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I actually had two distinct questions relating to circuit analysis and design. The first is theoretical and the second is a question about what I've observed on other circuits.

I'm reading some undergraduate EE books (I'm an EE student in Canada) and I've gotten to the point where transfer functions of circuits are discussed in the Laplace domain. In all the texts I've read it has been stated that if the poles (roots of the denominator) are in the left of the s-plane (i.e. the real parts are negative) then the transient response will be stable (that is, it goes to 0). I can show this by deriving the characteristic equation from the poles of a low- or high-pass filter and an LRC oscillator, but I can't immediately see that this is true for transfer functions with higher-degree denominators. In a similar vein (I think), is it possible to construct physically realizable circuits that have non-stable transient responses? What about the input function? Must the poles of an input function be on the right side of the s-plane? I'm in-between academic terms at the moment so I'm not able to conveniently ask a professor.

My second question has to do with the capacitors that are placed in large numbers next to power pins for ICs and other components such as power supplies. I've had it explained to me by some that these capacitors filter the noise in the power rails; others tell me that they provide needed voltage when the circuit is loaded because of IC current draw; still others have told me it's a combination of both. However, I'm still at a loss and it's something that's really bothering me. Can anyone explain (or point me in the direction of resources that explain) WHY capacitors are needed and maybe a brief mathematical or theoretical demonstration of the results when the capacitors are or aren't attached?

I'd be grateful for any responses or links to resources.

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# Two Questions: Transfer Functions and Capacitors

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