'''
.. module:: skrf.calibration.calibration
================================================================
calibration (:mod:`skrf.calibration.calibration`)
================================================================
This module provides objects for VNA calibration. Specific algorithms
inherit from the common base class :class:`Calibration`.
Base Class
--------------
.. autosummary::
:toctree: generated/
Calibration
One-port
----------------------
.. autosummary::
:toctree: generated/
OnePort
SDDL
PHN
Two-port
---------------------
.. autosummary::
:toctree: generated/
TwelveTerm
SOLT
EightTerm
UnknownThru
TRL
MultilineTRL
NISTMultilineTRL
SixteenTerm
LMR16
Three Receiver (1.5 port)
----------------------------------------------
.. autosummary::
:toctree: generated/
TwoPortOnePath
EnhancedResponse
Generic Methods
----------------
.. autosummary::
:toctree: generated/
terminate
unterminate
determine_line
PNA interaction
----------------
.. autosummary::
:toctree: generated/
convert_skrfcoefs_2_pna
convert_pnacoefs_2_skrf
'''
import numpy as npy
from numpy import linalg
from numpy.linalg import det
from numpy import mean, std, angle, real, imag, exp, ones, zeros, poly1d, invert, einsum, sqrt, unwrap,log,log10
import json
from numbers import Number
from collections import OrderedDict
import os
from copy import deepcopy, copy
import itertools
from warnings import warn
import six.moves.cPickle as pickle
from ..mathFunctions import complex_2_db, sqrt_phase_unwrap, \
find_correct_sign, find_closest, ALMOST_ZERO, rand_c, cross_ratio
from ..frequency import *
from ..network import *
from ..networkSet import func_on_networks as fon
from ..networkSet import NetworkSet
from .. import util
from ..io.touchstone import read_zipped_touchstones
from .. import __version__ as skrf__version__
## later imports. delayed to solve circular dependencies
#from io.general import write
#from io.general import read_all_networks
global coefs_list_12term
coefs_list_12term =[
'forward directivity',
'forward source match',
'forward reflection tracking',
'forward transmission tracking',
'forward load match',
'forward isolation',
'reverse directivity',
'reverse load match',
'reverse reflection tracking',
'reverse transmission tracking',
'reverse source match',
'reverse isolation'
]
global coefs_list_8term
'''
There are various notations used for this same model. Given that all
measurements have been unterminated properly the error box model holds
and the following equalities hold:
k = e10/e23 # in s-param
k = alpha/beta # in mark's notation
beta/alpha *1/Err = 1/(e10e32) # marks -> rytting notation
'''
coefs_list_8term = [
'forward directivity',
'forward source match',
'forward reflection tracking',
'reverse directivity',
'reverse load match',
'reverse reflection tracking',
'forward switch term',
'reverse switch term',
'k',
'forward isolation',
'reverse isolation'
]
global coefs_list_3term
coefs_list_3term = [
'directivity',
'source match',
'reflection tracking',
]
[docs]class Calibration(object):
'''
Base class for all Calibration objects.
This class implements the common mechanisms for all calibration
algorithms. Specific calibration algorithms should 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):
'''
Calibration initializer.
Notes
-------
About the order of supplied standards,
If the measured and ideals parameters are lists of Networks and
`sloppy_input=False`, then their elements must align. However,
if the measured and ideals are dictionaries, or
`sloppy_input=True`, then we will try to align them for you
based on the names of the networks (see `func:`align_measured_ideals`).
You do not want to use this `sloppy_input` feature if the
calibration depends on the standard order (like TRL).
Parameters
----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use `sloppy_input`)
sloppy_input : Boolean.
Allows ideals and measured lists to be 'aligned' based on
the network names.
is_reciprocal : Boolean
enables the reciprocity assumption on the calculation of the
error_network, which is only relevant for one-port
calibrations.
name: string
the name of this calibration instance, like 'waveguide cal'
this is just for convenience [None].
self_calibration: Boolean
True if there are less ideals than measurements.
Used in self-calibration such as LMR, LRRM, where some of the
standards can be unknown.
\*args, \*\*kwargs : key-word arguments
stored in self.kwargs, which may be used by sub-classes
most likely in `run`.
'''
# allow them to pass di
# lets make an ideal flush thru for them :
if hasattr(measured, 'keys'):
measured = measured.values()
if sloppy_input == False:
warn('dictionary passed, sloppy_input automatically activated')
sloppy_input = True
if hasattr(ideals, 'keys'):
ideals = ideals.values()
if sloppy_input == False:
warn('dictionary passed, sloppy_input automatically activated')
sloppy_input = True
# fill measured and ideals with copied lists of input
self.measured = [ntwk.copy() for ntwk in measured]
self.ideals = [ntwk.copy() for ntwk in ideals]
self.sloppy_input=sloppy_input
if sloppy_input:
self.measured, self.ideals = \
align_measured_ideals(self.measured, self.ideals)
self.self_calibration = self_calibration
if self_calibration == False and len(self.measured) != len(self.ideals):
raise(IndexError('The length of measured and ideals lists are different. Number of ideals must equal the number of measured. If you are using `sloppy_input` ensure the names are uniquely alignable.'))
# ensure all the measured Networks' frequency's are the same
for measure in self.measured:
if self.measured[0].frequency != measure.frequency:
raise(ValueError('measured Networks dont have matching frequencies.'))
# ensure that all ideals have same frequency of the measured
# if not, then attempt to interpolate
for k in list(range(len(self.ideals))):
if self.ideals[k].frequency != self.measured[0].frequency:
print('Warning: Frequency information doesn\'t match on ideals[{}], attempting to interpolate the ideal[{}] Network ..'.format(k,k))
try:
# try to resample our ideals network to match
# the measurement frequency
self.ideals[k].interpolate_self(\
self.measured[0].frequency)
print('Success')
except:
raise(IndexError('Failed to interpolate. Check frequency of ideals[{}].'.format(k)))
# passed to calibration algorithm in run()
self.kwargs = kwargs
self.name = name
self.is_reciprocal = is_reciprocal
# initialized internal properties to None
self._residual_ntwks = None
self._caled_ntwks =None
self._caled_ntwk_sets = None
def __str__(self):
if self.name is None:
name = ''
else:
name = self.name
if 'fromcoefs' in self.family.lower():
output = '%s Calibration: \'%s\', %s'\
%(self.family,name,str(self.frequency))
else:
output = '%s Calibration: \'%s\', %s, %i-standards'\
%(self.family,name,str(self.frequency),\
len(self.measured))
return output
def __repr__(self):
return self.__str__()
[docs] def run(self):
'''
Runs the calibration algorithm.
'''
raise NotImplementedError('The Subclass must implement this')
[docs] def apply_cal(self,ntwk):
'''
Apply correction to a Network
'''
raise NotImplementedError('The Subclass must implement this')
[docs] def apply_cal_to_list(self,ntwk_list):
'''
Apply correction to list of dict of Networks.
'''
if hasattr(ntwk_list, 'keys'):
return dict([(k, self.apply_cal(ntwk_list[k])) for k in ntwk_list])
else:
return [self.apply_cal(k) for k in ntwk_list]
[docs] def apply_cal_to_all_in_dir(self, *args, **kwargs):
'''
Apply correction to all touchstone files in a given directory.
See `skrf.io.general.read_all_networks`.
'''
from ..io.general import read_all_networks
ntwkDict = read_all_networks(*args, **kwargs)
return self.apply_cal_to_list(ntwkDict)
[docs] def apply_cal_to_network_set(self, ntwk_set):
'''
Apply correction to a NetworkSet.
'''
cal_ns = NetworkSet([self.apply_cal(ntwk) for ntwk in ntwk_set])
if hasattr(ntwk_set, 'name'):
cal_ns.name = ntwk_set.name
return cal_ns
[docs] def embed(self,ntwk):
'''
Embed an ideal response in the estimated error network[s]
'''
raise NotImplementedError('The Subclass must implement this')
[docs] def pop(self,std=-1):
'''
Remove and return tuple of (ideal, measured) at index.
Parameters
-------------
std : int or str
the integer of calibration standard to remove, or the name
of the ideal or measured calibration standard to remove.
Returns
-----------
ideal,measured : tuple of skrf.Networks
the ideal and measured networks which were popped out of the
calibration
'''
if isinstance(std, str):
for idx,ideal in enumerate(self.ideals):
if std == ideal.name:
std = idx
if isinstance(std, str):
for idx,measured in enumerate(self.measured):
if std == measured.name:
std = idx
if isinstance(std, str):
raise (ValueError('standard %s not found in ideals'%std))
return (self.ideals.pop(std), self.measured.pop(std))
[docs] def remove_and_cal(self, std):
'''
Remove a cal standard and correct it, returning correct and ideal
This requires requires overdetermination. Useful in
troubleshooting a calibration in which one standard is junk, but
you dont know which.
Parameters
-------------
std : int or str
the integer of calibration standard to remove, or the name
of the ideal or measured calibration standard to remove.
Returns
---------
ideal,corrected : tuple of skrf.Networks
the ideal and corrected networks which were removed out of the
calibration
'''
measured, ideals = copy(self.measured), copy(self.ideals)
i,m = self.pop(std)
self.run()
c = self.apply_cal(m)
self.measured = measured
self.ideals = ideals
self.run()
return c,i
[docs] @classmethod
def from_coefs_ntwks(cls, coefs_ntwks, **kwargs):
'''
Creates a calibration from its error coefficients
Parameters
-------------
coefs_ntwks : dict of Networks objects
error coefficients for the calibration
See Also
----------
Calibration.from_coefs
'''
# assigning this measured network is a hack so that
# * `calibration.frequency` property evaluates correctly
# * TRL.__init__() will not throw an error
if not hasattr(coefs_ntwks,'keys'):
# maybe they passed a list? lets try and make a dict from it
coefs_ntwks = NetworkSet(coefs_ntwks).to_dict()
coefs = NetworkSet(coefs_ntwks).to_s_dict()
frequency = list(coefs_ntwks.values())[0].frequency
cal= cls.from_coefs(frequency=frequency, coefs=coefs, **kwargs)
return cal
[docs] @classmethod
def from_coefs(cls, frequency, coefs, **kwargs):
'''
Creates a calibration from its error coefficients
Parameters
-------------
frequency : :class:`~skrf.frequency.Frequency`
frequency info, (duh)
coefs : dict of numpy arrays
error coefficients for the calibration
See Also
----------
Calibration.from_coefs_ntwks
'''
# assigning this measured network is a hack so that
# * `calibration.frequency` property evaluates correctly
# * TRL.__init__() will not throw an error
n = Network(frequency = frequency,
s = rand_c(frequency.npoints,2,2))
measured = [n,n,n]
if 'forward switch term' in coefs:
switch_terms = (Network(frequency = frequency,
s=coefs['forward switch term']),
Network(frequency = frequency,
s=coefs['reverse switch term']))
kwargs['switch_terms'] = switch_terms
cal = cls(measured, measured, **kwargs)
cal.coefs = coefs
cal.family += '(fromCoefs)'
return cal
@property
def frequency(self):
'''
:class:`~skrf.frequency.Frequency` object of the calibration
'''
return self.measured[0].frequency.copy()
@property
def nstandards(self):
'''
number of ideal/measurement pairs in calibration
'''
if len(self.ideals) != len(self.measured):
warn('number of ideals and measured don\'t agree')
return len(self.ideals)
@property
def coefs(self):
'''
Dictionary or error coefficients in form of numpy arrays
The keys of this will be different depending on the
Calibration Model. This dictionary should be populated
when the `run()` function is called.
Notes
-------
when setting this, property, the numpy arrays are flattened.
this makes accessing the coefs more concise in the code.
See Also
----------
coefs_3term
coefs_8term
coefs_12term
coefs_ntwks
'''
try:
return self._coefs
except(AttributeError):
self.run()
return self._coefs
@coefs.setter
def coefs(self,d):
'''
'''
for k in d:
d[k] = d[k].flatten()
self._coefs = d
[docs] def update_coefs(self, d):
'''
update current dict of error coefficients
'''
for k in d:
d[k] = d[k].flatten()
self._coefs.update(d)
@property
def output_from_run(self):
'''
Returns any output from the :func:`run`.
This just returns whats in _output_from_run, and calls
:func:`run` if that attribute is non-existent.
finally, returns None if run() is called, and nothing is in
_output_from_run.
'''
try:
return self._output_from_run
except(AttributeError):
# maybe i havent run yet
self.run()
try:
return self._output_from_run
except(AttributeError):
# i did run and there is no output_from_run
return None
@property
def coefs_ntwks(self):
'''
Dictionary of error coefficients in form of Network objects
See Also
-----------
coefs_3term_ntwks
coefs_12term_ntwks
coefs_8term_ntwks
'''
ns = NetworkSet.from_s_dict(d=self.coefs,
frequency=self.frequency)
return ns.to_dict()
@property
def coefs_3term(self):
'''
Dictionary of error coefficients for One-port Error model
Contains the keys:
* directivity
* source match
* reflection tracking'
'''
return dict([(k, self.coefs.get(k)) for k in [\
'directivity',
'source match',
'reflection tracking',
]])
@property
def coefs_3term_ntwks(self):
'''
Dictionary of error coefficients in form of Network objects
'''
ns = NetworkSet.from_s_dict(d=self.coefs_3term,
frequency=self.frequency)
return ns.to_dict()
@property
def normalized_directivity(self):
'''
the directivity normalized to the reflection tracking
'''
try:
return self.coefs_ntwks['directivity']/\
self.coefs_ntwks['reflection tracking']
except:
pass
try:
out = {}
for direction in ['forward','reverse']:
out[direction + ' normalized directivity'] =\
self.coefs_ntwks[direction + ' directivity']/\
self.coefs_ntwks[direction + ' reflection tracking']
return out
except:
raise ValueError('cant find error coefs')
@property
def coefs_8term(self):
'''
Dictionary of error coefficients for 8-term (Error-box) Model
Contains the keys:
* forward directivity
* forward source match
* forward reflection tracking
* reverse directivity
* reverse load match
* reverse reflection tracking
* forward switch term
* reverse switch term
* k
* forward isolation
* reverse isolation
Notes
--------
If this calibration uses the 12-term model, then
:func:`convert_12term_2_8term` is called. See [1]_
References
-------------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
'''
d = self.coefs
for k in coefs_list_8term:
if k not in d and k in coefs_list_12term:
return convert_12term_2_8term(d)
return d
@property
def coefs_8term_ntwks(self):
'''
Dictionary of error coefficients in form of Network objects
'''
ns = NetworkSet.from_s_dict(d=self.coefs_8term,
frequency=self.frequency)
return ns.to_dict()
@property
def coefs_12term(self):
'''
Dictionary of error coefficients for 12-term Model
Contains the keys:
* forward directivity
* forward source match
* forward reflection tracking
* forward transmission tracking
* forward load match
* forward isolation
* reverse directivity
* reverse load match
* reverse reflection tracking
* reverse transmission tracking
* reverse source match
* reverse isolation
Notes
--------
If this calibration uses the 8-term model, then
:func:`convert_8term_2_12term` is called. See [1]_
References
-------------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
'''
d = self.coefs
for k in coefs_list_12term:
if k not in d and k in coefs_list_8term:
return convert_8term_2_12term(d)
return d
@property
def coefs_12term_ntwks(self):
'''
Dictionary or error coefficients in form of Network objects
'''
ns = NetworkSet.from_s_dict(d=self.coefs_12term,
frequency=self.frequency)
return ns.to_dict()
@property
def verify_12term(self):
'''
'''
Edf = self.coefs_12term['forward directivity']
Esf = self.coefs_12term['forward source match']
Erf = self.coefs_12term['forward reflection tracking']
Etf = self.coefs_12term['forward transmission tracking']
Elf = self.coefs_12term['forward load match']
Edr = self.coefs_12term['reverse directivity']
Elr = self.coefs_12term['reverse load match']
Err = self.coefs_12term['reverse reflection tracking']
Etr = self.coefs_12term['reverse transmission tracking']
Esr = self.coefs_12term['reverse source match']
return Etf*Etr - (Err + Edr*(Elf - Esr))*(Erf + Edf *(Elr - Esf))
@property
def verify_12term_ntwk(self):
return Network(s= self.verify_12term, frequency = self.frequency)
@property
def residual_ntwks(self):
'''
Dictionary of residual Networks
These residuals are complex differences between the ideal
standards and their corresponding corrected measurements.
