Download This Notebook: Calibration.ipynb

# Calibration¶

## Introduction¶

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 [1]*, for an outline of different calibration algorithms see Doug Ryttings presentation [2]*. If you like to read books, then you may want to checkout [3]_ .

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¶

Calibrations are performed through a Calibration class. In General, Calibration objects require two arguments:

• a list of measured Network’s
• a list of ideal Network’s

The 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.

## One-Port Example¶

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 Networks. These 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 measured/ and 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'),
]

# a list of Network types, holding 'measured' responses
my_measured = [\
rf.Network('measured/short.s1p'),
rf.Network('measured/open.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()


## Concise One-port¶

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

## 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


## Two-port Calibrations¶

Naturally, two-port calibration is more involved than one-port. skrf supports a few different two-port algorithms. The traditional SOLT algorithm uses the 12-term error model. This algorithms is straightforward, and similar to the OnePort example.

The EightTerm calibration is based on the algorithm described in [4], 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. The 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.

## Switch-terms¶

Originally described by Roger Marks [5]_ , 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)


## SOLT Example¶

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'),
]

# 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'),
]

## 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 Calibration.write, or rf.write(), 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.

Bibliography

 [3] Dunsmore, Handbook of microwave component measurements: with advanced vna techniques. Hoboken, N.J: Wiley, 2012.
 [4] 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
 [5] 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
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