoints, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e
}
@property
def gamma(self):
"""
Propagation constant of the solved line.
"""
try:
return self._gamma
except(AttributeError):
self.run()
return self._gamma
@property
def er_eff(self):
"""
Relative effective permittivity of the solved line.
"""
try:
return self._er_eff
except(AttributeError):
self.run()
return self._er_eff
@property
def lambd(self):
"""
Eigenvalue of the weighted eigendecomposition.
The closer the eigenvalue to zero, the more sensitive the calibration to error.
Similar to the normalized standard deviation of NIST multiline TRL, but reversed.
"""
try:
return self._lambd
except(AttributeError):
self.run()
return self._lambd
[docs]
class UnknownThru(EightTerm):
"""
Two-Port Self-Calibration allowing the *thru* standard to be unknown.
This algorithm was originally developed in [1]_, and
is based on the 8-term error model (:class:`EightTerm`). It allows
the *thru* to be unknown, other than it must be reciprocal. This
is useful when when a well-known thru is not realizable.
References
----------
.. [1] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru,`"
IEEE Microwave and Guided Wave Letters, vol. 2, no. 12, pp. 505-507, 1992.
"""
family = 'UnknownThru'
[docs]
def __init__(self, measured, ideals, *args, **kwargs):
r"""
UnknownThru Initializer.
Note that the *thru* standard must be last in both measured, and
ideal lists. The ideal for the *thru* is only used to choose
the sign of a square root. Thus, it only has to be have s21, s12
known within :math:`\pi` phase.
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use `sloppy_input`)
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
"""
EightTerm.__init__(self, measured = measured, ideals = ideals,
**kwargs)
[docs]
def run(self):
p1_m = [k.s11 for k in self.measured_unterminated[:-1]]
p2_m = [k.s22 for k in self.measured_unterminated[:-1]]
p1_i = [k.s11 for k in self.ideals[:-1]]
p2_i = [k.s22 for k in self.ideals[:-1]]
thru_m = self.measured_unterminated[-1]
# create one port calibration for all reflective standards
port1_cal = OnePort(measured = p1_m, ideals = p1_i)
port2_cal = OnePort(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = port1_cal.coefs.copy()
p2_coefs = port2_cal.coefs.copy()
e_rf = port1_cal.coefs_ntwks['reflection tracking']
e_rr = port2_cal.coefs_ntwks['reflection tracking']
# create a fully-determined 8-term cal just get estimate on k's sign
# this is really inefficient, i need to work out the math on the
# closed form solution
et = EightTerm(
measured = self.measured,
ideals = self.ideals,
switch_terms= self.switch_terms)
k_approx = et.coefs['k'].flatten()
# this is equivalent to sqrt(detX*detY/detM)
e10e32 = np.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({f'forward {k}': p1_coefs[k] for k in p1_coefs})
coefs.update({f'reverse {k}': p2_coefs[k] for k in p2_coefs})
if self.switch_terms is not None:
coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
warn('No switch terms provided', stacklevel=2)
coefs.update({
'forward switch term': np.zeros(len(self.frequency), dtype=complex),
'reverse switch term': np.zeros(len(self.frequency), dtype=complex),
})
coefs.update({'k':k_})
self.coefs = coefs
[docs]
class LRM(EightTerm):
"""
Line-Reflect-Match self-calibration.
The required calibration standards are:
* Line: Fully known.
* Reflect: Unknown reflect, phase needs to be known within 90 degrees.
* Match: Fully known.
Reflect and match are assumed to be identical on both ports. The measured
and ideals lists must be given in LRM order.
Implementation is based on [1]_.
References
----------
.. [1] Zhao, W.; Liu, S.; Wang, H.; Liu, Y.; Zhang, S.; Cheng, C.; Feng,
K.; Ocket, I.; Schreurs, D.; Nauwelaers, B.; Qin, H.; Yang, X.
A Unified Approach for Reformulations of LRM/LRMM/LRRM Calibration
Algorithms Based on the T-Matrix Representation. Appl. Sci. 2017, 7,
866.
"""
family = 'LRM'
[docs]
def __init__(self, measured, ideals, switch_terms=None, isolation=None,
*args, **kwargs):
"""
LRM Initializer.
Parameters
----------
measured : list of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `measured` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports with a perfect isolation
between the ports. Used for determining the isolation error terms.
If no measurement is given leakage is assumed to be zero.
"""
super().__init__(
measured = measured,
ideals = ideals,
switch_terms = switch_terms,
isolation = isolation,
**kwargs)
[docs]
def run(self):
mList = [k for k in self.measured_unterminated]
lm = mList[0]
rm = mList[1]
mm = mList[2]
gm = self.ideals[2].s[:,0,0]
if self.ideals[2].nports > 1:
if any(gm != self.ideals[2].s[:,1,1]):
warnings.warn('Match ideal port 1 and port 2 are different. Using port 1 match also for port 2.',
stacklevel=2)
if self.ideals[1].nports > 1:
if any(self.ideals[1].s[:,0,0] != self.ideals[1].s[:,1,1]):
warnings.warn('Reflect ideal port 1 and port 2 are different. Using port 1 reflect also for port 2.',
stacklevel=2)
inv = np.linalg.inv
tl = self.ideals[0].t
fpoints = len(mList[0])
r1 = rm.s[:,0,0]
r2 = rm.s[:,1,1]
m1 = mm.s[:,0,0]
m2 = mm.s[:,1,1]
lm11 = lm.s[:,0,0]
lm12 = lm.s[:,0,1]
lm21 = lm.s[:,1,0]
lm22 = lm.s[:,1,1]
ones = np.ones(fpoints, dtype=complex)
zeros = np.zeros(fpoints, dtype=complex)
wlr1 = np.transpose(np.array([[ones, ones], [r1, m1]]), [2,0,1])
wll1 = np.transpose(np.array([[ones, zeros], [lm11, lm12]]), [2,0,1])
wll2 = np.transpose(np.array([[zeros, ones], [lm21, lm22]]), [2,0,1])
wlr2 = np.transpose(np.array([[ones, ones], [r2, m2]]), [2,0,1])
wl = inv(wlr1) @ wll1 @ inv(wll2) @ wlr2
# xyz2 == (x/y)*z**2
xyz2 = -np.linalg.det(tl) / np.linalg.det(wl)
c2 = wl[:, 0, 0]
c1 = -tl[:, 1, 0] - tl[:, 0, 1]
c0 = wl[:, 1, 1] * xyz2
z0 = -c1 + np.sqrt(c1**2 - 4*c2*c0)/(2*c2)
z1 = -c1 - np.sqrt(c1**2 - 4*c2*c0)/(2*c2)
zs = np.stack([z0, z1])
grs = np.zeros((2, fpoints), dtype=complex)
xs = np.zeros((2, fpoints), dtype=complex)
er = np.zeros((2, fpoints), dtype=complex)
for root in [0, 1]:
z = zs[root]
xyz = xyz2 / z
w11 = wl[:, 0, 0] * z
w21 = wl[:, 1, 0] * z
w12 = wl[:, 0, 1] * xyz
w22 = wl[:, 1, 1] * xyz
x = w12 / (tl[:, 1, 0] + tl[:, 1, 1]*gm - w22)
gr = (w11 - tl[:, 1, 0] + w21*x) / tl[:, 1, 1]
er[root] = np.abs(gr - self.ideals[1].s[:,0,0])
grs[root] = gr
xs[root] = x
root = er[0] < er[1]
gr = np.where(root, grs[0], grs[1])
x = np.where(root, xs[0], xs[1])
z = np.where(root, zs[0], zs[1])
y = x * z**2 / xyz2
self._solved_r = Network(s=gr, frequency=self.measured[0].frequency)
# Calculate error matrices
t10 = np.transpose(np.array([[ones, x], [gr, gm*x]]), [2,0,1]) \
@ inv(np.transpose(np.array([[ones,ones],[r1, m1]]), [2,0,1]))
t23 = np.transpose((1/z)*np.array([[ones, y], [gr, gm*y]]), [2,0,1]) \
@ inv(np.transpose(np.array([[ones,ones],[r2, m2]]), [2,0,1]))
Smat1 = t2s(t10)
Smat2 = t2s(t23)
# Convert the error coefficients to
# definitions used by the EightTerm class.
dx = linalg.det(Smat1)
dy = linalg.det(Smat2)
k = Smat1[:,0,1]/Smat2[:,0,1]
# Error coefficients
e = [Smat1[:,0,0],
Smat1[:,1,1],
dx,
Smat2[:,0,0],
Smat2[:,1,1],
dy,
k]
self._coefs = {\
'forward directivity':e[1],
'forward source match':e[0],
'forward reflection tracking':e[0]*e[1]-e[2],
'reverse directivity':e[4],
'reverse source match':e[3],
'reverse reflection tracking':e[4]*e[3]- e[5],
'k':e[6],
}
self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': np.zeros(fpoints, dtype=complex),
'reverse switch term': np.zeros(fpoints, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e
}
@property
def solved_r(self):
"""
Solved reflect
"""
try:
return self._solved_r
except(AttributeError):
self.run()
return self._solved_r
[docs]
class LRRM(EightTerm):
"""
Line-Reflect-Reflect-Match self-calibration.
The required calibration standards are:
* Line: Fully known.
* Reflect: Unknown reflect, phase needs to be known within 90 degrees.
* Reflect: Reflect with known absolute value of the reflection coefficient, \
phase needs to be known within 90 degrees. \
Different from the other reflect.