'''
return [caled - ideal for (ideal, caled) in zip(self.ideals, self.caled_ntwks)]
@property
def residual_ntwk_sets(self):
'''
Returns a NetworkSet for each `residual_ntwk`, grouped by their names
'''
residual_sets={}
std_names = list(set([k.name for k in self.ideals ]))
for std_name in std_names:
residual_sets[std_name] = NetworkSet(
[k for k in self.residual_ntwks if k.name.startswith(std_name)])
return residual_sets
@property
def caled_ntwks(self):
'''
List of the corrected calibration standards
'''
return self.apply_cal_to_list(self.measured)
@property
def caled_ntwk_sets(self):
'''
Returns a NetworkSet for each `caled_ntwk`, grouped by their names
'''
caled_sets={}
std_names = list(set([k.name for k in self.ideals ]))
for std_name in std_names:
caled_sets[std_name] = NetworkSet(
[k for k in self.caled_ntwks if k.name.startswith(std_name)])
return caled_sets
@property
def biased_error(self):
'''
Estimate of biased error for overdetermined calibration with
multiple connections of each standard
Returns
----------
biased_error : skrf.Network
Network with s_mag is proportional to the biased error
Notes
-------
Mathematically, this is
.. 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):
'''
Estimate of unbiased error for overdetermined calibration with
multiple connections of each standard
Returns
----------
unbiased_error : skrf.Network
Network with s_mag is proportional to the unbiased error
Notes
-------
Mathematically, this is
mean_s(std_c(r))
where:
* r : complex residual errors
* std_c : standard deviation taken across connections
* mean_s : complex mean taken across standards
See Also
---------
biased_error
unbiased_error
total_error
'''
rns = self.residual_ntwk_sets
out = NetworkSet([rns[k].std_s for k in rns]).mean_s_mag
out.name = 'Unbiased Error'
return out
@property
def total_error(self):
'''
Estimate of total error for overdetermined calibration with
multiple connections of each standard.This is the combined
effects of both biased and un-biased errors
Returns
----------
total_error : skrf.Network
Network with s_mag is proportional to the total error
Notes
-------
Mathematically, this is
std_cs(r)
where:
* r : complex residual errors
* std_cs : standard deviation taken across connections and standards
See Also
---------
biased_error
unbiased_error
total_error
'''
out = NetworkSet(self.residual_ntwks).mean_s_mag
out.name = 'Total Error'
return out
@property
def error_ntwk(self):
'''
The calculated error Network or Network[s]
This will return a single two-port network for a one-port cal.
For a 2-port calibration this will return networks
for forward and reverse excitation. However, these are not
sufficient to use for embedding, see the :func:`embed` function
for that.
'''
return error_dict_2_network(
self.coefs,
frequency = self.frequency,
is_reciprocal= self.is_reciprocal)
[docs] def write(self, file=None, *args, **kwargs):
'''
Write the Calibration to disk using :func:`~skrf.io.general.write`
Parameters
-----------
file : str or file-object
filename or a file-object. If left as None then the
filename will be set to Calibration.name, if its not None.
If both are None, ValueError is raised.
\*args, \*\*kwargs : arguments and keyword arguments
passed through to :func:`~skrf.io.general.write`
Notes
------
If the self.name is not None and file is can left as None
and the resultant file will have the `.ntwk` extension appended
to the filename.
Examples
---------
>>> cal.name = 'my_cal'
>>> cal.write()
See Also
---------
skrf.io.general.write
skrf.io.general.read
'''
# this import is delayed 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]class OnePort(Calibration):
'''
Standard algorithm for a one port calibration.
Solves the linear set of equations:
.. math::
e_{11}\mathbf{i_1m_1}-\Delta e\,\mathbf{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):
'''
'''
numStds = self.nstandards
numCoefs=3
mList = [self.measured[k].s.reshape((-1,1)) for k in list(range(numStds))]
iList = [self.ideals[k].s.reshape((-1,1)) for k in list(range(numStds))]
# ASSERT: mList and aList are now kx1x1 matrices, where k in frequency
fLength = len(mList[0])
#initialize outputs
abc = npy.zeros((fLength,numCoefs),dtype=complex)
residuals = npy.zeros((fLength,\
npy.sign(numStds-numCoefs)),dtype=complex)
parameter_variance = npy.zeros((fLength, 3,3),dtype=complex)
measurement_variance = npy.zeros((fLength, 1),dtype=complex)
# loop through frequencies and form m, a vectors and
# the matrix M. where M = i1, 1, i1*m1
# i2, 1, i2*m2
# ...etc
for f in list(range(fLength)):
#create m, i, and 1 vectors
one = npy.ones(shape=(numStds,1))
m = npy.array([ mList[k][f] for k in list(range(numStds))]).reshape(-1,1)# m-vector at f
i = npy.array([ iList[k][f] for k in list(range(numStds))]).reshape(-1,1)# i-vector at f
# construct the matrix
Q = npy.hstack([i, one, i*m])
# calculate least squares
abcTmp, residualsTmp = npy.linalg.lstsq(Q,m,rcond=None)[0:2]
if numStds > 3:
measurement_variance[f,:]= residualsTmp/(numStds-numCoefs)
parameter_variance[f,:] = \
abs(measurement_variance[f,:])*\
npy.linalg.inv(npy.dot(Q.T,Q))
abc[f,:] = abcTmp.flatten()
try:
residuals[f,:] = residualsTmp
except(ValueError):
raise(ValueError('matrix has singular values. ensure standards are far enough away on smith chart'))
# convert the abc vector to standard error coefficients
a,b,c = abc[:,0], abc[:,1],abc[:,2]
e01e10 = a+b*c
e00 = b
e11 = c
self._coefs = {\
'directivity':e00,\
'reflection tracking':e01e10, \
'source match':e11\
}
# output is a dictionary of information
self._output_from_run = {
'residuals':residuals,
'parameter variance':parameter_variance
}
return None
[docs] def apply_cal(self, ntwk):
er_ntwk = Network(frequency = self.frequency, name=ntwk.name)
tracking = self.coefs['reflection tracking']
s12 = npy.sqrt(tracking)
s21 = npy.sqrt(tracking)
s11 = self.coefs['directivity']
s22 = self.coefs['source match']
er_ntwk.s = npy.array([[s11, s21],[s12,s22]]).transpose().reshape(-1,2,2)
return er_ntwk.inv**ntwk
[docs] def embed(self,ntwk):
embedded = ntwk.copy()
embedded = self.error_ntwk**embedded
embedded.name = ntwk.name
return embedded
class SDDLWeikle(OnePort):
'''
Short Delay Delay Load (Oneport Calibration)
One-port self-calibration, which contains a short, a load, and
two delays shorts of unity magnitude but unknown phase. Originally
designed to be resistant to flange misalignment, see [1]_.
References
-------------
.. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment," Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006.
'''
family = 'SDDL'
def __init__(self, measured, ideals, *args, **kwargs):
'''
Short Delay Delay Load initializer
measured and ideal networks must be in the order:
* short
* delay short1
* delay short2
* load
Parameters
-----------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
args, kwargs :
passed to func:`Calibration.__init__`
See Also
---------
Calibration.__init__
'''
if (len(measured) != 4) or (len(ideals)) != 4:
raise IndexError('Incorrect number of standards.')
Calibration.__init__(self, measured = measured,
ideals =ideals, *args, **kwargs)
def run(self):
#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, *args, **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, *args, **kwargs)
[docs] def run(self):
# ideals (in impedance)
a = s2z(self.ideals[0].s,1).flatten() # half known
b = s2z(self.ideals[1].s,1).flatten() # half known
c = s2z(self.ideals[2].s,1).flatten() # fully known
d = s2z(self.ideals[3].s,1).flatten() # fully known
# measured (in impedances)
a_ = s2z(self.measured[0].s,1).flatten() # half known
b_ = s2z(self.measured[1].s,1).flatten() # half known
c_ = s2z(self.measured[2].s,1).flatten() # fully known
d_ = s2z(self.measured[3].s,1).flatten() # fully known
z = cross_ratio(a_,b_,c_,d_)
# intermediate variables
e = c-d-c*z
f = d-c-d*z
g = c*d*z
A = -real(f*z.conj())
B = 1j*imag( f*e.conj() + g.conj()*z)
C = real( g*e.conj())
npts = len(A)
b1,b2 = zeros(npts, dtype=complex), zeros(npts, dtype=complex)
for k in range(npts):
p = poly1d([A[k],B[k],C[k]])
b1[k],b2[k] = p.r
a1 = -(f*b1 + g)/(z*b1 + e)
a2 = -(f*b2 + g)/(z*b2 + e)
# temporarily translate into s-parameters so make the root-choice
# choosing a root in impedance doesnt generally work for typical
# calibration standards
b1_s = z2s(b1.reshape(-1,1,1),1)
b2_s = z2s(b2.reshape(-1,1,1),1)
a1_s = z2s(a1.reshape(-1,1,1),1)
a2_s = z2s(a2.reshape(-1,1,1),1)
b_guess = z2s(b.reshape(-1,1,1),1)
a_guess = z2s(a.reshape(-1,1,1),1)
distance1 = abs(a1_s - a_guess) + abs(b1_s - b_guess)
distance2 = abs(a2_s - a_guess) + abs(b2_s - b_guess)
b_found = npy.where(distance1<distance2, b1, b2)
a_found = npy.where(distance1<distance2, a1, a2)
self.ideals[0].s = z2s(a_found.reshape(-1,1,1),1)
self.ideals[1].s = z2s(b_found.reshape(-1,1,1),1)
OnePort.run(self)
## Two Ports
[docs]class TwelveTerm(Calibration):
'''
12-term, full two-port calibration.
`TwelveTerm` is the traditional, fully determined, two-port calibration
originally developed in [1]_.
`TwelveTerm` can accept any number of reflect and transmissive standards,
as well as arbitrary (non-flush) transmissive standards.
* If more than 3 reflect standards are provided, a least-squares
solution is implemented for the one-port stage of the calibration.
* If more than 1 transmissive standard is given the `load match`,
and `transmission tracking` terms are calculated multiple times
and averaged.
References
------------
.. [1] "Calibration Process of Automatic Network Analyzer Systems" by Stig Rehnmark
'''
family = 'TwelveTerm'
[docs] def __init__(self, measured, ideals, n_thrus=None, trans_thres=-40,
*args, **kwargs):
'''
TwelveTerm initializer
Use the `n_thrus` argument to explicitly define the number of
transmissive standards. Otherwise, if `n_thrus=None`, then we
will try and guess which are transmissive, by comparing the mean
:math:`|s21|` and :math:`|s12|` responses (in dB) to `trans_thres`.
Notes
------
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
-------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
n_thrus : int
Number of transmissive standards. If None, we will try and
guess for you by comparing measure transmission to trans_thres,
trans_thres: float
The minimum transmission magnitude (in dB) that is
the threshold for categorizing a transmissive standard.
Compared to the measured s21,s12 meaned over frequency
Only use if n_thrus=None.
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports with a perfect isolation
between the ports. Used for determining the isolation error terms.
If no measurement is given leakage is assumed to be zero.
Loads don't need to be same as the one used as a match standard or
even have similar reflection coefficients. Reflects can be also used,
but accuracy might not be as good.
See Also
-----------
Calibration.__init__
'''
kwargs.update({'measured':measured,
'ideals':ideals})
# note: this will enable sloppy_input and align stds if necessary
Calibration.__init__(self, *args, **kwargs)
# if they didnt tell us the number of thrus, then lets
# heuristically determine it
trans_thres_mag = 10 ** (trans_thres / 20)
if n_thrus is None:
warn('n_thrus is None, guessing which stds are transmissive')
n_thrus=0
for k in self.ideals:
mean_trans = NetworkSet([k.s21, k.s12]).mean_s_mag
trans_mag = npy.mean(mean_trans.s_mag.flatten())
# this number is arbitrary but reasonable
if trans_mag > trans_thres_mag:
n_thrus +=1
if n_thrus ==0:
raise ValueError('couldnt find a transmissive standard. check your data, or explicitly use `n_thrus` argument')
self.n_thrus = n_thrus
# if they didntly give explicit order, lets try and put the
# more transmissive standards last, by sorted measured/ideals
# based on mean s21
if self.sloppy_input is True:
trans = [npy.mean(k.s21.s_mag) for k in self.ideals]
# see http://stackoverflow.com/questions/6618515/sorting-list-based-on-values-from-another-list
# get order of indices of sorted means s21
order = [x for (y,x) in sorted(zip(trans, range(len(trans))),\
key=lambda pair: pair[0])]
self.measured = [self.measured[k] for k in order]
self.ideals = [self.ideals[k] for k in order]
[docs] def run(self):
'''
'''
n_thrus = self.n_thrus
p1_m = [k.s11 for k in self.measured[:-n_thrus]]
p2_m = [k.s22 for k in self.measured[:-n_thrus]]
p1_i = [k.s11 for k in self.ideals[:-n_thrus]]
p2_i = [k.s22 for k in self.ideals[:-n_thrus]]
thrus = self.measured[-n_thrus:]
ideal_thrus = self.ideals[-n_thrus:]
# create one port calibration for reflective standards
port1_cal = OnePort(measured = p1_m, ideals = p1_i)
port2_cal = OnePort(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = dict(port1_cal.coefs)
p2_coefs = dict(port2_cal.coefs)
if self.kwargs.get('isolation',None) is not None:
p1_coefs['isolation'] = self.kwargs['isolation'].s21.s.flatten()
p2_coefs['isolation'] = self.kwargs['isolation'].s12.s.flatten()
else:
p1_coefs['isolation'] = npy.zeros(len(self.frequency), dtype=complex)
p2_coefs['isolation'] = npy.zeros(len(self.frequency), dtype=complex)
# loop thru thrus, and calculate error terms for each one
# load match and transmission tracking for ports 1 and 2
lm1, lm2,tt1, tt2 = [],[],[],[]
for thru, thru_i in zip(thrus, ideal_thrus):
lm1.append(thru_i.inv**port1_cal.apply_cal(thru.s11))
lm2.append(thru_i.flipped().inv**port2_cal.apply_cal(thru.s22))
# forward transmission tracking
g = lm1[-1].s
d = p1_coefs['source match'].reshape(-1,1,1)
e,f,b,h = thru_i.s11.s, thru_i.s22.s,thru_i.s21.s,thru_i.s12.s
m = thru.s21.s - p1_coefs['isolation'].reshape(-1,1,1)
ac = m*1./b * (1 - (d*e + f*g + b*g*h*d) + (d*e*f*g) )
tt1.append(ac[:])
# reverse transmission tracking
thru.flip(),thru_i.flip() # flip thrus to keep same ports as above
g = lm2[-1].s
d = p2_coefs['source match'].reshape(-1,1,1)
e,f,b,h = thru_i.s11.s, thru_i.s22.s,thru_i.s21.s,thru_i.s12.s
m = thru.s21.s - p2_coefs['isolation'].reshape(-1,1,1)
ac = m*1./b * (1 - (d*e+f*g+b*g*h*d) + d*e*f*g)
tt2.append(ac[:])
thru.flip(), thru_i.flip() # flip em back
p1_coefs['transmission tracking'] = npy.mean(npy.array(tt1),axis=0).flatten()
p2_coefs['transmission tracking'] = npy.mean(npy.array(tt2),axis=0).flatten()
p1_coefs['load match'] = NetworkSet(lm1).mean_s.s.flatten()
p2_coefs['load match'] = NetworkSet(lm2).mean_s.s.flatten()
# update coefs
coefs = {}
coefs.update(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs]))
coefs.update(dict([('reverse %s'%k, p2_coefs[k]) for k in p2_coefs]))
eight_term_coefs = convert_12term_2_8term(coefs)
coefs.update(dict([(l, eight_term_coefs[l]) for l in \
['forward switch term','reverse switch term','k'] ]))
self._coefs = coefs
[docs] def apply_cal(self,ntwk):
'''
'''
caled = ntwk.copy()
s11 = ntwk.s[:,0,0]
s12 = ntwk.s[:,0,1]
s21 = ntwk.s[:,1,0]
s22 = ntwk.s[:,1,1]
Edf = self.coefs['forward directivity']
Esf = self.coefs['forward source match']
Erf = self.coefs['forward reflection tracking']
Etf = self.coefs['forward transmission tracking']
Elf = self.coefs['forward load match']
Eif = self.coefs.get('forward isolation',0)
Edr = self.coefs['reverse directivity']
Elr = self.coefs['reverse load match']
Err = self.coefs['reverse reflection tracking']
Etr = self.coefs['reverse transmission tracking']
Esr = self.coefs['reverse source match']
Eir = self.coefs.get('reverse isolation',0)
D = (1+(s11-Edf)/(Erf)*Esf)*(1+(s22-Edr)/(Err)*Esr) -\
((s21-Eif)/(Etf))*((s12-Eir)/(Etr))*Elf*Elr
caled.s[:,0,0] = \
(((s11-Edf)/(Erf))*(1+(s22-Edr)/(Err)*Esr)-\
Elf*((s21-Eif)/(Etf))*(s12-Eir)/(Etr)) /D
caled.s[:,1,1] = \
(((s22-Edr)/(Err))*(1+(s11-Edf)/(Erf)*Esf)-\
Elr*((s21-Eif)/(Etf))*(s12-Eir)/(Etr)) /D
caled.s[:,1,0] = \
( ((s21 -Eif)/(Etf))*(1+((s22-Edr)/(Err))*(Esr-Elf)) )/D
caled.s[:,0,1] = \
( ((s12 -Eir)/(Etr))*(1+((s11-Edf)/(Erf))*(Esf-Elr)) )/D
return caled
[docs] def embed(self, ntwk):
measured = ntwk.copy()
s11 = ntwk.s[:,0,0]
s12 = ntwk.s[:,0,1]
s21 = ntwk.s[:,1,0]
s22 = ntwk.s[:,1,1]
det = s11*s22 - s12*s21
Edf = self.coefs['forward directivity']
Esf = self.coefs['forward source match']
Erf = self.coefs['forward reflection tracking']
Etf = self.coefs['forward transmission tracking']
Elf = self.coefs['forward load match']
Eif = self.coefs.get('forward isolation',0)
Edr = self.coefs['reverse directivity']
Elr = self.coefs['reverse load match']
Err = self.coefs['reverse reflection tracking']
Etr = self.coefs['reverse transmission tracking']
Esr = self.coefs['reverse source match']
Eir = self.coefs.get('reverse isolation',0)
measured = ntwk.copy()
D1 = (1 - Esf*s11 - Elf*s22 + Esf*Elf*det)
D2 = (1 - Elr*s11 - Esr*s22 + Esr*Elr*det)
measured.s[:,0,0] = Edf + Erf * (s11 - Elf*det)/D1
measured.s[:,1,0] = Eif + Etf * s21/D1
measured.s[:,1,1] = Edr + Err * (s22 - Elr*det)/D2
measured.s[:,0,1] = Eir + Etr * s12/D2
return measured
[docs]class SOLT(TwelveTerm):
'''
Short Open Load Thru, Full two-port calibration.
