UNIT-4
TWO PORT NETWORKS
PREPARED BY
D V S RAMANJANEYULU
ASST.PROF
ACE ENGINEERING COLLEGE
Syllabus …… 2
Z,Y, ABCD and h- Parameters
Conversion of one parameter to
other
Condition for Reciprocity and
symmetry
Two port networks connected in
series, parallel and cascaded
configurations
Problem solving
3
4
Port A port is pair of terminals connecting an electrical network or
: circuit to an external circuit i.e it is a point of entry or exit for
electrical energy
Two Port network A two port network is an electrical network
: having two pair of terminals to connect to an external
circuit, with one pair at the input called input port and
other at out put called the output port .
Knowing the parameters of a two
port network enables us to treat
it as a black box when embedded
with in a larger network, thus
making analysis of network (large
circuits in particular) very easy .
This technique is well applied in areas of
Communication
Electronics
Control system
Power system
5
APPROACH TO TWO PORT PARAMETERS
There are four variables �1, �2 , �1 and �2 associated with a two
port network . Two of these variables can be 6 expressed in terms of other two
variables. Thus there will be two dependent variables and two independent
variables. The number of possible combinations generated by four variables taken
two at a time is six i.e there are 6 possible sets of equations describing a two-port
network 6
7
Z- PARAMETERS
(OPEN CIRCUIT PARAMETERS)
The Z-parameters of a two port network may be defined by expressing two port
voltages �1 𝑎𝑛𝑑 �2 in terms of two port currents �1 and �2
Matrix Form
Open circuit input
impedance
Open circuit reverse
transfer impedance
Open circuit forward
transfer impedance
Open circuit output
impedance
8
CONDITION FOR SYMMETRY
AND RECIPROCITY OF Z PARAMETERS
Symmetry : For the network to be symmetrical, the voltage-to-
current ratio at one port should be the same as the voltage-to-current ratio at
the other port with one of the port short circuited.
Condition for symmetry
9
A network is said to be reciprocal if the the ratio of
Reciprocity : excitation at one port to response at other port is same
if excitation and responses are interchanged
10
Condition for Reciprocity
Y- PARAMETERS
(SHORTCIRCUIT PARAMETERS)
The Y-parameters of a two port network may11be defined by expressing two port
currents �1 and �2 in terms of two port voltages �1 𝑎𝑛𝑑 �2
Matrix Form
Short circuit input
admittance
short circuit reverse
transfer admittance
short circuit forward
transfer admittance
short circuit output
admittance
CONDITION FOR SYMMETRY
AND RECIPROCITY OF Y PARAMETERS
Symmetry : For the network to be symmetrical, the voltage-to-
current ratio at one port should be the same as the voltage-to-current ratio at
the other port with one of the port short circuited.
Condition for symmetry
12
A network is said to be reciprocal if the the ratio of excitation at one
port to response at other port is same if excitation and responses are
interchanged
13
Condition for Reciprocity
ABCD - PARAMETERS
(TRANSMISSION LINE PARAMETERS)
The ABCD-parameters of a two port network 14 serve to relate the voltage and
currents of input port (�1 𝑎𝑛𝑑 �1) to voltage and currents of output port (�2and
� 2)
Matrix Form
CONDITION FOR SYMMETRY
AND RECIPROCITY OF Y PARAMETERS
Symmetry : For the network to be symmetrical, the voltage-to-
current ratio at one port should be the same as the voltage-to-current ratio at
the other port with one of the port short circuited.