* Match: Match with known resistance in series with unknown inductance.
Reflects are assumed to be identical on both ports. Note that the first
reflect's magnitude of the reflection coefficient can be unknown, but the
second reflect's magnitude of the reflection coefficient needs to be known.
Match needs to be only measured on the first port, the second port of match
measurement is not used during the calibration.
If match_fit == 'lc' then the second reflect is assumed to be a lossless
capacitor. Measurements should then include low frequencies for accurate
open capacitance determination. 'lc_fit_c_freq' argument can be given to
specify the maximum frequency in Hz where open looks like an ideal
capacitor, above this frequency open is assumed to only have known absolute
value similar to 'l' fit. Default is infinity.
Implementation is based on papers [1]_ and [2]_. 'lc' match_fit based on
[3]_.
References
----------
.. [1] Zhao, W.; Liu, S.; Wang, H.; Liu, Y.; Zhang, S.; Cheng, C.; Feng,
K.; Ocket, I.; Schreurs, D.; Nauwelaers, B.; Qin, H.; Yang, X.
A Unified Approach for Reformulations of LRM/LRMM/LRRM Calibration
Algorithms Based on the T-Matrix Representation. Appl. Sci. 2017, 7,
866.
.. [2] F. Purroy and L. Pradell, "New theoretical analysis of the LRRM
calibration technique for vector network analyzers," in IEEE
Transactions on Instrumentation and Measurement, vol. 50, no. 5,
pp. 1307-1314, Oct. 2001.
.. [3] S. Liu, I. Ocket, A. Lewandowski, D. Schreurs and B. Nauwelaers, "An
Improved Line-Reflect-Reflect-Match Calibration With an Enhanced Load
Model," in IEEE Microwave and Wireless Components Letters, vol. 27,
no. 1, pp. 97-99, Jan. 2017.
"""
family = 'LRRM'
[docs]
def __init__(self, measured, ideals, switch_terms=None, isolation=None,
z0=50, match_fit='l', *args, **kwargs):
"""
LRRM Initializer.
Parameters
----------
measured : list of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must be line, reflect, reflect, match and must align with the
`ideals` parameter
ideals : list of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `measured` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports with a perfect isolation
between the ports. Used for determining the isolation error terms.
If no measurement is given leakage is assumed to be zero.
z0 : int
Calibration reference impedance. Only affects the solved match
inductance. Has no effect on the solved calibration parameters.
match_fit : string or None
Match model. Valid choices are:
'l' to fit a single inductance over all frequencies.
'lc' to fit match with series inductor and parallel capacitor and
assuming that the second reflect is open with unknown capacitance.
'none' to not fit inductance and let it be different for each
frequency point.
'l' or 'lc' is recommended for normal use.
"""
self.z0 = z0
# TODO: Second port not implemented.
self.match_port = 0
# Maximum frequency to assume that open behaves like ideal capacitor when
# using match_fit == 'lc'.
self.lc_fit_c_freq = kwargs.get('lc_fit_c_freq', float('inf'))
self.match_fit = match_fit
if self.match_port not in [0, 1]:
raise ValueError('match_port must be either 0 or 1.')
super().__init__(
measured = measured,
ideals = ideals,
switch_terms = switch_terms,
isolation = isolation,
**kwargs)
[docs]
def run(self):
mList = [k for k in self.measured_unterminated]
lm = mList[0]
r1m = mList[1]
r2m = mList[2]
mm = mList[3]
inv = np.linalg.inv
tl = self.ideals[0].t
w = 2*np.pi*self.measured[0].f
fpoints = len(mList[0])
r11 = r1m.s[:,0,0]
r12 = r1m.s[:,1,1]
r21 = r2m.s[:,0,0]
r22 = r2m.s[:,1,1]
lm11 = lm.s[:,0,0]
lm12 = lm.s[:,0,1]
lm21 = lm.s[:,1,0]
lm22 = lm.s[:,1,1]
mm1 = mm.s[:,0,0]
thru_s21 = self.ideals[0].s[:,1,0]
ones = np.ones(fpoints, dtype=complex)
zeros = np.zeros(fpoints, dtype=complex)
wlr1 = np.transpose(np.array([[ones, ones], [r11, r21]]), [2,0,1])
wll1 = np.transpose(np.array([[ones, zeros], [lm11, lm12]]), [2,0,1])
wll2 = np.transpose(np.array([[zeros, ones], [lm21, lm22]]), [2,0,1])
wlr2 = np.transpose(np.array([[ones, ones], [r12, r22]]), [2,0,1])
wl = inv(wlr1) @ wll1 @ inv(wll2) @ wlr2
# xyz2 == (x/y)*z**2
xyz2 = -np.linalg.det(tl) / np.linalg.det(wl)
c2 = wl[:, 0, 0]
c1 = -tl[:, 1, 0] - tl[:, 0, 1]
c0 = wl[:, 1, 1] * xyz2
z0 = (-c1 + np.sqrt(c1**2 - 4*c2*c0))/(2*c2)
z1 = (-c1 - np.sqrt(c1**2 - 4*c2*c0))/(2*c2)
zs = np.stack([z0, z1])
# wm and solve_gr equations are different if match is on the second port.
assert self.match_port == 0
wm_t1 = inv(np.transpose(np.array([[ones, ones],[r11, r21]]), [2,0,1]))
wm_t2 = np.transpose(np.array([[ones], [mm1]]), [2,0,1])
wm = wm_t1 @ wm_t2
wm1 = wm[:, 0, 0]
wm2 = wm[:, 1, 0]
def solve_gr(gm):
gr1s = np.zeros((2, fpoints), dtype=complex)
gr2s = np.zeros((2, fpoints), dtype=complex)
xs = np.zeros((2, fpoints), dtype=complex)
er = np.zeros((2, fpoints), dtype=complex)
efs = np.zeros((2, 4, fpoints), dtype=complex)
for root in [0, 1]:
z = zs[root]
xyz = xyz2 / z
w11 = wl[:, 0, 0] * z
w21 = wl[:, 1, 0] * z
w12 = wl[:, 0, 1] * xyz
w22 = wl[:, 1, 1] * xyz
e1 = (tl[:, 1, 1]**2) * wm1
e0 = tl[:, 1, 1] * (tl[:, 1, 0] - w22) * wm1 + tl[:, 1, 1] * wm2 * w12
f1 = tl[:, 1, 1] * (w11 - tl[:, 1, 0]) * wm1 + tl[:, 1, 1] * wm2 * w12
f0 = (w11 - tl[:, 1, 0]) * (tl[:, 1, 0] - w22) * wm1 + wm1 * w21 * w12
gr2 = -(f0 - e0 * gm) / (f1 - e1 * gm)
x = w12 / (tl[:, 1, 0] + tl[:, 1, 1]*gr2 - w22)
gr1 = ((w11 - tl[:, 1, 0]) * (tl[:, 1, 0] + tl[:, 1, 1] * gr2 - w22) + w21*w12) \
/ (tl[:, 1, 1] * (tl[:, 1, 0] + tl[:, 1, 1] * gr2 - w22))
egr1 = np.abs(gr1 - self.ideals[1].s[:,0,0])
egr2 = np.abs(gr2 - self.ideals[2].s[:,0,0])
er[root] = egr1 + egr2
gr1s[root] = gr1
gr2s[root] = gr2
efs[root, 0, :] = e1
efs[root, 1, :] = e0
efs[root, 2, :] = f1
efs[root, 3, :] = f0
xs[root] = x
root = er[0] < er[1]
gr1 = np.where(root, gr1s[0], gr1s[1])
gr2 = np.where(root, gr2s[0], gr2s[1])
x = np.where(root, xs[0], xs[1])
z = np.where(root, zs[0], zs[1])
efs = np.where(root, efs[0], efs[1])
y = x * z**2 / xyz2
return gr1, gr2, x, y, z, efs
def calc_gm(R, l, c=0):
"""
Calculates reflection coefficient of resistor R in series with inductance
l in parallel with capacitor c.
"""
return (self.z0 + R*(-1 + 1j*c*w*self.z0) - l*w*(1j + c*w*self.z0)) \
/(-self.z0 + R*(-1 - 1j*c*w*self.z0) + l*w*(-1j + c*w*self.z0))
# First, solve reflects assuming ideal gm
gmi = self.ideals[3].s[:, self.match_port, self.match_port]
gr1, gr2, x, y, z, efs = solve_gr(gmi)
# Next solve for match inductance
R = (self.z0 * (1 + gmi)/(1 - gmi)).real # Resistance of the match
a = 2*gr2.real + np.abs(gr2)**2 - \
2*(gr2*thru_s21**(-2)).real - np.abs(gr2*thru_s21**(-2))**2
b = 4*R*(gr2.imag + (gr2*thru_s21**(-2)).imag)
c = 4*R**2*(np.abs(gr2)**2 - 1)
det = b**2 - 4*a*c
if np.any(det < 0):
warnings.warn('Load inductance determination failed. Calibration might be incorrect.', stacklevel=2)
det[det < 0] = 0
wL = [None, None]
wL[0] = (-b+np.sqrt(det))/(2*a)
wL[1] = (-b-np.sqrt(det))/(2*a)
gm_guess = [None, None]
for p in [0,1]:
gm_guess[p] = (R + 1j*wL[p] - self.z0)/(R + 1j*wL[p] + self.z0)
# Choose the root according to which one is closer to the ideal
m_ideal = self.ideals[3].s[:,0,0]
root = (np.abs(gm_guess[0] - m_ideal) > np.abs(gm_guess[1] - m_ideal)).astype(int)
# L from reactance
match_l = np.choose(root, wL)/w
match_c = zeros
# Weight L estimate by frequency
l0 = np.sum(w * match_l) / np.sum(w)
e1 = efs[0, :]
e0 = efs[1, :]
f1 = efs[2, :]
f0 = efs[3, :]
gr2_abs = np.abs(self.ideals[2].s[:,0,0])
if self.match_fit == 'l':
def min_l(l):
"""
Calculates gr2 absolute value error as a function of
the match inductance.
