Physical Derivation of Reflection Coefficient

Physically, the reflection coefficient seen at port is due to an impedance step from , that of the port interface, to a new impedance consisting of the parallel combination of all other port impedances meeting at the junction. Let

denote this parallel combination, in admittance form. Then we must have

Let's check this ``physical'' derivation against the formal definition Eq.(Q.20) leading to in Eq.(Q.22). Toward this goal, let

denote the parallel combination of all admittances connected to the junction. Then by Eq.(Q.24), we have for all . Now, from Eq.(Q.17),

and the result is verified.

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written by 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.