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# Multiple choice question for engineering

## Set 1

1. The key difference between circuit theory and transmission line theory is:
a) circuit elements
b) voltage
c) current
d) electrical size

Answer: d [Reason:] Circuit theory assumes physical dimensions of the network smaller than electrical wavelength, while transmission lines may be considerable fraction of wavelength.

2. Transmission line is a _________ parameter network.
a) lumped
b) distributed
c) active
d) none of the mentioned

Answer: b [Reason:] Since no lumped elements like resistors, capacitors are used at microwave frequencies, only transmission lines are used. Hence they are called distributed parameter network.

3. For transverse electromagnetic wave propagation, we need a minimum of:
a) 1 conductor
b) 2 conductors
c) 3 conductors
d) bunch of conductors

Answer: b [Reason:] With a single conductor, transverse electromagnetic wave propagation is not possible. Hence we need a minimum of 2 conductors.

4. To model a transmission line of infinitesimal length Δz, the lumped element that is not used is:
a) resistor
b) inductor
c) capacitor
d) transistor

Answer: d [Reason:] In the lumped element circuit model of a transmission line, we use only resistor, capacitor and inductor. Hence no transistor is used.

5. _________ and __________ contribute to the impedance of a transmission line in the lumped element representation.
a) resistor, inductor
b) resistor, capacitor
c) capacitor, inductor
d) transistor, capacitor

Answer: a [Reason:] Z=R+jωL. Hence, both resistor and inductor contribute to the impedance of the transmission line.

6. _________ and __________ contribute to the admittance of a transmission line in the lumped element representation.
a) conductance G, capacitor
b) conductance, inductor
c) resistor, capacitor
d) resistor, inductor

Answer: a [Reason:] Y=G+jωC. Hence, both conductance and capacitance contribute to the admittance of the transmission line.

7. Characteristic impedance of a transmission line is:
a) impedance Z of a transmission line
b) impedance which is a constant at any point on the transmission line
c) reciprocal of admittance of a transmission line
d) none of the mentioned

Answer: b [Reason:] Characteristic impedance is defined as that impedance of a line which is a constant when measured at any point on the line, Hence B.

8. Propagation constant γ is a :
a) real value
b) none of the mentioned
c) imaginary value
d) complex value

Answer: c [Reason:] Since propagation constant is a complex value, containing attenuation constant α, phase constant β respectively as their real and imaginary parts.

9. Attenuation constant α signifies:
a) real part of propagation constant
b) loss that the transmission line causes
c) none of the mentioned
d) all of the mentioned

Answer: d [Reason:] α is the real value of propagation constant, also signifies the loss that the transmission line causes and hence the total amount of energy transmitted. Hence all the mentioned.

10. Propagation constant γ is given by:
a) α+jβ
b) α-jβ
c) α/jβ
d) α.jβ

Answer: a [Reason:] Propagation constant is a complex sum of α and β, α being the real value and β being the complex part.

11. Characteristic impedance Zₒ is given by:
a) √Z/Y
b) √ZY
c) √Z+√Y
d) √Z-√Y

Answer: a [Reason:] Characteristic impedance Zₒ is the square root of ratio of impedance and admittance of the transmission line.

12. Propagation constant γ in terms of admittance and impedance of the transmission line is:
a) √Z/Y
b) √ZY
c) ZY
d) ZY*

Answer: b [Reason:] Propagation constant is the root of product of impedance and admittance of the transmission line.

## Set 2

1. Expression for input impedance of a transmission line in terms of load impedance and characteristic impedance is:
a) Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl)
b) (Z0+j ZLtan βl)/ (ZL+j Z0tan βl)
c) Z0 (ZL-j Z0tan βl)/ (Z0-j ZLtan βl)
d) (Z0-j ZLtan βl)/ (ZL-j Z0tan βl)

Answer: a [Reason:] Representing the input voltage as the ratio of voltage at current, representing voltage and currents in hyperbolic function form and simplifying, we get Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl).

2. Input impedance of a short circuited transmission line is :
a) -jZ0tanβl
b) jZ0tanβl
c) jZ0cotβl
d) – jZ0cotβl

Answer: b [Reason:] Since the load impedance of a short circuited transmission line is zero, substituting ZL=0 in the expression for input impedance of a transmission line Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl), input impedance of the transmission line comes out to be jZ0tanβl.

3. Input impedance of a transmission line can be represented in terms of this simple trigonometry function.
a) sine function
b) cosine function
c) cotangent function
d) tangent function

Answer: d [Reason:] The input impedance of a transmission line is expressed in the standard form as Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl) which is represented in terms of a tangent function.

