# Microwave Engineering Questions and Answers – Stability Circles

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

1. For a transistor amplifier to be stable, either the input or the output impedance must have a real negative part.
a) True
b) False

Explanation: For a transistor amplifier to be stable, either the input or the output impedance must have a real negative part. This would imply that │Гin│>1 or │Гout│>1, because these reflection coefficients depend on the source and load matching network.

2. ____________ condition, if met then the transistor can be impedance matched for any load.
a) Conditional stability
b) Unconditional stability
c) Infinite gain
d) Infinite input impedance

Explanation: A network is said to be unconditionally stable if │Гin│<1 and │Гout│<1 for all passive source and load impedance. Transistors that are unconditionally stable can be easily matched.

3. A network is said to be conditionally stable if:
a) │Гin│<1, │Гout│<1.
b) │Гin│>1, │Гout│>1
c) │Гin│>1, │Гout│<1
d) │Гin│<1, │Гout│>1

Explanation: For conditional stability, the condition to be satisfied is │Гin│<1, │Гout│<1. But this condition will be valid only for a certain range of passive source and load Impedance. His condition is also called potentially unstable.
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4. Stability condition of an amplifier is frequency independent and hence can be operated at any frequency.
a) True
b) False

Explanation: Stability condition of an amplifier is frequency dependent since the input and output matching networks generally depend on frequency. Hence it is possible for an amplifier to be stable at the designed frequency and unstable at other frequencies.

5. For a unilateral device condition for unconditional stability in terms of S parameters is:
a) │S11│<1, │S22│<1
b) │S11│>1, │S22│>1
c) │S11│>1, │S22│<1
d) │S11│<1, │S22│>1

Explanation: For a unilateral device, the condition for unconditional stability is │S11│<1, │S22│<1. S11 parameter signifies the amount of power reflected back to port 1, which is the input port of the transistor. If this S parameter is greater is than 1, more amount of power is reflected back implying the amplifier is unstable.

6. If │S11│>1 or │S22│>1, the amplifier cannot be unconditionally stable.
a) True
b) False

Explanation: If │S11│>1 or │S22│>1, the amplifier cannot be unconditionally stable because we can have a source or load impedance of Zₒ leading to Гs=0 or ГL=0, thus causing output and input reflection coefficients greater than 1.

7. For any passive source termination ГS, Unconditional stability implies that:
a) │Гout│<1
b) │Гout│>1
c) │Гin│<1
d) │Гin│>1

Explanation: Unconditional stability implies that │Гout│<1 for any passive source termination, Гs. The reflection coefficient for passive source impedance must lie within the unit circle of the smith chart, nd the other boundary of the circle is written as Гs=e.

8. The condition for unconditional stability of a transistor as per the K-∆ test is │∆│> 1 and K<1.
a) True
b) False

Explanation: The condition for unconditional stability of a transistor is │∆│< 1 and K>1. Here, │∆│ and K are defined in terms of the s parameters of the transistor by defining the S matrix. To determine the unconditional stability of a transistor in K-∆ method, the S matrix of the transistor must be known.

9. If the S parameters of a transistor given are
S11=-0.811-j0.311
S12= 0.0306+j0.0048
S21=2.06+j3.717
S22=-0.230-j0.4517
Then ∆ for the given transistor is:
a) 0.336
b) 0.383
c) 0.456
d) None of the mentioned

Explanation: Given the S parameters of a transistor, the ∆ value of the transistor is given by │S11S22-S12S21│. Substituting the given values in the above equation, the ∆ of the transistor is 0.336.

10. By performing the K-∆ test for a given transistor the values of K and ∆ were found to be equal to 0.383 and 0.334 respectively. The transistor with these parameters has unconditional stability.
a) True
b) False