Driving Point Impedance

Chapter Contents:

Search Introduction to Digital Filters

Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

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

, 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.

Previous: RC Filter Analysis
Next: Transfer Function

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

Sign in