"""
gm = (R + 1j*w*l - self.z0)/(R + 1j*w*l + self.z0)
return gr2_abs - np.abs((f0 - e0 * gm) / (f1 - e1 * gm))
# Try some alternative initial guesses
init_x = np.linspace(-10, 10, 10)
init_l = init_x / (w[-1])
init_guess = [np.mean(min_l(l)**2) for l in init_l]
li = np.argmin(init_guess)
best_guess = init_l[li]
# Choose the best guess for the least squares initial value
if init_guess[li] < np.mean(min_l(l0)**2):
l0 = best_guess
sol = least_squares(min_l, l0, method='lm')
match_l = sol.x * np.ones(match_l.shape)
match_c = zeros
elif self.match_fit == 'lc':
if self.ideals[2].s[0,0,0].real < 0:
warnings.warn("2nd reflect assumed to be open, but 2nd ideal ' \
'doesn't look like open. Calibration is likely incorrect.", stacklevel=2)
match_c = -1/(np.choose(root, wL)*w)
c0 = np.sum(w * match_c) / np.sum(w)
cw = w < 2 * np.pi * self.lc_fit_c_freq
cw = cw.astype(float)
def min_lc(x):
l, c = x
gm = calc_gm(R, l, c)
# Calculate open reflection coefficient from gm
gr2 = -(f0 - e0 * gm) / (f1 - e1 * gm)
# Fit capacitance to gr2
cgr2 = (1j*(-1 + gr2))/((1 + gr2)*w*self.z0)
cgr2 = np.mean(cgr2.real)
gr2_c = (1j + cgr2*w*self.z0)/(1j - cgr2*w*self.z0)
# Error between fitted open capacitor and calculated open
# capacitance
e_c = gr2_c + (f0 - e0 * gm) / (f1 - e1 * gm)
e_abs = gr2_abs - np.abs((f0 - e0 * gm) / (f1 - e1 * gm))
e = e_c * cw + (1 - cw) * e_abs
return np.abs(e)
# Biggest capacitance value assuming given gm matching.
worst_match = 0.4 # -7 dB
max_init_c = (2*worst_match)/(np.sqrt(1 - worst_match**2)*w[-1]*self.z0)
# Initial reactance guess, try to find positive L, C.
init_x = np.linspace(0, 20, 10)
init_l = init_x / (w[-1])
init_c = np.linspace(0, max_init_c, 10)
init_lc = [(l, c) for l in init_l for c in init_c]
if l0 > 0:
init_lc.append((l0, 0))
if c0 > 0:
init_lc.append((0, c0))
init_guess = [np.mean(min_lc(x)**2) for x in init_lc]
best_guess = init_lc[np.argmin(init_guess)]
l0 = best_guess[0]
c0 = best_guess[1]
sol = least_squares(min_lc, [l0, c0], method='lm')
match_l = sol.x[0] * np.ones(match_l.shape)
match_c = sol.x[1] * np.ones(match_l.shape)
elif self.match_fit == 'none' or self.match_fit is None:
pass
else:
raise ValueError(f'Unknown match_fit {self.match_fit}')
gamma_m = calc_gm(R, match_l, match_c)
# Solve finally reflects and calibration parameters using the solved match
gr1, gr2, x, y, z, _ = solve_gr(gamma_m)
freq = self.measured[0].frequency
self._solved_l = match_l
self._solved_c = match_c
self._solved_m = Network(s=gamma_m, frequency=freq, name='LRRM match')
self._solved_r1 = Network(s=gr1, frequency=freq, name='LRRM reflect 1')
self._solved_r2 = Network(s=gr2, frequency=freq, name='LRRM reflect 2')
# Calculate error matrices
t10 = np.transpose(np.array([[ones, x], [gr1, gr2*x]]), [2,0,1]) \
@ inv(np.transpose(np.array([[ones,ones],[r11, r21]]), [2,0,1]))
t23 = np.transpose((1/z)*np.array([[ones, y], [gr1, gr2*y]]), [2,0,1]) \
@ inv(np.transpose(np.array([[ones,ones],[r12, r22]]), [2,0,1]))
Smat1 = t2s(t10)
Smat2 = t2s(t23)
# Convert the error coefficients to
# definitions used by the EightTerm class.
dx = linalg.det(Smat1)
dy = linalg.det(Smat2)
k = Smat1[:,0,1]/Smat2[:,0,1]
# Error coefficients
e = [Smat1[:,0,0],
Smat1[:,1,1],
dx,
Smat2[:,0,0],
Smat2[:,1,1],
dy,
k]
self._coefs = {\
'forward directivity':e[1],
'forward source match':e[0],
'forward reflection tracking':e[0]*e[1]-e[2],
'reverse directivity':e[4],
'reverse source match':e[3],
'reverse reflection tracking':e[4]*e[3]- e[5],
'k':e[6],
}
self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': np.zeros(fpoints, dtype=complex),
'reverse switch term': np.zeros(fpoints, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e
}
@property
def solved_l(self):
"""
Solved inductance of the load
"""
try:
return self._solved_l
except(AttributeError):
self.run()
return self._solved_l
@property
def solved_c(self):
"""
Solved capacitance of the load.
Zero if match_fit != 'lc'.
"""
try:
return self._solved_c
except(AttributeError):
self.run()
return self._solved_c
@property
def solved_m(self):
"""
Solved match
"""
try:
return self._solved_m
except(AttributeError):
self.run()
return self._solved_m
@property
def solved_r1(self):
"""
Solved reflect1
"""
try:
return self._solved_r1
except(AttributeError):
self.run()
return self._solved_r1
@property
def solved_r2(self):
"""
Solved reflect2
"""
try:
return self._solved_r2
except(AttributeError):
self.run()
return self._solved_r2
[docs]
class MRC(UnknownThru):
"""
Misalignment Resistance Calibration.
This is an error-box based calibration that is a combination of the
SDDL[1]_ and the UnknownThru[2]_, algorithms.
The self-calibration aspects of these two algorithms alleviate the
need to know the phase of the delay shorts, as well as the exact
response of the thru. Thus the calibration is resistant to
waveguide flange misalignment.
References
----------
.. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment,"
Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006.
.. [2] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru,`"
IEEE Microwave and Guided Wave Letters, vol. 2, no. 12, pp. 505-507, 1992.
"""
family = 'MRC'
[docs]
def __init__(self, measured, ideals, *args, **kwargs):
r"""
MRC Initializer
This calibration takes exactly 5 standards, which must be in the
order:
[Short, DelayShort1, DelayShort1, Load, Thru]
The ideals for the delay shorts are not used and the ideal for
the *thru* is only used to choose
the sign of a square root. Thus, it only has to be have s21, s12
known within :math:`\pi` phase.
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
"""
UnknownThru.__init__(self, measured = measured, ideals = ideals,
**kwargs)
[docs]
def run(self):
p1_m = [k.s11 for k in self.measured_unterminated[:-1]]
p2_m = [k.s22 for k in self.measured_unterminated[:-1]]
p1_i = [k.s11 for k in self.ideals[:-1]]
p2_i = [k.s22 for k in self.ideals[:-1]]
thru_m = self.measured_unterminated[-1]
# create one port calibration for all reflective standards
port1_cal = SDDL(measured = p1_m, ideals = p1_i)
port2_cal = SDDL(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = port1_cal.coefs.copy()
p2_coefs = port2_cal.coefs.copy()
e_rf = port1_cal.coefs_ntwks['reflection tracking']
e_rr = port2_cal.coefs_ntwks['reflection tracking']
# create a fully-determined 8-term cal just get estimate on k's sign
# this is really inefficient, i need to work out the math on the
# closed form solution
et = EightTerm(
measured = self.measured,
ideals = self.ideals,
switch_terms= self.switch_terms)
k_approx = et.coefs['k'].flatten()
# this is equivalent to sqrt(detX*detY/detM)
e10e32 = np.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({f'forward {k}': p1_coefs[k] for k in p1_coefs})
coefs.update({f'reverse {k}': p2_coefs[k] for k in p2_coefs})
coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
warn('No switch terms provided', stacklevel=2)
coefs.update({
'forward switch term': np.zeros(len(self.frequency), dtype=complex),
'reverse switch term': np.zeros(len(self.frequency), dtype=complex),
})
coefs.update({'k':k_})
self.coefs = coefs
[docs]
class SixteenTerm(Calibration):
"""
General SixteenTerm (aka Error-box) Two-port calibration.
16-term error model is a complete error model that can solve for leakages between
the different VNA receivers.
There are several different combinations of calibration standards that can
be used. At least five two port measurements are needed. Using through, open,
short, and load standards some combinations result in singular matrix.
See [1]_ for list of non-singular combinations.