4. If a ƛ/3 transmission line is short circuited that has a characteristic impedance of 50 Ω, then its input impedance is:
a) -j100Ω
b) 50Ω
c) 86.60Ω
d) –j86.60Ω

Answer: d [Reason:] For a short circuited transmission line, the input impedance is given by jZ0tanβl.substituting for characteristic impedance and ‘l’ in the above equation, input impedance is –j86.60Ω.

5. Expression for input impedance of an Open circuited transmission line is:
a) -jZ0tanβl
b) jZ0tanβl
c) jZ0cotβl
d) -jZ0cotβl

Answer: d [Reason:] Since the load impedance of a open circuited transmission line is infinity, substituting ZL=infinity (1/ ZL =0) in the expression for input impedance of a transmission line Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl), input impedance of the open circuited transmission line comes out to be- jZ0cotβl.

6. Input impedance of a open circuited transmission line is represented using this trigonometric function:
a) sine function
b) cosine function
c) cotangent function
d) tangent function

Answer: c [Reason:] The input impedance of a transmission line is expressed in the standard form as Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl). With ZL equal to infinity for open circuit termination, 1/ ZL equal to 0, substituting this, we get input impedance in terms of a cotangent function.

7. For a λ/2 transmission line, if the characteristic impedance of the line is 50 Ω and the terminated with a load of 100 Ω, then its input impedance is:
a) 100Ω
b) 50Ω
c) 88.86Ω
d) none of the mentioned

Answer: a [Reason:] Input impedance of a transmission line is given by Z0 (ZL+j Z0tan βl)/ (Z0+j ZLtan βl). Substituting β=2π/λ, and l=λ/2, we get input impedance of the transmission line equal to the load impedance or the terminated load.

8. If a λ/3 transmission line is open circuited and has characteristic impedance of 50 Ω then the input impedance is:
a) j28.86Ω
b) 50Ω
c) j50Ω
d) 28.86Ω

Answer: a [Reason:] Input impedance of an open circuited transmission line is given by – jZ0cotβl. Substituting l=λ/3 and β=2π/λ in the above equation, input impedance is j28.86Ω.

9. Expression for a transmission co-efficient of a transmission line is :
a) 2ZL/ ( ZL+Z0)
b) (ZL-Z0)/ (ZL+Z0)
c) 2Z0/( ZL+Z0)
d) (ZL+Z0)/ (ZL-Z0)

Answer: a [Reason:] T=┌+1, where T is the transmission co-efficient and ┌ is the reflection co-efficient substituting ┌= (ZL-Z0)/ (ZL+Z0) in the equation for transmission co-efficient, we get 2ZL/ ( ZL+Z0).

10. For a transmission line, if the reflection coefficient is 0.4, then the transmission coefficient is:
a) 0.4
b) 1.4
c) 0.8
d) 2.8

Answer: b [Reason:] T=┌+1, where T is the transmission co-efficient and ┌ is the reflection co-efficient substituting ┌=0.4 in the above equation, transmission co-efficient is equal to 1.4.

11. If the transmission coefficient of a transmission line is 1.6, then the reflection co efficient is:
a) 0.8
b) 0.6
c) 0.4
d) 0.3

Answer: b [Reason:] T=┌+1, where T is the transmission co-efficient and ┌ is the reflection co-efficient substituting T=1.6, we get ┌=0.6.

12. For a transmission line, if the transmission coefficient is 1.4, then the insertion loss in dB is:
a) -2.922dB
b) 29dB
c) 1.46dB
d) -29dB

Answer: a [Reason:] Insertion loss for a transmission line is given by the expression -20loglTl in dB. Substituting T=1.4 and taking logarithm to base 10, insertion loss is -2.922dB.

13. The relation between nepers and decibels is:
a) 1 Np= 8.686 dB
b) 1 dB=8.868 dB
c) Np≥dB
d) dB≥Np

Answer: a [Reason:] 1 Np=10log e2 dB. Substituting e=2.718 in the above equation , 1Np=8.686 dB.

## Set 3

1. A T junction power divider can be used only for division of power.
a) True
b) False

Answer: b [Reason:] A T junction power divider is a 3 port network that can be used either for power dividing or power combining. For power division, one of the ports is excited with the source and the other two ports are used to receive power. For power combining, 2 ports are excited with the source and output is taken at the third port.

2. The lossless T junction dividers can be can all be modeled as a junction of three transmission lines.
a) True
b) False

Answer: a [Reason:] A T junction consists of three ports; hence they can be modeled with 3 transmission lines. However, they cannot be both lossless and matched simultaneously.

3. For the realization of lossless T-junction power divider using transmission lines, the characteristic impedance of the transmission line has to be real.
a) True
b) False

Answer: a [Reason:] From various analyses, it is found that for a transmission line must have real characteristic impedance. If they are not real, they capacitive and inductive passive elements result in retaining some energy in the junction making them lossy.

