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# Multiple choice question for engineering

## Set 1

1. Quadrature hybrids are those couplers which are:
a) 3 dB couplers
b) Directional couplers
c) They have a 900 phase difference between signals in through and coupled arms.
d) All of the mentioned

Answer: d [Reason:] Quadrature hybrids are directional couplers that have a phase difference of 900 between the signals obtained at through and coupled ports.

2. Branch-line couplers are also popular as Quadrature hybrids.
a) True
b) False

Answer: a [Reason:] Quadrature hybrids are also called as branch-line couplers. The other 3 dB couplers are coupled line couplers or Lange couplers. These couplers also can be Quadrature hybrids.

3. The S matrix of a Quadrature hybrid is of size 4×4 and the diagonal elements of a matched coupler are all:
a) 1
b) 0
c) Cannot be determined
d) None of the mentioned

Answer: b [Reason:] In a matched coupler, since all ports are matched, no power goes back to the port from which the flow of energy in the coupler occurred. Since the backward power flow is zero for matched network, the diagonal elements are zero.

4. A branch-line coupler is an asymmetric coupler.
a) True
b) False

Answer: b [Reason:] A branch-line coupler is a symmetric coupler that has all four ports placed symmetrically. Since the construction is symmetric, any port can be used as input and any port can be used as output.

5. Branch-line couplers are preferably made using waveguides so as to obtain high gain and simple construction.
a) True
b) False

Answer: b [Reason:] Branch-line couplers are mostly done using microstrip lines. They also reduce the complexity of the circuit and can be easily integrated with other microwave devices in all large scale applications.

6. A 50 Ω branch-line Quadrature hybrid has to be designed to operate over a range of frequencies. The branch-line impedance of this coupler so designed is:
a) 70.7 Ω
b) 35.4 Ω
c) 50 Ω
d) 100 Ω

Answer: b [Reason:] Each arm of a Quadrature hybrid is λ/4 long; λ is the wavelength at which the coupler is designed to operate. The branch-line impedance for a λ/4 line is Z0/√2. Substituting for Z0 in the equation, the impedance is 35.4 Ω.

7. The plot S11 v/s frequency for a branch-line coupler has a straight line characteristic for a wide range of frequency around the designed frequency range.
a) True
b) False

Answer: b [Reason:] S11 parameter signifies the power measured at port 1 when port 1 is used as an input port. When the ports of the coupler are matched, no power is reflected back to the port 1. Hence S11 curve has a dip at the frequency for which the coupler was operated to design. A fall and rise in the curve is seen at this point.

8. The curve of S14 for a branch-line coupler is similar to that of the S11 curve of the branch-line coupler.
a) True
b) False

Answer: a [Reason:] S14 parameter gives the power measured at the port 4 or the isolated port of the branch-line coupler. Since the signals that reach port 4 from 2 different arms are 900 out of phase with each other, theoretically power at port 4 is zero. Practically, it is zero for the designed frequency but some power is received at other frequencies.

9. S12 and S13 curves for branch-line couplers are almost a straight line parallel to X –axis. Both the curves are similar and follow same path.
a) True
b) False

Answer: a [Reason:] S13 and S12 parameters give the power measured at port 2 and port 3 of the branch-line coupler when port 1 is used as the input port. Since these are the through and coupled ports, power measured across these ports is almost constant and resemble a straight line parallel to X axis.

10. If the branch-line impedance of a coupler designed to operate at 1 GHz is 70.70 Ω, then the characteristic impedance of the material of the arms of the branch-line coupler is:
a) 70.7 Ω
b) 50 Ω
c) 100 Ω
d) None of the mentioned

Answer: c [Reason:] Given the branch impedance is 70.70 Ω; the characteristic impedance of the line is Z√2. This relation is used since all the arms of a branch-line coupler are λ/4 long. Substituting for Z, the characteristic impedance of the line is 100 Ω.

## Set 2

1. If a transmission line of characteristic impedance 50 Ω is to be matched to a load of 100Ω, then the characteristic impedance of the ƛ/4 transmission line to be used is:
a) 70.71 Ω
b) 50 Ω
c) 100 Ω
d) 75 Ω

Answer: a [Reason:] When a transmission line is not terminated with a matched load, it leads to losses and reflections. In order to avoid this, a λ/4 transmission line can be used for matching purpose. The characteristic impedance of the λ/4 transmission line is given by Z1=√(ZₒR)L. substituting the given values, we get Z1=70.71 Ω.