References
-----------
.. [1] K. J. Silvonen, "Calibration of 16-term error model (microwave measurement),"
in Electronics Letters, vol. 29, no. 17, pp. 1544-1545, 19 Aug. 1993.
"""
family = 'SixteenTerm'
[docs]
def __init__(self, measured, ideals, switch_terms=None,
*args, **kwargs):
"""
SixteenTerm Initializer.
Notes
-----
Switch terms are already assumed to be corrected since the ordinary
correction equations are not valid if the crosstalk is significant.
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
"""
self.switch_terms = switch_terms
if switch_terms is None:
warn('No switch terms provided', stacklevel=2)
Calibration.__init__(self,
measured = measured,
ideals = ideals,
**kwargs)
[docs]
def unterminate(self,ntwk):
"""
Unterminate switch terms from a raw measurement.
See Also
--------
calibration.unterminate
"""
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return unterminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
[docs]
def terminate(self, ntwk):
"""
Terminate a network with switch terms.
See Also
--------
calibration.terminate
"""
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return terminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
@property
def measured_unterminated(self):
return [self.unterminate(k) for k in self.measured]
[docs]
def run(self):
numStds = self.nstandards
numCoefs = 15
mList = [k.s for k in self.measured_unterminated]
iList = [k.s for k in self.ideals]
fLength = len(mList[0])
#initialize outputs
error_vector = np.zeros(shape=(fLength,numCoefs),dtype=complex)
residuals = np.zeros(shape=(fLength,4*numStds-numCoefs),dtype=complex)
Q = np.zeros((numStds*4, 15),dtype=complex)
M = np.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,:] = np.array([
[ i[0,0], i[1,0], 0 , 0 , 1, 0, 0, 0, -m[0,0]*i[0,0], -m[0,0]*i[1,0], -m[0,1]*i[0,0], -m[0,1]*i[1,0], -m[0,0] , 0 , -m[0,1] ], # noqa: E501
[ i[0,1], i[1,1], 0 , 0 , 0, 1, 0, 0, -m[0,0]*i[0,1], -m[0,0]*i[1,1], -m[0,1]*i[0,1], -m[0,1]*i[1,1], 0 , -m[0,0] , 0 ], # noqa: E501
[ 0 , 0 , i[0,0], i[1,0], 0, 0, 1, 0, -m[1,0]*i[0,0], -m[1,0]*i[1,0], -m[1,1]*i[0,0], -m[1,1]*i[1,0], -m[1,0] , 0 , -m[1,1] ], # noqa: E501
[ 0 , 0 , i[0,1], i[1,1], 0 ,0 ,0, 1, -m[1,0]*i[0,1], -m[1,0]*i[1,1], -m[1,1]*i[0,1], -m[1,1]*i[1,1], 0 , -m[1,0] , 0 ], # noqa: E501
])
#pdb.set_trace()
M[k*4:k*4+4,:] = np.array([\
[ 0 ],\
[ m[0,1] ],\
[ 0 ],\
[ m[1,1] ],\
])
## calculate least squares
error_vector_at_f, residuals_at_f = np.linalg.lstsq(Q,M,rcond=None)[0:2]
##if len (residualsTmp )==0:
## raise ValueError( 'matrix has singular values, check standards')
error_vector[f,:] = error_vector_at_f.flatten()
residuals[f,:] = residuals_at_f
e = error_vector
#Normalize e23 = 1
c = e[:,12]/(e[:,12]-e[:,13]*e[:,14])
for i in range(len(e[0])):
e[:,i] *= c
T1 = np.zeros(shape=(fLength, 2, 2), dtype=complex)
T2 = np.zeros(shape=(fLength, 2, 2), dtype=complex)
T3 = np.zeros(shape=(fLength, 2, 2), dtype=complex)
T4 = np.zeros(shape=(fLength, 2, 2), dtype=complex)
T1[:,0,0] = e[:,0]
T1[:,0,1] = e[:,1]
T1[:,1,0] = e[:,2]
T1[:,1,1] = e[:,3]
T2[:,0,0] = e[:,4]
T2[:,0,1] = e[:,5]
T2[:,1,0] = e[:,6]
T2[:,1,1] = e[:,7]
T3[:,0,0] = e[:,8]
T3[:,0,1] = e[:,9]
T3[:,1,0] = e[:,10]
T3[:,1,1] = e[:,11]
T4[:,0,0] = e[:,12]
T4[:,0,1] = e[:,13]
T4[:,1,0] = e[:,14]
T4[:,1,1] = c
# put the error vector into human readable dictionary
e1, e2, e3, e4 = self.E_matrices(T1, T2, T3, T4)
self._coefs = {\
'forward directivity':e1[:,0,0],
'reverse directivity':e1[:,1,1],
'forward source match':e4[:,0,0],
'reverse source match':e4[:,1,1],
'forward reflection tracking':e2[:,0,0]*e3[:,0,0],
'reverse reflection tracking':e2[:,1,1],
'k':e3[:,0,0],
'forward isolation':e1[:,1,0],
'reverse isolation':e1[:,0,1],
'forward port 1 isolation':e3[:,1,0],
'reverse port 1 isolation':e2[:,0,1],
'forward port 2 isolation':e2[:,1,0],
'reverse port 2 isolation':e3[:,0,1],
'forward port isolation':e4[:,1,0],
'reverse port isolation':e4[:,0,1],
}
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': np.zeros(fLength, dtype=complex),
'reverse switch term': np.zeros(fLength, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e,
'residuals':residuals
}
return None
[docs]
def apply_cal(self, ntwk):
"""Applies the calibration to the input network.
Inverse of `embed`.
Parameters
----------
ntwk : :class:`~skrf.network.Network`
Uncalibrated input network.
Returns
-------
caled : :class:`~skrf.network.Network`
Calibrated network.
"""
caled = ntwk.copy()
T1,T2,T3,T4 = self.T_matrices
caled = self.unterminate(caled)
caled.s = linalg.inv(-caled.s @ T3 + T1) @ (caled.s @ T4 - T2)
return caled
[docs]
def embed(self, ntwk):
"""Applies the error boxes to the calibrated input network.
Inverse of `apply_cal`.
Parameters
----------
ntwk : :class:`~skrf.network.Network`
Calibrated input network.
Returns
-------
embedded : :class:`~skrf.network.Network`
Network with error boxes applied.
"""
embedded = ntwk.copy()
T1,T2,T3,T4 = self.T_matrices
embedded.s = (T1 @ ntwk.s + T2) @ linalg.inv(T3 @ ntwk.s + T4)
embedded = self.terminate(embedded)
return embedded
@property
def T_matrices(self):
"""
Intermediate matrices used for embedding and de-embedding.
Returns
-------
T1,T2,T3,T4 : numpy ndarray
"""
ec = self.coefs
npoints = len(ec['forward directivity'])
e100 = ec['forward directivity']
e111 = ec['reverse directivity']
e400 = ec['forward source match']
e411 = ec['reverse source match']
e300 = ec['k']
e311 = np.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 = np.array([
[ e100 , e101],
[ e110 , e111]
]).transpose(2,0,1)
E2 = np.array([
[ e200 , e201],
[ e210 , e211]
]).transpose(2,0,1)
E3 = np.array([
[ e300 , e301],
[ e310 , e311]
]).transpose(2,0,1)
E4 = np.array([
[ e400 , e401],
[ e410 , e411]
]).transpose(2,0,1)
invE3 = linalg.inv(E3)
T1 = E2 - E1 @ invE3 @ E4
T2 = E1 @ invE3
T3 = -invE3 @ E4
T4 = invE3
return T1, T2, T3, T4
[docs]
def E_matrices(self, T1, T2, T3, T4):
"""
Convert solved calibration T matrices to S-parameters.
Returns
-------
E1,E2,E3,E4 : numpy ndarray
"""
invT4 = linalg.inv(np.array(T4))
E1 = T2 @ invT4
E2 = T1 - T2 @ invT4 @ T3
E3 = invT4
E4 = -invT4 @ T3
return E1, E2, E3, E4
[docs]
class LMR16(SixteenTerm):
"""
SixteenTerm Load-Match-Reflect self-calibration.
16-Term self calibration for leaky VNA. Implementation is based on [1]_.
Needs five standards to be measured and given in this order:
* Through
* Match-match
* Reflect-reflect
* Reflect-match
* Match-reflect
Reflect standard needs to be very reflective and same in all measurements.
Matching of through and match standards is assumed to be perfect.
Loss of the through is assumed to be zero, but its length can be non-zero.
Only reflect or through standard needs to be known and the other one will be
solved during the calibration. Solved S-parameters of the standards
can be accessed with LMR16.solved_through and LMR16.solved_reflect.
Switch termination is already assumed to be done either by the previous calibration or
during the measurements. Regular switch correction equations used with
EightTerm calibration can't be used if leakage is significant.
References
------------
.. [1] K. Silvonen, "LMR 16-a self-calibration procedure for a leaky network analyzer,"
in IEEE Transactions on Microwave Theory and Techniques, vol. 45, no. 7, pp. 1041-1049, Jul 1997
"""
family = 'SixteenTerm'
[docs]
def __init__(self, measured, ideals, ideal_is_reflect=True, sign=None,
switch_terms=None, *args, **kwargs):
r"""
LMR16 initializer.
Due to needing to solve a second order equation during the calibration a
choice must be taken on the correct root. Sign argument, +1 or -1, can be
given to make the root choice.
