The condition for symmetric property of ABCD parameter of two port network is:
A = D
Understanding the symmetric property of a two-port network described by ABCD parameters is essential in network analysis. The ABCD parameters, also known as transmission parameters, relate the input voltage and current (\(V_1, I_1\)) to the output voltage and current (\(V_2, I_2\)) as follows:
\[ V_1 = A V_2 - B I_2 \\ I_1 = C V_2 - D I_2 \]A two-port network is considered symmetric if its characteristics remain unchanged when the input and output ports are interchanged. If the network is symmetric, applying the same excitation at port 2 (now considered input) should produce the same response at port 1 (now considered output) as when the excitation was applied at port 1 and response measured at port 2.
Condition for Symmetric Property
For a two-port network represented by its ABCD parameters, the condition for the network to be symmetric is that the parameter A must be equal to the parameter D.
\[ A = D \]Let's examine why this is the case. If we swap the ports, the equations relating the new input (\(V_2, I_2\)) and new output (\(V_1, I_1\)) should have the same form as the original equations. The original matrix representation is:
\[ \begin{pmatrix} V_1 \\ I_1 \end{pmatrix} = \begin{pmatrix} A & B \\ C & D \end{pmatrix} \begin{pmatrix} V_2 \\ -I_2 \end{pmatrix} \]For symmetry, if we swap the ports, the new transmission matrix from port 2 to port 1 (with \(V_2, I_2\) as input-side variables and \(V_1, I_1\) as output-side variables) should be the same. Deriving the ABCD matrix from the perspective of port 2 as input leads to a matrix whose parameters are related to the original A, B, C, D. Comparing the new matrix to the original matrix shows that the condition for symmetry is indeed \(A = D\). Also, the determinant of the ABCD matrix, \(AD - BC\), must equal 1 for reciprocal networks, which is often the case in linear passive networks, but reciprocity and symmetry are independent properties.
Analyzing the Options
Let's look at the given options:
- Option 1: \(C=B\) - This is generally not the condition for symmetric property.
- Option 2: \(B=D\) - This is generally not the condition for symmetric property.
- Option 3: \(A=D\) - This is the standard condition for the symmetric property of a two-port network in terms of ABCD parameters.
- Option 4: \(A=B\) - This is generally not the condition for symmetric property.
Therefore, the condition for the symmetric property of ABCD parameters for a two-port network is \(A=D\).
Important Questions from Two Port Networks
A Two - port network is reciprocal if and only if:
Read the following statements regarding two port networks.
(A) The condition of reciprocity and symmetry for a two-port network with 'g' parameter representation can be deduced from the interrelationship of 'h' and g parameters.
(B) The condition of reciprocity for the h parameter representation leads to the condition of reciprocity for 'g' parameters representation as g 12 = −g 21 .
(C) The condition of symmetry in h-parameters representation never leads to the condition of symmetry in 'g' parameters representation.
(D) The symmetry condition in 'h' and 'g parameter representation can be deduced by putting h 11 = g 11 .
Choose the correct answer from the options given below:
A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer ________.
- When port 1 of two-port circuit is short-circuited, I 1 = 4I 2 & V 2 = 0.25 I 2 . Which of the following is true?
A two-port network has scattering parameters given \(\left[ s \right] = \left[ {\begin{array}{*{20}{c}} {{s_{11}}}&{{s_{12}}}\\ {{s_{211}}}&{{s_{22}}} \end{array}} \right]\). If the port 2 of the two-port is short-circuited, the s11 parameter for the resultant one-port network is
