My understanding is that "unknown thru" is based on the 8-term error model for a full two-port VNA. So I have doubts, that it can be used with the 1.5 port NanoVNA (whose 2nd port cannot transmit and has no directional coupler).
For true SOLR (aka "unknown thru") you do not only need a fully bidirectional two-port test set that can measure the full S-matrix (i.e. S11, S21, S12, S22), but actually a four receiver VNA.
There is no way around these hardware requirements. However, on a three receiver VNA, you can do a full two-port calibration (i.e. by a SOLT cal), and then determine certain parameters from the calibration data, the so-called switch terms. With the assumption that the switch terms are constant (this is usually a very good assumption), you can use them subsequently to do SOLR calibrations, even on a three receiver VNA. If I'm not mistaken this approach essentially is what Keysight calls "delta match method" which is available on their older or lower cost VNAs without four receivers.
A four receiver VNA has the ability to measure the switch terms directly. It does not need to assume that they are constant, and does not need to measure additional cal standards in a previous step to determine them.
Some more background about this: As you correctly say, SOLR is defined in terms of the 8-term error model. This model consists of two so-called error boxes at each port that correct for all imperfections. That means that it is assumed that the impedance of the physical VNA port does not change if it is switched from source to load configuration (the error boxes are constant and thus are unaware of the current port mode). The quantification of this model can be done in terms of measuring short, open, and load at each port, together with an unknown reciprocal thru. All that remains is a sign ambiguity, which essentially is due to the phase ambiguity in the thru of unknown length. Also, this step does not need a four receiver VNA. All of this is laid out in the original paper by Ferrero and Pisani which introduced the method ("Two-port network analyzer calibration using an unknown 'thru'", IEEE Microwave and Guided Wave Letters Volume 2, Issue 12, 1992).
To get rid of the assumption of a constant port match, commercial VNAs then transform the 8-term model to the conventional 12-term model (which is usually only a 10-term model by neglecting the crosstalk error terms which also do not exist in the 8-term model). The 12-term model has separate source and load port match errors for each direction. This of course, due to the larger number of unknowns, requires additional measurements: the switch terms.
The switch terms are defined as the ratio of outgoing wave and the incident wave
at one port, while the other port is configured as a source. Notice that a three receiver VNA has no way of measuring them. On four receiver VNAs they are usually measured along with the thru.
An implementation of SOLR will therefore consist of several steps: First quantify the 8-term error model by measuring SOL at each port as well as the unknown reciprocal thru. Then measure the switch terms (or recall them from memory if unable to measure them on a three receiver unit). Finally convert everything to the 12-term error model. Then the DUT can then be corrected in the usual way. Unfortunately this requires a bit more implementation effort than just using a single formula.
The switch terms only depend on the test set and should not vary much over time, at least in commercial lab grade VNAs. I have checked that with my VNA, they seem to be indeed very stable.
Home
Help
Search
Login
Register