If sign argument is not given it is tried to be solved automatically by
choosing the sign that makes :math:`k = \frac{t_{15}}{t_{12}}` closer to +1, which holds
if test fixture is symmetric.
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards.
ideals : list/dict of :class:`~skrf.network.Network` objects
Estimated response of the reflect or through calibration standard.
ideal_is_reflect : Boolean
True if given ideal is reflect and False if ideal is through
sign : +1,-1 or None
Sign to be used for the root choice.
"""
self.switch_terms = switch_terms
if switch_terms is None:
warn('No switch terms provided', stacklevel=2)
if isinstance(ideals, Network):
ideals = [ideals]
if len(ideals) != 1:
raise ValueError("One ideal must be given: Through or reflect definition.")
if not ideal_is_reflect:
self.through = ideals[0].copy()
self.reflect = None
self._solved_through = self.through
self._solved_reflect = Network(s=[0]*len(self.through.f), f=self.through.f, f_unit='Hz')
else:
self.through = None
self.reflect = ideals[0].copy()
self._solved_through = Network(s=[[[0,1],[1,0]]]*len(self.reflect.f), f=self.reflect.f, f_unit='Hz')
self._solved_reflect = self.reflect
if len(measured) != 5:
raise ValueError("5 Measurements are needed: T, M-M, R-R, R-M and M-R")
self.measured = measured
self.sign = sign
Calibration.__init__(self,
measured = measured,
ideals = ideals,
sloppy_input=False,
self_calibration=True,
**kwargs)
[docs]
def run(self):
mList = [k.s for k in self.measured_unterminated]
fLength = len(mList[0])
inv = linalg.inv
T1 = []
T2 = []
T3 = []
T4 = []
auto_sign = self.sign is None
for f in range(fLength):
ma = mList[0][f] #Through
mb = mList[1][f] #Match-match
mc = mList[2][f] #Reflect-reflect
md = mList[3][f] #Reflect-match
me = mList[4][f] #Match-reflect
nn = inv(me-ma).dot(mb-me)
mm = (ma-mc).dot(nn)
oo = mb-mc
rr = inv(md-ma).dot(mb-md)
pp = (ma-mc).dot(rr)
m = (pp[1,0] + oo[1,0])*mm[1,1] - (pp[1,1] + oo[1,1])*mm[1,0]
n = oo[1,0]*pp[0,1] - oo[1,1]*pp[0,0]
o = (mm[0,1]+ oo[0,1])*pp[0,0] - (mm[0,0] + oo[0,0])*pp[0,1]
p = oo[0,1]*mm[1,0] - oo[0,0]*mm[1,1]
#One of the coefficients is normalized to one
t12 = 1.0
auto_sign_abs = []
if auto_sign:
self.sign = 1
for sign_tries in [0,1,2]:
gt = self.sign*np.sqrt(m*o/(n*p))
if self.through is None:
g = self.reflect.s[f][0,0]
t = g/gt
self._solved_through.s[f] = np.array([[0,t],[t,0]])
else:
t = self.through.s[f][1,0]
g = gt*t
self._solved_reflect.s[f] = np.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(np.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*np.array([[t0,t1],[t2,t3]]) )
T2.append( c*np.array([[t4,t5],[t6,t7]]) )
T3.append( c*np.array([[t8,t9],[t10,t11]]) )
T4.append( c*np.array([[t12,t13],[t14,t15]]) )
T1 = np.array(T1)
T2 = np.array(T2)
T3 = np.array(T3)
T4 = np.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': np.zeros(fLength, dtype=complex),
'reverse switch term': np.zeros(fLength, dtype=complex),
})
return None
[docs]
@classmethod
def from_coefs(cls, frequency, coefs, **kwargs):
"""
Create a calibration from its error coefficients.
Parameters
----------
frequency : :class:`~skrf.frequency.Frequency`
frequency info, (duh)
coefs : dict of numpy arrays
error coefficients for the calibration
See Also
--------
Calibration.from_coefs_ntwks
"""
n = Network(frequency = frequency,
s = rand_c(frequency.npoints,2,2))
measured = [n,n,n,n,n]
if 'forward switch term' in coefs:
switch_terms = (Network(frequency = frequency,
s=coefs['forward switch term']),
Network(frequency = frequency,
s=coefs['reverse switch term']))
kwargs['switch_terms'] = switch_terms
cal = cls(measured, measured[0], **kwargs)
cal.coefs = coefs
cal.family += '(fromCoefs)'
return cal
@property
def residual_ntwks(self):
"""
Dictionary of residual Networks.
These residuals are complex differences between the ideal
standards and their corresponding corrected measurements.
"""
#Runs the calibration if needed
caled_ntwks = self.caled_ntwks
r = self.solved_reflect
m = Network(s=[0]*len(self.solved_reflect.f), f=self.solved_reflect.f, f_unit='Hz')
mm = two_port_reflect(m, m)
mr = two_port_reflect(m, r)
rm = two_port_reflect(r, m)
rr = two_port_reflect(r, r)
ideals = [self.solved_through, mm, rr, rm, mr]
return [caled - ideal for (ideal, caled) in zip(ideals, caled_ntwks)]
@property
def solved_through(self):
"""
Return the solved through or the ideal through if reflect was solved.
"""
if not hasattr(self, '_coefs'):
self.run()
return self._solved_through
@property
def solved_reflect(self):
"""
Return the solved reflect or the ideal reflect if through was solved.
"""
if not hasattr(self, '_coefs'):
self.run()
return self._solved_reflect
[docs]
class Normalization(Calibration):
"""
Simple Thru Normalization.
For calibration the S parameters of the network are divided by average of
the measured networks. The ideal networks are not used in the calibration.
"""
[docs]
def apply_cal(self, input_ntwk):
return input_ntwk/average(self.measured)
[docs]
class MultiportCal:
"""
Multi-port VNA calibration using two-port calibration method.
cal_dict should be a dictionary with key being two-tuples of port numbers,
such as (0, 1), (0, 2), ...
For each key it should have another dictionary as value. The two required
keys are 'method' that should be the two-port calibration class that is used
to calibrate that two-port combination (for example SOLT, EightTerm, TRL)
and 'measured' which is a list of measured Networks. Other inputs required
by the two-port calibration should be given as additional keys (for example
'ideals', 'switch_terms', ...).
There should be one common port in all measurements. For example in case of
4-port calibration one possible choice would be to make three measurements
between ports: 0-1, 0-2, and 0-3.
The list of measured networks can be given as either two-ports, in which
case it's assumed that the two ports corresponds to the ports in the key, or
multi-ports in which case a subnetwork is taken for calibration according to
the key.
Example cal_dict for three port measurement:
{(0,1): {'method':SOLT, 'measured': [list of measured networks], 'ideals': [list of ideal networks]},
(0,2): {'method':SOLT, 'measured': [list of measured networks], 'ideals': [list of ideal networks]}
}
`isolation` is optional N-port network of all ports matched for isolation
calibration. If None, no isolation calibration is performed.
Parameters
--------------
cal_dict : dictionary
Dictionary of port pair keys as specified above.
isolation: :class:`~skrf.network.Network` or None
N-port measurement of all matched ports for isolation calibration.
None to skip isolation calibration.
See Also
--------
calibration.MultiportSOLT
"""
family = 'Multiport'
[docs]
def __init__(self, cal_dict, isolation=None):
if not isinstance(cal_dict, dict):
raise ValueError("cal_dict not dictionary.")
nports = None
max_key_nports = 0
min_key_nports = float('inf')
z0 = None
frequency = None
for k, c in cal_dict.items():
if len(k) != 2:
raise ValueError(f"Invalid cal_dict key {k}. Expected tuple of length two.")
if not isinstance(k[0], int) or not isinstance(k[1], int):
raise ValueError("cal_dict key should be tuple of ints.")
max_key_nports = max(max_key_nports, max(k[0], k[1]))
min_key_nports = min(min_key_nports, min(k[0], k[1]))
if not isinstance(c, dict):
raise ValueError(f"cal_dict[{k}] not dictionary.")
if 'method' not in c:
raise ValueError(f"cal_dict[{k}] missing key 'method'.")
if 'measured' not in c:
raise ValueError(f"cal_dict[{k}] missing key 'measured'.")
for m in c['measured']:
if not isinstance(m, Network):
raise ValueError(f"Expected Network in cal_dict[{k}]['measured']")
if nports is None:
nports = m.nports
if m.nports not in [2, nports]:
raise ValueError("Measurement have inconsistent number of ports.")
if z0 is None:
z0 = m.z0[0,0]
elif m.z0[0,0] != z0:
raise ValueError("Inconsistent z0 in measured.")
if frequency is None:
frequency = m.frequency
elif m.frequency != frequency:
raise ValueError("Inconsistent frequency in measured.")
if "ideals" in c and z0 is not None:
for n in c["ideals"]:
if n.z0[0,0] != z0:
raise ValueError(f"Ideals and measured z0 doesn't match. {n.z0[0,0]} and {z0}")
self.nports = nports = max_key_nports + 1
if min_key_nports < 0:
raise ValueError("Negative port number found. Minimum should be zero.")
if min_key_nports != 0:
raise ValueError("Missing port 0. Make sure that ports are zero-indexed.")
if max_key_nports < 2:
raise ValueError("Less than three ports found. Use two-port or one-port calibration directly.")
if isolation is not None:
# Zero diagonal so that network can be simply subtracted
isolation = isolation.copy()
if isolation.nports != nports:
raise ValueError("Isolation network should have the same number of ports as measurements.")
for i in range(nports):
isolation.s[:,i,i] = 0
else:
s = np.zeros((len(frequency), nports, nports), dtype=complex)
isolation = Network(s=s, z0=z0, frequency=frequency)
self.isolation = isolation
self.cal_dict = cal_dict
self.z0 = z0
self.frequency = frequency
self.cals = {}
[docs]
def run(self):
"""
Run the calibration algorithm.
