Table of Contents
Introduction
Twoport networks simplify complex electrical circuits. They represent components like transmission lines and transformers, as well as electronic ones like transistors. This overview explains twoport network parameters, how to calculate them, and conditions for symmetry and reciprocity, aiding in network analysis.
What is a TwoPort Network?
A port is a pair of terminals where current enters one and exits the other. Components like resistors, inductors, and capacitors are examples of oneport networks, where electrical interactions occur at a single pair of terminals.
A twoport network has two pairs of terminals, here named port 1 and port 2. V_{1} and V_{2} represent the voltages at these ports, while I_{1} and I_{2} represent the currents flowing through the respective ports.
Two Port Network Example
A few examples of Two Port Network are:
 Filters,
 Smallsignal models for transistors
 Matching networks,
 Transmission lines,
 Transformers,
Two Port Network Parameters
In a twoport network, you can provide input to any port and extract output from any port. The parameters used to describe such networks are called twoport network parameters. There are six sets of these parameters, named Z, Y, T, T’, h, and g parameters, involving voltage (V) and current (I).
Z Parameters
In a twoport network, with I_{1} and I_{2} as inputs and V_{1} and V_{2} as outputs, the Z parameters describe the relationship:
 V_{1} = Z_{11} * I_{1} + Z_{12} * I_{2}
 V_{2} = Z_{21} * I_{1} + Z_{22} * I_{2}
Z_{11} is found by making port 2 an open circuit when I_{2} is 0, and Z_{12} is found by making port 1 an open circuit when I_{1} is 0. Similarly, Z_{21} and Z_{22} are obtained. These parameters are called impedance parameters or Z parameters. They represent the ratio of output voltage to input current and are measured in Ohms (Ω).
 A twoport network is symmetrical if Z_{11} equals Z_{22}.
 A twoport network is reciprocal if Z_{12} equals Z_{21}.
Y Parameters
In a twoport network, considering V_{1} and V_{2} as inputs and I_{1} and I_{2} as outputs, the Y parameters describe the relationship:
 I_{1} = Y_{11} * V_{1} + Y_{12} * V_{2}
 I_{2} = Y_{21} * V_{1} + Y_{22} * V_{2}
Y_{11} is found by making port 2 a short circuit when V_{2} is 0, and Y_{12} is found by making port 1 a short circuit when V_{1} is 0. Similarly, Y_{21} and Y_{22} are obtained. These parameters are called admittance parameters or Y parameters, representing the ratio of output current to input voltage, measured in mhos (℧).
 A twoport network is symmetrical if Y_{11} equals Y_{22}.
 A twoport network is reciprocal if Y_{12} equals Y_{21}.
T Parameters
In a twoport network, with V_{2} and I_{2} as inputs and V_{1} and I_{1} as outputs, the T parameters (Transmission parameters) describe the relationship:
 V_{1} = AV_{2} – BI_{2}
 I_{1} = CV_{2} – DI_{2}
Here, A, B, C, and D are constants obtained under specific conditions:
 A = V_{1}/V_{2} when I_{2} is 0
 B = V_{1}/I_{2} when V_{2} is 0
 C = I_{1}/V_{2} when I_{2} is 0
 D = I_{1}/I_{2} when V_{2} is 0
A and D have no units, while B and D have units of ohms (Ω) and mhos (℧), respectively. The ABCD parameters are also known as T parameters. A and C are obtained by making port 2 an open circuit, while B and D are obtained by making port 2 a short circuit.
 A twoport network is symmetrical if A equals D.
 A twoport network is reciprocal if AD – BC equals 1.
T’ Parameters
In a twoport network, with V_{1} and I_{1} as inputs and V_{2} and I_{2} as outputs, the T’ parameters (Inverse Transmission parameters) describe the relationship:
 V_{2} = A’V_{1} – B’I_{1}
