### Poles and Zeros

In the simple RC-filter example of §E.4.3, the transfer function is

*pole*at , and we can say there is one

*zero at infinity*as well. Since resistors and capacitors always have positive values, the time constant is always non-negative. This means the impulse response is always an exponential

*decay*--never a growth. Since the pole is at , we find that it is

*always in the left-half plane*. This turns out to be the case also for any

*complex*analog one-pole filter. By consideration of the partial fraction expansion of any , it is clear that, for stability of an analog filter,

*all poles must lie in the left half of the complex plane*. This is the analog counterpart of the requirement for digital filters that all poles lie inside the unit circle.

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Driving Point Impedance

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The Continuous-Time Impulse