NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 379

i 1 i 2

v 1 +
−

+

v 2 Port 2

Port 1 Two Port Network

−

Figure 9-27 Two-port network used to describe ABCD parameters.

9.2.3 ABCD Parameters

Consider the two-port network depicted in Figure 9-27. If the voltage and current
are measured at the input and output ports, the system can be characterized
in terms of its ABCD matrix. The ABCD parameters have several advantages
over other network parameters. They allow the full description of a network in
terms of input and output voltage and current, which makes them convenient for
cascading circuits; they are easily related to equivalent circuits; and they provide
a convenient basis for writing specialized programs that allow voltage and current
sources to drive channels constructed from cascaded ABCD elements. Two-port
ABCD parameters are developed here.
One significant difference between the ABCD matrix and the impedance matrix
is the direction of i 2 , which is pointing out of, not into, port 2. This allows easy
cascading of networks (which is addressed in Section 9.2.4). The ABCD values
are evaluated as

i 2 = 0 v 2 = 0 i 2 = 0 v 2 = 0

v 1
v 2

v 1
i 2

i 1
v 2

i 1
i 2

A = B = C = D = (9-38)

Using the definition shown in equations (9-38), a set of linear equations can be
written to describe the network:

v 1 = Av 2 + Bi 2

i 1 = Cv 2 + Di 2

which is more efficiently expressed in matrix form:

i 1 =

·

i 2

v 1 AB

CD

v 2

(9-39)

Consequently, if the ABCD matrix of a system is known, the response of the
system can be predicted for any input.
Since the ABCD parameters are evaluated with short and open circuits as
shown in equation (9-38), they are not practical to measure directly. However,
relationships exist that allow the ABCD matrix to be calculated directly from the
S -parameters as will be shown later.