Page 1
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
Page 2
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
Page 3
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
2 22 1 21 2
2 12 1 11 1
I z I z V
I z I z V
? ?
? ?
Putting the above equations in matrix form, we get
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
1
2
1
22 21
12 11
2
1
] [
I
I
z
I
I
z z
z z
V
V
the z terms are called the z parameters, and have units of ohms. The values of the parameters can
be evaluated by setting 0
1
? I or 0
2
? I .
The z parameters are defined as follows:
Thus
0
1
1
11
2
?
?
I
I
V
z
0
1
2
21
2
?
?
I
I
V
z
0
2
1
12
1
?
?
I
I
V
z
0
2
2
22
1
?
?
I
I
V
z
In the preceding equations, letting 0
1
? I or 0
2
? I is equivalent to open-circuiting the input or
output port. Hence, the z parameters are called open-circuit impedance parameters.
Here
11
z is defined as the open-circuit input impedance,
22
z is called the open-circuit output
impedance, and
12
z and
21
z are called the open-circuit transfer impedances.
If
12
z =
21
z , the network is said to be reciprocal network. Also, if
11
z =
22
z then the network is
called a symmetrical network.
We obtain
11
z and
21
z by connecting a voltage
1
V (or a current source
1
I ) to port 1 with port 2
open-circuited as in fig.
Similarly
12
z and
22
z by connecting a voltage
2
V (or a current source
2
I ) to port 2 with port 1
open-circuited as in fig.
A two-port is reciprocal if interchanging an ideal voltage source at one port with an ideal
ammeter at the other port gives the same ammeter reading.
Page 4
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
2 22 1 21 2
2 12 1 11 1
I z I z V
I z I z V
? ?
? ?
Putting the above equations in matrix form, we get
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
1
2
1
22 21
12 11
2
1
] [
I
I
z
I
I
z z
z z
V
V
the z terms are called the z parameters, and have units of ohms. The values of the parameters can
be evaluated by setting 0
1
? I or 0
2
? I .
The z parameters are defined as follows:
Thus
0
1
1
11
2
?
?
I
I
V
z
0
1
2
21
2
?
?
I
I
V
z
0
2
1
12
1
?
?
I
I
V
z
0
2
2
22
1
?
?
I
I
V
z
In the preceding equations, letting 0
1
? I or 0
2
? I is equivalent to open-circuiting the input or
output port. Hence, the z parameters are called open-circuit impedance parameters.
Here
11
z is defined as the open-circuit input impedance,
22
z is called the open-circuit output
impedance, and
12
z and
21
z are called the open-circuit transfer impedances.
If
12
z =
21
z , the network is said to be reciprocal network. Also, if
11
z =
22
z then the network is
called a symmetrical network.
We obtain
11
z and
21
z by connecting a voltage
1
V (or a current source
1
I ) to port 1 with port 2
open-circuited as in fig.
Similarly
12
z and
22
z by connecting a voltage
2
V (or a current source
2
I ) to port 2 with port 1
open-circuited as in fig.
A two-port is reciprocal if interchanging an ideal voltage source at one port with an ideal
ammeter at the other port gives the same ammeter reading.
Example 8.1
Determine the z parameters for the circuit in the following figure and then compute the
current in a 4O load if a
0
0 24 ? V source is connected at the input port.
To find
11
z and
21
z , the output terminals are open circuited. Also connect a voltage source
1
V to
the input terminals. This gives a circuit diagram as shown in Fig
Applying KVL to the left-mesh, we get
1 1 1
6 12 V I I ? ?
?
1 1
18I V ?
Hence ? ?
?0
1
1
11
2
I
I
V
z 18O
Applying KVL to the right-mesh, we get
0 6 0 3
1 2
? ? ? ? ? I V
?
1 2
6I V ?
Hence
0
1
2
21
2
?
?
I
I
V
z = 6 O
To find
12
z and
22
z , the input terminals are open circuited. Also connect a voltage source V
2
to
the output terminals. This gives a circuit diagram as shown in Fig.
Page 5
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
2 22 1 21 2
2 12 1 11 1
I z I z V
I z I z V
? ?
? ?
Putting the above equations in matrix form, we get
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
1
2
1
22 21
12 11
2
1
] [
I
I
z
I
I
z z
z z
V
V
the z terms are called the z parameters, and have units of ohms. The values of the parameters can
be evaluated by setting 0
1
? I or 0
2
? I .
The z parameters are defined as follows:
Thus
0
1
1
11
2
?
?
I
I
V
z
0
1
2
21
2
?
?
I
I
V
z
0
2
1
12
1
?
?
I
I
V
z
0
2
2
22
1
?
?
I
I
V
z
In the preceding equations, letting 0
1
? I or 0
2
? I is equivalent to open-circuiting the input or
output port. Hence, the z parameters are called open-circuit impedance parameters.
Here
11
z is defined as the open-circuit input impedance,
22
z is called the open-circuit output
impedance, and
12
z and
21
z are called the open-circuit transfer impedances.
If
12
z =
21
z , the network is said to be reciprocal network. Also, if
11
z =
22
z then the network is
called a symmetrical network.
We obtain
11
z and
21
z by connecting a voltage
1
V (or a current source
1
I ) to port 1 with port 2
open-circuited as in fig.
Similarly
12
z and
22
z by connecting a voltage
2
V (or a current source
2
I ) to port 2 with port 1
open-circuited as in fig.
A two-port is reciprocal if interchanging an ideal voltage source at one port with an ideal
ammeter at the other port gives the same ammeter reading.
Example 8.1
Determine the z parameters for the circuit in the following figure and then compute the
current in a 4O load if a
0
0 24 ? V source is connected at the input port.
To find
11
z and
21
z , the output terminals are open circuited. Also connect a voltage source
1
V to
the input terminals. This gives a circuit diagram as shown in Fig
Applying KVL to the left-mesh, we get
1 1 1
6 12 V I I ? ?
?
1 1
18I V ?
Hence ? ?
?0
1
1
11
2
I
I
V
z 18O
Applying KVL to the right-mesh, we get
0 6 0 3
1 2
? ? ? ? ? I V
?
1 2
6I V ?
Hence
0
1
2
21
2
?
?
I
I
V
z = 6 O
To find
12
z and
22
z , the input terminals are open circuited. Also connect a voltage source V
2
to
the output terminals. This gives a circuit diagram as shown in Fig.
Applying KVL to the left-mesh, we get
2 1
2 1
6
6 0 12
I V
I V
?
? ? ?
0
2
1
12
1
?
?
I
I
V
z =6 O
Applying KVL to the right-mesh, we get
0 6 3
2 2 2
? ? ? ? I I V
2 2
9I V ?
0
2
2
22
1
?
?
I
I
V
z =9 O
The equations for the two-port network are, therefore
2 1 1
6 18 I I V ? ? (1)
2 1 2
9 6 I I V ? ? (2)
The terminal voltages for the network shown in Fig.8.2 are
0
1
0 24 ? ? V (3)
2 2
4I V ? ? (4)
Fig.8.2
Combining equations (1) and (2) with equations (3) and (4) yields
2 1
0
6 18 0 24 I I ? ? ?
2 1
13 6 0 I I ? ?
On Solving, we get
0
2
0 73 . 0 ? ? ? I A
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