Download - Wolfram Research

2.9 Frequency-Domain Analysis of Linear Circuits 157
2.9.5 Two-Port Parameters
Two-Port Representations
It is easy to extend the analysis procedures for computing transfer functions to two-port parameter
analysis because two-port or, more generally, n-port matrices can be regarded as transfer functions
in several dimensions. Indeed, every single coefficient in a two-port matrix is a transfer function
from one port current or voltage to another, so we could obtain the four coefficients of a two-port
matrix by means of four separate transfer function analyses. However, we will apply a more efficient
strategy which allows for calculating complete n-port matrices in only one step.
I1
I2
V1
V2
Figure 9.8: Two-port current and voltage reference directions
Figure 9.8 shows the voltages and currents at the terminals of a two port. The relation between the
port quantities V , V , I , and I is generally given as a linear mapping of two equations in four
variables:
p
p
p
I
q
p I
q
q V
⩵
q V
Solving these equations for any combination of two-port voltages or currents yields one of six possible
two-port representations known as the admittance, impedance, hybrid I and II, and cascade I and II
forms. For example, solving for I and I in terms of V and V results in the admittance, or Y-matrix,
representation
I ⩵ y
I y
y
V
y V
whose coefficients y y are known as the Y-parameters of the two port. Similarly, solving for
V and V in terms of I and I yields the impedance, or Z-matrix, representation:
V ⩵ z
V z
z
I
z I