Question

The transfer impedances at a 2 port network remain constant when the position of excitation and response are interchanged if the network :
A. Is linear
B. Contains bilateral element
C. Has high impedance
D. Is resonant
E. Is non-linear Choose the correct answer from the options given below :

• A. A and B only
• B. A, B and C only
• C. A, B, C and D only
• D. A, C, D and E only

Hint:

Reciprocity theorem is valid only for:
• linear networks,
• bilateral networks. For reciprocal networks: \[ Z_{12}=Z_{21} \]

Answer 1

The Correct Option is A

Concept: The statement is based on the Reciprocity Theorem. According to reciprocity:
• transfer impedance remains unchanged when source and response positions are interchanged,
• the network must be linear and bilateral. This theorem does not require:
• high impedance,
• resonance,
• nonlinearity.

Step 1: Understanding reciprocity condition. For a reciprocal network: \[ Z_{12}=Z_{21} \] This means transfer impedance remains same when excitation and response are interchanged.

Step 2: Requirement of linearity. Reciprocity theorem is valid only for: \[ \text{Linear networks} \] because superposition and proportionality must hold. Hence statement \(A\) is correct.

Step 3: Requirement of bilateral elements. The network must contain bilateral elements such as:
• resistors,
• inductors,
• capacitors. Unilateral devices violate reciprocity. Hence statement \(B\) is correct.

Step 4: Checking high impedance condition. High impedance is not a requirement for reciprocity. Thus statement \(C\) is incorrect.

Step 5: Checking resonance condition. Resonance has no direct relation with reciprocity theorem. Hence statement \(D\) is incorrect.

Step 6: Checking non-linear condition. Reciprocity theorem does not apply to nonlinear networks. Therefore statement \(E\) is incorrect.

Step 7: Selecting the final answer. Correct statements are: \[ A,\;B \] Hence the correct option is: \[ \boxed{(1)\; A\text{ and }B\text{ only}} \]