4. The output power measured at the 2 ports of the T junction:
a) Is a constant
b) Variable
c) Is not real power
d) None of the mentioned

Answer: b [Reason:] The output line impedance determines the power delivered to the 2 output ports in a T junction coupler. Depending on the value of the power desired, the impedance can be changed and the corresponding power is obtained.

5. Hybrid couplers are also a type of directional couplers.
a) True
b) False

Answer: a [Reason:] Hybrid couplers are also a type of directional couplers that give a coupling factor of 3db) A coupling factor of 3dB means that 70.7% of the total input power is received at the output port.

6. If the input power is divided in the ratio of 2:1 in a T- junction coupler and the characteristic impedance of the 2 output lines is 150Ω and 75Ω, then the impedance of the input line is:
a) 100Ω
b) 50Ω
c) 150Ω
d) None of the mentioned

Answer: b [Reason:] The input impedance of the T junction is the equivalent of the 2 output impedances in parallel. That is 150││75. Solving this, (150*75/(150+75)), the input impedance is 50 Ω.

7. A lossy T junction can be matched at all the three ports.
a) True
b) False

Answer: a [Reason:] If a T junction is constructed using resistors, the T junction becomes lossy, but it can be simultaneously matched at all the three ports.

8. The diagonal elements of the s matrix of a resistive T junction are:
a) 0
b) 1
c) 0.5
d) 1.5

Answer: a [Reason:] A resistive junction can be matched at all the three ports of the junction. Hence no power is reflected back. As a result, the diagonal elements are all 0 for a resistive T junction.

9. The power delivered to the input port of a resistive power divider is equal to the source voltage applied.
a) True
b) False

Answer: b [Reason:] Since power is applied to a resistive power divider, there is loss and hence not all the supply power is delivered to the input port of the power divider.

10. The power input at the port 1 of resistive T junction is equally divided among the 2 output ports of the T junction.
a) True
b) False

Answer: b [Reason:] The power division ratio of a resistive T junction depends on the resistance of the resistors used in forming those junctions. Depending on the resistors used, the power gets divided accordingly.

## Set 4

1. As the beam area of an antenna decreases, the directivity of the antenna:
a) Increases
b) Decreases
c) Remains unchanged
d) Depends on the type of the antenna

Answer: a [Reason:] Beam area of an antenna and the directivity of the antenna are inversely proportional. As the beam area is reduced, the directivity increases, meaning smaller the radiating area of the transmitting antenna, more directed is the emitted energy.

2. If an antenna radiates over half a sphere, directivity of the antenna is:
a) Two
b) Four
c) Three
d) One

Answer: a [Reason:] Since the antenna radiates over half the sphere, beam area of the antenna is 2π, directivity of the antenna is given by 4π/ beam area. Substituting for beam area, the directivity of the antenna is two.

3. The half power beam width of an antenna in both θ and φ are 400 each. Then the gain of the antenna is:
a) 23
b) 25
c) 14
d) 27

Answer: b [Reason:] Approximate gain of an antenna is given by the expression 40000/ (HPBW) 2. Substituting the given values in the above expression, the gain of the antenna is 25. In dB scale the gain of the antenna is 14 dB.

4. The number N of radio transmitters or point sources of radiation distributed uniformly over the sky which an antenna can resolve is given by:
a) 4π/ ΩA
b) 2π/ ΩA
c) π/ ΩA
d) None of the mentioned

Answer: a [Reason:] Resolution may be defined as equal to half the beam width between first nulls. In the above expression the resolution N is given as 4π/ ΩA.. Here ΩA is the beam area.

5. Ideally, the number of point sources an antenna can resolve is numerically equal to:
a) Gain of the antenna
b) Directivity
c) Beam efficiency
d) Beam area

Answer: b [Reason:] The number of point source an antenna can resolve is given by 4π/ ΩA Directivity of an antenna is mathematically given by the relation 4π/ ΩA . Numerically resolution and directivity are equal.

6. Effective aperture is a parameter of the antenna that gives the physical aperture of the antenna.
a) True
b) False

Answer: b [Reason:] Effective aperture defines the amount of the total aperture of the antenna that is utilized for radiation of energy. Higher the effective aperture of an antenna, more is the aperture efficiency.

7. Effective aperture in terms of beam area and operating wavelength is given by the relation:
a) λ2/ ΩA
b) ΩA / λ2
c) λ2× ΩA
d) No such relationship exists

Answer: a [Reason:] Effective aperture is given as λ2/ ΩA. Here ΩA is the beam area. If the beam area is specified in terms of the operating wavelength λ, then effective are of the antenna can be made operating wavelength independent.