"""
nports = self.nports
p_count = defaultdict(int)
self.terminations = [None for i in range(nports)]
self._coefs = [{} for i in range(nports)]
for p in self.cal_dict.keys():
p_count[p[0]] += 1
p_count[p[1]] += 1
port_multiples = sorted(p_count.values())
if port_multiples[-2] != 1:
# It's easy to put `k` in non-repeated ports if one port is always used.
# I think this limitation could be removed if the `k` would be
# solved to be consistent in repeated ports.
raise ValueError("Invalid thru port combinations. One port should be common in all thru measurements.")
for p in self.cal_dict.keys():
c = self.cal_dict[p].copy()
if 'ideals' in c:
ideals = [i if i.nports == 2 else subnetwork(i, p) for i in c['ideals']]
c['ideals'] = ideals
c['measured'] = [m - subnetwork(self.isolation, p) if m.nports == 2 else subnetwork(m - self.isolation, p)
for m in c['measured']]
k_side = 0
if p_count[p[0]] > p_count[p[1]]:
k_side = 1
method = c.pop('method')
self.run_2port(method, p, k_side, **c)
[docs]
def run_2port(self, method, p, k_side, **kwargs):
r"""
Call the two-port calibration algorithm and populate multi-port error
coefficients for this port pair.
Parameters
----------
method: Two-port calibration class
Use to calibrate the port pair.
p: tuple of int
Length two tuple of port indices in the pair.
k_side: int
Port to put 'k' coefficient in the pair.
\*\*kwargs: Keyword arguments
Passed to the calibration method.
"""
cal = method(**kwargs)
cal.run()
self.cals[p] = cal
coefs = cal.coefs_8term
S1, S2 = self.coefs_to_ntwks(coefs, k_side=k_side)
one = np.ones(coefs['k'].shape, dtype=complex)
for c in cal.coefs_8term:
if 'forward' in c:
c2 = c.replace('forward ', '')
if 'switch term' in c:
self._coefs[p[1]][c2] = coefs[c]
else:
self._coefs[p[0]][c2] = coefs[c]
elif 'reverse' in c:
c2 = c.replace('reverse ', '')
if 'switch term' in c:
self._coefs[p[0]][c2] = coefs[c]
else:
self._coefs[p[1]][c2] = coefs[c]
elif c == 'k':
self._coefs[p[k_side]][c] = coefs[c]
if 'k' not in self._coefs[p[not k_side]].keys():
self._coefs[p[not k_side]][c] = one
else:
warn(f'Unknown coefficient in calibration {c}', stacklevel=2)
term1 = self.dut_termination(S1, coefs['reverse switch term'])
term2 = self.dut_termination(S2, coefs['forward switch term'])
f = self.frequency
self.terminations[p[0]] = Network(s=term1, z0=self.z0, frequency=f)
self.terminations[p[1]] = Network(s=term2, z0=self.z0, frequency=f)
@property
def coefs(self):
try:
return self._coefs
except(AttributeError):
self.run()
return self._coefs
@coefs.setter
def coefs(self, d):
self._coefs = d
[docs]
def unterminate_2port(self, ntwk, p1, p2):
"""
Unterminates switch terms from a raw measurement.
See Also
--------
calibration.unterminate
"""
gamma_f = Network(s=self.coefs[p2]['switch term'])
gamma_r = Network(s=self.coefs[p1]['switch term'])
return unterminate(ntwk, gamma_f, gamma_r)
[docs]
def terminate_2port(self, ntwk, p1, p2):
"""
Terminate a network with switch terms.
See Also
--------
calibration.terminate
"""
gamma_f = self.coefs[p2]['switch term']
gamma_r = self.coefs[p1]['switch term']
return terminate(ntwk, gamma_f, gamma_r)
[docs]
def T_matrices(self, p1, p2):
"""
Intermediate matrices used for embedding and de-embedding.
Returns
-------
T1,T2,T3,T4 : numpy ndarray
"""
npoints = len(self.coefs[0]['k'])
zero = np.zeros(npoints, dtype=complex)
Edf = self.coefs[p1]['directivity']
Esf = self.coefs[p1]['source match']
Erf = self.coefs[p1]['reflection tracking']
Edr = self.coefs[p2]['directivity']
Esr = self.coefs[p2]['source match']
Err = self.coefs[p2]['reflection tracking']
k1 = self.coefs[p1]['k']
k2 = self.coefs[p2]['k']
detX = Edf*Esf-Erf
detY = Edr*Esr-Err
T1 = np.array([
[ -k1*detX, zero ],
[ zero, -k2*detY ]
]).transpose(2,0,1)
T2 = np.array([
[ k1*Edf, zero ],
[ zero, k2*Edr ]
]).transpose(2,0,1)
T3 = np.array([
[ -k1*Esf, zero ],
[ zero, -k2*Esr ]
]).transpose(2,0,1)
T4 = np.array([
[ k1, zero ],
[ zero, k2 ]
]).transpose(2,0,1)
return T1, T2, T3, T4
[docs]
def apply_cal(self, ntwk):
"""
Apply correction to a Network.
"""
# A new copy of ntwk is created
ntwk = ntwk - self.isolation
caled = ntwk.copy()
# Use traveling definition since it can renormalize to negative real part impedance.
s_def = caled.s_def
caled.s_def = 'traveling'
fpoints = len(ntwk.frequency)
ports = np.arange(self.nports)
port_combos = list(combinations(ports, 2))
for p in port_combos:
T1, T2, T3, T4 = self.T_matrices(p[0], p[1])
caled_2p = subnetwork(ntwk, p).copy()
caled_2p.s_def = 'traveling'
caled_2p = self.unterminate_2port(caled_2p, p[0], p[1])
caled_2p.s = linalg.inv(-caled_2p.s @ T3 + T1) @ (caled_2p.s @ T4 - T2)
z = np.zeros((fpoints, 2), dtype=complex)
z[:,0] = self.terminations[p[0]].z[:,0,0]
z[:,1] = self.terminations[p[1]].z[:,0,0]
caled_2p.renormalize(z)
for ei, i in enumerate(p):
for ej, j in enumerate(p):
caled.s[:, i, j] = caled_2p.s[:, ei, ej]
for i in range(self.nports):
caled.z0[:,i] = self.terminations[i].z[:,0,0]
caled.renormalize(ntwk.z0, s_def=s_def)
return caled
[docs]
def embed(self, ntwk):
"""
Embed an ideal response in the estimated error network[s]
"""
fpoints = len(self.coefs[0]['k'])
nports = self.nports
nout = ntwk.copy()
Z = np.zeros((fpoints, 2*nports, 2*nports), dtype=complex)
gammas = []
for e, c in enumerate(self.coefs):
gammas.append(Network(s=c['switch term'], frequency=nout.frequency, z0=50))
Z[:, e, e] = c['directivity']
Z[:, nports+e, nports+e] = c['source match']
Z[:, e, nports+e] = c['reflection tracking'] * c['k'] / self.coefs[0]['k']
Z[:, nports+e, e] = self.coefs[0]['k'] / c['k']
# Consistent internal port Z0.
nout.z0 = 50
Z = Network(s=Z, frequency=nout.frequency, z0=50)
nout = connect(Z, nports, nout, 0, nports)
nout = terminate_nport(nout, gammas)
nout += self.isolation
nout.z0 = ntwk.z0
return nout
[docs]
def coefs_to_ntwks(self, coefs, k_side=0):
"""
Two-port 8-term error coefficients to Networks.
Parameters
----------
k_side: int, 0 or 1
Port to put 'k' coefficient.
"""
npoints = len(coefs['k'])
one = np.ones(npoints, dtype=complex)
Edf = coefs['forward directivity']
Esf = coefs['forward source match']
Erf = coefs['forward reflection tracking']
Edr = coefs['reverse directivity']
Esr = coefs['reverse source match']
Err = coefs['reverse reflection tracking']
k = coefs['k']
if k_side == 0:
S1 = np.array([
[ Edf, Erf/k ],
[ k, Esf ]
]).transpose(2,0,1)
S2 = np.array([
[ Edr, one ],
[ Err, Esr ]
]).transpose(2,0,1)
elif k_side == 1:
S1 = np.array([
[ Edf, Erf ],
[ one, Esf ]
]).transpose(2,0,1)
S2 = np.array([
[ Edr, one/k ],
[ Err*k, Esr ]
]).transpose(2,0,1)
else:
raise ValueError(f"Invalid k_side {k_side}, expected 0 or 1.")
return (S1, S2)
[docs]
def dut_termination(self, S, gamma):
"""Impedance looking from DUT to VNA terminated with switch term."""
term = S[:,1,1] + (S[:,0,1] * S[:,1,0] * gamma) / (1 - S[:,0,0] * gamma)
return term
[docs]
class MultiportSOLT(MultiportCal):
"""
Multi-port VNA calibration using two-port calibration method with one transmissive standard for each two-port pair.
`method` should be a two-port calibration method such as `EightTerm`,
`UnknownThru` or `SOLT`. This class calibrates a multi-port network using
the given two-port calibration method.