SOLT is the traditional, fully determined, two-port calibration
originally developed in [1]_.
Although the acronym SOLT implies the use of 4 standards, skrf's
algorithm can accept any number of reflect standards, If
more than 3 reflect standards are provided a least-squares solution
is implemented for the one-port stage of the calibration.
If your `thru` is not flush you need to use `TwelveTerm` instead of
SOLT.
Redundant flush thru measurements can also be used, through the `n_thrus`
parameter. See :func:`__init__`
References
------------
.. [1] W. Kruppa and K. F. Sodomsky, "An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence)," IEEE Transactions on Microwave Theory and Techniques, vol. 19, no. 1, pp. 122-123, Jan. 1971.
See Also
---------
TwelveTerm
'''
family = 'SOLT'
[docs] def __init__(self, measured, ideals, n_thrus=1, *args, **kwargs):
'''
SOLT initializer
If you arent using `sloppy_input`, then the order of the
standards must align.
If `n_thrus!=None`, then the thru standard[s] must be last in
the list. The `n_thrus` argument can be used to allow multiple
measurements of the flush thru standard.
If the ideal element for the thru is set to None, a flush thru
is assumed. If your `thru` is not flush you need
to use `TwelveTerm` instead of SOLT. Use
Notes
------
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
-------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use `sloppy_input`)
The thru standard can be None
n_thrus : int
number of thru 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('Cant use sloppy_input and have the ideal thru be None. measured and ideals must be lists, or dont use None for the thru ideal.')
ideal_thru = measured[0].copy()
ideal_thru.s[:,0,0] = 0
ideal_thru.s[:,1,1] = 0
ideal_thru.s[:,1,0] = 1
ideal_thru.s[:,0,1] = 1
ideals[k] = ideal_thru
kwargs.update({'measured':measured,
'ideals':ideals,
'n_thrus':n_thrus})
TwelveTerm.__init__(self,*args, **kwargs)
[docs] def run(self):
'''
'''
n_thrus = self.n_thrus
p1_m = [k.s11 for k in self.measured[:-n_thrus]]
p2_m = [k.s22 for k in self.measured[:-n_thrus]]
p1_i = [k.s11 for k in self.ideals[:-n_thrus]]
p2_i = [k.s22 for k in self.ideals[:-n_thrus]]
thru = NetworkSet(self.measured[-n_thrus:]).mean_s
# create one port calibration for reflective standards
port1_cal = OnePort(measured = p1_m, ideals = p1_i)
port2_cal = OnePort(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = port1_cal.coefs
p2_coefs = port2_cal.coefs
if self.kwargs.get('isolation',None) is not None:
p1_coefs['isolation'] = self.kwargs['isolation'].s21.s.flatten()
p2_coefs['isolation'] = self.kwargs['isolation'].s12.s.flatten()
else:
p1_coefs['isolation'] = npy.zeros(len(thru), dtype=complex)
p2_coefs['isolation'] = npy.zeros(len(thru), dtype=complex)
p1_coefs['load match'] = port1_cal.apply_cal(thru.s11).s.flatten()
p2_coefs['load match'] = port2_cal.apply_cal(thru.s22).s.flatten()
p1_coefs['transmission tracking'] = \
(thru.s21.s.flatten() - p1_coefs.get('isolation',0))*\
(1. - p1_coefs['source match']*p1_coefs['load match'])
p2_coefs['transmission tracking'] = \
(thru.s12.s.flatten() - p2_coefs.get('isolation',0))*\
(1. - p2_coefs['source match']*p2_coefs['load match'])
coefs = {}
coefs.update(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs]))
coefs.update(dict([('reverse %s'%k, p2_coefs[k]) for k in p2_coefs]))
eight_term_coefs = convert_12term_2_8term(coefs)
coefs.update(dict([(l, eight_term_coefs[l]) for l in \
['forward switch term','reverse switch term','k'] ]))
self._coefs = coefs
[docs]class TwoPortOnePath(TwelveTerm):
'''
Two Port One Path Calibration (aka poor man's TwelveTerm)
Provides full error correction on a switchless three receiver
system, i.e. you can only measure the waves a1,b1,and b2.
Given this architecture, the DUT must be flipped and measured
twice to be fully corrected.
To allow for this, the `apply_cal` method takes a tuple of
measurements in the order (forward,reverse), and creates a composite
measurement that is correctable.
'''
family = 'TwoPortOnePath'
[docs] def __init__(self, measured, ideals,n_thrus=None, source_port=1,
*args, **kwargs):
'''
initializer
Use the `n_thrus` argument to explicitly define the number of
transmissive standards. Otherwise, if `n_thrus=None`, then we
will try and guess which are transmissive, by comparing the mean
: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__
'''
self.sp = source_port-1
self.rp = 1 if self.sp == 0 else 0
kwargs.update({'measured':measured,
'ideals':ideals,
'n_thrus':n_thrus})
TwelveTerm.__init__(self,*args, **kwargs)
[docs] def run(self):
'''
run
'''
'''
if self.sp !=0:
raise NotImplementedError('not implemented yet. you can just flip() all your data though. ')
n_thrus = self.n_thrus
p1_m = [k.s11 for k in self.measured[:-n_thrus]]
p1_i = [k.s11 for k in self.ideals[:-n_thrus]]
thru = NetworkSet(self.measured[-n_thrus:]).mean_s
# create one port calibration for reflective standards
port1_cal = OnePort(measured = p1_m, ideals = p1_i)
# cal coefficient pdictionaries
p1_coefs = port1_cal.coefs
if self.kwargs.get('isolation',None) is not None:
raise NotImplementedError()
p1_coefs['isolation'] = isolation.s21.s.flatten()
else:
p1_coefs['isolation'] = npy.zeros(len(thru), dtype=complex)
p1_coefs['load match'] = port1_cal.apply_cal(thru.s11).s.flatten()
p1_coefs['transmission tracking'] = \
(thru.s21.s.flatten() - p1_coefs.get('isolation',0))*\
(1. - p1_coefs['source match']*p1_coefs['load match'])
coefs = {}'''
# run a full twelve term then just copy all forward error terms
# over reverse error terms
TwelveTerm.run(self)
out_coefs = self.coefs.copy()
if self.sp ==0:
forward = 'forward'
reverse = 'reverse'
elif self.sp ==1:
forward = 'reverse'
reverse = 'forward'
else:
raise('source_port is out of range. should be 1 or 2.')
for k in self.coefs:
if k.startswith(forward):
k_out = k.replace(forward,reverse)
out_coefs[k_out] = self.coefs[k]
eight_term_coefs = convert_12term_2_8term(out_coefs)
out_coefs.update(dict([(l, eight_term_coefs[l]) for l in \
['forward switch term','reverse switch term','k'] ]))
self._coefs = out_coefs
[docs] def apply_cal(self, ntwk_tuple):
'''
apply the calibration to a measurement
Notes
-------
Full correction is possible given you have measured your DUT
in both orientations. Meaning, you have measured the device,
then physically flipped the device and made a second measurement.
This tuple of 2-port Networks is what is meant by
(forward,reverse), in the docstring below
If you pass a single 2-port Network, then the measurement will
only be partially corrected using what is known as the
`EnhancedResponse` calibration.
Parameters
-----------
network_tuple: tuple, or Network
tuple of 2-port Networks in order (forward, reverse) OR
a single 2-port Network.
'''
if isinstance(ntwk_tuple,tuple) or isinstance(ntwk_tuple,list):
f,r = ntwk_tuple[0].copy(), ntwk_tuple[1].copy()
sp,rp = self.sp,self.rp
ntwk = f.copy()
ntwk.s[:,sp,sp] = f.s[:,sp,sp]
ntwk.s[:,rp,sp] = f.s[:,rp,sp]
ntwk.s[:,rp,rp] = r.s[:,sp,sp]
ntwk.s[:,sp,rp] = r.s[:,rp,sp]
out = TwelveTerm.apply_cal(self, ntwk)
return out
else:
warnings.warn('only gave a single measurement orientation, error correction is partial without a tuple')
ntwk = ntwk_tuple.copy()
sp,rp = self.sp,self.rp
ntwk.s[:,rp,rp] = 0
ntwk.s[:,sp,rp] = 0
out = TwelveTerm.apply_cal(self, ntwk)
out.s[:,rp,rp] = 0
out.s[:,sp,rp] = 0
return out
[docs]class EnhancedResponse(TwoPortOnePath):
'''
Enhanced Response Partial Calibration
Why are you using this?
For full error you correction, you can measure the DUT in both
orientations and instead use TwoPortOnePath
Accuracy of correct measurements will rely on having a good match
at the passive side of the DUT.
For code-structuring reasons, this is a dummy placeholder class.
Its just TwoPortOnePath, which defaults to enhancedresponse correction
when you apply the calibration to a single network, and not a tuple
of networks.
'''
family = 'EnhancedResponse'
[docs]class EightTerm(Calibration):
'''
General EightTerm (aka Error-box) Two-port calibration
This is basically an extension of the one-port algorithm to two-port
measurements, A least squares estimator is used to determine the
error coefficients. No self-calibration takes place.
The concept is presented in [1]_ , but implementation follows that
of [2]_ .
See :func:`__init__`
Notes
-------
An important detail of implementing the error-box
model is that the internal switch must be correctly accounted for.
This is done through the measurement of :term:`switch terms`.
References
------------
.. [1] Speciale, R.A.; , "A Generalization of the TSD Network-Analyzer Calibration Procedure, Covering n-Port Scattering-Parameter Measurements, Affected by Leakage Errors," Microwave Theory and Techniques, IEEE Transactions on , vol.25, no.12, pp. 1100- 1115, Dec 1977. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1129282&isnumber=25047
.. [2] Rytting, D. (1996) Network Analyzer Error Models and Calibration Methods. RF 8: Microwave Measurements for Wireless Applications (ARFTG/NIST Short Course Notes)
'''
family = 'EightTerm'
[docs] def __init__(self, measured, ideals, switch_terms=None,
isolation=None, ut_hook=None,*args, **kwargs):
'''
EightTerm Initializer
Notes
------
See func:`Calibration.__init__` for details about automatic
standards alignment (aka `sloppy_input`).
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
isolation : :class:`~skrf.network.Network` object
Measurement with loads on both ports with a perfect isolation
between the ports. Used for determining the isolation error terms.
If no measurement is given leakage is assumed to be zero.
Loads don't need to be same as the one used as a match standard or
even have similar reflection coefficients. Reflects can be also used,
but accuracy might not be as good.
'''
self.switch_terms = switch_terms
if switch_terms is None:
warn('No switch terms provided')
if isolation is None:
self.isolation = measured[0].copy()
self.isolation.s[:,:,:] = 0
else:
self.isolation = isolation.copy()
#Zero port matching so that networks can be simply subtracted
self.isolation.s[:,0,0] = 0
self.isolation.s[:,1,1] = 0
self.ut_hook=ut_hook
Calibration.__init__(self,
measured = measured,
ideals = ideals,
*args, **kwargs)
[docs] def unterminate(self,ntwk):
'''
Unterminates switch terms from a raw measurement.
See Also
---------
calibration.unterminate
'''
if self.ut_hook is not None:
return self.ut_hook(self,ntwk)
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return unterminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
[docs] def terminate(self, ntwk):
'''
Terminate a network with switch terms
See Also
--------
calibration.terminate
'''
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return terminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
@property
def measured_unisolated(self):
return [k-self.isolation for k in self.measured]
@property
def measured_unterminated(self):
return [self.unterminate(k) for k in self.measured_unisolated]
[docs] def run(self):
numStds = self.nstandards
numCoefs = 7
mList = [k.s for k in self.measured_unterminated]
iList = [k.s for k in self.ideals]
fLength = len(mList[0])
#initialize outputs
error_vector = npy.zeros(shape=(fLength,numCoefs),dtype=complex)
residuals = npy.zeros(shape=(fLength,4*numStds-numCoefs),dtype=complex)
Q = npy.zeros((numStds*4, 7),dtype=complex)
M = npy.zeros((numStds*4, 1),dtype=complex)
# loop through frequencies and form m, a vectors and
# the matrix M. where M = e00 + S11i
# i2, 1, i2*m2
# ...etc
for f in list(range(fLength)):
# loop through standards and fill matrix
for k in list(range(numStds)):
m,i = mList[k][f,:,:],iList[k][f,:,:] # 2x2 s-matrices
Q[k*4:k*4+4,:] = npy.array([\
[ 1, i[0,0]*m[0,0], -i[0,0], 0, i[1,0]*m[0,1], 0, 0 ],\
[ 0, i[0,1]*m[0,0], -i[0,1], 0, i[1,1]*m[0,1], 0, -m[0,1] ],\
[ 0, i[0,0]*m[1,0], 0, 0, i[1,0]*m[1,1], -i[1,0], 0 ],\
[ 0, i[0,1]*m[1,0], 0, 1, i[1,1]*m[1,1], -i[1,1], -m[1,1] ],\
])
#pdb.set_trace()
M[k*4:k*4+4,:] = npy.array([\
[ m[0,0]],\
[ 0 ],\
[ m[1,0]],\
[ 0 ],\
])
# calculate least squares
error_vector_at_f, residuals_at_f = npy.linalg.lstsq(Q,M,rcond=None)[0:2]
#if len (residualsTmp )==0:
# raise ValueError( 'matrix has singular values, check standards')
error_vector[f,:] = error_vector_at_f.flatten()
residuals[f,:] = residuals_at_f
e = error_vector
# put the error vector into human readable dictionary
self._coefs = {\
'forward directivity':e[:,0],
'forward source match':e[:,1],
'forward reflection tracking':(e[:,0]*e[:,1])-e[:,2],
'reverse directivity':e[:,3]/e[:,6],
'reverse source match':e[:,4]/e[:,6],
'reverse reflection tracking':(e[:,4]/e[:,6])*(e[:,3]/e[:,6])- (e[:,5]/e[:,6]),
'k':e[:,6],
}
self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': npy.zeros(fLength, dtype=complex),
'reverse switch term': npy.zeros(fLength, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e,
'residuals':residuals
}
return None
[docs] def apply_cal(self, ntwk):
caled = ntwk.copy()
inv = linalg.inv
T1,T2,T3,T4 = self.T_matrices
ntwk.s[:,1,0] -= self.coefs['forward isolation']
ntwk.s[:,0,1] -= self.coefs['reverse isolation']
ntwk = self.unterminate(ntwk)
for f in list(range(len(ntwk.s))):
t1,t2,t3,t4,m = T1[f,:,:],T2[f,:,:],T3[f,:,:],\
T4[f,:,:],ntwk.s[f,:,:]
caled.s[f,:,:] = inv(-1*m.dot(t3)+t1).dot(m.dot(t4)-t2)
return caled
[docs] def embed(self, ntwk):
'''
'''
embedded = ntwk.copy()
inv = linalg.inv
T1,T2,T3,T4 = self.T_matrices
for f in list(range(len(ntwk.s))):
t1,t2,t3,t4,a = T1[f,:,:],T2[f,:,:],T3[f,:,:],\
T4[f,:,:],ntwk.s[f,:,:]
embedded.s[f,:,:] = (t1.dot(a)+t2).dot(inv(t3.dot(a)+t4))
embedded = self.terminate(embedded)
embedded.s[:,1,0] += self.coefs['forward isolation']
embedded.s[:,0,1] += self.coefs['reverse isolation']
return embedded
@property
def T_matrices(self):
'''
Intermediate matrices used for embedding and de-embedding.
