Homemade VNA calibration kit

Under construction...

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.
The measurements results for the SMA female standards and for the SMA male standards are shown in the following paragraphs below.
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).
A section below shows the models for the HP 8753C VNA.

SMA female calibration kit measurements

The following chapter shows several reference impedances having an SMA female port.
Some time ago I found on ebay a quite cheap lot of new old stock Molex 73251-1260 female SMA connectors; they are well suited to build some simple loads as they have a very short center pin and four standard ground legs, as they were intended to be mounted on a PCB while minimizing the connection parasitics (hence the surface-mount style center conductor).

Open

This is simply a bare SMA connector - no additional components. In theory the center conductor should be shielded from the external environment, i.e. enclosed in a conductive case, but in practice, at the relatively low frequencies involved here, this has been found to make no difference.

Molex_73251-1260_open reference load Molex_73251-1260_open reflection coefficient

Short - style 1 (SnPb solder only)

This reference short circuit was built by simply flooding the back of the connector with enough solder to fill the void between the center conductor and ground. Not a very elegant way, but seems to work quite well.

Molex_73251-1260_short_SnPb reference load Molex_73251-1260_short_SnPb reflection coefficient

Short - style 2 (Cu disk)

This is another version of the short circuit reference; a small copper disk was cut out from a thin copper tape with just the right size to fill the void between the center conductor and the surrounding ground and then soldered down. Performances seems about the same as the first version or maybe even a little worse (!).

Molex_73251-1260_short_Cu reference load Molex_73251-1260_short_Cu reflection coefficient

50 Ω loads

For the 50 Ω load several possibilities were tried, using a different number of resistors in parallel, since the common wisdom is that two or three resistor in parallel are better than a single one, but I did not find any actual measurements to support this statement. Not surprisingly, that seems to be true...

Load - 1 x 49.9 ohm

A reference load built using a single Panasonic ERA3AEB49R9V resistor (49.9Ω 0.1 %, 0603 size, 100 mW max).

Molex_73251-1260_1x49.9ohm reference load Molex_73251-1260_1x49.9ohm reflection coefficient

Load - 2 x 100 ohm

A reference load built using two Panasonic ERA3AEB101V resistors (100Ω 0.1 %, 0603 size, 100 mW max) in parallel.

Molex_73251-1260_2x100ohm reference load Molex_73251-1260_2x100ohm reflection coefficient

Load - 3 x 150 ohm

A reference load built using three Panasonic ERA3AEB151V resistors (150Ω 0.1 %, 0603 size, 100 mW max) in parallel.

Molex_73251-1260_3x150ohm reference load Molex_73251-1260_3x150ohm reflection coefficient

Load - 4 x 200 ohm

A reference load built using four Panasonic ERA3AEB201V resistors (200Ω 0.1 %, 0603 size, 100 mW max) in parallel.

Molex_73251-1260_4x200ohm reference load Molex_73251-1260_4x200ohm reflection coefficient

SMA male

The following chapter shows several reference impedances having an SMA male port.
Unfortunately I was not able to find some quality surface-mount style SMA male connectors, so I had to resort to using some cheap PCB-mount types that can be found on many places on the internet under the part number S01-SPPT4-11BS00. By simply looking at them, it's clear that their quality is far inferior to the nice Molex female SMA mentioned previously; every connector has some different issues, like dielectric protruding slightly from the body, not cleanly cut, center conductor slightly recessed and so on. For sure I would be very worried at the thought of using them on a professional VNA equipped with precision 3.5 mm connectors!

Open

Simply a bare SMA connector with the center pin trimmed down with a rotary tool the be flush to the dielectric. Also in this case, having a shield or not around the ground pins made no difference, at the frequencies used here.

S01-SPPT4-11BS00_open reference load S01-SPPT4-11BS00_open reflection coefficient

Short (copper disk)

A connector shorted on the back with a small copper disk cut out from thin copper tape; the copper disk just filled the void between the center conductor and the surrounding ground and was then covered with tin-lead solder.

