IN3LBQ on the Hühnerspiel (Amthorspitze) - photo by IN3OTD

Homemade VNA calibration kit

Having built a couple of vector network analyzers (VNAs), the N2PK design and a homemade one based on the six-port concept and having also recently bought one, a venerable 8753C, I needed some known reference impedances to properly calibrate them. The most common VNA calibration method (aptly named SOLT) uses three reference loads to calibrate each port, which usually are (approximately) a short circuit an open circuit and a 50 Ω load; an additional standard, a thru, is used to connect the two ports together for characterizing the transmission path. These known reference impedances are called the calibration kit.
While, in principle, perfect reference impedances could be built, in practice the short, open and load are only approximations of the ideal impedances they should represent and most of the difficulty in building a calibration kit is in characterizing these imperfections; I had the opportunity to do some measurements with a lab-grade VNA, which, after a proper calibration with its own calibration kit, was used to characterize my homemade reference impedances. This allows to obtain a sort of "secondary standards", which, considering the amateur radio use, will be of good enough quality, at least at not-too-high frequencies.
Separate pages show the measurements results for homemade SMA female and SMA male standards (and for not-so-good SMA male standards).
To be able to use these loads as calibration standards for a VNA, they characteristics must be expressed in terms of the standards model every VNA implements; for historical and practical reasons, many VNAs need to have the calibration standards defined in terms of a simple model - only modern VNA can directly use the S-parameters of the calibration standards (the so-called data-based model).
The next section describes how to derive the standards models for the HP 8753C VNA.

Calibration kit modeling for the HP 8753C

The old HP VNAs, like the 8753 family, have always used the same model for the calibration standards definition [1], [2]; newer VNAs (PNAs, ENAs, etc.) allow using also additional models.
For the 1-port standards considered here the model is a lossy transmission line terminated by a defined load; the lossy transmission line characteristics are described by using the offset delay, offset loss and offset Z0 terms, while the termination loads are defined using a frequency-dependent inductance and capacitance respectively for the short and open standards and a perfect termination for the load standard (see [2] for all the details).
Moreover, it turns out that some early HP network analyzers designed for the lower microwave frequencies do not use the frequency-dependent inductance model, but just assume an ideal short [3]; this because below approximately 6 GHz the inductance term can be modeled using the offset delay (while the open standard capacitance starts to become important much lower in frequency) [4].

The allowable ranges for the various parameters for the HP8753C are summarized in the following tables:

Short model

offset delay offset loss offset Z0 L0 L1 L2 L3
± 9 s 0 to 10000 TΩ/s 1e-3 to 500 Ω ± 0 pH ± 0 1e-24 F/Hz ± 0 1e-33 F/Hz2 ± 0 1e-42 F/Hz3

Open model

offset delay offset loss offset Z0 C0 C1 C2 C3
± 9 s 0 to 10000 TΩ/s 1e-3 to 500 Ω ± 10000 fF ± 10000 1e-27 F/Hz ± 10000 1e-36 F/Hz2 ± 10000 1e-45 F/Hz3

GNU Octave script for computing the models coefficients

Under construction...

Here is a script for GNU Octave to compute the standard models coefficients from the measured loads S-parameters.
To run the script, the nonlinear optimization library NLopt and the S-parameter toolbox by Tudor Dima (contact him to obtain a copy) are needed.

References:

[1] Agilent, "Specifying Calibration Standards for the Agilent 8510 Network Analyzer," Application Note 8510-5B
[2] Agilent, "Specifying Calibration Standards and Kits for Agilent Vector Network Analyzers," Application Note 1287-11
[3] Agilent Technical Forum, "HP 85032F Cal Kit" thread
[4] Agilent Technical Forum, "Type N cal kit data needed" thread