Attia, John Okyere. “Two-Port Networks.”
Electronics and Circuit Analysis using MATLAB.
Ed. John Okyere Attia
Boca Raton: CRC Press LLC, 1999

CHAPTER SEVEN

TWO-PORT NETWORKS This chapter discusses the application of MATLAB for analysis of two-port
networks. The describing equations for the various two-port network represen-
tations are given. The use of MATLAB for solving problems involving paral-
lel, series and cascaded two-port networks is shown. Example problems in-
volving both passive and active circuits will be solved using MATLAB.
7.1 TWO-PORT NETWORK REPRESENTATIONS

A general two-port network is shown in Figure 7.1.

Linear
two-port
network
I
2
V
2
V
1
+
-
+
-


VzIzI
1 11 1 12 2
=+
(7.1) VzIzI
2 21 1 22 2
=+
(7.2)

In matrix form, the above equation can be rewritten as

© 1999 CRC Press LLC© 1999 CRC Press LLC
V
V
zz
zz
I
I
1
2
11 12

I
11
1
1
0
2
=
=
(7.4) z
V
I
I
12
1
2
0
1
=
=
(7.5) z
V
I
I
21

= 0). The following exam-
ple shows a technique for finding the z-parameters of a simple circuit. Example 7.1

For the T-network shown in Figure 7.2, find the z-parameters. +
-
V
1
V
2
+
-
I
1
I
2
Z
1
Z
2
Z
3

Figure 7.2 T-Network


I
I
1
2
13 3
323
1
2






=
+
+












(7.10)

=+
(7.12) IyVyV
2 21 1 22 2
=+
(7.13)
where V
1
and
V
2
are independent variables and
I
1
and
I
2
are dependent variables.

In matrix form, the above equations can be rewritten as I
I
yy

The y-parameters can be found as follows: © 1999 CRC Press LLC© 1999 CRC Press LLC

y
I
V
V
11
1
1
0
2
=
=
(7.15) y
I
V
V
12
1
2
0

(7.18)

The y-parameters are also called short-circuit admittance parameters. They are
obtained as a ratio of current and voltage and the parameters are found by
short-circuiting port 2 (
V
2
= 0) or port 1 (
V
1
= 0). The following two exam-
ples show how to obtain the y-parameters of simple circuits. Example 7.2

Find the y-parameters of the pi (π) network shown in Figure 7.3.

+
-
V
1
V
2
+
-
I
1
I
2

22 21 1 2
=+− =−+ +
() ()
(7.20)

Comparing Equations (7.19) and (7.20) to Equations (7.12) and (7.13), the y-
parameters are []
Y
YY Y
YYY
ab b
bbc
=
+−
−+






(7.21) Example 7.3

Figure 7.4 shows the simplified model of a field effect transistor. Find its y-

I V sC V V sC V sC sC V sC
111 12311 3 2 3
=+− = ++−
() ( )()
(7.22)

IVYgVVVsCVgsC VYsC
mm
222 1 2131 3 22 3
=++− = −+ +
() ( )( )
(7.23)

Comparing the above two equations to Equations (7.12) and (7.13), the y-
parameters are © 1999 CRC Press LLC© 1999 CRC Press LLC[]
Y
sC sC sC
gsCYsC
m
=
+−

where

I
1
and
V
2
are independent variables and
V
1
and
I
2
are dependent variables.

In matrix form, the above two equations become V
I
hh
hh
I
V
1
2
11 12
21 22
1
2

0
2
=
=
(7.28) h
V
V
I
12
1
2
0
1
=
=
(7.29) h
I
I
V21
2
1
0
2
=

= 0 ). The
h-parameters of a bipolar junction transistor are determined in the following
example. Example 7.4

A simplified equivalent circuit of a bipolar junction transistor is shown in Fig-
ure 7.5, find its h-parameters.
+
-
V
1
V
2
+
-
I
1
I
2
Y
2
I
1
Z
1
β
=






1
2
0
β
` (7.34)

© 1999 CRC Press LLC© 1999 CRC Press LLC

7.1.4 Transmission parameters

A two-port network can be described by transmission parameters. The de-
scribing equations are VaVaI
1 11 2 12 2
=−
(7.35)
1
11 12
21 22
2
2






=






−






(7.37)

The transmission parameters can be found as

a

21
1
2
0
2
=
=
(7.40) a
I
I
V
22
1
2
0
2
=−
=
(7.41)

The transmission parameters express the primary (sending end) variables
V
1

and
I
1

2
+
-
I
1
I
2
Z
1 Figure 7.6 Simple Impedance Network Solution

By inspection, II
12
=−
(7.42)

Using KVL, VVZI
1211
=+
© 1999 CRC Press LLC

Example 7.6

Find the transmission parameters for the network shown in Figure 7.7.
+
-
V
1
V
2
+
-
I
1
I
2
Y
2 Figure 7.7 Simple Admittance Network

Solution

By inspection,
V
1
V
2
+
-
I
1
I
2
Z
11
Z
22
Z
12
I
1
Z
21
I
1 (a) © 1999 CRC Press LLC