Question

Consider the following statements associated with two-port reciprocal networks : A. \[ Z_{12}=Z_{21} \] B. \[ Y_{12}=Y_{21} \] C. \[ h_{12}=h_{21} \] D. \[ AD-BC=1 \] Choose the correct answer from the options given below :

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

Hint:

Reciprocity conditions: \[ Z_{12}=Z_{21} \] \[ Y_{12}=Y_{21} \] \[ AD-BC=1 \] For h-parameters: \[ h_{12}=-h_{21} \]

Answer 1

The Correct Option is D

Concept: A reciprocal network is one in which transfer characteristics remain unchanged when input and output are interchanged. Reciprocity conditions for two-port parameters are: \[ Z_{12}=Z_{21} \] \[ Y_{12}=Y_{21} \] \[ AD-BC=1 \] However: \[ h_{12}\neq h_{21} \] for reciprocal networks.

Step 1: Analyze statement A. For reciprocal networks: \[ Z_{12}=Z_{21} \] This is a standard reciprocity condition. Hence: \[ A \text{ is correct} \]

Step 2: Analyze statement B. Similarly: \[ Y_{12}=Y_{21} \] is also a reciprocity condition. Hence: \[ B \text{ is correct} \]

Step 3: Analyze statement C. For h-parameters, reciprocity condition is: \[ h_{12}=-h_{21} \] not: \[ h_{12}=h_{21} \] Therefore: \[ C \text{ is incorrect} \]

Step 4: Analyze statement D. For ABCD transmission parameters: \[ AD-BC=1 \] is the reciprocity condition. Hence: \[ D \text{ is correct} \]

Step 5: Write the final answer. Correct statements are: \[ A,\ B,\ D \] Hence, the correct option is: \[ \boxed{(D)\ A,B,D\text{ only}} \]