# Microwave Engineering Questions and Answers – Transmission Matrix(ABCD)

This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Transmission Matrix(ABCD)”.

1. ABCD matrix is used:
a) When there is two or more port networks in the cascade
b) To represent a 2 port network
c) To represent a 2 port network
d) To represent the impedance of a microwave network

Explanation: The Z, Y, and S parameter representation can be used to characterize a microwave network with an arbitrary number of ports. But most microwave networks consist of cascade of two or more two port networks. In this case it is convenient to use ABCD matrix for network representations.

2. The voltage equation for a 2 port network that can be represented as a matrix is:
a) V1=AV2 + BI2
b) V1=CV2 + DI2
c) V1=BV2 +AI2
d) V1=DV2+CI2

Explanation: In the equation, V1 is the voltage measured at port 1 and V2 is the voltage measured at port 2 and I2 is the current measured at the second port. A and B are the network constants.

3. ABCD matrix of the cascade connection of 2 networks is equal to:
a) Product of ABCD matrices representing the individual two ports
b) Sum of the ABCD matrices representing the individual two ports
c) Difference of the ABCD matrices representing the individual two ports
d) Sum of transpose of ABCD matrices representing the individual two ports

Explanation: When two networks are connected in cascade, each of the two networks are represented as a 2×2 square matrix. Then to obtain the equivalent matrix of the cascade, the product of the ABCD matrices of each stage is taken.

4. For simple impedance Z, the ABCD parameters are:
a) A=1, Z=B, C=0, D=1
b) A=0, B=1, C=1, D=0
c) A=Z, B=1, C=1, D=0
d) A=1, B=0, C=Z, D=1

Explanation: If simple impedance or an equivalent impedance of a network is represented as a ABCD matrix, writing the equations in terms of voltage and current and setting each variable to zero, the four constants are obtained. For an impedance Z, the constants are A=1, Z=B, C=0, D=1.

5. For a simple admittance Y, the ABCD parameters are:
a) A=1, B=0, C=Y, D=1
b) A=Z, B=1, C=1, D=0
c) A=1, B=0, C=Z, D=1
d) A=1, Y=B, C=0, D=1

Explanation: If simple admittance or an equivalent admittance of a network is represented as a ABCD matrix, writing the equations in terms of voltage and current and setting each variable to zero, the four constants are obtained. For an admittance Y, the constants are A=1, Z=B, C=0, D=1.
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6. C parameter for a transmission line of characteristic impedance Zₒ, phase constant β and length ‘l’ is:
a) j Yₒ Sin βl
b) j Zₒ Sin βl
c) j Zₒ tan βl
d) j Yₒ tan βl

Explanation: If a transmission line is represented as two port network, constants can be derived in terms of the A, B, C, D constants for the network. But setting each electrical parameter to zero, this constant is found. By doing so, the C parameter of transmission line is j Yₒ Sin βl.

7. For a 2 port network if Z₁₁=1.5 and Z₁₂=1.2, A parameter for the same 2 port network is:
a) 1.5
b) 1.25
c) 0.75
d) 1.75

Explanation: A parameter for the two port network is the ratio of the impedance Z11 and the impedance Z12. Substituting in this equation,’ A’ parameter of the network is 1.25.

8. For a 2 port network, if the admittance parameter Y₁₂=0.4, then B among the ABCD, parameters for the 2 port network is:
a) 2.5
b) 4.5
c) 5
d) 6

Explanation: For a two port network, B parameter is defined as the reciprocal of the admittance Y12. Taking the reciprocal of the given value, the B parameter of the network is 2.5.

9. If D=1.6 and B=2.8 for a 2 port network, then Y₁₁=?
a) 0.5714
b) 0.987
c) 0.786
d) 1.75

Explanation: The admittance Y11 of the network is defined as the ratio of B parameter to the D parameter of the network. Taking the ratio of the given values, admittance Y11 is 0.5714.

10. If A=2.8 and B=1.4 for a 2 port network then Z₁₁=?
a) 0.5
b) 2
c) 4.2
d) 2.7

Explanation: Z11 parameter of a two port network is the ratio of the A parameter of the network to the B parameter of the network. Taking the ratio of the given values, Z11 is 2.

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