8.________ of an antenna is defined as the ratio of the induced voltage to the incident electric field.
a) Effective height
b) Gain
c) Directivity
d) Loss

Answer: a [Reason:] At the receiving end, effective height of an antenna is defined as the ratio of the induced voltage to the incident electric field. Otherwise, if the effective length of the receiving antenna is known and if the induced voltage is measured, then the field strength can be determined.

9. The directivity of an antenna in terms of the aperture efficiency and operating wavelength is given by:
a) 4πAe/λ2
b) 2πAe/λ2
c) πAe/λ2
d) None of the mentioned

Answer: a [Reason:] The directivity of an antenna in terms of aperture efficiency is given by 4πAe/λ2. Here Ae is the aperture efficiency. λ is the operating frequency. With an increase in the effective aperture area of an antenna, directivity of the antenna can be increased making the radiated beam narrower.

10. A radio link has 15 W transmitter connected to an antenna of 2.5 m2 effective aperture at 5 GHz. The receiving antenna has an effective aperture of 0.5 m2 and is located at a 15 Km line of sight distance from transmitting antenna. Assuming lossless, matched antennas, the power delivered to the receiver is:
a) 20 µW
b) 15 µm
c) 23 µm
d) 25 µm

Answer: c [Reason:] The power delivered to the receiving antenna is Pt (A1 A2/ r2λ2). Substituting the given values in the above equation, the power at the receiver is 23 µm.

## Set 5

1. A practical oscillator has a frequency spectrum consisting of a single delta function at its operating frequency.
a) True
b) False

Answer: b [Reason:] An ideal oscillator has a frequency spectrum consisting of a single delta function at its operating frequency, but a practical oscillator has a spectrum in the form of a Gaussian curve consisting of some noise component.

2. ____________ due to random fluctuations caused by thermal and other noise sources appear as broad continuous distribution localized about the output signal.
a) Phase noise
b) White noise
c) Thermal noise
d) Shot noise

Answer: a [Reason:] Phase noise is defined as the ratio of power in one phase modulation sideband to the total signal power per unit bandwidth at a particular offset fm. phase noise due to random fluctuations caused by thermal and other noise sources appear as broad continuous distribution localized about the output signal.

3. The phase variation for an oscillator or synthesizer is given by:
a) ∆f*sin ωmt/ fm
b) ∆f / fm
c) Sin ωmt/ fm
d) None of the mentioned

Answer: a [Reason:] The phase variation for an oscillator or synthesizer is given by ∆f*sin ωmt/ fm. here, fm is the modulating signals frequency, ∆f is the change in the frequency.

4. The expression for phase noise in an oscillator is given by:
a) θrms2
b) θrms2/√2
c) θrms2/2
d) θrms2/ 3

Answer: c [Reason:] The expression for phase noise in an oscillator is given by θrms2/2. θrms is the rms value of the phase deviation. Phase noise is directly proportional to the square of the RMS value of the phase deviation. Greater the deviation, higher is the phase noise.

5. Phase noise at the output of an oscillator is given by:
a) kBFGT0
b) kT0F/Pc
c) kT0F/Pc
d) None of the mentioned

Answer: b [Reason:] Phase noise at the output of an oscillator is given by kT0F/Pc. here k is the Boltzmann’s constant. B is the operating bandwidth of the system, here the equation is considered for a bandwidth of 1 Hz as per the definition of phase noise. F is the figure of merit of system.

6. Noise power versus frequency for an amplifier has spikes at the operating frequency without the application of an input voltage.
a) True
b) False

Answer: b [Reason:] Noise power versus frequency for an amplifier has spikes at the operating frequency with the application of an input voltage. When an input voltage is applied to the amplifier, noise component also is added. Along with the signal, noise is also amplified and peaks at the operating frequency.

7. An idealized power spectral density of amplifier has a straight line parallel to X axis and the noise is constant at all frequencies.
a) True
b) False

Answer: b [Reason:] The curve has a negative slope up to a frequency called fα due to the thermal noise also called as 1/f noise. Above this frequency, the graph is a straight line parallel to X axis.

8. At higher frequencies of operation of an oscillator, induced noise is mostly:
a) Thermal noise
b) White noise
c) Shot noise
d) Flicker noise

Answer: a [Reason:] At higher frequencies of operation of an oscillator, induced noise is mostly thermal, and constant with frequency. This noise is also proportional to the noise figure of the amplifier.

9. A GSM cellular telephone standard requires a minimum of 9 dB rejection of interfering signal levels of -23 dBm at 3 MHz from the carrier, -33 dBm at 1.6 MHz from the carrier, and -43 dBm at 0.6 MHz from the carrier, for a carrier level of -99 dBm. Determine the required local oscillator phase noise at 3 MHz carrier frequency offset.
a) -138 dBc/Hz
b) -128 dBc/Hz
c) -118 dBc/Hz
d) None of the mentioned