Y,Z,H parameter

1. GANDHINAGAR INSTITUTE OF
TECHNOLOGY
Sub – Circuit and Network (2130901)
Topic – Z,H,Y and ABCD Parameter
Guided by – Prof. Kushan Vadwala
Sem – 3rd
Branch – Electrical (b3)
Academic year – 2015&2016

2. PREPARED BY
Sodha Manthansinh (140120109057)

3. TWO PORT
NETWORKS

4. SUB - TOPICS
Z – PARAMETER
Y – PARAMETER
T (ABCD) – PARAMETER
TERMINATED TWO PORT NETWORKS

5. TWO – PORT NETWORKS
A pair of terminals through which a current may enter or leave a
network is known as a port.
Two terminal devices or elements (such as resistors, capacitors,
and inductors) results in one – port network.
Most of the circuits we have dealt with so far are two – terminal
or one – port circuits.
A two – port network is an electrical network with two separate
ports for input and output.
It has two terminal pairs acting as access points. The current
entering one terminal of a pair leaves the other terminal in the
pair.

6. Linear network
+
V
-
I
I
One – port network
Linear network
+
V1
-
I1
I1 I2
I2
+
V2
-
Two – port network

7. Two (2) reason why to study two port – network:
Such networks are useful in communication, control system,
power systems and electronics.
Knowing the parameters of a two – port network enables us to
treat it as a “black box” when embedded within a larger
network.
From the network, we can observe that there are 4 variables that
is I1, I2, V1and V2, which two are independent.
The various term that relate these voltages and currents are
called parameters.

8. Z – PARAMETER
Z – parameter also called as impedance parameter and
the units is ohm (Ω)
Impedance parameters is commonly used in the synthesis
of filters and also useful in the design and analysis of
impedance matching networks and power distribution
networks.
The two – port network may be voltage – driven or
current – driven.

9. Two – port network driven by voltage source.
Two – port network driven by current sources.
Linear network
I1 I2
+

+

V1 V2
I1 I2
+
V1
-
Linear network
+
V2
-

10. The “black box” is replace with Z-parameter is as shown
below.
The terminal voltage can be related to the terminal
current as:
+
V1
-
I1
I2
+
V2
-
Z11
Z21
Z12
Z22
2221212
2121111
IzIzV
IzIzV

 (1)
(2)

11. In matrix form as:
The Z-parameter that we want to determine are z11, z12, z21, z22.
The value of the parameters can be evaluated by setting:
1. I1= 0 (input port open – circuited)
2. I2= 0 (output port open – circuited)


















2
1
2221
1211
2
1
I
I
zz
zz
V
V

12. Thus,
01
2
21
01
1
11
2
2




I
I
I
V
z
I
V
z
02
2
22
02
1
12
1
1




I
I
I
V
z
I
V
z
Where;
z11 = open – circuit
input
impedance.
z12 = open – circuit
transfer
impedance from
port 1 to port 2.
z21 = open – circuit
transfer
impedance from
port 2 to port 1.
z22 = open – circuit
output impedance.

13. EXAMPLE
Find the Z – parameter of the circuit below.
40Ω
240Ω
120Ω
+
V1
_
+
V2
_
I1
I2

14. SOLUTION
i) I2 = 0(open circuit port 2). Redraw the circuit.
40Ω
240Ω
120Ω
+
V1
_
+
V2
_
I1
Ia
Ib




84
(2)(1)sub
)2......(
400
280
)1.......(120
1
1
11
1
1
I
V
Z
II
IV
b
b




72
(3)(4)sub
)4.......(
400
120
.......(3)240
1
2
21
1
2
I
V
Z
II
IV
a
a

15. ii) I1 = 0 (open circuit port 1). Redraw the circuit.
40Ω
240Ω
120Ω
+
V1
_
+
V2
_
Iy I2
Ix




96Z
(2)(1)sub
)2.......(
400
160
)1.......(240
2
2
22
2
2
I
V
II
IV
x
x




72
(3)(4)sub
)4.......(
400
240
)3.......(120
2
1
12
2
1
I
V
Z
II
IV
y
y
In matrix form:
  






9672
7284
Z

16. Y - PARAMETER
Y – parameter also called admittance parameter and the
units is siemens (S).
The “black box” that we want to replace with the Y-
parameter is shown below.
+
V1
-
I1
I2
+
V2
-
Y11
Y21
Y12
Y22

