When we study about calibration, usually 12 error terms 8 error term are found along with various method like TRL , LRL , SOLT etc.
When we see any two port VNA we have a1,a2,b1,b2, r1, r2 . we need to calibrate using these terms only.
1. How can we find calibration parameters from the above 4 parameters (a1,b1, etc) like ESR，ESF ,ELF etc?
2. What minimum parameters I need to use from 12 error terms for manual calibration?#
I totally agree, but i think i am not so good in mathematics , let us consider PNA series two port network analyzer with one source, we only have a,b, r1,r2 receivers。 or for further simplicity let us consider old 8530 or 8510 which has same receiver's name as described Dr Joel books, i just want to ask we have only a1, a2, b1 , b2, (before S parameter's unit) . how to actually calculate E11, E01 or E22 , E23 ? do we have any other way to calculate ?
i want to calculate them for free space measurement , your alternative solution for calibration of free space measurement is greatly appreciated.
@ Zee on Sep 6, 2018 10:26 AMFirstly, here is how you associate the PNA receiver names with the more common receiver names used in most calibration literature:
PNA Rcvr Name Common Rcvr Name
------------------------------------------------------------
A b1
B b2
C b3
D b4
R1 a1
R2 a2
R3 a3
R4 a4
The error terms you are asking about are computed from solving a matrix of equations based on measurements of known standards. So for example if you consider a 1 port calibration scenario, the following equations give you the 3 error terms you need Directivity (e00), Port Match (e11) and Tracking (e10e01):
the slide above is from a lecture by Doug Rything, who basically spearheaded the introduction of modern automated VNAs. the Full presentation can be found here.
As for free-space measurements, that's not my area of expertise, but maybe one of the other folks on the forum might chime in here.
Chapter 3 of the book "Handbook of Microwave Component Measurements" by Dr. Joel Dunsmore has an extensive coverage of various VNA calibration techniques that the formulas for calculating the error terms from the standard measurements.