Passive Impedances

It is well known that a real impedance $R$ (in Ohms, e.g.) is passive so long as $R\geq 0$. A passive impedance cannot create energy. On the other hand, if $R<0$, the impedance is said to be active, and it must be connected to some energy source. The concept of passivity can be extended to complex impedances $R(j\omega)$ as well: We say that a complex impedance is passive if $R(s)$ is positive real, where $s$ is the Laplace-transform variable. In the discrete-time case, $R(z)$ must be positive real using an analogous definition (given in §K.4 below).

This appendix explores some implications of the positive real condition for passive impedance. Section K.1 considers the nature of waves reflecting from a passive impedance, while §K.2 considers the particular passive impedance created by a moving termination. Next, §K.3 looks at the acoustic guitar bridge, including a look at some laboratory measurements. Finally, §K.4 provides a review of some mathematical properties of positive real functions in the