Returns
--------
T1,T2,T3,T4 : numpy ndarray
'''
ec = self.coefs
npoints = len(ec['k'])
one = npy.ones(npoints,dtype=complex)
zero = npy.zeros(npoints,dtype=complex)
Edf = self.coefs['forward directivity']
Esf = self.coefs['forward source match']
Erf = self.coefs['forward reflection tracking']
Edr = self.coefs['reverse directivity']
Esr = self.coefs['reverse source match']
Err = self.coefs['reverse reflection tracking']
k = self.coefs['k']
detX = Edf*Esf-Erf
detY = Edr*Esr-Err
T1 = npy.array([\
[ -1*detX, zero ],\
[ zero, -1*k*detY]])\
.transpose().reshape(-1,2,2)
T2 = npy.array([\
[ Edf, zero ],\
[ zero, k*Edr]])\
.transpose().reshape(-1,2,2)
T3 = npy.array([\
[ -1*Esf, zero ],\
[ zero, -1*k*Esr]])\
.transpose().reshape(-1,2,2)
T4 = npy.array([\
[ one, zero ],\
[ zero, k ]])\
.transpose().reshape(-1,2,2)
return T1,T2,T3,T4
[docs] def renormalize(self, z0_old, z0_new, powerwave=False):
"""Renormalizes the calibration error boxes to a new reference impedance.
Useful for example after doing a TRL calibration with non-50 ohm
transmission lines. After the TRL calibration reference impedance is the
line characteristic impedance. If the transmission line characteristic
impedance is known this function can be used to renormalize the
reference impedance to 50 ohms or any other impedance.
"""
ec = self.coefs
npoints = len(ec['k'])
one = npy.ones(npoints,dtype=complex)
Edf = self.coefs['forward directivity']
Esf = self.coefs['forward source match']
Erf = self.coefs['forward reflection tracking']
Edr = self.coefs['reverse directivity']
Esr = self.coefs['reverse source match']
Err = self.coefs['reverse reflection tracking']
k = self.coefs['k']
S1 = npy.array([\
[ Edf, k ],\
[ Erf/k, Esf ]])\
.transpose().reshape(-1,2,2)
S2 = npy.array([\
[ Edr, Err ],\
[ one, Esr ]])\
.transpose().reshape(-1,2,2)
#Port impedances before renormalization.
#Only the DUT side (port 2) is renormalized.
#VNA side (port 1) stays unchanged.
z = npy.array([z0_new, z0_old]).transpose()
if powerwave:
S1 = renormalize_s(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
A Similar self-calibration algorithm as developed by Engen and
Hoer [1]_, more closely following into a more matrix form in [2]_.
Reference impedance of the calibration is characteristic impedance of the
transmission lines. If the characteristic impedance is known, reference
impedance can be renormalized using `EightTerm.renormalize` function.
See Also
------------
determine_line function which actually determines the line s-parameters
References
------------
.. [1] G. F. Engen and C. A. Hoer, "Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer," IEEE Transactions on Microwave Theory and Techniques, vol. 27, no. 12, pp. 987-993, 1979.
.. [2] H.-J. Eul and B. Schiek, "A generalized theory and new calibration procedures for network analyzer self-calibration," IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 4, pp. 724-731, 1991.
'''
family = 'TRL'
[docs] def __init__(self, measured, ideals=None, estimate_line=False,
n_reflects=1,solve_reflect=True, *args,**kwargs):
'''
Initialize a TRL calibration
Note that the order of `measured` and `ideals` is strict.
It must be [Thru, Reflect, Line]. A multiline algorithms is
used if more than one line is passed. A multi-reflect algorithm
is used if multiple reflects are passed, see `n_reflects` argument.
All of the `ideals` can be 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 : and approximately 90deg matched line (can be lossy)
The reflect ideals can also be given as a +-1.
Note you can also use the `estimate_line` option to
automatically estimate the initial guess for the line length
from measurements . This is sensible
if you have no idea what the line length is, but your **error
networks** are well 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
'''
#warn('Value of Reflect is not solved for yet.')
self.n_stds = n_stds = len(measured)
self.n_reflects = n_reflects
self.estimate_line = estimate_line
self.solve_reflect = solve_reflect
## generate ideals, given various inputs
if ideals is None:
ideals = [None]*len(measured)
if ideals[0] is None:
# lets make an ideal flush thru for them
ideal_thru = measured[0].copy()
ideal_thru.s[:,0,0] = 0
ideal_thru.s[:,1,1] = 0
ideal_thru.s[:,1,0] = 1
ideal_thru.s[:,0,1] = 1
ideals[0] = ideal_thru
for k in range(1,n_reflects+1):
if ideals[k] is None:
# default assume they are using flushshorts
ideals[k] =-1
if isinstance(ideals[k], Number):
ideal_reflect = measured[k].copy()
ideal_reflect.s[:,0,0] = ideals[k]
ideal_reflect.s[:,1,1] = ideals[k]
ideal_reflect.s[:,1,0] = 0
ideal_reflect.s[:,0,1] = 0
ideals[k] = ideal_reflect
for k in range(n_reflects+1,n_stds):
if ideals[k] is None:
# lets make an 90deg line for them
ideal_line = measured[k].copy()
ideal_line.s[:,0,0] = 0
ideal_line.s[:,1,1] = 0
ideal_line.s[:,1,0] = -1j
ideal_line.s[:,0,1] = -1j
ideals[k] = ideal_line
EightTerm.__init__(self,
measured = measured,
ideals = ideals,
*args, **kwargs)
[docs] def run(self):
m_ut = self.measured_unterminated
n_reflects = self.n_reflects
n_stds = self.n_stds
estimate_line = self.estimate_line
solve_reflect = self.solve_reflect
ideals = self.ideals
## Solve for the line[s]
for k in range(n_reflects+1,n_stds):
if estimate_line:
# setting line_approx to None causes determine_line() to
# estimate the line length from raw measurements
line_approx = None
else:
line_approx = ideals[k]
self.ideals[k] = determine_line(m_ut[0], m_ut[k], line_approx) # find line
## Solve for the reflect[s]
if solve_reflect:
for k in range(1,n_reflects+1):
# solve for reflect using the last line if they pass >1
r = determine_reflect(m_ut[0],m_ut[k],m_ut[-1],reflect_approx=ideals[k], line_approx=self.ideals[-1])
self.ideals[k] = two_port_reflect(r,r)
return EightTerm.run(self)
MultilineTRL = TRL
[docs]class NISTMultilineTRL(EightTerm):
'''
NIST Multiline TRL calibration.
Multiline TRL can use multiple lines to extend bandwidth and accuracy of the
calibration. Different line measurements are combined in a way that minimizes
the error in calibration.
At every frequency point there should be at least one line pair that has phase
difference that is not 0 degrees or a multiple of 180 degrees otherwise
calibration equations are singular and accuracy is very poor.
By default the reference impedance of the calibration is the characteristic
impedance of the transmission lines. If the characteristic impedance is
known reference impedance can be renormalized by giving `z0_ref` and
`z0_line`. Alternatively if capacitance/length of the transmission line is
given with `c0` argument, characteristic impedance can be solved assuming
that conductance/length is zero.
Algorithm is the one published in [0]_, but implementation is based on [1]_.
References
------------
.. [0] D. C. DeGroot, J. A. Jargon and R. B. Marks, "Multiline TRL revealed," 60th ARFTG Conference Digest, Fall 2002., Washington, DC, USA, 2002, pp. 131-155.
.. [1] K. Yau "On the metrology of nanoscale Silicon transistors above 100 GHz" Ph.D. dissertation, Dept. Elec. Eng. and Comp. Eng., University of Toronto, Toronto, Canada, 2011.
'''
family = 'TRL'
[docs] def __init__(self, measured, Grefls, l,
er_est=1, refl_offset=None, ref_plane=0,
gamma_root_choice='estimate', k_method='multical', c0=None,
z0_ref=50, z0_line=None, *args, **kwargs):
'''
NISTMultilineTRL initializer
Note that the order of `measured` is strict.
It must be [Thru, Reflect, Line]. Multiple reflects can
also be used, see `n_reflects` argument.
Notes
-------
This implementation inherits from :class:`EightTerm`. Don't
forget to pass switch_terms.
Parameters
--------------
measured : list of :class:`~skrf.network.Network`
must be in order [Thru, Reflect, Line]
Grefls : complex or list of complex
Estimated reflection coefficients of reflect standards.
Usually -1 for short or +1 for open.
l : list of float
Lengths of through and lines.
er_est : complex
Estimated effective permittivity of the lines.
Imaginary part is the loss at 1 GHz.
Negative imaginary part indicates losses.
refl_offset : float or list of float
Estimated offsets of the reflect standards from the center of the through.
Negative length is towards the VNA. Units are in meters.
ref_plane : float or list of float
Reference plane shift after the calibration.
Negative length is towards the VNA. Units are in meters.
Different shifts can be given to different ports by giving a two element list.
First element is shift of port 1 and second is shift of port 2.
gamma_root_choice : string
Method to use for choosing the correct eigenvalue for propagation
constant.
'estimate' : Choose the root that is closer to the estimated propagation
constant. Best choice when data is of good quality. To improve the
performance in phatological cases it's possible to give estimate
of the propagation constant as a keyword argument with 'gamma_est'.
'real' : Force the real part of the gamma to be positive corresponding
to a lossy line. Imaginary part can be negative.
This is the suggested method when lines have moderate loss and the
measurement noise is low. This is the default method.
'auto' : Use heuristics to choose the eigenvalue.
'imag' : Force the imaginary part of the gamma to be positive,
corresponding to a positive length line. Real part can be positive.
May choose incorrectly when the line is long due to phase wrapping.
k_method : string
Method to use for determining the 'k' error coefficient.
Currently valid choices are 'marks' or 'multical'.
The default method is 'multical'.
c0 : None, float or list of float
Capacitance/length of the transmission line in units F/m used for
reference impedance renormalization.
Characteristic impedance of the transmission lines can be determined
from the solved propagation constant if capacitance per length is known.
After the characteristic impedance is solved reference impedance of
the calibration is changed to `z0_ref`.
Solved characteristic impedance can be accessed with `cal.z0`.
Assumes TEM mode and conductance/length to be zero.
If `c0` == `z0_line` == None, the characteristic impedance is not renormalized.
In this case reference impedance of the calibration is characteristic
impedance of the transmission lines.
z0_ref : None, complex or list of complex
New reference impedance for the characteristic impedance renormalizarion.
No effect if `c0` == None and `z0_line` == None.
If `z0_ref` == None, no renormalization is done.
z0_line : None, complex or list of complex
Characteristic impedance of the transmission lines. Used for reference
impedance renormalization.
If `z0` == `z0_line` == None, the characteristic impedance is not renormalized.
In this case reference impedance of the calibration is characteristic
impedance of the transmission lines.
\*args, \*\*kwargs : passed to EightTerm.__init__
dont forget the `switch_terms` argument is important
'''
self.refl_offset = refl_offset
self.ref_plane = ref_plane
self.er_est = er_est
self.l = l
self.Grefls = Grefls
self.gamma_root_choice = gamma_root_choice
self.k_method = k_method
self.z0_ref = z0_ref
self.c0 = c0
self.z0_line = z0_line
try:
self.Grefls[0]
except TypeError:
self.Grefls = [self.Grefls]
if self.refl_offset == None:
self.refl_offset = [0]*len(self.Grefls)
try:
self.refl_offset[0]
except TypeError:
self.refl_offset = [self.refl_offset]
if len(measured) != len(self.Grefls) + len(l):
raise ValueError("Amount of measurements doesn't match amount of line lengths and reflection coefficients")
#Not used, but needed for Calibration class init
ideals = measured
#EightTerm applies the switch correction
EightTerm.__init__(self,
measured = measured,
ideals = ideals,
self_calibration=True,
*args, **kwargs)
m_sw = [k for k in self.measured_unterminated]
n_reflects = len(self.Grefls)
self.measured_reflects = m_sw[1:1+n_reflects]
self.measured_lines = [m_sw[0]]
self.measured_lines.extend(m_sw[1+n_reflects:])
if len(l) != len(self.measured_lines):
raise ValueError("Different amount of lines and line lengths found")
[docs] def run(self):
c = 299792458.0
pi = npy.pi
inv = linalg.inv
exp = npy.exp
log = npy.log
abs = npy.abs
det = linalg.det
gamma_est_user = self.kwargs.get('gamma_est', None)
measured_reflects = self.measured_reflects
measured_lines = self.measured_lines
measured_lines_t = list(map(lambda x: s2t(x.s), self.measured_lines))
l = self.l
er_est = self.er_est
freqs = measured_lines[0].f
fpoints = len(freqs)
lines = len(l)
gamma = npy.zeros(fpoints, dtype=npy.complex)
z0 = npy.zeros(fpoints, dtype=npy.complex)
gamma_est = (1j*2*pi*freqs[0]/c)*npy.sqrt(er_est.real + 1j*er_est.imag/(freqs[0]*1e-9))
line_c = npy.zeros(fpoints, dtype=int)
er_eff = npy.zeros(fpoints, dtype=npy.complex)
Tmat1 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex)
