Feedback amplifiers comprising long feedback paths can be coined with the name of delayed feedback amplifiers, in the sense that, the long feedback acts as a delay element inside the feedback loop of the amplifier.
Looking into the dynamics of such an amplifier, it is easily recognized that the characteristic equation is no longer polynomial. Having this in mind, what would be the impact of the delay (long path) on the amplifiers closed-loop bandwidth? Will it be different than the bandwidth of a reference amplifier with the same closed loop gain, but a shorter feedback path?
This may seem rather strange and even contrary to common knowledge. It is widely accepted, that long paths contribute with large parasitic effects which contribute to reduce bandwidth in amplifiers. However, when considering feedback amplifiers, this may not be the case. From the bandwidth point of view, long feedback paths can represent advantages.
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I would expect that a long feedback path would pose some issues with transient stability of the circuit, depending on the situation the circuit is designed to address. A low bandwidth on the feedback path is necessary to ensure cicuit stability in this case. There is a fair amount of theory on infinite impulse response circuits that would be insightful in regards to the tradeoffs in this situation.
I'll chip in an answer. While I have engineering friends who claim pure time-delay elements deserves special attention when analyzing feedback-amplifier stability, I think in general it's not always necessary to make a big deal about it. Keep in mind that a simple pole, such as from an R-C filter, has an associated time delay t = RC. The pole frequency for this time delay is f = 1 / 2pi RC = 1/2pi t. Aha, there you have it, for starts just add another feedback pole in your analysis with the long-path delay element, at f = 1/2pi t.
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