A TDR gives you the characteristic impedance of a transmission line as a function of position. You can also measure the characteristic impedance of a uniform transmission line using a VNA, which gives you Zc as a function of frequency. How do the two compare? I assume that the TDR gives me a weighted sum of the frequency-dependent value, based on the rise time that I'm using -- but I'm not sure how.
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I assume that the TDR gives me a weighted sum of the frequency-dependent value, based on the rise time that I'm using -- but I'm not sure how.
Given that a DFT, Discrete Fourier Transform, is fundamentally a 'weighted sum', yes.
It's not quite as simple as just doing the FFT of one to get the other. There are some normalisations to do, and the restricted frequency ranges cause problems.
The finite rise time of the TDR limits the high frequency response. Even if the VNA itself goes down to very low frequencies (some microwave ones still go down to 9 kHz), it's still not DC, so you have to make an assumption if you are trying to go VNA -> TDR.
If you're measuring in waveguide, the frequency dispersion needs to be handled, and the frequency range is very narrow, but it can still be done with suitable assumptions.
While a VNA + suitable transform can do everything that a TDR can do, remember that a TDR is quite limited. For instance, it does not 'give you the characteristic impedance of a transmission line as a function of position' as you assert, without qualifications. Its main use is to work with a near lossless line, and show reflections that generally indicate point-like discontinuities. If there is any loss at the near end of the line, this will attenuate the reflections from the far end, distorting their amplitude. You have to make some assumptions about the line to interpret the trace from a TDR. A VNA+transform is no different, it cannot magic visibility to the far end of a lossy line, so still needs to be interpreted. Consider a length of line, an attenuator, another length of line, and a load. There is no way for any instrument, TDR or VNA, to disambiguate the combination of the attenuator, second line, and load parameters.
Neil_UK
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Thanks for your answer, Neil. Say that I have Zc from DC to 10 GHz from some EM simulation software. Do you know how I could calculate the expected TDR response (assuming a given rise time)? – qtc0 Jun 02 '23 at 17:32
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1I don't, it's been decades since being involved with that stuff at calculation level, but this might be useful, or this which has a bunch of further links in it. – Neil_UK Jun 02 '23 at 18:14
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Does a VNA allow you to locate the discontinuity? I thought it just gave you the relevant S parameter value for a unit under test. At least that's the VNA results I've seen (not an expert). – SteveSh Jun 02 '23 at 18:38
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@SteveSh You can locate discontinuities by transforming S11 to the time-domain. Some VNAs have that feature built in. Of course, you'll need to know the wave velocity to work out the physical location. There are also special transforms for dispersive transmission lines (e.g., https://ieeexplore.ieee.org/document/9447194) – qtc0 Jun 02 '23 at 19:23
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@qtco - Thanks. Sounds like that's only applicable for (uniform?) transmission lines? I don't see how that would work for something like an RF module with many active (amplifiers) and passives (switches, attenuators, etc) in the path. – SteveSh Jun 02 '23 at 19:29
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@SteveSh you can still get useful information, but yes the time-domain gets very cluttered if there are multiple paths/reflections. – qtc0 Jun 02 '23 at 21:56
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@SteveSh As soon as you hit the first loss, or gain, everything beyond that has an unknown scaling applied to it. So you have to either assume a gain, or you give up on magnitudes and just be happy with hints of positional information. That's why the main application of TDR is to find small discontinutities in an assumed lossless transmission line. – Neil_UK Jun 03 '23 at 05:39