 I_{2} = C’V_{1} – D’I_{1}
Here, A’, B’, C’, and D’ are constants obtained under specific conditions:
 A’ = V_{2}/V_{1} when I_{1} is 0
 B’ = V_{2}/I_{1} when V_{1} is 0
 C’ = I_{2}/V_{1} when I_{1} is 0
 D’ = I_{2}/I_{1} when V_{1} is 0
A’ and D’ have no units, while B’ and D’ have units of ohms (Ω) and mhos (℧), respectively. The A’B’C’D’ parameters are also known as Inverse Transmission parameters or T’ parameters. A’ and C’ are obtained by making port 1 an open circuit, while B’ and D’ are obtained by making port 1 a short circuit.
 A twoport network is symmetrical if A’ equals D’.
 A twoport network is reciprocal if A’D’ – B’C’ equals 1.
h Parameters
In a twoport network with I_{1} and V_{2} as inputs and V_{1} and I_{2} as outputs, the h parameters (Hybrid parameters) describe the relationship:
 V_{1} = h_{11} + h_{12}V_{2}
 I_{2} = h_{21}I_{1} + h_{22}V_{2}
Here, h_{12} and h_{21} are unitless, and the units of h_{11} and h_{22} are ohms (Ω) and mhos (℧), respectively. The h parameters can be obtained under specific conditions:
 h_{11} = V_{1}/I_{1} when V_{2} is 0
 h_{12} = V_{1}/V_{2} when I_{1} is 0
 h_{21} = I_{2}/I_{1} when V_{2} is 0
 h_{22} = I_{2}/V_{2} when I_{1} is 0
Two h parameters, h_{11}, and h_{21}, can be found by making port 2 a short circuit, and the other two, h_{12} and h_{22}, can be found by making port 1 an open circuit.
 A twoport network is symmetrical if h = 1, i.e., h_{11}h_{22} – h_{21}h_{12} = 1.
 A twoport network is reciprocal if h_{12} equals h_{21}.
g Parameters
In a twoport network with V_{1 }and I_{2} as inputs and I_{1} and V_{2} as outputs, the g parameters (Inverse Hybrid parameters) describe the relationship:
 I_{1} = g_{11}V_{1} + g_{12}I_{2}
 V_{2} = g_{21}V_{1} + g_{22}I_{2}
Here, g_{12} and g_{21} are unitless, and the units of g_{11} and g_{22} are mhos (℧) and ohms (Ω), respectively. The g parameters can be obtained under specific conditions:
 g_{11} = I_{1}/V_{1} when I_{2} is 0
 g_{12} = I_{1}/I_{2} when V_{1} is 0
 g_{21} = V_{2}/V_{1} when I_{2} is 0
 g_{22} = V_{2}/I_{2} when V_{1} is 0
Two g parameters, g_{11}, and g_{21}, can be found by making port 2 an open circuit, and the other two, g_{12} and g_{22}
Two g parameters, g_{11}, and g_{21}, can be found by making port 2 an open circuit, and the other two, g_{12} and g, can be found by making port 1 a short circuit.
, can be found by making port 1 a short circuit.
 A twoport network is symmetrical if g = 1, i.e., g_{11}g_{22} – g_{12}g_{21} = 1.
 A twoport network is reciprocal if g_{12} equals g_{21}.
Frequently Asked Questions (FAQs)

What is meant by the twoport network?
A twoport network is an electrical network or circuit with two pairs of terminals, allowing independent input and output variables. It’s commonly used to model complex systems in a simplified manner.

What is the use of twoport?
A twoport is used to model and analyze complex electrical systems, simplifying their representation. It aids in understanding and designing circuits, facilitating the study of signal flow and interactions.

What is the formula for 2 ports?
The general representation of a twoport network involves four variables: V1 and I1 as input voltage and current, and V2 and I2 as output voltage and current. Different parameter sets like Z, Y, T, h, and g parameters express the relationships between these variables.

How many numbers is a port?
A port in a twoport network consists of a pair of terminals through which electrical signals enter and exit. A twoport network has two such ports, providing input and output connections.
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