Re: Negative Group Delay: A -180° Phase Shift After All?


Clay wrote:
Andor wrote:
A while back, Jani posted a link to an interesting paper:

Also this enlightening paper about negative group delays in electronic
circuits might be of intrest to you:

http://www.physics.berkeley.edu/research/chiao/morgan/supcir.html

In it is described a simple active resonance filter with some
initeresting properties. After reading more closely, as usual, I'm
confused. Formula (4) states the transfer function of the filter
depicted in Fig. 1. My electronic days are a while back, yet I find the
two minus signs in the denominator of the transfer function in (4)
suspicious. Can someone more knowledgable in electronics verify this
transfer function?

Regards,
Andor

Andor,

I agree with you about the two minus signs in the denominator. When I
work it out I have plus signs in the denominator on the reactive
elements.

This kind of begs the question how the author arrived at the
measurements depcited in Fig. 2. The phase response of the system as
you and I see it is the inverted (multiplied by -1) phase response
shown in Fig. 2. The only possible way to measure the inverted phase
response is to have swapped the reference output and the device under
test output into the oscilloscope (makes one wonder about the
measurements shown in Fig. 5).

Luckily, he introduces a second sign error in (7) (definition of the
group delay), so the theoretical group delay shown in Fig. 3 is correct
again.

It should also be interesting to hear the author explain how a real
input signal into the resonance filter produces a complex output, see
eq. (8).

Regards,
Andor

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