Question

Statement I: A symmetrical two-port network is bound to be reciprocal.

Statement II: A symmetrical network will have the same magnitude of image impedance at both the ports.

Choose the correct option:

1. Both statement I and statement II are true and statement II is the correct explanation of statement I.
2. Both statement I and statement II  are true but statement II is not the correct explanation of statement I.
3. Statement I is true but statement II is false.
4. Statement I is false but statement II is true.

Answer 1

Correct Answer - Option 4 : Statement I is false but statement II is true.

Statement 1:

If any Two-port network is symmetrical than the network doesn't need to be reciprocal because the condition for the network to be symmetrical and reciprocal is different. The Conditions for a network to be symmetrical and reciprocal are:

Reciprocal	Symmetrical
Z12 = Z21	Z11 = Z22
Y12 = Y21	Y11 = Y22
\(\left| {\begin{array}{*{20}{c}} A&B\\ C&D \end{array}} \right| = 1\)	A = D
h12 = -h21	\(\left| {\begin{array}{*{20}{c}} h_{11}&h_{12}\\ h_{21}&h_{22} \end{array}} \right| = 1\)
g12 = -g21	\(\left| {\begin{array}{*{20}{c}} g_{11}&g_{12}\\ g_{21}&g_{22} \end{array}} \right| = 1\)

Hence, statement 1 is incorrect.

Statement 2:

The image impedance in terms of ABCD parameter is given as:

At input port: 

\({Z_1} = \sqrt { \frac{{AB}}{{CD}}} \)

At output port:

\({Z_2} = \sqrt { \frac{{DB}}{{AC}}} \)

If this network is symmetrical then,

A = D

So, Z₁ = Z₂

Hence, statement 2 is correct.