Condition for symmetry
15
A network is said to be reciprocal if the the ratio of
excitation at one portReciprocity
to response at
: other port is same
if excitation and responses are interchanged
16
Condition for Reciprocity
h – PARAMETERS
(Hybrid PARAMETERS)
The h -parameters of a two port network serve
17 to relate the voltage of input port
(�1) 𝑎𝑛𝑑 current of output port ( �2) in terms of currents of input port (�1) and
voltage of output port (�2)
Matrix Form
CONDITION FOR SYMMETRY
AND RECIPROCITY OF h PARAMETERS
Condition for symmetry
18
A network is said to be reciprocal if the the ratio of
excitation at one portReciprocity
to response at
: other port is same
if excitation and responses are interchanged
19
Condition for Reciprocity
SYNOPSIS OF ALL PARAMETERS
20
EQUIVALENT CIRCUITS OF ALL
PARAMETERS
21
Transmission
line parameters
NOT POSSIBLE
Example 1 : Find Z-parameters for the circuit shown below and
comment on symmetry and reciprocity of circuit
22
Ans : �𝟏𝟏 = �𝟏 +��
�𝟏� = ��
��𝟏 = ��
��� = �� +��
RECIPROCAL
SYMMETRICAL IF �𝟏 = ��
23
24
Example 2 : Find Z-parameters for the circuit shown below and
comment on symmetry and reciprocity of circuit
Ans : �𝟏𝟏= 11/5
�𝟏� = 4/5
��𝟏 = 4/5
��� = 6/5
25
26
Example 3 : Find open circuit parameters for the circuit shown
27
ANS
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Example
4
:
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Example 1 : Find Y-parameters for the circuit shown below and
comment on symmetry and reciprocity of circuit
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Ans : �𝟏𝟏 = 5/11
�𝟏� = -2/11
��𝟏 = -2/11
��� = 3/11
Circuit is reciprocal (since �𝟏� = ��𝟏 ) Non
symmetrical (since �𝟏𝟏 ≠ ��� )
31
Example 2 : Find Y-parameters for the circuit shown below and
comment on symmetry and reciprocity of circuit
32
Ans : �𝟏𝟏 = 1/2
�𝟏� = -1/4
��𝟏 = -1/4
��� = 5/8
Circuit is reciprocal (since �𝟏� = ��𝟏 ) Not
symmetrical (since �𝟏𝟏 ≠ ��� )
33
Example 3 : Find Y-parameters for the circuit shown below and
comment on symmetry and reciprocity of circuit
34
ANS
35
Example 1 : Find transmission parameters for the circuit shown
below and comment on symmetry and reciprocity of circuit
36
Ans : A= 6/5
B= 17/5 C= 1/5 D= 7/5
Circuit is NOT reciprocal (since AD-BC ≠ 1) Not
symmetrical (since A ≠ D)
37
38
Example 2 : Find ABCD parameters for the circuit shown below
and comment on symmetry and reciprocity of
circuit 39
Ans : A= 11/4
B= 5/2 C= 5/4 D= 3/2
Circuit is NOT reciprocal (since AD-BC ≠ 1)
Not symmetrical (since A ≠ D)
40
Example 3 : Find ABCD parameters for the circuit shown below
41
Ans :
42
Example
1:
43
Example 2 : Find hybrid parameters for the circuit shown below
and comment on symmetry and reciprocity of
circuit 44
Ans : �𝟏𝟏 = 2
�𝟏𝟐 = 1/2
�𝟐𝟏 = -1/2
�𝟐𝟐 = 1/2
Circuit is reciprocal (since �𝟏𝟐 = − �𝟐𝟏 )
Non symmetrical (since �𝟏𝟏 �𝟐𝟐 − �𝟐𝟏 �𝟏𝟐 ≠1)
45
46
INTER-RELATIONSHIPS BETWEEN PARAMETERS
47
Objective :When it is required to find out two or more parameters of a
particular network then finding each parameter will be
tedious. But if we find a particular parameter then the other
parameters can be found if the inter-relation ship between
them in known.
Z-Parameters Y-Parameters T-Parameters H-Parameters
Wher 48
∆𝒁 = 𝒁𝟏𝟏 𝒁𝟐𝟐− 𝒁𝟏𝟐 𝒁𝟐𝟏 , ∆𝒚 = �𝟏𝟏 �𝟐𝟐- �𝟏𝟐 �𝟐𝟏 , ∆𝑯 = �𝟏𝟏 �𝟐𝟐− �𝟏𝟐 �𝟐𝟏 , ∆�=AD-BC
1. Z-Parameters in terms of Y-Parameters
49
2. Z-Parameters in terms of ABCD -Parameters
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3. Z-Parameters in terms of H-Parameters
51
1. Y-Parameters in terms of z-Parameters
52
2. Y-Parameters in terms of T-Parameters
53
3. Y-Parameters in terms of H -Parameters
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1. ABCD -Parameters in terms of z-Parameters
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2. ABCD -Parameters in terms of Y-Parameters
56
3. ABCD -Parameters in terms of H-Parameters
57
1. H -Parameters in terms of z-Parameters
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2. H -Parameters in terms of Y-Parameters
59
3. H -Parameters in terms of ABCD -Parameters
60
Example 1 : The Z-Parameters of 2 port network are �11= 20ohm,
�12= �21= 10ohm, �22= 30 ohm. Find Y and
61
ABCD Parameters.
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Example 2 : Currents �1 and �2 entering at port1 and port2
respectively of a 2 port network is given by following equation
Find Y , Z and ABCD Parameters of
network. 63
64
65
Example 1 : Two identical sections of the network shown in figure are
connected in series .Obtain Z parameters of over all
network
66
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Example 2 : Obtain Z parameters of following network.
68
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Example 3 : Obtain Y parameters of following network.
70
71
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Example 4: Two identical sections of the network shown are
connected
in cascade. Obtain the transmission parameters of over all network
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