For an ideal transmission line, is the time delay at DC and RF frequencies the same?

For an ideal transmission line, is the time delay at DC and RF frequencies the same?

What is exactly going on with the delay at the static DC frequency?

first of all, what is static DC frequency? if it is DC, then how it could have frequency?
i think, in case of DC time delay is less than that in rf signal.

This is group delay which defines how long it takes a signal to traverse a network, or its transit time.

Group delay (s) = ΔΦ/Δω

You compute it from S21 phase.

Simulate it in AWR, you can find result. For ideal trans line, it's same for DC and any freq. But if your delay network is not ideal, say have capacitor or inductor, the result is different. DC delay should be greater than RF.

Dispersion - Microwave Encyclopedia - MicroWaves101.com

Could be more precise?

DC carries no signal I thought? Plus, there is no wave can propagate at DC, so it bothers me when thinking of delay at DC。

---------- Post added at 17:03 ---------- Previous post was at 16:55 ----------

i tend to think they are the same, but haven't straight out the reAsoning yet. I am referring to the perfect TEM line case. Let's not consider secondary parasitic effects yet.

CNM, If you look at the group delay definition, there is a Δω which refers to frequency, why did you talk about DC signal?
There is no sense to speak about group delay with DC signal.

If you simply replace DC by low frequency, many words could be safed.

You are absolutely right. It is the special frequency of "DC" that is giving trouble.

Any comments on what happens at "DC"?

To transform a complex time domain signal into frequency domain, it is often true that it contains DC component. Static field establishes at the speed of light. I don't know...I am just asking for different opinions on this.

Delay at DC frequency is a contradiction in terms, because you can't determine a delay of a steady quantity.

And it's of no practical or theoretical interest, in my opinion.

That is very interesting. So AWR tells us delay is the same for DC and any frequency.

I suspect ADS will tell the same story. If this is true, I speculate that at DC the field establishment time is the same as signal propagation time.

It is difficult to deal with DC frequency. However if we consider the problem in time domain: suppose a voltage pulse is feed into one side, we can get the the pulse after a delay on the other side. A pulse does include DC components. I think the group delay may originally come from energy transferring.

I think, there's no doubt about the propagation speed of TEM waves at low frequencies, and there's no discontinunity on the passage to the limit to zero. I guess, you'll find the answer in any theoretical electrical engineering textbook. But what's the actual problem you're chasing after?

P.S.: I assume, that φ(ω) of the "delayed" TEM wave is continuous and continuously differentiable at ω=0. Then the group delay dφ/dω exists and is equal for zero and "near zero" frequencies.

Thank you. There is something in your comment..

---------- Post added at 07:55 ---------- Previous post was at 07:48 ----------

It is just one of those very basic thing in our everyday engineering life....that many people (include myself) takes for granted. I do find myself not really understand this. I would like to find the correct answer and also understand the answer better. It calls for extensive and in-depth physics knowledge to get a clear idea on what is right, and why it is right.

So far, I am still thinking the delay at DC is the same as that at any other frequency. By the way, I am not religious about any EDA tool, but I have to give some credits to MWO or ADS, unless some one can give me a good reason for not to trust the results from MWO or ADS on this.

---------- Post added at 08:07 ---------- Previous post was at 07:55 ----------

Are you saying that there is a step in delay, at non-DC frequency having a fixed delay, but at DC frequency, it suddenly jumps down to 0 delay?

At DC, I would say that delay is defined by electrons speed? I'm wrong?

How fast do they travel? Should be a very small delay close to zero as everybody say.

If you're familiar with the mathematical terms, you'll understand, that I said just the opposite. It's a reasoning, why you can assume the delay at DC to be equal to the value at frequencies > 0, although it can't be observed.

You didn't tell about an actual problem, just a general remark about things taken as granted.

I read your comments again, yes, you said the opposite. I am not assuming they are the same, but trying to find if they are the same. It is not a general remark. It is more like a practical bandwidth definition for many practical TRL delay configurations. It probably can be observed, not directly by human being, but indirectly with the help of equipment, since the delay time is too small for most occasions.

---------- Post added at 08:04 ---------- Previous post was at 08:01 ----------

It is the field speed, not the electron drift speed. It is very small (pS, nS etc...) compared to the "second" that human are normally used to.

I guess it depends on how you defind "delay".

If you had a battery and a switch at one end of a cable, and closed the switch at time 0+, the voltage at the far end of a cable will show up at a time that is approximately C/√εr of the cable (C=speed of light in a vacuum)

On the other hand, if you stuffed one electron into one end of the cable, and let current flow, it would take MUCH longer for THAT one specific electron to pop out the other end (if you can even really think that way considering quantum mechanics).