2. If a λ/4 transmission line is 100Ω is used to match a transmission line to a load of 100Ω, then the characteristic impedance of the transmission line is:
a) 100 Ω
b) 50 Ω
c) 70.71 Ω
d) 200 Ω

Answer: a [Reason:] When a transmission line is not terminated with a matched load, it leads to losses and reflections. In order to avoid this, a λ/4 transmission line can be used for matching purpose. The characteristic impedance of the λ/4 transmission line is given by Z1=√(ZₒR)L. substituting the given values, Z0=100 Ω.

3. Expression for the characteristic impedance of a transmission line(λ/4) used for impedance matching is:
a) Z1=√(ZₒR)L
b) Z1=√(Zₒ/R)L
c) Z1=√(Zₒ+R)L
d) None of the mentioned

Answer: a [Reason:] When a transmission line is not terminated with a matched load, it leads to losses and reflections. In order to avoid this, a λ/4 transmission line can be used for matching purpose. Hence the expression used to find the characteristic impedance of the λ/4 transmission line is Z1=√(ZₒR)L.

4. If there is no standing wave on a transmission line, then the value of SWR is:
a) 1
b) 0
c) Infinity
d) Insufficient data

Answer: a [Reason:] When there are no standing waves in the transmission line, the reflection co-efficient is zero and hence input impedance of the transmission line is equal to the characteristic impedance of the line. Hence the relation between SWR and reflection co-efficient yields SWR as 1.

5. When a λ/4 transmission line is used for impedance matching, then which of the following is valid?
a) Standing waves are present on the λ/4 transmission line
b) No standing waves on the λ/4 transmission line
c) Standing waves are not present both on the feed line and the matching λ/4 line
d) Standing waves are present on both the feed line and the matching λ/4 line

Answer: a [Reason:] λ/4 transmission line is used to match the load impedance to the characteristic impedance of the transmission line. Hence, standing waves are present on the λ/4 transmission line, but not on the transmission line since it is matched

6. For a transmission line , if the input impedance of the transmission line is 100Ω with a characteristic impedance of 150Ω, then the magnitude of the reflection co efficient:
a) 0.5
b) 1
c) 0.2
d) 0

Answer: c [Reason:] The expression for reflection co-efficient of a transmission line in terms input and characteristic impedance is (Zin-Zₒ)/(Zin+ Zₒ). Substituting the given values in the above expression, reflection co-efficient is 0.2.

7. If the reflection co-efficient of a transmission line is 0.334 with a characteristic impedance of 50Ω then the input impedance of the transmission line is:
a) 100 Ω
b) 50 Ω
c) 150 Ω
d) None of the mentioned

Answer: a [Reason:] Substituting the given voltage reflection co-efficient and the characteristic impedance of the transmission line in ┌= (Zin-Zₒ)/(Zin+ Zₒ). The input impedance of the transmission line is 100Ω

8. When a transmission line of characteristic impedance(50Ω) zₒ is matched to a load by a λ/4 transmission line of characteristic impedance 100Ω, then the transmission co efficient is:
a) 1.5
b) 0.5
c) 1.333
d) 2

Answer: c [Reason:] When a transmission line is matched to a load by using a λ/4 transmission line, the transmission co-efficient T1 of the line is obtained using the expression 2Z1/ (Z1+Z0). Here Z1 is the characteristic impedance of the λ/4 transmission line and Z1 is the characteristic impedance of the transmission line. Substituting the given values, we get T1=1.3333.

9. If a transmission line of zₒ=50Ω is matched using λ/4 transmission line of z₁=100Ω, then the transmission co efficient T₂ is:
a) 1
b) 0.6667
c) 1.3333
d) 2

Answer: b [Reason:] When a transmission line is matched to a load by using a λ/4 transmission line, the transmission co-efficient T2 of the line is obtained using the expression 2Z0/ (Z1+Z0). Here Z1 is the characteristic impedance of the λ/4 transmission line and Z0 is the characteristic impedance of the transmission line. Substituting the given values, we get T2=0.6667.

