For the two-port network shown in figure, the z-parameter matrix is given by
\(\begin{bmatrix} 6 & 2 \\ 2 & 3 \end{bmatrix}\,\Omega\)
The network. It is a T-network: a 4 Ω resistor in series with port 1, a 2 Ω resistor shunting from the middle node down to the common rail, and a 1 Ω resistor in series with port 2.
Definition of the z-parameters. The impedance (open-circuit) parameters are defined by
\(V_1 = Z_{11}I_1 + Z_{12}I_2, \qquad V_2 = Z_{21}I_1 + Z_{22}I_2\)
so each parameter is measured with one port left open:
\(Z_{11}=\left.\dfrac{V_1}{I_1}\right|_{I_2=0},\ Z_{12}=\left.\dfrac{V_1}{I_2}\right|_{I_1=0},\ Z_{21}=\left.\dfrac{V_2}{I_1}\right|_{I_2=0},\ Z_{22}=\left.\dfrac{V_2}{I_2}\right|_{I_1=0}\)
Z11 — drive port 1, port 2 open. With I2 = 0 no current flows in the 1 Ω arm, so it drops no voltage and can be ignored. The current I1 flows through the 4 Ω series arm and then through the 2 Ω shunt arm:
\(Z_{11} = 4 + 2 = 6\ \Omega\)
Z22 — drive port 2, port 1 open. Now the 4 Ω arm carries no current, and I2 flows through the 1 Ω series arm and the 2 Ω shunt arm:
\(Z_{22} = 1 + 2 = 3\ \Omega\)
Z21 — transfer impedance. With port 2 open, all of I1 flows through the shunt 2 Ω resistor, and the open-circuit voltage at port 2 is the voltage across that shunt element (the 1 Ω arm drops nothing):
\(V_2 = 2 I_1 \Rightarrow Z_{21} = 2\ \Omega\)
Z12. The network contains only resistors, so it is reciprocal and \(Z_{12} = Z_{21} = 2\ \Omega\). Physically, the 2 Ω shunt arm is the branch common to both loops, and for a T-network the mutual term is always the shunt element.
Assemble the matrix.
\([Z] = \begin{bmatrix} 6 & 2 \\ 2 & 3 \end{bmatrix}\Omega\)
Quick check on the options. A reciprocal network must give a symmetric matrix (Z12 = Z21), which immediately rules out options 2, 3 and 4; only option 1 is symmetric, and its diagonal entries 6 Ω and 3 Ω match the series-plus-shunt sums computed above.
Shortcut worth memorising. For a T-network with series arms ZA (port 1), ZB (port 2) and shunt arm ZC: \(Z_{11}=Z_A+Z_C\), \(Z_{22}=Z_B+Z_C\), \(Z_{12}=Z_{21}=Z_C\).
Hence, the z-parameter matrix is [[6, 2], [2, 3]] Ω.
Similar Questions
Assertion (A) : In a two port network, with 4 terminals four types of parameters like impedance, admittance, hybrid and transmission are considered and they are related to each other.
Reason (R) : The assumption made for the above statement is that there are no independent sources and non-zero initial conditions within the linear port network.
Select your answer using the codes given below :
Read the following statements :
ST 1 : y-parameters can be obtained from Z parameters.
ST 2 : It is not necessary to define y-parameters separately.Match the given lists :
List – I List – II a. Condition of reciprocity i. \(\dfrac{Z_{12}}{Z_{22}}\) b. h12 ii. Z12 = Z21 c. 
\(\begin{bmatrix}R&R\\R&R\end{bmatrix}\)iii. Z d. Condition of symmetry iv. Z11 = Z22 Codes :
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 ________.
The condition for symmetric property of ABCD parameter of two port network is:
- 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?
