# Microwave Engineering Questions and Answers – Scattering Matrices

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This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Scattering Matrices”.

1. S parameters are expressed as a ratio of:
a) Voltage and current
b) Impedance at different ports
c) Indecent and the reflected voltage waves
d) None of the mentioned

Explanation: S matrix can be used to represent any n port network. S parameters are defined for microwave networks. Hence instead of voltage and current measurement, the amplitude of the incident and reflected voltage waves is measured.

2. The relation between incident voltage matrix , reflected voltage matrix and S matrix for a microwave network:
a) [v-] = [s] [v+].
b) [v+] = [s] [v-].
c) [v-] [v] = [s].
d) [s] = [v] [v-].

Explanation: S parameter for a microwave network is defined as the ratio of reflected voltage wave to the incident voltage wave. When represented in the form of a matrix, reflected voltage matrix is the product of S parameter and the incident voltage wave at that port.

3. The specific element Sij of the scattering matrix can be determined as:
a) SIJ= Vi-/Vj+
b) SIJ= Vi+/Vj-
c) S= Vj+/Vi-
d) None of the mentioned

Explanation: The parameter Sij is found by driving port j with an incident wave of voltage Vj+ coming out of ports i. The incident waves on all ports except the jth port are set to zero.

4. The device used to get the measurement of S parameters of n- port micro wave network is:
a) CRO
b) Network analyzer
c) Circulator
d) Attenuator

Explanation: Network analyzer is a device to which any microwave network can be externally connected with the help of probes and the s parameters of the network can be obtained.

5. For a one port network , the scattering parameter S₁₁ in terms of impedance parameter Z₁₁ is:
a) (Z11-1)/ (Z11+1)
b) (Z11+1)/ (Z11-1)
c) (Z11+1) (Z11-1)
d) Z11

Explanation: If Z matrix of a one port network is computed, then the s matrix of the same can be computed using the Z11 coefficient. To compute the S11 parameter of the network, the relation used is (Z11-1)/ (Z11+1).

6. Scattering matrix for a reciprocal network is:
a) Symmetric
b) Unitary
c) Skew symmetric
d) Identity matrix

Explanation: For a reciprocal network, the input to port I and output at port j is the same as the input at port j and output measured at port i. Hence, the ports are interchangeable. As the ports are interchangeable, this is reflected in the matrix and the matrix becomes symmetric.

7. S₁₂=0.85-45⁰ and S₁₂=0.85 +45⁰ for a two port network. Then the two port network is:
a) Non-reciprocal
b) Lossless
c) Reciprocal
d) Lossy

Explanation: For a reciprocal network, the S matrix is symmetric. For the matrix to be symmetric, Sij=Sji. Since this condition is not satisfied in the above case, the matrix is non reciprocal.

8. Scattering matrix for a lossless matrix is:
a) Unitary
b) Symmetric
c) Identity matrix
d) Null matrix

Explanation: For a lossless network, the scattering matrix has to be unitary. That is, the law of conservation of energy is to be verified for this case. Using appropriate formula, this condition can be verified.

9. If the reflection co efficient of a 2 port network is 0.5 then the return network loss in the network is:
a) 6.5 dB
b) 0.15 dB
c) 6.020 dB
d) 10 dB

Explanation: Given the reflection coefficient of the network, return loss of the network is calculated using the formula -20 log │Г│. Substituting for reflection coefficient, the return loss of the network is 6.02 dB.

10. If the reflection co efficient of a 2 port network is 0.25 then the return network loss in the network is:
a) 12.05 dB
b) 0.15 dB
c) 20 dB
d) 10 dB