S01-SPPT4-11BS00_short_Cu reference load S01-SPPT4-11BS00_short_Cu reflection coefficient

note that the return loss goes positive at high frequency; as this is not actually possible with a passive load, this likely means there was some issue with the VNA calibration... did not have time to investigate.

50 Ω loads

Also in this case several styles were tried to build a 50 Ω load, using a different number of resistors in parallel. Again, not surprisingly it was found that paralleling a few resistors gives better performances than a single one..
Some of the loads apparently has a low-frequency return loss better than 70 dB; while this number might not be accurate, since it depends a lot on the quality of the initial VNA calibration, it indicates that at low frequency the load is indeed very close to 50 Ω.

Load - 1 x 49.9 ohm

A reference load built using a single Panasonic ERA3AEB49R9V resistor (49.9Ω 0.1 %, 0603 size, 100 mW max).

S01-SPPT4-11BS00_1x49.9ohm reference load S01-SPPT4-11BS00_1x49.9ohm reflection coefficient

Load - 2 x 100 ohm

A reference load built using two Panasonic ERA3AEB101V resistors (100Ω 0.1 %, 0603 size, 100 mW max) in parallel.

S01-SPPT4-11BS00_2x100ohm reference load S01-SPPT4-11BS00_2x100ohm reflection coefficient

Load - 3 x 150 ohm

A reference load built using three Panasonic ERA3AEB151V resistors (150Ω 0.1 %, 0603 size, 100 mW max) in parallel.

S01-SPPT4-11BS00_3x150ohm reference load S01-SPPT4-11BS00_3x150ohm reflection coefficient

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

SMA female short model

As said above, the HP 8753C does not allow to specify a parasitic inductance for the short as this is assumed to be zero, so only the offset transmission line parameter can be used to model this standard behavior. Here are the optimization results

offset delay offset loss offset Z0 L0 L1 L2 L3
32.6 ps 42.1 MΩ/s 52.4 Ω 0 pH 0e-24 H/Hz 0e-33 H/Hz2 0e-42 H/Hz3

Fitting results:

This is the residual error across the whole frequency range: the overall RMS error is around -55 dB but the error at high frequencies becomes quite high..

SMA female open model

The open model includes a frequency-dependent parasitic capacitance, which allows to obtain good results over a wide frequency range. In the optimization results below the offset Z0 has been fixed at 50 Ω since its value did not influence much the final results:

offset delay offset loss offset Z0 C0 C1 C2 C3
35.5 ps 10.9 MΩ/s 50 Ω -4.8 fF -1071.7e-27 F/Hz 2228.6e-36 F/Hz2 -218.4e-45 F/Hz3

Fitting results:

This is the residual error across the whole frequency range: the overall RMS error is around -64.5 dB.

Extreme optimization

These are the model parameters using an "extreme" optimization - setting the optimization goal to the minimum RMS error over the entire frequency range and without constraining the parameters to assume only "physical" values.

offset delay offset loss offset Z0 C0 C1 C2 C3
10.6 ps 9.96 MΩ/s 111.7 Ω 613.9 fF 1806.7e-27 F/Hz -9027.7e-36 F/Hz2 718.4e-45 F/Hz3

Note that the offset delay and impedance are quite far from the actual values, but this allowed a better fit at high frequencies:

This is the residual error across the whole frequency range: the overall RMS error is around -70 dB.

SMA female load model

Of all the loads built, the one that fitted best the 8753C load model is the one made with two 100Ω resistors in parallel, so only the results for this load are presented.

offset delay offset loss offset Z0
76.6 ps 5.03 MΩ/s 50.9 Ω

Fitting results:

This is the residual error across the whole frequency range: the overall RMS error is around -47 dB but the error at high frequencies becomes quite high, probably because of the parasitic capacitance that cannot be accounted for in the model.


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