17. The terminal current can be expressed in term of terminal
voltage as:
In matrix form:
2221212
2121111
VyVyI
VyVyI

 (1)
(2)


















2
1
2221
1211
2
1
V
V
yy
yy
I
I

18. The y-parameter that we want to determine are Y11, Y12, Y21, Y22.
The values of the parameters can be evaluate by setting:
i) V1 = 0 (input port short – circuited).
ii) V2 = 0 (output port short – circuited).
Thus;
01
2
21
01
1
11
2
2




V
V
V
I
Y
V
I
Y
02
2
22
02
1
12
1
1




V
V
V
I
Y
V
I
Y

19. EXAMPLE
Find the Y – parameter of the circuit shown
below.
5Ω
15Ω20Ω
+
V1
_
+
V2
_
I1
I2

20. SOLUTION
i) V2 = 0
5Ω
20Ω
+
V1
_
I1
I2
Ia
S
V
I
Y
II
IV
a
a
4
1
(2)(1)sub
)2.......(
25
5
)1.......(20
1
1
11
1
1




S
V
I
Y
IV
5
1
5
1
2
21
21



21. ii) V1 = 0
In matrix form;
5Ω
15Ω
+
V2
_
I1
I2
Ix
S
V
I
Y
II
IV
x
x
15
4
(4)(3)sub
)4.......(
25
5
)3.......(15
2
2
22
2
2




S
V
I
Y
IV
5
1
5
2
1
12
12


  SY













15
4
5
1
5
1
4
1

22. H - PARAMETER
In these network there are four parameters called the hybrid
parameters or H-parameters, one is measured in terms of ohm,
one in mho and other two are dimension less. Since these
parameters has mixed dimensions, so they are called as hybrid
parameters.
The “black box” that we want to replace with T – parameter is as
shown below.

23. 2221212
2121111
VhIhI
VhIhV


  























2
1
2
1
2221
1211
2
1
V
I
h
V
I
hh
hh
I
V
02
2
22
01
2
12
02
1
12
01
1
11
12
12
,
,




IV
IV
V
I
h
I
I
h
V
V
h
I
V
h
h11 = Short-circuit input
impedance
h12 = Open-circuit reverse
voltage gain
h21 = Short-circuit forward
current gain
h22 = Open-circuit output
admittance

25. T (ABCD) PARAMETER
T – parameter or ABCD – parameter is a another set of
parameters relates the variables at the input port to those
at the output port.
T – parameter also called transmission parameters because
this parameter are useful in the analysis of transmission
lines because they express sending – end variables (V1
and I1) in terms of the receiving – end variables (V2 and -
I2).

26. The “black box” that we want to replace with T – parameter
is as shown below.
The equation is:
+
V1
-
I1
I2
+
V2
-
A11
C21
B12
D22
)2.......(
)1.......(
221
221
DICVI
BIAVV



27. In matrix form is:
The T – parameter that we want determine are A, B, C and D
where A and D are dimensionless, B is in ohm (Ω) and C is in
siemens (S).
The values can be evaluated by setting
i) I2 = 0 (input port open – circuit)
ii) V2 = 0 (output port short circuit)


















2
2
1
1
I
V
DC
BA
I
V

28. Thus;
In term of the transmission parameter, a network is reciprocal if;02
1
02
1
2
2




I
I
V
I
C
V
V
A
02
1
02
1
2
2




V
V
I
I
D
I
V
B
1BC-AD 

29. EXAMPLE
Find the ABCD – parameter of the circuit
shown below.
2Ω
10Ω
+
V2
_
I1 I2
+
V1
_
4Ω

30. SOLUTION
i) I2 = 0,
2Ω
10Ω
+
V2
_
I1
+
V1
_
2.1
5
6
10
2
2
1.0
10
2
1
22
2
1
211
2
1
12











V
V
A
VV
V
V
VIV
S
V
I
C
IV

31. ii) V2 = 0,
 












8.6
10
10
14
12
1012
102
4.1
14
10
2
1
221
211
2111
2
1
12
I
V
B
IIV
IIV
IIIV
I
I
D
II
2Ω
10Ω
I1 I2
+
V1
_
4Ω
I1 + I2
  






4.11.0
8.62.1
T

32. THANK YOU
FOR
LISTENING