Tmat2 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex)
Smat1 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex)
Smat2 = npy.ones(shape=(fpoints, 2, 2), dtype=npy.complex)
e = npy.zeros(shape=(fpoints, 7), dtype=npy.complex)
nstd = npy.zeros(shape=(fpoints), dtype=npy.float)
def t2s_single(t):
return t2s(t[npy.newaxis,:,:])[0]
def s2t_single(s):
return s2t(s[npy.newaxis,:,:])[0]
def root_choice(Mij, dl, gamma_est):
e_val = linalg.eigvals(Mij)
Da = [0,0]
Db = [0,0]
ga = [0,0]
gb = [0,0]
for i in [0,1]:
if i == 0:
eij1 = e_val[0]
eij2 = e_val[1]
else:
eij1 = e_val[1]
eij2 = e_val[0]
ea = (eij1 + 1/eij2)/2
periods = npy.round(((gamma_est*dl).imag - (-log(ea)).imag)/(2*pi))
ga[i] = (-log(ea) + 1j*2*pi*periods)/dl
Da[i] = abs(ga[i]*dl - gamma_est*dl)/abs(gamma_est*dl)
eb = (eij2 + 1/eij1)/2
periods = npy.round(((gamma_est*dl).imag - (-log(eb)).imag)/(2*pi))
gb[i] = (-log(eb) + 1j*2*pi*periods)/dl
Da[i] = abs(gb[i]*dl + gamma_est*dl)/abs(-gamma_est*dl)
if Da[0] + Db[0] < 0.1*(Da[1] + Db[1]):
return e_val
if Da[1] + Db[1] < 0.1*(Da[0] + Db[0]):
return e_val[::-1]
if npy.sign((ga[0]).real) != npy.sign((gb[0]).real):
if Da[0] + Db[0] < Da[1] + Db[1]:
return e_val
else:
return e_val[::-1]
else:
if abs((ga[0]-gb[0]).real) < 0.1*abs((ga[1] + gb[1]).real) \
and abs(ga[0].real/ga[0].imag) > 0.001 \
and ga[0].real > 0:
if Da[0] + Db[0] < 0.2:
return e_val
else:
return e_val[::-1]
else:
if Da[0] + Db[0] < Da[1] + Db[1]:
return e_val
else:
return e_val[::-1]
#Unreachable
return e_val
V_inv = npy.eye(lines-1, dtype=npy.complex) \
- (1.0/lines)*npy.ones(shape=(lines-1, lines-1), dtype=npy.complex)
b1_vec = npy.zeros(lines-1, dtype=npy.complex)
b2_vec = npy.zeros(lines-1, dtype=npy.complex)
CoA1_vec = npy.zeros(lines-1, dtype=npy.complex)
CoA2_vec = npy.zeros(lines-1, dtype=npy.complex)
b1_vec2 = npy.zeros(lines-1, dtype=npy.complex)
b2_vec2 = npy.zeros(lines-1, dtype=npy.complex)
CoA1_vec2 = npy.zeros(lines-1, dtype=npy.complex)
CoA2_vec2 = npy.zeros(lines-1, dtype=npy.complex)
for m in range(fpoints):
min_phi_eff = pi*npy.ones(lines)
#Find the best common line to use
for n in range(lines):
for k in range(n-1):
dl = l[k] - l[n]
pd = abs(exp(-gamma_est*dl) - exp(gamma_est*dl))/2
if -1 <= pd <= 1:
phi_eff = npy.arcsin( pd )
else:
phi_eff = 0
min_phi_eff[n] = min(min_phi_eff[n], phi_eff)
#Common line is selected to be one with the largest phase difference
line_c[m] = npy.argmax(min_phi_eff)
#Pre-calculate inverse T-matrix of the common line
inv_line_c = inv(measured_lines_t[line_c[m]][m])
#Propagation constant extraction
#Compute eigenvalues of each line pair
g_dl = npy.zeros(lines-1, dtype=npy.complex)
dl_vec = npy.zeros(lines-1, dtype=npy.complex)
k = 0
for n in range(lines):
#Skip the common line
if n == line_c[m]:
continue
dl = l[n] - l[line_c[m]]
Mij = (measured_lines_t[n][m]).dot(inv_line_c)
if 'estimate' in self.gamma_root_choice:
#Choose the correct root later
e_val = linalg.eigvals(Mij)
else:
#Choose the correct root using heuristics
e_val = root_choice(Mij, dl, gamma_est)
g_dl1 = -log(0.5*(e_val[0] + 1.0/e_val[1]))
g_dl2 = -log(0.5*(e_val[1] + 1.0/e_val[0]))
g_dl[k] = g_dl1
if 'real' in self.gamma_root_choice and (g_dl1/dl).real < 0:
#Choose root that has bigger real part (more lossier)
g_dl[k] = g_dl2
if 'imag' in self.gamma_root_choice and (g_dl1/dl).imag < 0:
#Choose root that has larger imaginary part
#Only works for short lines
g_dl[k] = g_dl2
if 'estimate' in self.gamma_root_choice:
#Choose root that is closer to the estimate
if gamma_est_user is not None:
g_est = gamma_est_user[m]
else:
#Use estimate from earlier iterations
g_est = gamma_est
periods1 = npy.round( ((gamma_est*dl).imag - g_dl1.imag)/(2*pi))
periods2 = npy.round( ((gamma_est*dl).imag - g_dl2.imag)/(2*pi))
g_dl1 += 1j*2*pi*periods1
g_dl2 += 1j*2*pi*periods2
if abs(g_dl1 - g_est*dl) < abs(g_dl2 - g_est*dl):
g_dl[k] = g_dl1
else:
g_dl[k] = g_dl2
else:
periods = npy.round(((gamma_est*dl).imag - (g_dl[k].imag))/(2*pi))
g_dl[k] += 1j*2*pi*periods
dl_vec[k] = dl
k = k + 1
gamma[m] = (dl_vec.transpose().dot(V_inv).dot(g_dl))/(dl_vec.transpose().dot(V_inv).dot(dl_vec))
if m != fpoints-1:
gamma_est = gamma[m].real + 1j*gamma[m].imag*freqs[m+1]/freqs[m]
er_eff[m] = -(gamma[m]/(2*pi*freqs[m]/c))**2
root1 = []
root2 = []
d1 = [0,0]
d2 = [0,0]
S_thru = measured_lines[0].s[m]
p = 0
for n in range(lines):
if n == line_c[m]:
continue
#Port 1
T = measured_lines_t[n][m].dot(inv_line_c)
T = measured_lines[n].s[m,1,0]*measured_lines[line_c[m]].s[m,0,1]*T
e_val = linalg.eigvals(T)
B1 = npy.array([\
[T[0,1]/(e_val[0]-T[0,0]), T[0,1]/(e_val[1]-T[0,0])],
[(e_val[0]-T[1,1])/T[1,0], (e_val[1]-T[1,1])/T[1,0]]])
CoA1 = npy.array([\
[T[1,0]/(e_val[1]-T[1,1]), T[1,0]/(e_val[0]-T[1,1])],
[(e_val[1]-T[0,0])/T[0,1], (e_val[0]-T[0,0])/T[0,1]]])
B_est1 = T[0,1]/(exp(gamma[m]*(l[n]-l[line_c[m]]) - T[0,0]))
CoA_est1 = T[1,0]/(exp(-gamma[m]*(l[n]-l[line_c[m]]) - T[1,1]))
dB1 = abs(B1 - B_est1)/abs(B_est1)
dCoA1 = abs(CoA1 - CoA_est1)/abs(CoA_est1)
if abs(B1[0,1] - B_est1) < abs(B1[1,1] - B_est1):
b1_vec[p] = B1[0,1]
b1_vec2[p] = B1[0,0]
root1.append([0,1])
else:
b1_vec[p] = B1[1,1]
b1_vec2[p] = B1[1,0]
root1.append([1,1])
if abs(CoA1[0,1] - CoA_est1) < abs(CoA1[1,1] - CoA_est1):
CoA1_vec[p] = CoA1[0,1]
CoA1_vec2[p] = CoA1[0,0]
else:
CoA1_vec[p] = CoA1[1,1]
CoA1_vec2[p] = CoA1[1,0]
d1[0] += npy.sum(dB1[:,root1[-1][1]]) + npy.sum(dCoA1[:,root1[-1][1]])
d1[1] += npy.sum(dB1[:,int(not root1[-1][1])]) + npy.sum(dCoA1[:,int(not root1[-1][1])])
#Port 2
k = npy.array([[0,1],[1,0]], dtype=npy.complex)
T = s2t_single(k.dot(measured_lines[n].s[m]).dot(k)).dot(\
inv(s2t_single(k.dot(measured_lines[line_c[m]].s[m]).dot(k))))
T = measured_lines[n].s[m][0,1]*measured_lines[line_c[m]].s[m][1,0]*T
e_val = linalg.eigvals(T)
B2 = npy.array([\
[T[0,1]/(e_val[0]-T[0,0]), T[0,1]/(e_val[1]-T[0,0])],
[(e_val[0]-T[1,1])/T[1,0], (e_val[1]-T[1,1])/T[1,0]]])
CoA2 = npy.array([\
[T[1,0]/(e_val[1]-T[1,1]), T[1,0]/(e_val[0]-T[1,1])],
[(e_val[1]-T[0,0])/T[0,1], (e_val[0]-T[0,0])/T[0,1]]])
B_est2 = T[0,1]/(exp(gamma[m]*(l[n]-l[line_c[m]]) - T[0,0]))
CoA_est2 = T[1,0]/(exp(-gamma[m]*(l[n]-l[line_c[m]]) - T[1,1]))
dB2 = abs(B2 - B_est2)/abs(B_est2)
dCoA2 = abs(CoA2 - CoA_est2)/abs(CoA_est2)
if abs(B2[0,1] - B_est2) < abs(B2[1,1] - B_est2):
b2_vec[p] = B2[0,1]
b2_vec2[p] = B2[0,0]
root2.append([0,1])
else:
b2_vec[p] = B2[1,1]
b2_vec2[p] = B2[1,0]
root2.append([1,1])
if abs(CoA2[0,1] - CoA_est2) < abs(CoA2[1,1] - CoA_est2):
CoA2_vec[p] = CoA2[0,1]
CoA2_vec2[p] = CoA2[0,0]
else:
CoA2_vec[p] = CoA2[1,1]
CoA2_vec2[p] = CoA2[1,0]
d2[0] += npy.sum(dB2[:,root2[-1][1]]) + npy.sum(dCoA2[:,root2[-1][1]])
d2[1] += npy.sum(dB2[:,int(not root2[-1][1])]) + npy.sum(dCoA2[:,int(not root2[-1][1])])
p += 1
Vb = npy.zeros(shape=(lines-1,lines-1), dtype=npy.complex)
Vc = npy.zeros(shape=(lines-1,lines-1), dtype=npy.complex)
#Fill in upper triangular matrix
l_not_common = [i for i in l if i != l[line_c[m]]]
for b in range(len(l_not_common)):
for a in range(b+1):
if a == b: #Diagonal
len_l = l_not_common[a]
exp_factor = exp(-gamma[m]*(len_l - l[line_c[m]]))
Vb[a,b] = abs(exp_factor)**2 + 1/abs(exp_factor)**2 + \
2*( abs(exp(-gamma[m]*len_l))*\
abs(exp(-gamma[m]*l[line_c[m]])) )**2
n = abs(exp_factor - 1/exp_factor)**2
Vb[a,b] /= n
Vc[a,b] = abs(exp_factor)**2 + 1/(abs(exp_factor))**2 + \
2/( abs(exp(-gamma[m]*l[line_c[m]]))*\
abs(exp(-gamma[m]*len_l)) )**2
Vc[a,b] /= n
elif a < b:
len_a = l_not_common[a]
len_b = l_not_common[b]
exp_factor = exp(-gamma[m]*(len_a -l[line_c[m]]))
exp_factor2 = exp(-gamma[m]*(len_b -l[line_c[m]]))
Vb[a,b] = exp_factor2*exp_factor.conjugate() + \
(abs(exp(-gamma[m]*l[line_c[m]])))**2 * \
exp(-gamma[m]*len_b)*(exp(-gamma[m]*len_a)).conjugate()
n = (exp_factor - 1/exp_factor).conjugate()* \
(exp_factor2-1/exp_factor2)
Vb[a,b] /= n
Vb[b,a] = Vb[a,b].conjugate()
Vc[a,b] = 1/(exp_factor2*exp_factor.conjugate()) + \
1/( (abs(exp(-gamma[m]*l[line_c[m]])))**2 * \
exp(-gamma[m]*len_b)*(exp(-gamma[m]*len_a)).conjugate() )
Vc[a,b] /= n
Vc[b,a] = Vc[a,b].conjugate()
def solve_A(B1, B2, CoA1, CoA2):
#Determine A using unknown reflect
Ap = B1*B2 - B1*S_thru[1,1] - B2*S_thru[0,0] + linalg.det(S_thru)
Ap = -Ap/(1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*linalg.det(S_thru))
A1_vals = npy.zeros(len(measured_reflects), dtype=npy.complex)
A2_vals = npy.zeros(len(measured_reflects), dtype=npy.complex)
for n in range(len(measured_reflects)):
S_r = measured_reflects[n].s[m]
S_r11 = S_r[0,0]
S_r22 = S_r[1,1]
Arr = (S_r11 - B1)/(1 - S_r11*CoA1)* \
(1 - S_r22*CoA2)/(S_r22 - B2)
Gr_est = self.Grefls[n]*exp(-2*gamma[m]*(self.refl_offset[n] - l[0]/2.))
G_trial = (S_r[0,0] - B1)/(npy.sqrt(Ap*Arr)*(1 - S_r[0,0]*CoA1))
if abs( Gr_est/abs(Gr_est) - G_trial/abs(G_trial) ) > npy.sqrt(2):
A1_vals[n] = -npy.sqrt(Ap*Arr)
else:
A1_vals[n] = npy.sqrt(Ap*Arr)
A2_vals[n] = A1_vals[n]/Arr
A1 = npy.mean(A1_vals)
A2 = npy.mean(A2_vals)
return A1, A2
values = []
#List possible root choices for B and CoA
for i in [(0,0), (0,1), (1,0), (1,1)]:
if i[0] == 0:
b1 = b1_vec
coa1 = CoA1_vec
else:
b1 = b1_vec2
coa1 = CoA1_vec2
if i[1] == 0:
b2 = b2_vec
coa2 = CoA2_vec
else:
b2 = b2_vec2
coa2 = CoA2_vec2
inv_Vb = inv(Vb)
inv_Vc = inv(Vc)
sum_inv_Vb = npy.sum(inv_Vb)
sum_inv_Vc = npy.sum(inv_Vc)
B1 = npy.sum(inv_Vb.dot(b1))/sum_inv_Vb
B2 = npy.sum(inv_Vb.dot(b2))/sum_inv_Vb
CoA1 = npy.sum(inv_Vc.dot(coa1))/sum_inv_Vc
CoA2 = npy.sum(inv_Vc.dot(coa2))/sum_inv_Vc
denom = 1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*\
(S_thru[0,0]*S_thru[1,1] - S_thru[0,1]*S_thru[1,0])
values.append( (abs(denom), B1, B2, CoA1, CoA2) )
if abs(values[0][0]) > 1e-9 and d1[1]/d1[0] > 10 and d2[1]/d2[0] > 10:
#Estimate seems to be correct
B1, B2, CoA1, CoA2 = values[0][1:]
A1, A2 = solve_A(B1, B2, CoA1, CoA2)
else:
#Estimation is incorrect or the accuracy is bad
#Choose the root that minimizes error to measurements
best_error = None
best_values = []
for v in values:
if abs(v[0]) < 1e-9:
continue
B1, B2, CoA1, CoA2 = v[1:]
A1, A2 = solve_A(B1, B2, CoA1, CoA2)
C1 = CoA1*A1
C2 = CoA2*A2
R = S_thru[0,1]*(1 - C1*C2)/(A1 - B1*C1)
T1 = R*npy.array([[A1, B1],[C1, 1]])
g = npy.array([[0,1],[1,0]])
T2 = npy.array([[A2, B2],[C2, 1]])
error = 0
for n in range(lines):
meas = measured_lines[n].s[m]
ideal = npy.array([[exp(-gamma[m]*l[n]), 0],[0,exp(gamma[m]*l[n])]])
embedded = t2s_single(T1.dot(ideal).dot(g.dot(inv(T2).dot(g))))
error += npy.sum(abs(embedded - meas))
if best_error == None or error < best_error:
best_error = error
best_values = v
B1, B2, CoA1, CoA2 = best_values[1:]
A1, A2 = solve_A(B1, B2, CoA1, CoA2)
sigmab = npy.sqrt(1/(npy.sum(inv(Vb)).real))
sigmac = npy.sqrt(1/(npy.sum(inv(Vc)).real))
nstd[m] = (sigmab + sigmac)/2
C1 = CoA1*A1
C2 = CoA2*A2
#Determine R1, R2
if self.k_method == 'marks':
p1_len_est = self.kwargs.get('p1_len_est', 0)
p2_len_est = self.kwargs.get('p2_len_est', 0)
z0_phase = npy.angle( npy.sqrt(er_eff[m]) )
Qox = ( 1 - 1j*z0_phase)
Qoy = ( 1 - 1j*z0_phase)
R1R2 = (S_thru[1,0]*(1 - C1*C2))**-1
gam = A2 - B2*C2
de = (A1-B1*C1)*(R1R2*(A2-B2*C2))**2
beta_sqr = (abs(de)**2 + abs(gam)**2)/\
(de.conjugate()*Qox + de.conjugate()*Qoy)
s21y = npy.sqrt( beta_sqr )
R2 = ((A2 -B2*C2)/s21y)**-1
R2_est = exp(gamma[m]*p2_len_est)
if abs( R2_est/abs(R2_est) -R2/abs(R2) ) > npy.sqrt(2):
R2 = -R2
R1 = R1R2/R2
R1_est = exp(gamma[m]*p1_len_est)
if abs( R1_est/abs(R1_est) - R1/abs(R1) ) > npy.sqrt(2):
warn('Inconsistencies detected')
elif self.k_method == 'multical':
denom = 1 - CoA1*S_thru[0,0] - CoA2*S_thru[1,1] + CoA1*CoA2*\
(S_thru[0,0]*S_thru[1,1] - S_thru[0,1]*S_thru[1,0])
R1 = S_thru[0,1]/denom
R2 = S_thru[1,0]/denom
else:
raise ValueError('Unknown k_method: {}'.format(self.k_method))
#Reference plane shift
if self.ref_plane != 0:
try:
shift1 = exp(-2*gamma[m]*self.ref_plane[0])
shift2 = exp(-2*gamma[m]*self.ref_plane[1])
except TypeError:
shift1 = exp(-2*gamma[m]*self.ref_plane)
shift2 = exp(-2*gamma[m]*self.ref_plane)
A1 *= shift1
A2 *= shift2
C1 *= shift1
C2 *= shift2
R1 *= shift1
R2 *= shift2
if self.c0 is not None:
#Estimate the line characteristic impedance
#using known capacitance/length
if self.z0_line is not None:
raise ValueError('Only one of c0 or z0_line can be given.')
try:
c0m = self.c0[m]
except TypeError:
c0m = self.c0
z0[m] = gamma[m]/(1j*2*npy.pi*freqs[m]*c0m)
else:
#Set the known line characteristic impedance
if self.z0_line is not None:
try:
z0[m] = self.z0_line[m]
except TypeError:
z0[m] = self.z0_line
else:
try:
z0[m] = self.z0_ref[m]
except TypeError:
z0[m] = self.z0_ref
#Error matrices
Tmat1[m,:,:] = R1*npy.array([[A1, B1],[C1, 1]])
Tmat2[m,:,:] = R2*npy.array([[A2, B2],[C2, 1]])
Smat1[m,:,:] = t2s_single(Tmat1[m,:,:])
Smat2[m,:,:] = t2s_single(Tmat2[m,:,:])
#Convert the error coefficients to
#definitions used by the EightTerm class.
