Computing uncertainty of S21dB, from measured 2-port S-parameters

[Tomo Yokoyama]

Hi, I have the corrected 2-port S-parameters, with rep n = 30.  I am trying to compute the uncertainty for S11dB and S21 dB.  I am doing this with Matlab, using Matlab-UncLib, outside of VNA tools.  Looks like S11dB uncertainty is believable.   I am having problems with S21dB uncertainty and also computing the mean value.  Here are my computing steps"

1)  compute the mean across n = 30, per freq

meas(k,:)  = [meas_s11r meas_s11i  meas_s21r ...  meas_s22r meas_s22i]  % 8 variables

input_values = mean(meas,1);

input_covar = cov(meas) ./ size(meas,1);

inputs = unc(input_values, inputs_covar);

2) define output variables; s21dB

 

s21r=inputs(3); s21i=inputs(4);

s21dB= 20.*log10(sqrt(s21r.^2 + s21i.^2))

the computed s21dB has the standard uncertainty, but it is too large than expected.

Also, the computed s21dB (center) value from the mean of s21r and s12r are too large.

the mean of S21dB, computed from the individual s21 (i.e., not from the mean of s21) is much less.  

Pls help me to correctly compute the uncertainty of S21dB.  I think I am missing some important steps.    Thanks. Tomo

[Tomo Yokoyama]

Follow up:  Looks like my covariance for S21 r/ i is very large.

I think conversion may be right U(s21dB) = 8.686* u(|s21|) / |S21|?

[Michael Wollensack METAS]

Hi,

your conversion looks right, see

https://www.wolframalpha.com/input?i=D%5B20*log10%5Bx%5D%5D

Regards

Michael