# Microwave Engineering Questions and Answers – Binomial Multi-section Matching Transformers

This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Binomial Multi-section Matching Transformers”.

1. The passband response of a binomial matching transformer can be called optimum:
a) if the roll off in the response curve is high
b) if the response is flat in the impedance matched region
c) if the matching network is frequency sensitive
d) none of the mentioned

Explanation: The response curve of a binomial matching transformer ( θ v/s │Г (θ) │) must be flat at the frequency for which impedance matching is performed and for those frequencies that lie in the required bandwidth. This is one of the most important characteristic of a good matching circuit.

2. If a quality binomial matching transformer gives a good flat response curve, it is called “maximally flat”.
a) true
b) false

Explanation: A binomial matching section can be termed efficient when it is less frequency sensitive and gives a constant gain over a wide range of frequencies. This constant gain implies a flat curve over a wide range of frequencies. This is termed as “maximally flat”.

3. The response curve of a binomial matching transformer is plotted for each section of the matching network individually and then analyzed for optimum solution.
a) true
b) false

Explanation: The response curve of a binomial multisection transformer is determined for an N-section transformer by setting the first N-1 derivatives of │Г (θ) │ to zero at the center frequency, fₒ.

4. To obtain a flat curve in the response of a binomial multisection transformer, N-1 derivatives of │Г (θ) │are set to zero. This implies:
a) the frequency sensitivity of the matching section is increased linearly
b) the frequency sensitivity of the matching section is increased exponentially
c) roll off in the curve is increased
d) none of the mentioned

Explanation: The derivatives of │Г (θ) │ show the rate of change of reflection co-efficient with distance. If this derivative is not zero, the matching circuit becomes more sensitive and a higher bandwidth cannot be obtained. Hence to make the matching network frequency independent, the derivatives are set to zero.

5. The condition │Г (θ) │=0 for θ=π/2 of a binomial multi section transformer corresponds to the:
a) upper cutoff frequency
b) lower cutoff frequency
c) center frequency
d) none of the mentioned

Explanation: θ=π/2 corresponds to the center frequency at which │Г (θ) │=0. θ=βl. β=2 π/λ and l=λ/4. Substituting for β and λ in the equation for θ, θ=π/2. This is the center frequency at which impedance matching is done at which the reflection coefficient is zero and perfect match is achieved.
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6. The reflection co-efficient magnitude of a binomial multisection transformer is:
a) 2N│A││cos (θ)│N
b) 2N│A│
c) 2N│cos (θ) │N
d) none of the mentioned

Explanation: The reflection co-efficient of a binomial multisection transformer is dependent on the length of the matching section, operating frequency and load impedance and characteristic impedance. A is a constant defined as A=2-N (ZL– Z0)/ (ZL+ Z0).

7. The reflection coefficient ГN in terms of successive impedances Zn and Zn+1 when multisection transformers are used in a binomial matching transformer is given by:
a) 0.5ln (Zn+1/Zn)
b) ln (Zn+1/Zn)
c) 0.5ln (Zn/Zn+1)
d) (Zn/Zn+1)

Explanation: After binomial expansion of the equation for Г(θ), the maximum power is N, where N is the number of the sections in the transformer. After making suitable approximations so that the approximated values are in well agreement with actual values, the expression for reflection coefficient is 0.5ln (Zn+1/Zn).

8. In the plot of normalized frequency v/s reflection co-efficient for a binomial multisection filter, the curve has a dip at:
a) center frequency
b) upper cutoff frequency
c) lower cutoff frequency
d) none of the mentioned

Explanation: Since the impedance matching circuit is used to match the load to the transmission line, there will be perfect match in the circuit resulting in zero or low reflection. Hence, there is a dip at the center frequency.

9. As the number of sections in the binomial multisection transformer increases the plot of normalized frequency v/s reflection co-efficient has a wider open curve.
a) true
b) false

Explanation: When more number of sections are used for matching, the reflection co-efficient is low for neighboring frequencies as well. Hence, the network can be used for a wide range of operating frequencies. Hence, this increases the bandwidth.

10. A three section binomial transformer is used to match a 100Ω transmission line to a 50Ω transmission line. Then the value of the constant ‘A’ for this design is:
a) -0.0433
b) 0.0433
c) 0.01
d) -0.01

Explanation: ‘A’ is given by the expression 2-(n+1)ln (ZL/Z0), Where N is the number of sections in the matching network. Substituting the given values in the equation for ‘A’, the value of A is -0.0433.

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