Group delay from S21

LvW said:

* In your post #4 and post#6 you spoke about the propagation delay (in space between A and B), which in this context is very „questionable“ (as prooved by other thread contributors).

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I think it's time to get back to (a) the textbooks or (b) your network analyzer and do the experiment. For propagation in space and other non-dispersive media, group delay is constant over frequency, and equal to the propagation delay.

LvW said:

Hi albbg,

*The original question was about the concept/meaning of the term group delay (post#1).
* In your post #4 and post#6 you spoke about the propagation delay (in space between A and B), which in this context is very „questionable“ (as prooved by other thread contributors).

But I think, the questioner would like to know: Which signal is delayed if compared with which other signal?
And this cannot be answered using only the phase properties (delay) of two discrete frequencies f1 and f2 at the output of a system.

LvW

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Instead of debating here, go on the web and search the definition of GD. I posted one link by Wikipedia, read that. This is a forum with people giving their own opinion only. GD has been described in detail in many books that have gone through peer reviews. I think you'll find your answer there.

Far as my concern, GD is time domain issue. Maybe you can represent by changing phase or what not, I really have not look into this. There is already a straight correlation of velocity of propagation for different frequency with the dielectric loss as I posted in post #15. Those are formulas widely accepted and are in most EM text books that clearly explained the velocity varies for different frequency under lossy medium. I don't know what else to clarify.

Of cause, people can force the issue of change in velocity with frequency can be interpreted as change of phase with change of frequency \[ \frac {\partial \varphi}{\partial \omega}\]!!!!

LvW said:

Hi albbg,

Of course, I agree to your calculation in post#38. However, I am afraid, there is something like a misunderstanding between us.

LvW

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Hi LvW,

Yes, I think there is some misunderstanding.
However i think my contributes are pertinent. In fact there is no difference considering just one frequency at a time (as I did) or a spectrum of simultaneous frequencies; of course everything must be linear (no IM) products.
We are not comparing the phase of two generic different frequencies (makes no sense), but how the phase of two different frequency behaves applying a time delay: is very different.
So if we consider instead of two CW, as in my previuos post, a composite signal, f.i. an AM modulation still the GD applies to the frequencies composing the AM spectrum, that is comparing the output signal with the input one you will see:

the ouput modulation envelope delayed with respect of the input evelope if GD is positive
the ouput modulation envelope anticipated with respect of the input evelope if GD is negative

This second apparently contradict the causality. In effect the modulant signal is slower than the modulation frequency. Let's consider in input a peak at a certain value of envelope; this value (or a value very close to it) is already present within a period of the modulation frequency before this peak. When a negative GD is applied this value is just carried before with respect to the input due to the phase shift of the sine function acting as carrier. This means the information (evelope level) is already there, but is only carried before due to the phase shift of the carrier function (since it is periodic, anticipation can be seen as delay of more tha a semiperiod). Then no causality principle is violated. Probably I've been not so clear as I hoped to be, but I'm not able to explain it better, at least in English.

Alan0354, I think this discussion is interesting more than searching here and there. You are not costrained to follow it.

albbg said:

the ouput modulation envelope delayed with respect of the input evelope if GD is positive
the ouput modulation envelope anticipated with respect of the input evelope if GD is negative

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Yes - this exactly describes my understanding of the term "group delay" (in accordance with the mathematical derivation of this term, which is the negative slope of the corresponding system phase function).
As a special case - this "envelope" can be the compound signal of two frequencies only.
During discussion of all the delays (propagation delay, group delay, signal delay,..) we always have to ask WHICH physical quantity is delayed.