Properties of Passive Impedances

It is well known that a real impedance
(in Ohms, for example) is
*passive* so long as
. A passive impedance cannot
create energy. On the other hand, if
, the impedance is
*active* and has some energy source. The concept of
passivity can be extended to complex frequency-dependent impedances
as well: A complex impedance
is
*passive* if
is *positive real*, where
is the
Laplace-transform variable. The positive-real property is discussed in
§C.11.2 below.

This section explores some implications of the positive real condition
for passive impedances. Specifically, §C.11.1 considers the
nature of waves reflecting from a passive impedance in general,
looking at the *reflection transfer function*, or
*reflectance*, of a passive impedance. To provide further
details, Section C.11.2 derives some mathematical properties of positive
real functions, particularly for the discrete-time case. Application
examples appear in §9.2.1 and §9.2.1.

- Passive Reflectances
- Reflectance and Transmittance of a Yielding String Termination
- Power-Complementary Reflection and Transmission

- Positive Real Functions

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