Two Port Networks Questions and Answers

Answer: B

The key marks II and IV as the correct statements. The reasoning behind the key is that the two sets of parameters are not interchangeable in every case: the Z-parameters are defined by open-circuit conditions, which cannot be realised at high frequency, where the open-circuited port has stray capacitance and the test condition fails, and the hybrid pi model gives a direct way to obtain Z from the admittance form of the device. The statement that Y and Z need not be defined separately because Y = 1/Z is not accepted, since for a two-port the matrices are inverses only if the inverse exists, and the statement that conversion is not valid at low frequency is the reverse of what applies. I could not verify every step of the key's argument from a standard text, so the answer rests on the official key. The answer is that options II and IV are correct.

Answer: D

A two-port network is reciprocal when the transfer quantities in the two directions are related. In h-parameters the condition is \(h_{21} = -h_{12}\), which is option (D).

For comparison, the condition in Z-parameters is \(Z_{12} = Z_{21}\), and in Y-parameters it is \(Y_{12} = Y_{21}\). Options A and B compare driving-point quantities (\(Z_{11}\) with \(Z_{22}\), \(Y_{21}\) with \(Y_{22}\)), which describes a symmetrical network and not a reciprocal one. Option C has the wrong sign for the h-parameter condition.

Answer: A

The correct match is zeroes and poles with stability (iv), ramp with \(1/s^{2}\) (iii), superposition with linear elements (i) and transmission parameters with ABCD (ii), so the code is iv iii i ii, option (A).

The locations of poles and zeros decide stability, the Laplace transform of a unit ramp is \(1/s^{2}\), superposition holds for linear elements, and the ABCD parameters are the transmission parameters. Options B, C and D each break at least one of these pairs.

Answer: C

Assertion (A) is true, since ABCD parameters are called the transmission parameters of a two port network. Reason (R) is false as printed: the matrix relation of the ABCD parameters takes the output current in the direction leaving the port, so it reads [V1, I1] = [[A, B], [C, D]] [V2, -I2], with a minus sign on I2, which the printed relation lacks. So (A) is true and (R) is false.

Answer: A

Both statements are true and (R) explains (A). The impedance, admittance, hybrid and transmission parameter sets all describe the same four-terminal network, so each set can be converted into any other.

The conversions hold under the assumption stated in the reason: a linear network with no independent sources inside, with the initial conditions taken as zero, which is the standard basis on which port parameters are defined. The wording of the printed reason on initial conditions is awkward, but the key takes it as this assumption. Hence option (A).