Classical network theory [12] is partly concerned with the properties of connections of N-port devices. In the abstract, an -port is a mathematical entity whose internal behavior is only accessible through its
ports. With the
th port is associated a current
, a voltage
, and two terminals (see Figure 2.1). The two terminals of any port must always be connected to the terminals of another port. A network is simply a collection of
-ports connected such that no port is left free
.
For lumped networks, the voltages, currents and possibly element values in the networks are allowed to be real-valued functions of a sole real parameter
If an -port is linear and time-invariant (LTI), then the port quantities may exhibit a purely exponential time-dependence at a single complex frequency
. For such an exponential state [12], it is also useful to define, for any port with voltage
and current
, the complex amplitudes
and
. We can then write
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In most cases of interest, the entries of
will be rational functions of
. An
-port so defined is called real if the coefficients of these rational functions are real numbers. In this case, there is no loss in generality [12] in considering the port voltages and currents to be real-valued functions of
, in which case we may write, for an exponential state,
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