In general, S21 is the measurement of the complex output/Input transfer function. Complex means that it represents both amplitude (that is gain or attenuation) and phase relationship between the input and the output signals.
The group delay is the variation of the phase due to the variation of the angular frequency (with the sign changed), that is:
GD = -dφ/dω
if we know S21 at two different frequencies, let say "f1" and "f2", since ω=2•Π•f, then:
GD ≈ -phase[S21(f1)-S21(f2)]/[2•Π•(f1-f2)]
I used "≈" because the exact definition requires the limit f2 --> f1
From the s2p parameters the phase of S21 can be known directly; if instead you have imaginary and real part of S21, then:
phase(S21)=arctg[Im(S21)/Re(S21)]
you can have a huge group delay, like going from the earth to the moon, and the modulation will get thru just fine!
Sound like an incorrect generalization at first sight. I presume you mean "the group delay of this specific system". For a system that is only causing delay time, group delay is equal to delay time. But there are other possible causes of group delay respectively phase dispersion dφ/dω than delay time.This means the group delay is the time required to travel from A to B.
Yes I was just answering the sentence of LvW that said "I think, group delay has nothing to do with the time a signal needs to travel from A to B."I presume you mean "the group delay of this specific system". For a system that is only causing delay time, group delay is equal to delay time.
Please help me to clarify my view:Group delay is a useful measure of time distortion, and is calculated by differentiating, with respect to frequency, the phase response versus frequency of the device under test (DUT). The group delay is a measure of the slope of the phase response at any given frequency. Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion.
I agree to the viewpoint, that group delay has something to do with delay time (travel time, flight time, whatsoever...), because it's the same value for a class of systems. But it's a different quantity, in so far LvW is systematically right. He's referring to an important property of group delay. It's defined for systems where a delay time can be neither measured nor theoretically derived. It can be understood it as a generalization of delay time. It's mainly useful for the description of systems with frequency dependend transfer function, e.g. filters or band limited channels as mentioned by LvW. They generally expose a non-constant group delay, except for those that are designed purposeful with linear phase like FIR filters with symmetrical impulse response.Yes I was just answering the sentence of LvW that said "I think, group delay has nothing to do with the time a signal needs to travel from A to B."
I presume you meaned to write "a condition for constant group delay".A condition for GD is that the phase response of the system is a linear function of the frequency. That is if we take the dφ/dω of a linear function we get a constant.
Yes I was just answering the sentence of LvW that said "I think, group delay has nothing to do with the time a signal needs to travel from A to B."
Units of Group delay as defined is Rad/(Rad/Sec)=seg. So it is consistent with the time to travel.
here...the group delay. It is a function of the frequency ω and we colloquially say it is "'the time delay of
the amplitude envelope of a sinusoid at frequency ω".
You can read it as a prove that group delay is a different quantity respectively has "nothing to do" with signal travel time.is a discussion of negative GD which (for me) clears up my confusion regarding time delay.
I agree with your consideration except for "must ... only". The group delay plot of a low-pass filter is an example how group delay can be determined for wide band signals as well. As previously mentioned, my viewpoint is the other way around. Group delay can be applied to small band signals, where an exact absolute signal delay or "travel time" can't be determined by nature of the signal, but isn't restricted to it. In the cases, where group delay is constant over frequency, it's effectively identical to a signal delay.The parameter "group delay" must be applied to a "group" of frequencies only (e.g. a modulation signal), which are very close to each other if compared with the corresponding mean value.
I agree with your consideration except for "must ... only". The group delay plot of a low-pass filter is an example how group delay can be determined for wide band signals as well.
In the cases, where group delay is constant over frequency, it's effectively identical to a signal delay.
At first sight, I don't see a reason why group delay can't be calculated e.g. for a delay line?Yes, also agreed - with one single restriction: This kind of signal delay must be caused by phase shifts only (and not by another type of delay: storage effects, travelling time of electromagnetic waves,..)
At first sight, I don't see a reason why group delay can't be calculated e.g. for a delay line?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?