dx = linalg.det(Smat1[m,:,:])
dy = linalg.det(Smat2[m,:,:])
if self.k_method == 'marks':
k = Smat1[m,1,0]/Smat2[m,0,1]
else:
k = dx*dy*Smat1[m,1,0]/(Smat2[m,0,1]*Smat2[m,1,0])
#Error coefficients
e[m] = [Smat1[m,0,0],
Smat1[m,1,1],
dx,
Smat2[m,0,0],
Smat2[m,1,1],
dy,
k]
self._z0 = z0
self._gamma = gamma
self._er_eff = er_eff
self._nstd = nstd
self._coefs = {\
'forward directivity':e[:,0],
'forward source match':e[:,1],
'forward reflection tracking':e[:,0]*e[:,1]-e[:,2],
'reverse directivity':e[:,3],
'reverse source match':e[:,4],
'reverse reflection tracking':e[:,4]*e[:,3]- e[:,5],
'k':e[:,6],
}
self._coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
self._coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': npy.zeros(fpoints, dtype=complex),
'reverse switch term': npy.zeros(fpoints, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e
}
#Reference impedance renormalization
if self.z0_ref is not None and npy.any(z0 != self.z0_ref):
powerwave = self.kwargs.get('powerwave', False)
if npy.shape(self.z0_ref) != (fpoints,):
z0_ref = self.z0_ref*npy.ones(fpoints, dtype=npy.complex)
self.renormalize(z0, z0_ref, powerwave=powerwave)
[docs] @classmethod
def from_coefs(cls, frequency, coefs, **kwargs):
'''
Creates a calibration from its error coefficients
Parameters
-------------
frequency : :class:`~skrf.frequency.Frequency`
frequency info, (duh)
coefs : dict of numpy arrays
error coefficients for the calibration
See Also
----------
Calibration.from_coefs_ntwks
'''
# assigning this measured network is a hack so that
# * `calibration.frequency` property evaluates correctly
# * __init__() will not throw an error
n = Network(frequency = frequency,
s = rand_c(frequency.npoints,2,2))
measured = [n,n,n]
if 'forward switch term' in coefs:
switch_terms = (Network(frequency = frequency,
s=coefs['forward switch term']),
Network(frequency = frequency,
s=coefs['reverse switch term']))
kwargs['switch_terms'] = switch_terms
#Fill the required __init__ fields with garbage
#and assign the coefficients manually
cal = cls(measured, [-1], [0,1], **kwargs)
cal.coefs = coefs
cal.family += '(fromCoefs)'
return cal
@property
def gamma(self):
'''
Propagation constant of the solved line.
'''
try:
return self._gamma
except(AttributeError):
self.run()
return self._gamma
@property
def er_eff(self):
'''
Effective permittivity of the solved line.
Currently, this only works for TEM media. If you are using
non-TEM media (ie rectangular waveguide) then you need to compute
er yourself from gamma.
'''
try:
return self._er_eff
except(AttributeError):
self.run()
return self._er_eff
@property
def z0(self):
'''
Solved characteristic impedance of the transmission lines.
This is only solved if C0 parameter (Capacitance/length in units F/m) is given.
Solved Z0 assumes that conductance/length is zero and line supports TEM mode.
'''
try:
return self._z0
except(AttributeError):
self.run()
return self._z0
@property
def nstd(self):
'''
Normalized standard deviation of the calibration error.
Normalization is done such that 90 degree long single line gives
a standard deviation of 1.
'''
try:
return self._nstd
except(AttributeError):
self.run()
return self._nstd
[docs] def save_calibration(self, filename):
"""
save calibration as an archive containing the standards, parameters and calibration results
Parameters
----------
filename : str
the path of the zip archive to save
"""
parameters = OrderedDict()
parameters["file type"] = "skrf calibration"
parameters["calibration class"] = self.__class__.__name__
parameters["skrf version"] = skrf__version__
parameters["measured"] = ntwk_names = [ntwk.name for ntwk in self.measured]
for i, name in enumerate(ntwk_names):
ntwk_names[i] = util.unique_name(name, ntwk_names, i)
parameters["ideals"] = None
if self.switch_terms:
fswitch, rswitch = self.switch_terms # type: Network
fswitch.name = "forward switch terms"
rswitch.name = "reverse switch terms"
parameters["switch terms"] = fswitch.name, rswitch.name
else:
parameters["switch terms"] = None
parameters["kwargs"] = {
"Grefls": self.Grefls,
"l": self.l,
"er_est": self.er_est,
"refl_offset": self.refl_offset,
"ref_plane": self.ref_plane,
"gamma_root_choice": self.gamma_root_choice,
"k_method": self.k_method
}
with zipfile.ZipFile(filename, 'w', compression=zipfile.ZIP_DEFLATED) as archive:
archive.writestr("parameters.json", json.dumps(parameters, indent=2))
if self.switch_terms:
fswitch.write_touchstone(dir="switch terms", to_archive=archive)
rswitch.write_touchstone(dir="switch terms", to_archive=archive)
for i, ntwk in enumerate(self.measured): # type: int, Network
ntwk.write_touchstone(ntwk_names[i] + ".s2p", dir="measured", to_archive=archive)
for key, ntwk in self.coefs_ntwks.items():
ntwk.write_touchstone(dir="coefs", to_archive=archive)
gamma_ntwk = Network(f=self.measured[0].f, s=self.gamma, z0=50., comments="propagation constant")
gamma_ntwk.write_touchstone("gamma.s1p", to_archive=archive)
[docs] @classmethod
def load_calibration_archive(cls, filename):
with zipfile.ZipFile(filename) as archive:
parameters = json.loads(archive.open("parameters.json").read().decode("ascii"))
measured_dict = read_zipped_touchstones(archive, "measured")
switch_terms_dict = read_zipped_touchstones(archive, "switch terms")
coefs_dict = read_zipped_touchstones(archive, "coefs") # not used currently
gamma_ntwk = Network.zipped_touchstone("gamma.s1p", archive)
measured = list()
for name in parameters["measured"]:
measured.append(measured_dict[name])
if parameters["switch terms"] is None:
switch_terms = None
else:
switch_terms = [
switch_terms_dict[parameters["switch terms"][0]],
switch_terms_dict[parameters["switch terms"][1]]
]
kwargs = parameters["kwargs"]
cal = cls(measured, switch_terms=switch_terms, **kwargs)
cal.coefs = NetworkSet(coefs_dict).to_s_dict()
cal._gamma = gamma_ntwk.s.flatten()
return cal
[docs]class UnknownThru(EightTerm):
'''
Two-Port Self-Calibration allowing the *thru* standard to be unknown.
This algorithm was originally developed in [1]_, and
is based on the 8-term error model (:class:`EightTerm`). It allows
the *thru* to be unknown, other than it must be reciprocal. This
is useful when when a well-known thru is not realizable.
References
-----------
.. [1] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru,`" IEEE Microwave and Guided Wave Letters, vol. 2, no. 12, pp. 505-507, 1992.
'''
family = 'UnknownThru'
[docs] def __init__(self, measured, ideals, *args, **kwargs):
'''
Initializer
Note that the *thru* standard must be last in both measured, and
ideal lists. The ideal for the *thru* is only used to choose
the sign of a square root. Thus, it only has to be have s21, s12
known within :math:`\pi` phase.
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter ( or use `sloppy_input`)
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list ( or use sloppy_input
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
'''
EightTerm.__init__(self, measured = measured, ideals = ideals,
*args, **kwargs)
[docs] def run(self):
p1_m = [k.s11 for k in self.measured_unterminated[:-1]]
p2_m = [k.s22 for k in self.measured_unterminated[:-1]]
p1_i = [k.s11 for k in self.ideals[:-1]]
p2_i = [k.s22 for k in self.ideals[:-1]]
thru_m = self.measured_unterminated[-1]
thru_approx = self.ideals[-1]
# create one port calibration for all reflective standards
port1_cal = OnePort(measured = p1_m, ideals = p1_i)
port2_cal = OnePort(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = port1_cal.coefs.copy()
p2_coefs = port2_cal.coefs.copy()
e_rf = port1_cal.coefs_ntwks['reflection tracking']
e_rr = port2_cal.coefs_ntwks['reflection tracking']
X = port1_cal.error_ntwk
Y = port2_cal.error_ntwk
# create a fully-determined 8-term cal just get estimate on k's sign
# this is really inefficient, i need to work out the math on the
# closed form solution
et = EightTerm(
measured = self.measured,
ideals = self.ideals,
switch_terms= self.switch_terms)
k_approx = et.coefs['k'].flatten()
# this is equivalent to sqrt(detX*detY/detM)
e10e32 = npy.sqrt((e_rf*e_rr*thru_m.s21/thru_m.s12).s.flatten())
k_ = e10e32/e_rr.s.flatten()
k_ = find_closest(k_, -1*k_, k_approx)
#import pylab as plb
#plot(abs(k_-k_approx))
#plb.show()
# create single dictionary for all error terms
coefs = {}
coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
coefs.update(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs]))
coefs.update(dict([('reverse %s'%k, p2_coefs[k]) for k in p2_coefs]))
if self.switch_terms is not None:
coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
warn('No switch terms provided')
coefs.update({
'forward switch term': npy.zeros(len(self.frequency), dtype=complex),
'reverse switch term': npy.zeros(len(self.frequency), dtype=complex),
})
coefs.update({'k':k_})
self.coefs = coefs
class MRC(UnknownThru):
'''
Misalignment Resistance Calibration
This is an error-box based calibration that is a combination of the
SDDL[1]_ and the UnknownThru[2]_, algorithms.
The self-calibration aspects of these two algorithms alleviate the
need to know the phase of the delay shorts, as well as the exact
response of the thru. Thus the calibration is resistant to
waveguide flange misalignment.
References
-----------
.. [1] Z. Liu and R. M. Weikle, "A reflectometer calibration method resistant to waveguide flange misalignment," Microwave Theory and Techniques, IEEE Transactions on, vol. 54, no. 6, pp. 2447-2452, Jun. 2006.
.. [2] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru,`" IEEE Microwave and Guided Wave Letters, vol. 2, no. 12, pp. 505-507, 1992.
'''
family = 'MRC'
def __init__(self, measured, ideals, *args, **kwargs):
'''
Initializer
This calibration takes exactly 5 standards, which must be in the
order:
[Short, DelayShort1, DelayShort1, Load, Thru]
The ideals for the delay shorts are not used and the ideal for
the *thru* is only used to choose
the sign of a square root. Thus, it only has to be have s21, s12
known within :math:`\pi` phase.
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
'''
UnknownThru.__init__(self, measured = measured, ideals = ideals,
*args, **kwargs)
def run(self):
p1_m = [k.s11 for k in self.measured_unterminated[:-1]]
p2_m = [k.s22 for k in self.measured_unterminated[:-1]]
p1_i = [k.s11 for k in self.ideals[:-1]]
p2_i = [k.s22 for k in self.ideals[:-1]]
thru_m = self.measured_unterminated[-1]
thru_approx = self.ideals[-1]
# create one port calibration for all reflective standards
port1_cal = SDDL(measured = p1_m, ideals = p1_i)
port2_cal = SDDL(measured = p2_m, ideals = p2_i)
# cal coefficient dictionaries
p1_coefs = port1_cal.coefs.copy()
p2_coefs = port2_cal.coefs.copy()
e_rf = port1_cal.coefs_ntwks['reflection tracking']
e_rr = port2_cal.coefs_ntwks['reflection tracking']
X = port1_cal.error_ntwk
Y = port2_cal.error_ntwk
# create a fully-determined 8-term cal just get estimate on k's sign
# this is really inefficient, i need to work out the math on the
# closed form solution
et = EightTerm(
measured = self.measured,
ideals = self.ideals,
switch_terms= self.switch_terms)
k_approx = et.coefs['k'].flatten()
# this is equivalent to sqrt(detX*detY/detM)
e10e32 = npy.sqrt((e_rf*e_rr*thru_m.s21/thru_m.s12).s.flatten())
k_ = e10e32/e_rr.s.flatten()
k_ = find_closest(k_, -1*k_, k_approx)
#import pylab as plb
#plot(abs(k_-k_approx))
#plb.show()
# create single dictionary for all error terms
coefs = {}
coefs.update(dict([('forward %s'%k, p1_coefs[k]) for k in p1_coefs]))
coefs.update(dict([('reverse %s'%k, p2_coefs[k]) for k in p2_coefs]))
coefs['forward isolation'] = self.isolation.s[:,1,0].flatten()
coefs['reverse isolation'] = self.isolation.s[:,0,1].flatten()
if self.switch_terms is not None:
coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
warn('No switch terms provided')
coefs.update({
'forward switch term': npy.zeros(len(self.frequency), dtype=complex),
'reverse switch term': npy.zeros(len(self.frequency), dtype=complex),
})
coefs.update({'k':k_})
self.coefs = coefs
[docs]class SixteenTerm(Calibration):
'''
General SixteenTerm (aka Error-box) Two-port calibration
16-term error model is a complete error model that can solve for leakages between
the different VNA receivers.
There are several different combinations of calibration standards that can
be used. At least five two port measurements are needed. Using through, open,
short, and load standards some combinations result in singular matrix.
See [1]_ for list of non-singular combinations.
References
-----------
.. [1] K. J. Silvonen, "Calibration of 16-term error model (microwave measurement)," in Electronics Letters, vol. 29, no. 17, pp. 1544-1545, 19 Aug. 1993.
'''
family = 'SixteenTerm'
[docs] def __init__(self, measured, ideals, switch_terms=None,
*args, **kwargs):
'''
SixteenTerm Initializer
Notes
------
Switch terms are already assumed to be corrected since the ordinary
correction equations are not valid if the crosstalk is significant.
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards. The order
must align with the `ideals` parameter
ideals : list/dict of :class:`~skrf.network.Network` objects
Predicted ideal response of the calibration standards.
The order must align with `ideals` list
switch_terms : tuple of :class:`~skrf.network.Network` objects
the pair of switch terms in the order (forward, reverse)
'''
self.switch_terms = switch_terms
if switch_terms is None:
warn('No switch terms provided')
Calibration.__init__(self,
measured = measured,
ideals = ideals,
*args, **kwargs)
[docs] def unterminate(self,ntwk):
'''
Unterminates switch terms from a raw measurement.
See Also
---------
calibration.unterminate
'''
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return unterminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
[docs] def terminate(self, ntwk):
'''
Terminate a network with switch terms
See Also
--------
calibration.terminate
'''
if self.switch_terms is not None:
gamma_f, gamma_r = self.switch_terms
return terminate(ntwk, gamma_f, gamma_r)
else:
return ntwk
@property
def measured_unterminated(self):
return [self.unterminate(k) for k in self.measured]
[docs] def run(self):
numStds = self.nstandards
numCoefs = 15
mList = [k.s for k in self.measured_unterminated]
iList = [k.s for k in self.ideals]
fLength = len(mList[0])
#initialize outputs
error_vector = npy.zeros(shape=(fLength,numCoefs),dtype=complex)
residuals = npy.zeros(shape=(fLength,4*numStds-numCoefs),dtype=complex)
Q = npy.zeros((numStds*4, 15),dtype=complex)
M = npy.zeros((numStds*4, 1),dtype=complex)
