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 :
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both statements are true, and the reason states the very condition that makes the assertion possible.
Why there are four parameter sets. A two-port has four terminal variables — V1, I1, V2, I2 — of which any two may be chosen as independent and the other two expressed in terms of them. Each choice gives a different description:
| Set | Independent | Equations | Where used |
|---|---|---|---|
| z | I1, I2 | V = zI | Series-connected networks |
| y | V1, V2 | I = yV | Parallel-connected networks |
| h | I1, V2 | Hybrid | Transistor models |
| ABCD | V2, −I2 | Transmission | Cascaded networks, lines |
Since all four describe the same network, they must be interconvertible, and the standard conversion tables express any set in terms of any other — for example \(h_{11}=\dfrac{\Delta z}{z_{22}}\) and \(y=z^{-1}\).
Now the reason, which is the precondition for all of it. Each description takes the form of a homogeneous linear relation — a 2 × 2 matrix with no constant term. Two things would destroy that:
• an independent source inside the network would add a constant, so V1 would not be zero when both currents were zero, and the matrix form could not hold;
• a non-zero initial condition — charge on a capacitor, current in an inductor — would add a similar constant term in the s domain.
Excluding both is exactly what allows the network to be characterised by four numbers, and hence what allows the four sets to be related to one another. So (R) explains (A) and the code is 1.
What is not excluded : dependent (controlled) sources are perfectly permissible, because their value is proportional to a terminal variable and so contributes to the matrix rather than to a constant term. Their presence simply makes the network non-reciprocal, so \(z_{12}\ne z_{21}\) and the matrix loses its symmetry. That is precisely how a transistor is modelled.
A caution on existence : the four sets are interconvertible but not all of them always exist. A network whose z matrix is singular has no y parameters, and an ideal transformer has neither z nor y but perfectly good ABCD parameters — which is a further reason for keeping all four in the toolkit.
Hence, both (A) and (R) are true and (R) is the correct explanation of (A).
Similar Questions
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?