10. If the transmission co-efficient T₁ of a transmission line is 1.333 and the characteristic impedance of the λ/4 transmission line used is 100Ω, then the characteristic impedance of the transmission line is:
a) 50Ω
b) 100Ω
c) 70.71Ω
d) None of the mentioned

Answer: a [Reason:] Expression for transmission co-efficient of a transmission line matched using a λ/4 transmission line is 2Z1/ (Z1+Z0). Substituting the known values, the characteristic impedance of the transmission line is 50Ω.

## Set 3

1. A quarter wave transformer is useful for matching any load impedance to a transmission line.
a) True
b) False

Answer: b [Reason:] Quarter wave transformers are a simple circuit that can be used to match real load impedance to a transmission line. Quarter wave transformers cannot be used to match complex load impedances to a transmission line.

2. Major advantage of a quarter wave transformer is:
a) It gives proper matching
b) It gives high gain
d) None of the mentioned

Answer: c [Reason:] Quarter-wave transformers can be extended to multi section designs in a methodical manner to provide a broader bandwidth.

3. If a narrow band impedance match is required, then more multi section transformers must be used.
a) True
b) False

Answer: b [Reason:] If a narrow band impedance match is required, then a single section of quarter wave transformer is used. When a wideband impedance match is required, then multi-section quarter wave transformers must be used for impedance matching.

4. The major drawback of the quarter wave transformer that it cannot match complex load to a transmission line cannot be overcome.
a) True
b) False

Answer: b [Reason:] The major drawback of the quarter wave transformer that it cannot match complex load to a transmission line can be overcome by transforming complex load impedance to real load impedance.

5. Complex load impedance can be converted to real load impedance by:
a) Scaling down the load impedance
b) By introducing an approximate length of transmission line between load and quarter wave transformer
c) Changing the operating wavelength
d) None of the mentioned

Answer: b [Reason:] By introduction of a transmission line of suitable length between the load and the quarter wave transformer, the reactive component of the load that is the complex value can be nullified thus leaving behind only real load impedance to be matched.

6. Converting complex load into real load for impedance matching has no effect on the bandwidth of the match.
a) True
b) False

Answer: b [Reason:] Adding a length of line to the transmission line between the load and quarter wave transformer alters the frequency dependence of the load thus altering the bandwidth of the match.

7. If a single section quarter wave transformer is used for impedance matching at some frequency, then the length of the matching line is:
a) Is different at different frequencies
b) Is a constant
c) Is λ/2 for other frequencies
d) None of the mentioned

Answer: a [Reason:] The length of the matching section is λ/4 for the frequency at which it is matched. For other frequencies, the electrical length varies. For multi section transformers, a wide bandwidth can be achieved.

8. Quarter wave transformers cannot be used for non-TEM lines for impedance matching.
a) True
b) False

Answer: a [Reason:] For non-TEM lines, propagation constant is not a linear function of frequency and the wave impedance is frequency dependent. These factors complicate the behavior of the quarter wave transformer for non-TEM lines.

9. The reactances associated with the transmission line due to discontinuities:
a) Can be ignored
b) Have to matched
C Discontinuities do not exist
d) None of the mentioned

Answer: b [Reason:] Reactance due to discontinuities in the transmission line contribute to the impedance, they can be matched by altering the length of the matching section.

10. If a load of 10Ω has to be matched to a transmission line of characteristic impedance of 50Ω, then the characteristic impedance of the matching section of the transmission line is:
a) 50Ω
b) 10Ω
c) 22.36Ω
d) 100Ω

Answer: c [Reason:] Characteristic impedance of the matching section of a transmission line is given by Z1=√Zₒ.ZL. Substituting the given impedance values, the characteristic impedance of the matching section is 22.36 Ω.

## Set 4

1. The modes of propagation supported by a rectangular wave guide is:
a) TM, TEM, TE modes
b) TM, TE
c) TM, TEM
d) TE, TEM

Answer: b [Reason:] A hollow rectangular waveguide can propagate TE and TM modes. Since only a single conductor is present, it does not support TEM mode of propagation.