# loop through frequencies and form m, a vectors and
# the matrix M.
#i[j,k] = Actual S-parameters
#m[j,k] = Measured S-parameters
#t15 is normalized to one
for f in list(range(fLength)):
# loop through standards and fill matrix
for k in list(range(numStds)):
m,i = mList[k][f,:,:],iList[k][f,:,:] # 2x2 s-matrices
Q[k*4:k*4+4,:] = npy.array([\
[ i[0,0], i[1,0], 0 , 0 , 1, 0, 0, 0, -m[0,0]*i[0,0], -m[0,0]*i[1,0], -m[0,1]*i[0,0], -m[0,1]*i[1,0], -m[0,0] , 0 , -m[0,1] ],\
[ i[0,1], i[1,1], 0 , 0 , 0, 1, 0, 0, -m[0,0]*i[0,1], -m[0,0]*i[1,1], -m[0,1]*i[0,1], -m[0,1]*i[1,1], 0 , -m[0,0] , 0 ],\
[ 0 , 0 , i[0,0], i[1,0], 0, 0, 1, 0, -m[1,0]*i[0,0], -m[1,0]*i[1,0], -m[1,1]*i[0,0], -m[1,1]*i[1,0], -m[1,0] , 0 , -m[1,1] ],\
[ 0 , 0 , i[0,1], i[1,1], 0 ,0 ,0, 1, -m[1,0]*i[0,1], -m[1,0]*i[1,1], -m[1,1]*i[0,1], -m[1,1]*i[1,1], 0 , -m[1,0] , 0 ],\
])
#pdb.set_trace()
M[k*4:k*4+4,:] = npy.array([\
[ 0 ],\
[ m[0,1] ],\
[ 0 ],\
[ m[1,1] ],\
])
## calculate least squares
error_vector_at_f, residuals_at_f = npy.linalg.lstsq(Q,M,rcond=None)[0:2]
##if len (residualsTmp )==0:
## raise ValueError( 'matrix has singular values, check standards')
error_vector[f,:] = error_vector_at_f.flatten()
residuals[f,:] = residuals_at_f
e = error_vector
#Normalize e23 = 1
c = e[:,12]/(e[:,12]-e[:,13]*e[:,14])
for i in range(len(e[0])):
e[:,i] *= c
T1 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.complex)
T2 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.complex)
T3 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.complex)
T4 = npy.zeros(shape=(fLength, 2, 2), dtype=npy.complex)
T1[:,0,0] = e[:,0]
T1[:,0,1] = e[:,1]
T1[:,1,0] = e[:,2]
T1[:,1,1] = e[:,3]
T2[:,0,0] = e[:,4]
T2[:,0,1] = e[:,5]
T2[:,1,0] = e[:,6]
T2[:,1,1] = e[:,7]
T3[:,0,0] = e[:,8]
T3[:,0,1] = e[:,9]
T3[:,1,0] = e[:,10]
T3[:,1,1] = e[:,11]
T4[:,0,0] = e[:,12]
T4[:,0,1] = e[:,13]
T4[:,1,0] = e[:,14]
T4[:,1,1] = c
# put the error vector into human readable dictionary
e1, e2, e3, e4 = self.E_matrices(T1, T2, T3, T4)
self._coefs = {\
'forward directivity':e1[:,0,0],
'reverse directivity':e1[:,1,1],
'forward source match':e4[:,0,0],
'reverse source match':e4[:,1,1],
'forward reflection tracking':e2[:,0,0]*e3[:,0,0],
'reverse reflection tracking':e2[:,1,1],
'k':e3[:,0,0],
'forward isolation':e1[:,1,0],
'reverse isolation':e1[:,0,1],
'forward port 1 isolation':e3[:,1,0],
'reverse port 1 isolation':e2[:,0,1],
'forward port 2 isolation':e2[:,1,0],
'reverse port 2 isolation':e3[:,0,1],
'forward port isolation':e4[:,1,0],
'reverse port isolation':e4[:,0,1],
}
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': npy.zeros(fLength, dtype=complex),
'reverse switch term': npy.zeros(fLength, dtype=complex),
})
# output is a dictionary of information
self._output_from_run = {
'error vector':e,
'residuals':residuals
}
return None
[docs] def apply_cal(self, ntwk):
caled = ntwk.copy()
inv = linalg.inv
T1,T2,T3,T4 = self.T_matrices
ntwk = self.unterminate(ntwk)
for f in list(range(len(ntwk.s))):
t1,t2,t3,t4,m = T1[f,:,:],T2[f,:,:],T3[f,:,:],\
T4[f,:,:],ntwk.s[f,:,:]
caled.s[f,:,:] = inv(-1*m.dot(t3)+t1).dot(m.dot(t4)-t2)
return caled
[docs] def embed(self, ntwk):
'''
'''
embedded = ntwk.copy()
inv = linalg.inv
T1,T2,T3,T4 = self.T_matrices
for f in list(range(len(ntwk.s))):
t1,t2,t3,t4,a = T1[f,:,:],T2[f,:,:],T3[f,:,:],\
T4[f,:,:],ntwk.s[f,:,:]
embedded.s[f,:,:] = (t1.dot(a)+t2).dot(inv(t3.dot(a)+t4))
embedded = self.terminate(embedded)
return embedded
@property
def T_matrices(self):
'''
Intermediate matrices used for embedding and de-embedding.
Returns
--------
T1,T2,T3,T4 : numpy ndarray
'''
ec = self.coefs
npoints = len(ec['forward directivity'])
inv = linalg.inv
e100 = ec['forward directivity']
e111 = ec['reverse directivity']
e400 = ec['forward source match']
e411 = ec['reverse source match']
e300 = ec['k']
e311 = npy.ones(npoints)
e200 = ec['forward reflection tracking']/e300
e211 = ec['reverse reflection tracking']
e110 = ec['forward isolation']
e101 = ec['reverse isolation']
e301 = ec['reverse port 2 isolation']
e310 = ec['forward port 1 isolation']
e201 = ec['reverse port 1 isolation']
e210 = ec['forward port 2 isolation']
e401 = ec['reverse port isolation']
e410 = ec['forward port isolation']
E1 = npy.array([\
[ e100 , e110], \
[ e101 , e111]])\
.transpose().reshape(-1,2,2)
E2 = npy.array([\
[ e200 , e210], \
[ e201 , e211]])\
.transpose().reshape(-1,2,2)
E3 = npy.array([\
[ e300 , e310], \
[ e301 , e311]])\
.transpose().reshape(-1,2,2)
E4 = npy.array([\
[ e400 , e410], \
[ e401 , e411]])\
.transpose().reshape(-1,2,2)
T1 = npy.zeros(E1.shape, dtype=npy.complex)
T2 = T1.copy()
T3 = T1.copy()
T4 = T1.copy()
invE3 = inv(E3)
for i in range(npoints):
T1[i] = E2[i] - E1[i].dot(invE3[i]).dot(E4[i])
T2[i] = E1[i].dot(invE3[i])
T3[i] = -invE3[i].dot(E4[i])
T4[i] = invE3[i]
return T1, T2, T3, T4
[docs] def E_matrices(self, T1, T2, T3, T4):
'''
Convert solved calibration T matrices to S-parameters.
'''
inv = linalg.inv
E1 = npy.zeros(T1.shape, dtype=npy.complex)
E2 = npy.zeros(T2.shape, dtype=npy.complex)
E3 = npy.zeros(T3.shape, dtype=npy.complex)
E4 = npy.zeros(T4.shape, dtype=npy.complex)
invT4 = inv(npy.array(T4))
for i in range(len(T1)):
E1[i] = T2[i].dot(invT4[i])
E2[i] = T1[i] - T2[i].dot(invT4[i]).dot(T3[i])
E3[i] = invT4[i]
E4[i] = -invT4[i].dot(T3[i])
return E1, E2, E3, E4
[docs]class LMR16(SixteenTerm):
'''
SixteenTerm Load-Match-Reflect self-calibration.
16-Term self calibration for leaky VNA. Implementation is based on [1]_.
Needs five standards to be measured and given in this order:
* Through
* Match-match
* Reflect-reflect
* Reflect-match
* Match-reflect
Reflect standard needs to be very reflective and same in all measurements.
Matching of through and match standards is assumed to be perfect.
Loss of the through is assumed to be zero, but its length can be non-zero.
Only reflect or through standard needs to be known and the other one will be
solved during the calibration. Solved S-parameters of the standards
can be accessed with LMR16.solved_through and LMR16.solved_reflect.
Switch termination is already assumed to be done either by the previous calibration or
during the measurements. Regular switch correction equations used with
EightTerm calibration can't be used if leakage is significant.
References
------------
.. [1] K. Silvonen, "LMR 16-a self-calibration procedure for a leaky network analyzer," in IEEE Transactions on Microwave Theory and Techniques, vol. 45, no. 7, pp. 1041-1049, Jul 1997
'''
family = 'SixteenTerm'
[docs] def __init__(self, measured, ideals, ideal_is_reflect=True, sign=None,
switch_terms=None, *args, **kwargs):
"""
LMR16 initializer
Due to needing to solve a second order equation during the calibration a
choice must be taken on the correct root. Sign argument, +1 or -1, can be
given to make the root choice.
If sign argument is not given it is tried to be solved automatically by
choosing the sign that makes :math:`k = \\frac{t_{15}}{t_{12}}` closer to +1, which holds
if test fixture is symmetric.
Parameters
--------------
measured : list/dict of :class:`~skrf.network.Network` objects
Raw measurements of the calibration standards.
ideals : list/dict of :class:`~skrf.network.Network` objects
Estimated response of the reflect or through calibration standard.
ideal_is_reflect : Boolean
True if given ideal is reflect and False if ideal is through
sign : +1,-1 or None
Sign to be used for the root choice.
"""
self.switch_terms = switch_terms
if switch_terms is None:
warn('No switch terms provided')
if type(ideals) == Network:
ideals = [ideals]
if len(ideals) != 1:
raise ValueError("One ideal must be given: Through or reflect definition.")
if ideal_is_reflect == False:
self.through = ideals[0].copy()
self.reflect = None
self._solved_through = self.through
self._solved_reflect = Network(s=[0]*len(self.through.f), f=self.through.f, f_unit='Hz')
else:
self.through = None
self.reflect = ideals[0].copy()
self._solved_through = Network(s=[[[0,1],[1,0]]]*len(self.reflect.f), f=self.reflect.f, f_unit='Hz')
self._solved_reflect = self.reflect
if len(measured) != 5:
raise ValueError("5 Measurements are needed: T, M-M, R-R, R-M and M-R")
self.measured = measured
self.sign = sign
Calibration.__init__(self,
measured = measured,
ideals = ideals,
sloppy_input=False,
self_calibration=True,
*args, **kwargs)
[docs] def run(self):
mList = [k.s for k in self.measured_unterminated]
fLength = len(mList[0])
inv = linalg.inv
T1 = []
T2 = []
T3 = []
T4 = []
auto_sign = self.sign == None
for f in range(fLength):
ma = mList[0][f] #Through
mb = mList[1][f] #Match-match
mc = mList[2][f] #Reflect-reflect
md = mList[3][f] #Reflect-match
me = mList[4][f] #Match-reflect
nn = inv(me-ma).dot(mb-me)
mm = (ma-mc).dot(nn)
oo = mb-mc
rr = inv(md-ma).dot(mb-md)
pp = (ma-mc).dot(rr)
m = (pp[1,0] + oo[1,0])*mm[1,1] - (pp[1,1] + oo[1,1])*mm[1,0]
n = oo[1,0]*pp[0,1] - oo[1,1]*pp[0,0]
o = (mm[0,1]+ oo[0,1])*pp[0,0] - (mm[0,0] + oo[0,0])*pp[0,1]
p = oo[0,1]*mm[1,0] - oo[0,0]*mm[1,1]
#One of the coefficients is normalized to one
t12 = 1.0
auto_sign_abs = []
if auto_sign:
self.sign = 1
for sign_tries in [0,1,2]:
gt = self.sign*npy.sqrt(m*o/(n*p))
if self.through == None:
g = self.reflect.s[f][0,0]
t = g/gt
self._solved_through.s[f] = npy.array([[0,t],[t,0]])
else:
t = self.through.s[f][1,0]
g = gt*t
self._solved_reflect.s[f] = npy.array([g])
t15 = -(p/o)*(pp[0,0]/mm[1,1])*gt*t12
#If correct sign is not specified try to choose it based
#on the fact that with correct sign t15/t12 ~= +1
#Assuming that test fixtures are symmetric
if auto_sign:
auto_sign_abs.append(npy.abs(1 - t15/t12))
if sign_tries == 0:
self.sign = -self.sign
if sign_tries == 1:
if auto_sign_abs[0] < auto_sign_abs[1]:
self.sign = 1
else:
self.sign = -1
else:
break
t13 = -pp[0,1]/pp[0,0]*t15
t14 = -mm[1,0]/mm[1,1]*t12
#Normalize e23 = 1
c = 1/(t15 - t13*t14)
t8 = (rr[0,0]*t12 + rr[0,1]*t14)*(1./g) - t13/t
t9 = (nn[0,0]*t13 + nn[0,1]*t15)*(1./g) - t12/t
t10 = (rr[1,0]*t12 + rr[1,1]*t14)*(1./g) - t15/t
t11 = (nn[1,0]*t13 + nn[1,1]*t15)*(1./g) - t14/t
t0 = mc[0,0]*t8 + mc[0,1]*t10 - (1./g)*(oo[0,0]*t12+oo[0,1]*t14)
t1 = mc[0,0]*t9 + mc[0,1]*t11 - (1./g)*(oo[0,0]*t13+oo[0,1]*t15)
t2 = mc[1,0]*t8 + mc[1,1]*t10 - (1./g)*(oo[1,0]*t12+oo[1,1]*t14)
t3 = mc[1,0]*t9 + mc[1,1]*t11 - (1./g)*(oo[1,0]*t13+oo[1,1]*t15)
t4 = mb[0,0]*t12 + mb[0,1]*t14
t5 = mb[0,0]*t13 + mb[0,1]*t15
t6 = mb[1,0]*t12 + mb[1,1]*t14
t7 = mb[1,0]*t13 + mb[1,1]*t15
T1.append( c*npy.array([[t0,t1],[t2,t3]]) )
T2.append( c*npy.array([[t4,t5],[t6,t7]]) )
T3.append( c*npy.array([[t8,t9],[t10,t11]]) )
T4.append( c*npy.array([[t12,t13],[t14,t15]]) )
T1 = npy.array(T1)
T2 = npy.array(T2)
T3 = npy.array(T3)
T4 = npy.array(T4)
#Convert T-matrix to S-parameters
#and put error terms in human readable form
e1,e2,e3,e4 = self.E_matrices(T1, T2, T3, T4)
self._coefs = {\
'forward directivity':e1[:,0,0],
'reverse directivity':e1[:,1,1],
'forward source match':e4[:,0,0],
'reverse source match':e4[:,1,1],
'forward reflection tracking':e2[:,0,0]*e3[:,0,0],
'reverse reflection tracking':e2[:,1,1],
'k':e3[:,0,0],
'forward isolation':e1[:,1,0],
'reverse isolation':e1[:,0,1],
'forward port 1 isolation':e3[:,1,0],
'reverse port 1 isolation':e2[:,0,1],
'forward port 2 isolation':e2[:,1,0],
'reverse port 2 isolation':e3[:,0,1],
'forward port isolation':e4[:,1,0],
'reverse port isolation':e4[:,0,1],
}
if self.switch_terms is not None:
self._coefs.update({
'forward switch term': self.switch_terms[0].s.flatten(),
'reverse switch term': self.switch_terms[1].s.flatten(),
})
else:
self._coefs.update({
'forward switch term': npy.zeros(fLength, dtype=complex),
'reverse switch term': npy.zeros(fLength, dtype=complex),
})
return None
[docs] @classmethod
def from_coefs(cls, frequency, coefs, **kwargs):
'''
Creates a calibration from its error coefficients
Parameters
-------------
frequency : :class:`~skrf.frequency.Frequency`
frequency info, (duh)
coefs : dict of numpy arrays
error coefficients for the calibration
See Also
----------
Calibration.from_coefs_ntwks
'''
n = Network(frequency = frequency,
s = rand_c(frequency.npoints,2,2))
measured = [n,n,n,n,n]
if 'forward switch term' in coefs:
switch_terms = (Network(frequency = frequency,
s=coefs['forward switch term']),
Network(frequency = frequency,
s=coefs['reverse switch term']))
kwargs['switch_terms'] = switch_terms
cal = cls(measured, measured[0], **kwargs)
cal.coefs = coefs
cal.family += '(fromCoefs)'
return cal
@property
def residual_ntwks(self):
'''
Dictionary of residual Networks
These residuals are complex differences between the ideal
standards and their corresponding corrected measurements.
'''
#Runs the calibration if needed
caled_ntwks = self.caled_ntwks
r = self.solved_reflect
m = Network(s=[0]*len(self.solved_reflect.f), f=self.solved_reflect.f, f_unit='Hz')
mm = two_port_reflect(m, m)
mr = two_port_reflect(m, r)
rm = two_port_reflect(r, m)
rr = two_port_reflect(r, r)
ideals = [self.solved_through, mm, rr, rm, mr]
return [caled - ideal for (ideal, caled) in zip(ideals, caled_ntwks)]
@property
def solved_through(self):
'''
Return the solved through or the ideal through if reflect was solved
'''
if not hasattr(self, '_coefs'):
self.run()
return self._solved_through
@property
def solved_reflect(self):
'''
Return the solved reflect or the ideal reflect if through was solved
'''
if not hasattr(self, '_coefs'):
self.run()
return self._solved_reflect
class Normalization(Calibration):
'''
Simple Thru Normalization
'''
def run(self):
pass
def apply_cal(self, input_ntwk):
return input_ntwk/average(self.measured)
## Functions
def ideal_coefs_12term(frequency):
'''
An ideal set of 12term calibration coefficients
Produces a set of error coefficients, that would result if the
error networks were matched thrus
'''
zero = zeros(len(frequency), dtype='complex')
one = ones(len(frequency), dtype='complex')
ideal_coefs = {}
ideal_coefs.update({k:zero for k in [\
'forward directivity',
'forward source match',
'forward load match',
'reverse directivity',
'reverse load match',
'reverse source match',
]})
ideal_coefs.update({k:one for k in [\
'forward reflection tracking',
'forward transmission tracking',
'reverse reflection tracking',
'reverse transmission tracking',
]})
return ideal_coefs
[docs]def unterminate(ntwk, gamma_f, gamma_r):
'''
Unterminates switch terms from a raw measurement.
