Question

For a transmission line the constant A, B, C and D are related as:
1. AD - BC = 1
2. BC - AD = 1
3. \(\sqrt{AD - BC}= 0.5\)
4. None of these

Answer 1

Correct Answer - Option 1 : AD - BC = 1

Conditions for Reciprocity and Symmetry:

1) A network is said to be reciprocal if the ratio of the response to the excitation is invariant to an interchange of the positions of the excitation and response of the network.

2) A two-port network is said to be symmetrical if the input and output ports can be interchanged without altering the port voltages and currents.

• ABCD parameters are generalized circuit constants used to develop the model for transmission lines, i.e. ABCD parameters are used in the two-port network representation of a transmission line.
• ABCD parameters are also known as transmission line parameters.
• The symmetry condition for a two-port network in terms of transmission parameters is: A = D
• The Reciprocity condition for a two-port in terms of transmission parameters is AD - BC = 1

 

Conditions of reciprocity and symmetry in terms of different two-port parameters are:

Parameter	Conditions of reciprocity	Conditions of symmetry
Z	z12 = z21	z11 = z22
Y	y12 = y21	y11 = y22
T(ABCD)	(AD – BC) = 1	A = D
h	h12 = -h21	(h11h22 – h12h21) = 1