2. A hollow rectangular waveguide cannot propagate TEM waves because:
a) Of the existence of only one conductor
b) Of the losses caused
c) It is dependent on the type of the material used
d) None of the mentioned

Answer: a [Reason:] A rectangular hollow waveguide can propagate both TE and TM modes of propagation. But due the presence of only one conductor, rectangular waveguide does not support the propagation of TEM mode.

3. For any mode of propagation in a rectangular waveguide, propagation occurs:
a) Above the cut off frequency
b) Below the cut off frequency
c) Only at the cut-off frequency
d) Depends on the dimension of the waveguide

Answer: a [Reason:] Both TE and TM modes of propagation in rectangular waveguide have certain separate and specific cut off frequencies below which propagation is not possible. Hence propagation of signal occurs above the cut off frequency.

4. In TE mode of wave propagation in a rectangular waveguide, what is the equation that has to be satisfied?
a) (∂2/ ∂x2 + ∂2/ ∂y2+ kC2).HZ(x, y) =0
b) (∂2/ ∂x2 + ∂2/ ∂y2– kC2).HZ(x, y) =0
c) (∂2/ ∂x2 – ∂2/ ∂y2+ kC2).HZ(x, y) =0
d) None of the mentioned

Answer: a [Reason:] For TE mode of propagation in a rectangular waveguide, electric field along the direction of propagation is 0. Hence for propagation, the above partial differential equation in terms of magnetic field along Z direction has to be satisfied.

5. Dominant mode is defined as:
a) Mode with the lowest cut off frequency
b) Mode with the highest cut off frequency
c) Any TEM mode is called a dominant mode
d) None of the mentioned

Answer: a [Reason:] Among the various modes of propagation in a rectangular waveguide, the mode of propagation having the lowest cutoff frequency or the highest wavelength of propagation among the other propagating modes is called dominant mode.

6. For TE1ₒ mode, if the waveguide is filled with air and the broader dimension of the waveguide is 2 cm, then the cutoff frequency is:
a) 5 MHz
b) 7.5 MHz
c) 7.5 GHz
d) 5 GHz

Answer: c [Reason:] The cutoff frequency for TE 10 mode of propagation in a rectangular waveguide is 1/2a√(∈μ) where ‘a’ is the broader dimension of the waveguide. Substituting for the given value and 1/√(∈μ)=3*108. The cutoff frequency is 7.5 GHz.

7. TEₒₒ mode for a rectangular waveguide:
a) Exists
b) Exists but defined only under special cases
c) Does not exist
d) Cannot be determined

Answer: c [Reason:] The field expressions for TEₒₒ mode disappears or becomes zero theoretically. Hence, TEₒₒ mode does not exist.

8. For dominant mode propagation in TE mode, if the rectangular waveguide has a broader dimension of 31.14 mm , then the cutoff wave number:
a) 100
b) 500
c) 50
d) 1000

Answer: a [Reason:] The cutoff wave number for the dominant mode of a rectangular waveguide is given by π/a where ‘a’ is the broader dimension of the waveguide, substituting the given values, the wave number 100.

9. The lowest mode of TM wave propagation is:
a) TM10 mode
b) TM01 mode
c) TM11 mode
d) TM12 mode

Answer: c [Reason:] The field components for other lower modes of propagation in TM mode disappear for other lower modes of propagation. Hence, the lowest mode of propagation is TM11 mode.

10. The cutoff frequency for the dominant mode in TM mode propagation for a rectangular waveguide of dimension of 30mm*40mm is:
a) 2 GHz
b) 1 GHz
c) 2 MHz
d) 4 MHz

Answer: a [Reason:] The cutoff frequency of dominant mode in TM mode is √((π/a)2 + (π/b)2). Here, ‘a’ and ‘b’ are the dimensions of the waveguide. Substituting the corresponding values, the cutoff frequency is 2 GHz.

11. In TE10 mode of wave propagation in a rectangular waveguide, if the broader dimension of the waveguide is 40 cm, then the cutoff wavelength for that mode is:
a) 8 cm
b) 6 cm
c) 4 cm
d) 2 cm

Answer: a [Reason:] In TE10 mode of propagation in a rectangular waveguide, the cutoff wavelength of the waveguide is given by 2a where ‘a’ is the broader dimension of the waveguide. Substituting, the cutoff wavelength is 8 cm.

