Calibration ¶

Contents

Calibration

Intro ¶

This tutorial illustrates how to use skrf to calibrate data taken from a VNA. The explanation of calibration theory and calibration kit design is beyond the scope of this tutorial. Instead, this tutorial describes how to calibrate a device under test (DUT), assuming you have measured an acceptable set of standards, and have a coresponding set ideal responses.

skrf‘s default calibration algorithms are generic in that they will work with any set of standards. If you supply more calibration standards than is needed, skrf will implement a simple least-squares solution.

Creating a Calibration ¶

Calibrations are performed through a Calibration class. Creating a Calibration object requires at least two pieces of information:

a list of measured Network‘s
a list of ideal Network‘s

The Network elements in each list must all be similar (same #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.

Optionally, other information can be provided when relevent such as,

calibration algorithm
enforce eciprocity of embedding networks
etc

When this information is not provided skrf will determine it through inspection, or use a default value.

Saving and Recalling a Calibration ¶

Like other skrf objects, Calibration‘s can be written-to and read-from disk. Writing can be accomplished by using Calibration.write(), or rf.write(), and reading is done with rf.read().

One-Port ¶

This example is written to be instructive, not concise.

import skrf as rf


## 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.Calibration(\
        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)

# plot results
dut_caled.plot_s_db()
# save results
dut_caled.write_touchstone()

Concise One-port ¶

This example is the same as the first except more concise.

import skrf as rf

my_ideals = rf.load_all_touchstones_in_dir('ideals/')
my_measured = rf.load_all_touchstones_in_dir('measured/')


## create a Calibration instance
cal = rf.Calibration(\
        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 ¶

Two-port calibration is more involved than one-port. skrf supports two-port calibration using a 8-term error model based on the algorithm described in [1], by R.A. Speciale.

Like the one-port algorithm, the two-port calibration can handle 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.

One draw-back of using the 8-term error model formulation (which is the same formulation used in TRL) is that switch-terms may need to be measured in order to achieve a high quality calibration (this was pointed out to me by Dylan Williams).

Switch-terms ¶

Originally described by Roger Marks [2] , switch-terms account for the fact that the 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 measured with a custom measurement configuration on the VNA itself. skrf has support for switch terms for the HP8510C class, which you can use or extend to different VNA. Without switch-term measurements, your calibration quality will vary depending on properties of you VNA.

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


## created necessary data for Calibration class

# a list of Network types, holding 'ideal' responses
my_ideals = [\
        rf.Network('ideal/thru.s2p'),
        rf.Network('ideal/line.s2p'),
        rf.Network('ideal/short, short.s2p'),
        ]

# a list of Network types, holding 'measured' responses
my_measured = [\
        rf.Network('measured/thru.s2p'),
        rf.Network('measured/line.s2p'),
        rf.Network('measured/short, short.s2p'),
        ]


## create a Calibration instance
cal = rf.Calibration(\
        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()

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. There is a function in the WorkingBand Class which will do this for you, called two_port_reflect.:

short = rf.Network('ideals/short.s1p')
load = rf.Network('ideals/load.s1p')
short_load = rf.two_port_reflect(short, load)

Bibliography

[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]	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