My question deals with the calculation of the measurement uncertainty with using the time-domain (TD) option of VNAs (in my case 8510C or PNA). There exist sophisticated ways how to calculate the measurement uncertainty in the frequency domain (FD) and the main sources of the uncertainty are usually known.

On the other hand, there exist ways how to improve the results obtained in the FD with use of TD techniques and how to minimize several systematic errors (either directly in VNA, or by subsequent computer postprocessing). The question is, what is the uncertainty of such TD corrected data when I know the uncertainty of the data obtained in FD?

For me there are too many unknowns in the process: to calculate the uncertainty resulting from the DFT algorithms, I have to know the A/D converter quantization uncertainty, effective number of bits, parameters of the window used for gating etc. Also I have problems with the conversion of the uncertainties between TD and FD, since they are correlated in a complicated manner.

Does anyone have experience with that? I have found only works dealing with TD correction techniques of data from FD, but no uncertainty analysis of such process.

Martin Hudlicka

Czech Metrology Institute

Prague, Czech Republic

On the other hand, there exist ways how to improve the results obtained in the FD with use of TD techniques and how to minimize several systematic errors (either directly in VNA, or by subsequent computer postprocessing). The question is, what is the uncertainty of such TD corrected data when I know the uncertainty of the data obtained in FD?

For me there are too many unknowns in the process: to calculate the uncertainty resulting from the DFT algorithms, I have to know the A/D converter quantization uncertainty, effective number of bits, parameters of the window used for gating etc. Also I have problems with the conversion of the uncertainties between TD and FD, since they are correlated in a complicated manner.

Does anyone have experience with that? I have found only works dealing with TD correction techniques of data from FD, but no uncertainty analysis of such process.

Martin Hudlicka

Czech Metrology Institute

Prague, Czech Republic

First, you really need to be more specific when you say "uncertainty in time domain". As an analogy, if you asked, "what is the uncertainty of an S-parameter measurement", I would tell you "It's between 0.02 dB and 100 dB)" (now is that any help? no).

Each parameter will have it's own uncertainty, and the uncertainty will depend upon the parameter measured.

Next, uncertainty in the frequency domain depends upon the standards used to correct, but there is strong correlation. For example, if you use and open and short for the 1 port cal, which have uncertainty in the length, the uncertainty in the frequency domain is given as uncorrelated, but in fact it is strongly correlated across frequency, and therefor results in a very specific delay error. On the other hand, if you used data based standards, the uncertainty across frequency may not be correlated, and so you cannot say anything about the effect on time domain.

The above refers to time domain data, but you imply that you are using time domain gating to improve frequency domain data. Just FYI, in the 8410 and PNA, gating is performed in the frequency domain, not the time domain, through a convolution process. It's mathematically equivalent, but the data is never really converted to the time domain. In gating, masking is a big effect. The masking effect can be determined in some specific cases (I demonstrated one in my thesis),but in general it's quite complicated as well.

You might try looking at some of the peeling algorithm work that has been done (in the time domain), or something called "pencil-matrix" algorithms (I don't have much experience in these).

Sorry if this is a long list of "how hard it is" but it is a pretty broad question, good grist for new research.