There should be `Nports - 1` thru standards and the number of other
standards depending on the number of standards required by the chosen
calibration method. Standards should be always given thrus first. Thru
standards are used to find the port connections during the calibration and
all standards should be N-ports.
There should be one common port in all thru measurements. For
example in case of 4-port calibration one possible choice would be to make
three thru measurements between ports: 0-1, 0-2, and 0-3.
If isolation calibration is used it should be not passed as an argument to
the two-port calibration and N-port isolation measurement should be instead
given as an argument for this class.
`switch_terms` should be a list of switch terms with nth entry being the
switch term an/bn with source from any other port. Note that in case of
two-port this is the reversed order than what two-port calibration would
require. If calibration is a 12-term calibration such as `SOLT` or
`TwelveTerm` no switch terms are required.
`thru_pos` argument can be used to change the order of thru given to the
calibration method. `auto` will try to determine it automatically from the
calibration method. Other options are `first` and `last`. Other standards
are given in the same order they are given to this class.
`cal_args` can be used to give addition arguments to the calibration method.
If no arguments are given it should be None, otherwise a dictionary of
arguments and values.
See Also
--------
calibration.MultiportCal
Lower level multi-port calibration class. This needs to be used for TRL
calibration as it has also lines between ports which doesn't fit the
interface of this class.
"""
family = 'Multiport'
[docs]
def __init__(
self,
method,
measured: Network,
ideals: list[Network],
isolation=None,
switch_terms=None,
thru_pos: Literal["first", "last", "auto"] = "auto",
cal_args: dict | None = None,
):
self.ideals = ideals
self.measured = measured
self.nports = ideals[0].nports
nports = self.nports
if nports < 3:
raise ValueError("Too few ports in input networks. At least 3 required.")
self.switch_terms = switch_terms
if thru_pos == 'auto':
if method in [LRM, LRRM]:
thru_pos = 'first'
elif method in [SOLT, EightTerm, UnknownThru, MRC, TwelveTerm]:
thru_pos = 'last'
else:
raise ValueError(
"Unable to determine 'thru_pos' automatically. Set it manually to either 'first' or 'last'"
)
if thru_pos not in ['last', 'first']:
raise ValueError("thru_pos must be either 'first' or 'last'")
if cal_args is None:
cal_args = {}
for i in ideals:
if i.nports != self.nports:
raise ValueError("Inconsistent number of ports in ideals.")
if not issubclass(method, Calibration):
raise ValueError("method must be Calibration subclass.")
if issubclass(method, SixteenTerm):
warn("SixteenTerm calibration is reduced to 8-terms.", stacklevel=2)
if len(ideals) < nports - 1:
raise ValueError(f"Invalid number of ideals. Expected at least {nports-1} but got {len(ideals)}.")
self.thru_ports = []
for thru in ideals[:nports-1]:
nonzero = []
for i in range(nports):
for j in range(i+1, nports):
if thru.s[-1, i, j] != 0:
nonzero.append([i, j])
if len(nonzero) != 1:
raise ValueError("Invalid thru ideal. Thru should connect exactly two ports.")
self.thru_ports.append(tuple(nonzero[0]))
#Generate cal_dict in the format required by MultiportCal.
nports = self.nports
nthrus = nports - 1
cal_dict = {}
for e, p in enumerate(self.thru_ports):
ideals = [subnetwork(self.ideals[e], p)]
ideals_sol = [subnetwork(i, p) for i in self.ideals[nthrus:]]
ideals.extend(ideals_sol)
measured = [subnetwork(self.measured[e], p)]
measured_sol = [subnetwork(i, p) for i in self.measured[nthrus:]]
measured.extend(measured_sol)
if self.switch_terms is None:
sw_terms = None
else:
sw_terms = [self.switch_terms[i] for i in p][::-1]
if thru_pos == 'last':
ideals = ideals[1:] + [ideals[0]]
measured = measured[1:] + [measured[0]]
cal_dict[p] = {}
cal_dict[p]['method'] = method
cal_dict[p]['ideals'] = ideals
cal_dict[p]['measured'] = measured
if sw_terms is not None:
cal_dict[p]['switch_terms'] = sw_terms
for k, v in cal_args.items():
cal_dict[p][k] = v
super().__init__(cal_dict=cal_dict, isolation=isolation)
## Functions
def ideal_coefs_12term(frequency):
"""
An ideal set of 12term calibration coefficients.
Produces a set of error coefficients, that would result if the
error networks were matched thrus
"""
zero = zeros(len(frequency), dtype='complex')
one = ones(len(frequency), dtype='complex')
ideal_coefs = {}
ideal_coefs.update({k:zero for k in [\
'forward directivity',
'forward source match',
'forward load match',
'reverse directivity',
'reverse load match',
'reverse source match',
]})
ideal_coefs.update({k:one for k in [\
'forward reflection tracking',
'forward transmission tracking',
'reverse reflection tracking',
'reverse transmission tracking',
]})
return ideal_coefs
[docs]
def unterminate(ntwk, gamma_f, gamma_r):
r"""
Unterminate switch terms from a raw measurement.
In order to use the 8-term error model on a VNA which employs a
switched source, the effects of the switch must be accounted for.
This is done through `switch terms` as described in [1]_ . The
two switch terms are defined as,
.. math ::
\Gamma_f = \frac{a2}{b2} ,\qquad\text{sourced by port 1}\
\Gamma_r = \frac{a1}{b1} ,\qquad\text{sourced by port 2}
These can be measured by four-sampler VNA's by setting up
user-defined traces onboard the VNA. If the VNA doesnt have
4-samplers, then you can measure switch terms indirectly by using a
two-tier two-port calibration. First do a SOLT, then convert
the 12-term error coefs to 8-term, and pull out the switch terms.
Parameters
----------
two_port : 2-port Network
the raw measurement
gamma_f : 1-port Network
the measured forward switch term.
gamma_f = a2/b2 sourced by port1
gamma_r : 1-port Network
the measured reverse switch term
gamma_r = a1/b1 sourced by port2
Returns
-------
ntwk : Network object
References
----------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
"""
unterminated = ntwk.copy()
# extract scattering matrices
m, gamma_r, gamma_f = ntwk.s, gamma_r.s, gamma_f.s
u = m.copy()
one = np.ones(ntwk.frequency.npoints)
d = one - m[:,0,1]*m[:,1,0]*gamma_r[:,0,0]*gamma_f[:,0,0]
u[:,0,0] = (m[:,0,0] - m[:,0,1]*m[:,1,0]*gamma_f[:,0,0])/(d)
u[:,0,1] = (m[:,0,1] - m[:,0,0]*m[:,0,1]*gamma_r[:,0,0])/(d)
u[:,1,0] = (m[:,1,0] - m[:,1,1]*m[:,1,0]*gamma_f[:,0,0])/(d)
u[:,1,1] = (m[:,1,1] - m[:,0,1]*m[:,1,0]*gamma_r[:,0,0])/(d)
unterminated.s = u
return unterminated
[docs]
def terminate(ntwk, gamma_f, gamma_r):
"""
Terminate a network with switch terms.
see [1]_
Parameters
----------
two_port : 2-port Network
an unterminated network
gamma_f : 1-port Network
measured forward switch term.
gamma_f = a2/b2 sourced by port1
gamma_r : 1-port Network
measured reverse switch term
gamma_r = a1/b1 sourced by port2
Returns
-------
ntwk : Network object
See Also
--------
unterminate_switch_terms
References
----------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
"""
m = ntwk.copy()
m.s[:,0,0] = ntwk.s[:,0,0] + ntwk.s[:,1,0]*ntwk.s[:,0,1]*gamma_f.s[:,0,0]/(1-ntwk.s[:,1,1]*gamma_f.s[:,0,0])
m.s[:,1,1] = ntwk.s[:,1,1] + ntwk.s[:,1,0]*ntwk.s[:,0,1]*gamma_r.s[:,0,0]/(1-ntwk.s[:,0,0]*gamma_r.s[:,0,0])
m.s[:,1,0] = ntwk.s[:,1,0]/(1-ntwk.s[:,1,1]*gamma_f.s[:,0,0])
m.s[:,0,1] = ntwk.s[:,0,1]/(1-ntwk.s[:,0,0]*gamma_r.s[:,0,0])
return m
def terminate_nport(ntwk, gammas):
"""
Terminate N-port network with switch terms.
Note that for 2-port the order `gammas` is opposite of terminate.
Correct order for 2-port is [gamma_r, gamma_f].
See [1]_
Parameters
----------
two_port : Network
an unterminated network.
gammas : list of 1-port Network
measured switch term.
gammas[i] = ai/bi sourced by any other port.
Returns
-------
ntwk : Network object
See Also
--------
terminate
References
----------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
"""
nin = ntwk.copy()
# Assign fixed z0 for connections for inner ports.
nin.z0 = 50
nout = ntwk.copy()
nports = ntwk.nports
fpoints = len(ntwk.frequency)
if len(gammas) != ntwk.nports:
raise ValueError("len(gammas) doesn't match the number of network ports")
ones = np.ones(len(ntwk.s))
for i in range(nports):
term = np.zeros((fpoints, 2*nports, 2*nports), dtype=complex)
for j in range(nports):
if i == j:
term[:,nports+j,j] = ones
term[:,j,j+nports] = ones
continue
term[:,j,j] = gammas[j].s[:,0,0]
term[:,nports+j,j] = ones
net = Network(s=term, frequency=nin.frequency, z0=50)
net = connect(nin, 0, net, 0, nports)
for j in range(nports):
nout.s[:,j,i] = net.s[:,j,i]
nout.z0 = ntwk.z0
return nout
def compute_switch_terms(ntwks):
"""
A method for indirectly computing the switch terms of a VNA using measurements of at least three transmissive
reciprocal devices. The VNA does not need to be calibrated, and more than three reciprocal devices can be used.
