Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


Driving Point Impedance

Taking the Laplace transform of both sides of Eq.$ \,$ (E.1) gives

$\displaystyle V_e(s) = V_R(s) + V_C(s) = R\, I(s) + \frac{1}{Cs} I(s)
$

where we made use of the fact that the impedance of a capacitor is $ 1/(Cs)$ , as derived above. The driving point impedance of the whole RC filter is thus

$\displaystyle R_d(s) \isdef \frac{V_e(s)}{I(s)} = R + \frac{1}{Cs}.
$

Alternatively, we could simply note that impedances always sum in series and write down this result directly.


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``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
CCRMA