Question

The values of B and D of ABCD parameters of two port network respectively are

• A. 9/4, 5/4
• B. 35/2, 5/2
• C. 11/4, 5/2
• D. 15/4, 35/2

Hint:

For a T-network (series arm \(Z_1\), shunt \(Z_2\), series arm \(Z_3\)): A = \(1+Z_1/Z_2\), B = \(Z_1+Z_3+Z_1Z_3/Z_2\), C = \(1/Z_2\), D = \(1+Z_3/Z_2\).
For a symmetric T-network (\(Z_1=Z_3\)), A=D.

Answer 1

The Correct Option is A

The given two-port network is a symmetric T-network with series arms \(Z_1 = 1\Omega\), \(Z_3 = 1\Omega\) and shunt arm \(Z_2 = 4\Omega\).

ABCD parameters for a T-network: 

\(A = 1 + \frac{Z_1}{Z_2}\)

\(B = Z_1 + Z_3 + \frac{Z_1 Z_3}{Z_2}\)

\(C = \frac{1}{Z_2}\)

\(D = 1 + \frac{Z_3}{Z_2}\)

Here, \(Z_1 = 1\Omega\), \(Z_2 = 4\Omega\), \(Z_3 = 1\Omega\).

B =

\(1 + 1 + \frac{1 \times 1}{4} = 2 + \frac{1}{4} = \frac{8+1}{4} = \frac{9}{4} \Omega\)

D =

\(1 + \frac{1}{4} = \frac{4+1}{4} = \frac{5}{4}\) (dimensionless)

\[ \boxed{\text{B = 9/4, D = 5/4}} \]