2-Port Network becomes the important topic for gate aspirants. Every year one or two question is expected from this topic. The article is framed to help you to solve questions on 2-port network.
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A 2-port is an electrical circuit or device with 2 pairs of terminals. They find application in transistors, filters etc.
A two-port network is represented by four external variables: voltage and current at the input port, and voltage and current at the output port.
In this two of the four variables are given, while the other two can always be derived. The parameters used in order to describe a two-port network are the following:
Z, Y, A , h, g
They are usually expressed in matrix notation and they establish relations between the following parameters.
we know I1 and I2 That means they are independent variables and V1 and V2 are dependent variables. Here we use KVL to evaluate V1 and V2.
V1 = Z11 I1+Z12I2
V2 = Z21 I1+Z22I2
All four parameters Z11,Z12 ,Z21 , and Z22 represent impedance. In particular, Z21 and Z12 are transfer impedances.
we know V1 and V2 That means they are independent variables and I1 and I2 are dependent variables. Here we use KCL to evaluate I1 and I2
I1 = Y11 V1+Y12V2
I2 = Y21 V1+Y22V2
These four parameters Y11,Y12 ,Y21 , and Y22 represent admittance. In particular, Y21 and Y12 are transfer admittances.
ABCD -model (Transmission Model):
we know V1 and I1 That means they are independent variables and V2 and I2 are dependent variables. Here we use KVL to evaluate V2 and KCL to evaluate I2
A and D are dimensionless coefficients, B is impedance and C is admittance .A negative sign is there to the output current I2 in the model, as the direction of the current is out-ward, for easy analysis of a cascade of multiple network models.
Also read : How to solve questions on Flip flops
H-model (Hybrid Model) :
In the H-model or hybrid model,V2 and I1 are known, and find V1 by KVL and I2 by KCL:
Here h12 and h21 are dimensionless coefficients, h11 is impedance and h22 is admittance
g model (inverse hybrid model) :
V1 and I2 are known, and find V2 and I1 by :
Here g12 and g21 are dimensionless coefficients, g22 is impedance and g11 is admittance.
Important Tips to Remember:
We must know important tips that must be considered to solve questions of two ports network.
When I2 = 0, it means line at output port is at open circuit. There is only one current I1. Similarly if I1 =0 , it means line at input port is at open circuit. This is assumptions we use to find impedance.
when impedance or any other coefficients is to be find, try to find out its equation using KVL or KCL as required. For voltage KVL will be used, for current KCL will be used. For example,
V1 = Z11 I1+Z12I2
If Z11 is to be find. Try to find V1 using KVL, then subsequently we will get Z11. Similarly ,
I2 = Y21 V1+Y22V2,
If Y21 is to be find then find I2 using KCL. Then subsequently we will get Y21
Before solving , simplify the circuit as possible. For this you may have to convert delta to start conversion. If two resistance are in parallel , convert them into single resistance.
Similarly if two resistance are in series convert into single resistance.
Example From Gate :
In the h – parameter model of 2 – port network given in the figure shown
the value of h22 (in siemens) is _____________
We know formula of
I2 = h21 I1+h22V2
We can redraw the figure as :
As the resistors are in parellel,We can redraw this in to :
Further, solving we can solve (2*3)/(2+3) this in to :
In order to find h22, we have to apply KCL.
I2 = h21 I1+h22V2
Assuming I1 =0,
I2 = V2/(6/5 +6/5) +V2/(6/5).
12 I2 = 15 V2
h22 = I2 / V2 = 1.25
Suppose if we need to calculate impedance , then we had to apply KVL, Before apply KVL (if we had to apply in above final circuit), to simplify convert delta to star conversion for simplification.
We hope you got a detailed idea how questions can be solved.
Best Wishes !!
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