Group delay in a receiver

• 3
Suppose you had an ideal mixer, operating with fixed LO on the high side.... and you added a "real" IF amplifier. That amplifier has negative phase slope, which is used to calculate receiver group delay. But in this case, as you sweep the RF signal, you are sweeping the IF amplifier phase backwards. Seems like this causes a negative group delay, but I am not ready to believe in time travel. Thoughts on this? Thanks for your help.

Steve
• 0
The phase response might be tricking the VNA into aliasing your measurement.
• 0
If it's a high sided LO, that mean the output frequency is being swept backwards too. So the GD (derivative of phase wrt. freq) still comes out positive.

R&S has a two-tone GD measurement technique. I have never used it, but they say it can even be used to measure satellite links. In this they talk about using a reference mixer fed from the same LO as your mixer, bringing it back up to RF, and I assume that would take care of the frequency inversion as well.

https://cdn.rohde-schwarz.com/pws/dl_downloads/dl_application/application_notes/1ef98/1EF98_1e.pdf
• 3
OK, I think I get it. The reason I asked is because of an "Excel mixer" I am playing with. Here is a page on it, it is still a mess

https://www.microwaves101.com/encyclopedias/excel-s-parameter-mixer

when I "mix" and amplifier's S-parameters to another frequency using high-side LO and look at group delay it is negative. But that is not a physical thing, just a figment of a slightly bogus way to simulate a receiver, right?

Thanks
• 0
You can achieve negative group delay in a medium with anomalous dispersion (like seawater). This just means the signal arrives prior to the carrier (group velocity > phase velocity; what makes it anomalous). Media with high insertion loss can also yield negative group delay such as just outside a bandpass filters passband.
• 3
It turns out that when you "mix" S-parameters with high-side LO, you need to take the conjugate of S21 and S12, and then group delay comes out as expected. I did not make this up, it is detailed in a paper by Dr. Dylan Williams...I'll post some updates on this shortly....

Thanks to Frauke for pointing this out. Here is the reference:

D. F. Williams, F. Ndagijimana, K. A. Remley, J. A. Dunsmore and S. Hubert, "Scattering-parameter models and representations for microwave mixers," in IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 1, pp. 314-321, Jan. 2005,
• 3
Out mixer spreadsheet has been updated to fix the high-side group delay issue, grab a copy here.

https://www.microwaves101.com/download-area#SparMixer
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