The z parameters z11 and z21 for the 2-port network shown in the given figure respectively are :
\(z_{11}=\dfrac{6}{11}\ \Omega;\ z_{21}=\dfrac{-16}{11}\ \Omega\)
Both parameters are open-circuit parameters, so set \(I_{2}=0\) and keep it that way throughout. By definition
\(z_{11}=\left.\dfrac{E_{1}}{I_{1}}\right|_{I_{2}=0}\qquad z_{21}=\left.\dfrac{E_{2}}{I_{1}}\right|_{I_{2}=0}\)
Step 1 — trace the current. With port 2 open, the whole of I1 flows through the 2 Ω series resistor, then down through the 4 Ω shunt resistor, and finally through the dependent source back to the input terminal.
Step 2 — apply KVL round the input loop. Adding the two resistive drops and the controlled source,
\(E_{1}=2I_{1}+4I_{1}-10E_{1}\)
\(E_{1}+10E_{1}=6I_{1}\)
\(11E_{1}=6I_{1}\quad\Rightarrow\quad z_{11}=\dfrac{E_{1}}{I_{1}}=\dfrac{6}{11}\ \Omega\)
The 11 in every option is the signature of this step — it comes from the \(1+10\) produced by the controlled source acting back on its own controlling variable.
Step 3 — write the output voltage. E2 is measured from the shunt node to the reference terminal, so it is the 4 Ω drop plus the source voltage:
\(E_{2}=4I_{1}-10E_{1}\)
Substituting \(E_{1}=\dfrac{6}{11}I_{1}\),
\(E_{2}=4I_{1}-10\left(\dfrac{6}{11}\right)I_{1}=\dfrac{44-60}{11}I_{1}=-\dfrac{16}{11}I_{1}\)
\(z_{21}=-\dfrac{16}{11}\ \Omega\)
which is option 3.
| Parameter | Definition | Value |
|---|---|---|
| z11 | Open-circuit input impedance | +6/11 Ω |
| z21 | Open-circuit forward transfer impedance | −16/11 Ω |
Two checks worth making. First, z11 must be positive here, because the input still looks resistive from the source's point of view — a negative value would mean the network was delivering power back, which this passive-plus-controlled-source combination does not do at the input. Second, z21 may perfectly well be negative: it is a transfer quantity, and the dependent source inverts the sense of the output. That sign is also why the network is non-reciprocal; with a controlled source present \(z_{12}\ne z_{21}\), and reciprocity, which holds for any network of R, L, C and transformers alone, is lost.
Hence, z11 = 6/11 Ω and z21 = −16/11 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?