12. In TE01 mode of wave propagation in a rectangular waveguide, if the smaller dimension of the waveguide is 2 cm, then the cutoff wavelength for that mode is:
a) 4 cm
b) 8 cm
c) 1 cm
d) 2 cm

Answer: a [Reason:] For TE01 mode of wave propagation in a rectangular wave guide, if the smaller dimension of the wave guide is 2 cm, then the cut off wavelength is 2b where b is the smaller dimension of the waveguide. substituting, the cutoff wavelength is 4 cm.

## Set 5

1. Discontinuities in the matching quarter wave transformer are not of considerable amount and are negligible.
a) True
b) False

Answer: b [Reason:] Discontinuities in the matching network cause reflections which result in considerable attenuation of the transmitted signal. Hence, discontinuities in transformers are not negligible.

2. The overall reflection coefficient of a matching quarter wave transformer cannot be calculated because of physical constraints.
a) True
b) False

Answer: b [Reason:] Though the computation of total reflection is complex, the total reflection can be computed in two ways. They are the impedance method and the multiple reflection method.

3. In the multiple reflections analysis method, the total reflection is:
a) An infinite sum of partial reflections
b) An infinite sum of partial reflection and transmissions
c) Constant value
d) Finite sum of partial reflections

Answer: b [Reason:] The number of discontinuities in the matching circuit (quarter wave transmission line) is theoretically infinite since the exact number cannot be practically determined. Hence, the total reflection is an infinite sum of partial reflections and transmission.

4. The expression for total reflection in the simplified form is given by:
a) Г=Г1+ Г3e-2jθ
b) Г=Г113
c) Г=Г12+ Г3e-2jθ
d) Г= Г1+ Г2e-2jθ

Answer: a [Reason:] This expression dictates that the total reflection is dominated by the reflection from the initial discontinuity between Z1 and Z2 (Г1), and the first reflection from the discontinuity between Z2 and ZL (Г3e-2jθ).

5. The e-2jθ term in the expression for total reflection in a single section quarter wave transformer impedance matching network Г=Г1+ Г3e-2jθ signifies:
a) Phase delay
b) Frequency change
c) Narrowing bandwidth
d) None of the mentioned

Answer: a [Reason:] The term e-2jθ in Г=Г1+ Г3e-2jθ accounts for phase delay when the incident wave travels up and down the line. This factor is a result of multiple reflections.

6. If the first and the third reflection coefficients of a matched line is 0.2 and 0.01, then the total reflection coefficient if quarter wave transformer is used for impedance matching is:
a) 0.2
b) 0.01
c) 0.21
d) 0.19

Answer: d [Reason:] The total reflection co-efficient of a matched line due to discontinuities is given by Г=Г1+ Г3e-2jθ. Given that Г1=0.2 and Г3=0.01, β=2π/λ, l=λ/4. θ=βl, Substituting the given values in the above 2 given equations, the total reflection coefficient is 0.19.

7. If a λ/4 transmission line is used for impedance matching, then always Г1> Г3.
a) True
b) False

Answer: a [Reason:] Since the load is matched to the transmission line the reflection from the load towards the source will be very less (Г3). Г1 is the reflection from the junction of the transmission line and the λ/4 matching section. Since this end will have some improper matching and discontinuities, Г1 is always greater than Г3.

8. To compute the total reflection of a multi-section transmission line, the lengths of the transmission lines considered are all unequal.
a) True
b) False

Answer: b [Reason:] The computation of total reflection of a matched line due to discontinuities is theoretically complex. In order to obtain an approximated simple expression, the lengths of the multi section matching transformers is a constant or all of them are equal.

9. If ZL< Z0, then the reflection coefficient at that junction is:
a) ГN<0
b) ГN>0
c) ГN>1
d) None of the mentioned

Answer: a [Reason:] When there is no proper matching between load impedance and the characteristic impedance of a transmission line and given the condition that ZL< Z0, then the reflection coefficient at that junction is always negative. That is, ГN<0.

10. The total approximate reflection coefficient is a finite sum of reflection co-efficient of individual matching section of the matching network.
a) True
b) False