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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) \eqsp \frac{V_C(s)}{V_e(s)}
\eqsp \frac{\frac{1}{Cs}}{R+\frac{1}{Cs}}
\eqsp \frac{1}{RCs+1}
\eqsp \frac{1}{RC}\frac{1}{s+\frac{1}{RC}}
\isdefs \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 © 2024-09-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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