In order to use the 8-term error model on a VNA which employs a
switched source, the effects of the switch must be accounted for.
This is done through `switch terms` as described in [1]_ . The
two switch terms are defined as,
.. math ::
\\Gamma_f = \\frac{a2}{b2} ,\\qquad\\text{sourced by port 1}\\
\\Gamma_r = \\frac{a1}{b1} ,\\qquad\\text{sourced by port 2}
These can be measured by four-sampler VNA's by setting up
user-defined traces onboard the VNA. If the VNA doesnt have
4-samplers, then you can measure switch terms indirectly by using a
two-tier two-port calibration. First do a SOLT, then convert
the 12-term error coefs to 8-term, and pull out the switch terms.
Parameters
-------------
two_port : 2-port Network
the raw measurement
gamma_f : 1-port Network
the measured forward switch term.
gamma_f = a2/b2 sourced by port1
gamma_r : 1-port Network
the measured reverse switch term
gamma_r = a1/b1 sourced by port2
Returns
-----------
ntwk : Network object
References
------------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
'''
unterminated = ntwk.copy()
# extract scattering matrices
m, gamma_r, gamma_f = ntwk.s, gamma_r.s, gamma_f.s
u = m.copy()
one = npy.ones(ntwk.frequency.npoints)
d = one - m[:,0,1]*m[:,1,0]*gamma_r[:,0,0]*gamma_f[:,0,0]
u[:,0,0] = (m[:,0,0] - m[:,0,1]*m[:,1,0]*gamma_f[:,0,0])/(d)
u[:,0,1] = (m[:,0,1] - m[:,0,0]*m[:,0,1]*gamma_r[:,0,0])/(d)
u[:,1,0] = (m[:,1,0] - m[:,1,1]*m[:,1,0]*gamma_f[:,0,0])/(d)
u[:,1,1] = (m[:,1,1] - m[:,0,1]*m[:,1,0]*gamma_r[:,0,0])/(d)
unterminated.s = u
return unterminated
[docs]def terminate(ntwk, gamma_f, gamma_r):
'''
Terminate a network with switch terms
see [1]_
Parameters
-------------
two_port : 2-port Network
an unterminated network
gamma_f : 1-port Network
measured forward switch term.
gamma_f = a2/b2 sourced by port1
gamma_r : 1-port Network
measured reverse switch term
gamma_r = a1/b1 sourced by port2
Returns
-----------
ntwk : Network object
See Also
--------
unterminate_switch_terms
References
------------
.. [1] "Formulations of the Basic Vector Network Analyzer Error
Model including Switch Terms" by Roger B. Marks
'''
m = ntwk.copy()
ntwk_flip = ntwk.copy()
ntwk_flip.flip()
m.s[:,0,0] = (ntwk**gamma_f).s[:,0,0]
m.s[:,1,1] = (ntwk_flip**gamma_r).s[:,0,0]
m.s[:,1,0] = ntwk.s[:,1,0]/(1-ntwk.s[:,1,1]*gamma_f.s[:,0,0])
m.s[:,0,1] = ntwk.s[:,0,1]/(1-ntwk.s[:,0,0]*gamma_r.s[:,0,0])
return m
[docs]def determine_line(thru_m, line_m, line_approx=None):
'''
Determine S21 of a matched line.
Given raw measurements of a `thru` and a matched `line` with unknown
s21, this will calculate the response of the line. This works for
lossy lines, and 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 thru
line_m : :class:`~skrf.network.Network`
raw measurement of a matched transmissive standard
line_approx : :class:`~skrf.network.Network`
approximate network the ideal line response. if None, then
the response is approximated by line_approx = line/thru. This
makes the assumption that the error networks have much larger
transmission than reflection
References
--------------
'''
npts = len(thru_m)
zero = npy.zeros(npts)
if line_approx is None:
# estimate line length, by assuming error networks are well
# matched
line_approx = line_m/thru_m
C = thru_m.inv**line_m
# the eigen values of the matrix C, are equal to s12,s12^-1)
# we need to choose the correct one
w,v = linalg.eig(C.t)
s12_0, s12_1 = w[:,0], w[:,1]
s12 = find_correct_sign(s12_0, s12_1, line_approx.s[:,1,0])
found_line = line_m.copy()
found_line.s = npy.array([[zero, s12],[s12,zero]]).transpose().reshape(-1,2,2)
return found_line
def determine_reflect(thru_m, reflect_m, line_m, reflect_approx=None,
line_approx=None, return_all=False):
'''
Determine reflect from a thru, reflect, line 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
line_m : :class:`~skrf.network.Network`
raw measurement of a matched transmissive standard
reflect_m: :class:`~skrf.network.Network`
raw measurement of a reflect standard
reflect_approx : :class:`~skrf.network.Network`
approximate One-port network for the reflect. if None, then
we assume its a flush short (gamma=-1)
return_all: bool
return all possible values fo reflect, one for each root-choice.
useful for troubleshooting.
Returns
-------
reflect : :class:`~skrf.network.Network`
a One-port network for the found reflect.
'''
#Call determine_line first to solve root choice of the propagation constant
line = determine_line(thru_m, line_m, line_approx)
inv = linalg.inv
rt = thru_m.t
rd = line_m.t
tt = einsum('ijk,ikl -> ijl', rd, inv(rt))
a = tt[:,1,0]
b = tt[:,1,1]-tt[:,0,0]
c = -tt[:,0,1]
sol1 = (-b-sqrt(b*b-4*a*c))/(2*a)
sol2 = (-b+sqrt(b*b-4*a*c))/(2*a)
e2 = line.s[:,0,1]**2
x1 = (tt[:,1,0]*sol1 + tt[:,1,1])/(tt[:,0,1]/sol2 + tt[:,0,0])
x2 = (tt[:,1,0]*sol2 + tt[:,1,1])/(tt[:,0,1]/sol1 + tt[:,0,0])
rootChoice = [abs(x1[i] - e2[i]) < abs(x2[i] - e2[i]) for i in range(len(x1))]
y = sol1*invert(rootChoice) + sol2*rootChoice
x = sol1*rootChoice + sol2*invert(rootChoice)
b = y
e = thru_m.s[:,0,0]
d = -det(thru_m.s)
f = -thru_m.s[:,1,1]
gam = (f-d/x)/(1-e/x)
b_A = (e-y)/(d-b*f)
w1 = reflect_m.s[:,0,0]
w2 = reflect_m.s[:,1,1]
a = sqrt(((w1-y)*(1+w2*b_A)*(d-y*f))/\
((w2+gam)*(1-w1/x)*(1-e/x)))
out = []
for rootChoice2 in [1,-1] :
a= a*rootChoice2
unknownReflectS = (w1-y)/(a*(1-w1/x))
out.append(unknownReflectS)
if return_all:
return [Network(frequency=thru_m.frequency, s = k) for k in out]
if reflect_approx is None:
reflect_approx = reflect_m.copy()
reflect_approx.s[:,0,0]=-1
closer = find_closest(out[0], out[1], reflect_approx.s11.s.flatten())
reflect = reflect_approx.copy()
reflect.s[:,0,0]=closer
return reflect.s11
def convert_12term_2_8term(coefs_12term, redundant_k = False):
'''
Convert the 12-term and 8-term error coefficients.
Derivation of this conversion can be found in [#]_ .
References
------------
.. [#] Marks, Roger B.; , "Formulations of the Basic Vector Network Analyzer Error Model including Switch-Terms," ARFTG Conference Digest-Fall, 50th , vol.32, no., pp.115-126, Dec. 1997. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4119948&isnumber=4119931
'''
# Nomenclature taken from Roger Marks
Edf = coefs_12term['forward directivity']
Esf = coefs_12term['forward source match']
Erf = coefs_12term['forward reflection tracking']
Etf = coefs_12term['forward transmission tracking']
Elf = coefs_12term['forward load match']
Eif = coefs_12term.get('forward isolation',0)
Edr = coefs_12term['reverse directivity']
Esr = coefs_12term['reverse source match']
Err = coefs_12term['reverse reflection tracking']
Elr = coefs_12term['reverse load match']
Etr = coefs_12term['reverse transmission tracking']
Eir = coefs_12term.get('reverse isolation',0)
# these are given in eq (30) - (33) in Roger Mark's paper listed in
# the docstring
# NOTE: k = e10/e23 = alpha/beta
# the 'k' nomenclature is from Soares Speciale
gamma_f = (Elf - Esr)/(Err + Edr*(Elf - Esr))
gamma_r = (Elr - Esf)/(Erf + Edf*(Elr - Esf))
k_first = Etf/(Err + Edr*(Elf - Esr) )
k_second =1/(Etr/(Erf + Edf *(Elr - Esf)))
k = k_first #npy.sqrt(k_second*k_first)# (k_first +k_second )/2.
coefs_8term = {}
for l in ['forward directivity','forward source match',
'forward reflection tracking','reverse directivity',
'reverse reflection tracking','reverse source match',
'forward isolation', 'reverse isolation']:
coefs_8term[l] = coefs_12term[l].copy()
coefs_8term['forward switch term'] = gamma_f
coefs_8term['reverse switch term'] = gamma_r
coefs_8term['k'] = k
if redundant_k:
coefs_8term['k first'] = k_first
coefs_8term['k second'] = k_second
return coefs_8term
def convert_8term_2_12term(coefs_8term):
'''
'''
Edf = coefs_8term['forward directivity']
Esf = coefs_8term['forward source match']
Erf = coefs_8term['forward reflection tracking']
Edr = coefs_8term['reverse directivity']
Esr = coefs_8term['reverse source match']
Err = coefs_8term['reverse reflection tracking']
gamma_f = coefs_8term['forward switch term']
gamma_r = coefs_8term['reverse switch term']
k = coefs_8term['k']
# taken from eq (36)-(39) in the Roger Marks paper given in the
# docstring
Elf = Esr + (Err*gamma_f)/(1. - Edr * gamma_f)
Elr = Esf + (Erf *gamma_r)/(1. - Edf * gamma_r)
Etf = ((Elf - Esr)/gamma_f) * k
Etr = ((Elr - Esf )/gamma_r) * 1./k
coefs_12term = {}
for l in ['forward directivity','forward source match',
'forward reflection tracking','reverse directivity',
'reverse reflection tracking','reverse source match',
'forward isolation', 'reverse isolation']:
coefs_12term[l] = coefs_8term[l].copy()
coefs_12term['forward load match'] = Elf
coefs_12term['reverse load match'] = Elr
coefs_12term['forward transmission tracking'] = Etf
coefs_12term['reverse transmission tracking'] = Etr
return coefs_12term
[docs]def convert_pnacoefs_2_skrf(coefs):
'''
Convert PNA error coefficients to skrf error coefficients
Parameters
------------
coefs : dict
coefficients as retrieved from PNA
ports : tuple
port indices. in order (forward, reverse)
Returns
----------
skrf_coefs : dict
same error coefficients but with keys matching skrf's convention
'''
coefs_map ={'Directivity':'directivity',
'SourceMatch':'source match',
'ReflectionTracking':'reflection tracking',
'LoadMatch':'load match',
'TransmissionTracking':'transmission tracking',
'CrossTalk':'isolation'}
skrf_coefs = {}
if len(coefs) ==3:
for k in coefs:
coef= k[:-5]
coef_key = coefs_map[coef]
skrf_coefs[coef_key] = coefs[k]
else:
ports = list(set([k[-2] for k in coefs]))
ports.sort(key=int)
port_map ={ports[0]: 'forward',
ports[1]: 'reverse'}
for k in coefs:
coef,p1,p2 = k[:-5],k[-4],k[-2]
# the source port has a different position for reflective
# and transmissive standards
if coef in ['Directivity','SourceMatch','ReflectionTracking']:
coef_key = port_map[p1]+' '+coefs_map[coef]
elif coef in ['LoadMatch','TransmissionTracking','CrossTalk']:
coef_key = port_map[p2]+' '+coefs_map[coef]
skrf_coefs[coef_key] = coefs[k]
return skrf_coefs
[docs]def convert_skrfcoefs_2_pna(coefs, ports = (1,2)):
'''
Convert skrf error coefficients to pna error coefficients
Notes
--------
The skrf calibration terms can be found in variables
* skrf.calibration.coefs_list_3term
* skrf.calibration.coefs_list_12term
Parameters
------------
coefs : dict
complex ndarrays for the cal coefficients as defined by skrf
ports : tuple
port indices. in order (forward, reverse)
Returns
----------
pna_coefs : dict
same error coefficients but with keys matching skrf's convention
'''
if not hasattr(ports, '__len__'):
ports = ports,
coefs_map ={'directivity':'Directivity',
'source match':'SourceMatch',
'reflection tracking':'ReflectionTracking',
'load match':'LoadMatch',
'transmission tracking':'TransmissionTracking',
'isolation':'CrossTalk'}
pna_coefs = {}
if len(coefs)==3:
for k in coefs:
coef_key = coefs_map[k] + '(%i,%i)'%(ports[0],ports[0])
pna_coefs[coef_key] = coefs[k]
else:
port_map_trans ={'forward':ports[1],
'reverse':ports[0]}
port_map_refl ={'forward':ports[0],
'reverse':ports[1]}
for k in coefs:
fr = k.split(' ')[0] # remove 'forward|reverse-ness'
eterm = coefs_map[k.lstrip(fr)[1:] ]
# the source port has a different position for reflective
# and transmissive standards
if eterm in ['Directivity','SourceMatch','ReflectionTracking']:
coef_key= eterm+'(%i,%i)'%(port_map_refl[fr],
port_map_refl[fr])
elif eterm in ['LoadMatch','TransmissionTracking','CrossTalk']:
receiver_port = port_map_trans[fr]
source_port = port_map_refl[fr]
coef_key= eterm+'(%i,%i)'%(receiver_port,source_port)
pna_coefs[coef_key] = coefs[k]
return pna_coefs
def align_measured_ideals(measured, ideals):
'''
Aligns two lists of networks based on the intersection of their names.
'''
measured = [ measure for measure in measured\
for ideal in ideals if ideal.name in measure.name]
ideals = [ ideal for measure in measured\
for ideal in ideals if ideal.name in measure.name]
return measured, ideals
def two_port_error_vector_2_Ts(error_coefficients):
ec = error_coefficients
npoints = len(ec['k'])
one = npy.ones(npoints,dtype=complex)
zero = npy.zeros(npoints,dtype=complex)
#T_1 = npy.zeros((npoints, 2,2),dtype=complex)
#T_1[:,0,0],T_1[:,1,1] = -1*ec['det_X'], -1*ec['k']*ec['det_Y']
#T_1[:,1,1] = -1*ec['k']*ec['det_Y']
T1 = npy.array([\
[ -1*ec['det_X'], zero ],\
[ zero, -1*ec['k']*ec['det_Y']]]).transpose().reshape(-1,2,2)
T2 = npy.array([\
[ ec['e00'], zero ],\
[ zero, ec['k']*ec['e33']]]).transpose().reshape(-1,2,2)
T3 = npy.array([\
[ -1*ec['e11'], zero ],\
[ zero, -1*ec['k']*ec['e22']]]).transpose().reshape(-1,2,2)
T4 = npy.array([\
[ one, zero ],\
[ zero, ec['k']]]).transpose().reshape(-1,2,2)
return T1,T2,T3,T4
def error_dict_2_network(coefs, frequency, is_reciprocal=False, **kwargs):
'''
Create a Network from a dictionary of standard error terms
'''
if len (coefs.keys()) == 3:
# ASSERT: we have one port data
ntwk = Network(**kwargs)
if is_reciprocal:
#TODO: make this better and maybe have phase continuity
# functionality
tracking = coefs['reflection tracking']
#s12 = npy.sqrt(tracking)
#s21 = npy.sqrt(tracking)
s12 = sqrt_phase_unwrap(tracking)
s21 = sqrt_phase_unwrap(tracking)
else:
s21 = coefs['reflection tracking']
s12 = npy.ones(len(s21), dtype=complex)
s11 = coefs['directivity']
s22 = coefs['source match']
ntwk.s = npy.array([[s11, s21],[s12,s22]]).transpose().reshape(-1,2,2)
ntwk.frequency = frequency
return ntwk
else:
p1,p2 = {},{}
for k in ['source match','directivity','reflection tracking']:
p1[k] = coefs['forward '+k]
p2[k] = coefs['reverse '+k]
forward = error_dict_2_network(p1, frequency = frequency,
name='forward', is_reciprocal = is_reciprocal,**kwargs)
reverse = error_dict_2_network(p2, frequency = frequency,
name='reverse', is_reciprocal = is_reciprocal,**kwargs)
return (forward, reverse)