However, the accuracy of the computed switch terms depends on the uniqueness of the measured reciprocal devices.
Devices with asymmetric structure and semi-reflective properties can help ensure the conditioning of the system
matrix, which solves the switch terms.
See [1]_ and [2]_
Parameters
----------
ntwks : List of networks
measured reciprocal devices. At least 3 required.
Returns
-------
Gammas : List of one-port networks of the switch terms.
The order is [Gamma21, Gamma12]. Gamma21 is forward and Gamma12 is reverse.
References
----------
.. [1] Z. Hatab, M. E. Gadringer, and W. Bösch, "Indirect Measurement of Switch Terms of a Vector Network Analyzer
with Reciprocal Devices," 2023, e-print: https://arxiv.org/abs/2306.07066
.. [2] https://ziadhatab.github.io/posts/vna-switch-terms/
See Also
--------
terminate
unterminate
"""
if len(ntwks) < 3:
raise ValueError("At least three networks are required.")
fpoints = len(ntwks[0].frequency)
Gamma21_fill = np.zeros(shape=(fpoints,), dtype=complex) # forward switch term
Gamma12_fill = np.zeros(shape=(fpoints,), dtype=complex) # reverse switch term
for inx in range(fpoints): # iterate through all frequency points
# create the system matrix
H = np.array([
[-ntwk.s[inx,0,0]*ntwk.s[inx,0,1]/ntwk.s[inx,1,0], -ntwk.s[inx,1,1], 1, ntwk.s[inx,0,1]/ntwk.s[inx,1,0]]
for ntwk in ntwks])
_,_,vh = np.linalg.svd(H) # compute the SVD
nullspace = vh[-1,:].conj() # get the nullspace
Gamma21_fill[inx] = nullspace[1]/nullspace[2]
Gamma12_fill[inx] = nullspace[0]/nullspace[3]
Gamma21 = Network(s=Gamma21_fill, frequency=ntwks[0].frequency, name='Gamma21')
Gamma12 = Network(s=Gamma12_fill, frequency=ntwks[0].frequency, name='Gamma12')
return [Gamma21, Gamma12]
[docs]
def determine_line(thru_m, line_m, line_approx=None):
r"""
Determine S21 of a matched line.
Given raw measurements of a `thru` and a matched `line` with unknown
s21, this will calculate the response of the line. This works for
lossy lines, and attenuators. The `line_approx`
is an approximation to line, this used to choose the correct
root sign. If left as `None`, it will be estimated from raw measurements,
which requires your error networks to be well matched (S_ij >>S_ii).
This is possible because two measurements can be combined to
create a relationship of similar matrices, as shown below. Equating
the eigenvalues between these measurements allows one to solve for S21
of the line.
.. math::
M_t = X \cdot A_t \cdot Y \\
M_l = X \cdot A_l \cdot Y\\
M_t \cdot M_{l}^{-1} = X \cdot A_t \cdot A_{l}^{-1} \cdot X^{-1}\\
eig(M_t \cdot M_{l}^{-1}) = eig( A_t \cdot A_{l}^{-1})\\
which can be solved to yield S21 of the line
Notes
-----
This relies on the 8-term error model, which requires that switch
terms are accounted for. specifically, thru and line have their
switch terms unterminated.
Parameters
----------
thru_m : :class:`~skrf.network.Network`
raw measurement of a flush thru
line_m : :class:`~skrf.network.Network`
raw measurement of a matched transmissive standard
line_approx : :class:`~skrf.network.Network`
approximate network the ideal line response. if None, then
the response is approximated by line_approx = line/thru. This
makes the assumption that the error networks have much larger
transmission than reflection
References
----------
"""
npts = len(thru_m)
zero = np.zeros(npts)
if line_approx is None:
# estimate line length, by assuming error networks are well
# matched
line_approx_s21 = line_m.s[:,1,0] / thru_m.s[:,1,0]
else:
line_approx_s21 = line_approx.s[:,1,0]
C = thru_m.inv**line_m
# the eigen values of the matrix C, are equal to s12,s12^-1)
# we need to choose the correct one
w,v = linalg.eig(C.t)
s12_0, s12_1 = w[:,0], w[:,1]
s12 = find_correct_sign(s12_0, s12_1, line_approx_s21)
found_line = line_m.copy()
found_line.s = np.array([[zero, s12],[s12,zero]]).transpose(2,0,1)
return found_line
def _regularize_inplace(z : ComplexArray, epsilon : float=1e-7) -> ComplexArray:
""" Regularize an array inplace around zero """
zero_idx = np.abs(z)<epsilon
z[zero_idx] = .5*(epsilon * np.exp(np.angle(z[zero_idx])*1j)+z[zero_idx])
return z
def determine_reflect(thru_m, reflect_m, line_m, reflect_approx=None,
line_approx=None, return_all=False):
"""
Determine reflect from a thru, reflect, line measurements.
This is used in the TRL algorithm, but is made modular for
multi-line, multi-reflect options.
Parameters
----------
thru_m : :class:`~skrf.network.Network`
raw measurement of a thru
reflect_m: :class:`~skrf.network.Network`
raw measurement of a reflect standard
line_m : :class:`~skrf.network.Network`
raw measurement of a matched transmissive standard
reflect_approx : :class:`~skrf.network.Network`
approximate One-port network for the reflect. if None, then
we assume its a flush short (gamma=-1)
return_all: bool
return all possible values fo reflect, one for each root-choice.
useful for troubleshooting.
Returns
-------
reflect : :class:`~skrf.network.Network`
a One-port network for the found reflect.
The equations are from "Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port
Automatic Network Analyzer", G.F. Engen et al., 1979
"""
# regularize the parameters in case of matched thru and line. see gh-870
thru_m = thru_m.copy()
thru_m.s[:, 0, 0] = _regularize_inplace(thru_m.s[:, 0, 0])
thru_m.s[:, 1, 1] = _regularize_inplace(thru_m.s[:, 1, 1])
#Call determine_line first to solve root choice of the propagation constant
line = determine_line(thru_m, line_m, line_approx)
inv = linalg.inv
rt = thru_m.t
rd = line_m.t
# tt is equal to T from equation (24) in the paper
tt = einsum('ijk,ikl -> ijl', rd, inv(rt))
a = tt[:,1,0]
b = tt[:,1,1]-tt[:,0,0]
c = -tt[:,0,1]
sqrtD = sqrt(b*b-4*a*c)
# The variables a, b, c define a quadratic equation for which the solutions sol1 and sol2 correspond to the
# ratios (r11/r21) and (r12/r22) from equations (30) and (31) in the paper
# The quadratic equation has solutions sol1 = (-b-sqrt(b*b-4*a*c))/(2*a), sol2 = (-b+sqrt(b*b-4*a*c))/(2*a)
# For a=0 these become degenerate. Also the consequtive equations for x1 and x2 contain singularities for a=0 or c=0
sol1 = (-b-sqrtD)/(2*a)
sol2 = (-b+sqrtD)/(2*a)
# equation (32)
x1 = (tt[:,1,0]*sol1 + tt[:,1,1])/(tt[:,0,1]/sol2 + tt[:,0,0])
x2 = (tt[:,1,0]*sol2 + tt[:,1,1])/(tt[:,0,1]/sol1 + tt[:,0,0])
e2 = line.s[:,0,1]**2
rootChoice = abs(x1 - e2) < abs(x2 - e2) # see gh-870
y = sol1*invert(rootChoice) + sol2*rootChoice
x = sol1*rootChoice + sol2*invert(rootChoice)
b = y
e = thru_m.s[:,0,0]
d = -det(thru_m.s)
f = -thru_m.s[:,1,1]
gam = (f-d/x)/(1-e/x) # equation (40)
b_A = (e-b)/(d-b*f) # equation (41): beta/alpha
w1 = reflect_m.s[:,0,0]
w2 = reflect_m.s[:,1,1]
# equation (45)
a = sqrt(((w1-b)*(1+w2*b_A)*(d-b*f))/\
((w2+gam)*(1-w1/x)*(1-e/x)))
out = [(w1-b)/(a*(1-w1/x)), (w1-b)/(-a*(1-w1/x))] # equation (47)
if return_all:
return [Network(frequency=thru_m.frequency, s = k) for k in out]
if reflect_approx is None:
reflect_approx = reflect_m.copy()
reflect_approx.s[:,0,0]=-1
closer = find_closest(out[0], out[1], reflect_approx.s11.s.flatten())
reflect = reflect_approx.copy()
reflect.s[:,0,0] = closer
return reflect.s11
def convert_12term_2_8term(coefs_12term, redundant_k = False):
"""
Convert the 12-term and 8-term error coefficients.
Derivation of this conversion can be found in [#]_ .
References
----------
.. [#] Marks, Roger B.; , "Formulations of the Basic Vector Network Analyzer Error Model including Switch-Terms,"
ARFTG Conference Digest-Fall, 50th , vol.32, no., pp.115-126, Dec. 1997.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4119948&isnumber=4119931
"""
# Nome