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Transfer Function

Since the input and output signals are defined as $ v_e(t)$ and $ v_C(t)$ , respectively, the transfer function of this analog filter is given by, using voltage divider rule,

$\displaystyle H(s) = \frac{V_C(s)}{V_e(s)}
= \frac{\frac{1}{Cs}}{R+\frac{1}{Cs}},
= \frac{1}{RCs+1}
= \frac{1}{RC}\frac{1}{s+\frac{1}{RC}}
\isdef \frac{1}{\tau} \frac{1}{s+\frac{1}{\tau}}.
$

The parameter $ \tau\isdef RC$ is called the RC time constant, for reasons we will soon see.


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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