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This tutorial describes how to use skrf to calibrate data taken from a VNA. For an introduction to VNA calibration see this article by Rumiantsev and Ridler *, for an outline of different calibration algorithms see Doug Ryttings presentation *. If you like to read books, then you may want to checkout _ .
What follows is are various examples of how to calibrate a device under test (DUT), assuming you have measured an acceptable set of standards, and have a corresponding set ideal responses. This may be reffered to as offline calibration, because it is not occuring onboard the VNA itself. One benefit of this technique is that it provides maximum flexibilty for non-conventional calibrations, and preserves all raw data.
Creating a Calibration¶
- a list of measured
- a list of ideal
Network elements in each list must all be similar (same number
of ports, frequency info, etc) and must be aligned to each other,
meaning the first element of ideals list must correspond to the first
element of measured list. Self calibration algorithms, such as TRL, do
not require predefined ideal responses.
This example code is written to be instructive, not concise. To
construct a one-port calibration you need to have measured at least
three standards and have their known ideal responses in the form of
Network can be created from touchstone files,
a format all modern VNA’s support.
In the following script the measured and ideal touchstone files for a
conventional short-open-load (SOL) calkit are in folders
ideal/, respectively. These are used to create a OnePort
Calibration and correct a measured DUT
import skrf as rf from skrf.calibration import OnePort ## created necessary data for Calibration class # a list of Network types, holding 'ideal' responses my_ideals = [\ rf.Network('ideal/short.s1p'), rf.Network('ideal/open.s1p'), rf.Network('ideal/load.s1p'), ] # a list of Network types, holding 'measured' responses my_measured = [\ rf.Network('measured/short.s1p'), rf.Network('measured/open.s1p'), rf.Network('measured/load.s1p'), ] ## create a Calibration instance cal = rf.OnePort(\ ideals = my_ideals, measured = my_measured, ) ## run, and apply calibration to a DUT # run calibration algorithm cal.run() # apply it to a dut dut = rf.Network('my_dut.s1p') dut_caled = cal.apply_cal(dut) dut_caled.name = dut.name + ' corrected' # plot results dut_caled.plot_s_db() # save results dut_caled.write_touchstone()
This example achieves the same task as the one above except in a more concise programmatic way.
import skrf as rf from skrf.calibration import OnePort my_ideals = rf.load_all_touchstones_in_dir('ideals/') my_measured = rf.load_all_touchstones_in_dir('measured/') ## create a Calibration instance cal = rf.OnePort(\ ideals = [my_ideals[k] for k in ['short','open','load']], measured = [my_measured[k] for k in ['short','open','load']], ) ## what you do with 'cal' may may be similar to above example
Naturally, two-port calibration is more involved than one-port. skrf
supports a few different two-port algorithms. The traditional
algorithm uses the 12-term error model. This algorithms is
straightforward, and similar to the OnePort example.
EightTerm calibration is based on the algorithm described in
, by R.A. Speciale. It can be constructed from any number of
standards, providing that some fundamental constraints are met. In
short, you need three two-port standards; one must be transmissive, and
one must provide a known impedance and be reflective. Note, that the
word 8-term is used in the literature to describe a specific error
model used by a variety of calibration algorihtms, like TRL, LRM, etc.
EightTerm class, is an implementation of the algorithm cited
above, which does not use any self-calibration.
One important detail of using the 8-term error model formulation is that switch-terms may need to be measured in order to achieve a high quality calibration (thanks to Dylan Williams for pointing this out). These are described next.
Originally described by Roger Marks _ , switch-terms account for the fact that the 8-term (aka error-box ) model is overly simplified. The two error networks change slightly depending on which port is being excited. This is due to the internal switch within the VNA.
Switch terms can be directly measured with a custom measurement
configuration on the VNA itself. skrf has support for measuring
switch terms in the
skrf.vi.vna module, see the HP8510’s
skrf.vi.vna.HP8510C.switch_terms, or PNA’s
skrf.vi.vna.PNA.get_switch_terms . Without switch-term measurements,
your calibration quality will vary depending on properties of you VNA.
Using one-port ideals in two-port Calibration¶
Commonly, you have data for ideal data for reflective standards in the
form of one-port touchstone files (ie
.s1p). To use this with skrf’s
two-port calibration method you need to create a two-port network that
is a composite of the two networks. The function
skrf.network.two_port_reflect does this
short = rf.Network('ideals/short.s1p') shorts = rf.two_port_reflect(short, short)
Two-port calibration is accomplished in an identical way to one-port, except all the standards are two-port networks. This is even true of reflective standards (S21=S12=0). So if you measure reflective standards you must measure two of them simultaneously, and store information in a two-port. For example, connect a short to port-1 and a load to port-2, and save a two-port measurement as ‘short,load.s2p’ or similar
import skrf as rf from skrf.calibration import SOLT # a list of Network types, holding 'ideal' responses my_ideals = [ rf.Network('ideal/thru.s2p'), rf.Network('ideal/short, short.s2p'), rf.Network('ideal/open, open.s2p'), rf.Network('ideal/load, load.s2p'), ] # a list of Network types, holding 'measured' responses my_measured = [ rf.Network('measured/thru.s2p'), rf.Network('measured/short, short.s2p'), rf.Network('measured/open, open.s2p'), rf.Network('measured/load, load.s2p'), ] ## create a SOLT instance cal = SOLT( ideals = my_ideals, measured = my_measured, ) ## run, and apply calibration to a DUT # run calibration algorithm cal.run() # apply it to a dut dut = rf.Network('my_dut.s2p') dut_caled = cal.apply_cal(dut) # plot results dut_caled.plot_s_db() # save results dut_caled.write_touchstone()
Saving and Recalling a Calibration¶
Calibration’s can be written-to and
read-from disk using the temporary storage container of pickles. Writing
can be accomplished by using
and reading is done with
rf.read(). Since these functions rely on
pickling, they are not recomended for long-term data storage. Currently
there is no way to achieve long term storage of a Calibration object,
other than saving the script used to generate it.
|||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|
|||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|