GATE EC 2025 Set 1 — Question 40
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Network Theory → Two-Port Networks → Z, Y, h & ABCD Parameters
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Question
The -parameter matrix of a two port network relates the port voltages and port currents as follows:The -parameter matrix (with each entry in Ohms) of the network shown below is __________.
Correct answer
(A) bmatrix 10/3 & 2/3 \ 2/3 & 10/3 bmatrix
Solution
To find the -parameters, we use the definitions:
When , the last series resistor carries no current. The network seen from port 1 consists of a series resistor, followed by a shunt resistor in parallel with a series combination of a resistor and another shunt resistor.To find , we first find the voltage at the first shunt node ():Since , is the voltage across the second shunt resistor. By voltage division:Thus, .Step 2: Use symmetry and reciprocity.
The network is symmetric, so .
The network is reciprocal (made of linear resistors), so .Final Matrix:This matches option (A).
1.
2.
Step 1: Calculate and by setting .When , the last series resistor carries no current. The network seen from port 1 consists of a series resistor, followed by a shunt resistor in parallel with a series combination of a resistor and another shunt resistor.To find , we first find the voltage at the first shunt node ():Since , is the voltage across the second shunt resistor. By voltage division:Thus, .Step 2: Use symmetry and reciprocity.
The network is symmetric, so .
The network is reciprocal (made of linear resistors), so .Final Matrix:This matches option (A).
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