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QUESTION: 1

Z_{L} = 200 Ω and it is desired that Z_{i} = 50 Ω The quarter wave transformer should have a characteristic impedance of

Solution:

Z_{0} = Z_{i} . Z_{L}

QUESTION: 2

A broadside array consisting of 200 cm wavelength with 10 half-wave dipole spacing 10 cm. And if each array element feeding with 1 amp. current and operating at same frequency then find the half power beamwidth

Solution:

.

QUESTION: 3

Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of 10^{14} Hz in glass. Assume velocity of light is 3 x 10^{8} m/sec in vacuum.

Solution:

Given, μ = 1.6, *f* = 10^{14} Hz, *v* = 3 x 10^{8} m/sec.

QUESTION: 4

The function *f*(*x* - *v*_{ot}) represent which of the following?

Solution:

*f*(*x* - *v _{ot}*) represents in +ve direction while

QUESTION: 5

A broadside array operating at 100 cm wavelength consist of 4 half-wave dipoles spaced 50 cm apart. Each element carries radio frequency current in the same phase and of magnitude 0.5 A. The radiated power will be

Solution:

P = *n* . I^{2} . R_{r}, where R_{r} = 80p^{2} Ω.

*n* = 4.

QUESTION: 6

The input impedance of short-circuited line of length *l* where λ/4 < *l* < λ/2, is

Solution:

*l* < λ/4, Z_{L} = 0

, if Z_{d} comes +*j* *k*Z_{C} then inductive,

If Z_{d} comes -*j* *k*Z_{C} then capacitive.

for 0 ≤ *l* ≤ 1/4, λ ≤ *l* ≤ 3λ/4 will be inductive.

QUESTION: 7

A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls find cut off wavelength for dominant mode.

Solution:

.

QUESTION: 8

Find the radiation resistance of an antenna of length λ/10 meter?

Solution:

.

QUESTION: 9

Charge needed within a unit sphere centred at the origin for producing a potential field,

Solution:

*q* = 120p coulomb, *r* = 1 meter.

QUESTION: 10

A rectangular metal waveguide filled with a dielectric of relative permittivity ε_{r} = 4, has the inside dimensions 3 x 1.2 cm, the cut off frequency for the dominant mode is

Solution:

for dominant mode.

QUESTION: 11

A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls Calculate group velocity for dominant mode.

Solution:

V_{g} . V_{p} = C^{2}

where

.

QUESTION: 12

For F_{1} layer the maximum ionic density is 2.3 x 10^{4} electrons per cc. The critical frequency for this layer will be

Solution:

*f _{c}* = 9N

QUESTION: 13

Which one of the following does represents the electric field lines for the TE_{02} mode in the cross section of a hollow rectangular metallic waveguide?

Solution:

TE_{02} *m* = 0, *n* = 2

in *x* direction no propagation, only in *y*, and normal to the waveguide, tangential component is continuous.

QUESTION: 14

The velocity of electromagnetic wave in a good conductor is

Solution:

, for good conductor ε_{r} >> 1.

QUESTION: 15

Radiation intensity of a dipole depends strongly on frequency. If at a frequency *f*, the intensity of radiation is 'I'. Then at a frequency of *f*/2, the intensity will be

Solution:

I ∝ *f*.

QUESTION: 16

Consider a 300 Ω, quarter wave long at 1 GHz transmission line as shown in figure. It is connected to a 10 V, 50 Ω source at one end is left open circuited at the other end. The magnitude of the voltage at the open circuit end of the line is

Solution:

γ = a + *j*β a = 0 γ = *j*β

Propagating wave

*v* = V_{I} *e*^{-rz} + V_{R} *e*^{rz}

No change in the voltage at the open end it will same,

*v _{r}* = 10 volt.

QUESTION: 17

The phase angle corresponding to λ/4 in a standing-wave pattern is

Solution:

QUESTION: 18

A hollow rectangular waveguide has dimensions *a* = 2*b*. Calculate the amount of attenuation, if the frequency is 3 GHz, and *b* = 1 cm.

Solution:

Since, wave is attenuated hence β = 0

and Take, dominant mode *m* = 1,

*n* = 0

.

QUESTION: 19

Calculate the directivity of an antenna for θ_{E} = 30º, θ_{H} = 60

Solution:

.

QUESTION: 20

Most antenna consisting of a 50 meter long vertical conductor operates over a perfectly conducting ground plane. It is base fed at a frequency of 600 kHz. The radiation resistance of the antenna in ohms is

Solution:

QUESTION: 21

A (75 - *j* 40) W load is connected to a co-axial line of *z*_{0} = 75ω at 6 MHz. The load matching on the line can be accomplished by connecting

Solution:

Z_{L} = 75 - J . 40, Z_{C} = 75 W, *f* = 6 mHz

Given Z_{L} is capacitive, so proper matching, load must be inductive.

QUESTION: 22

A plane wave is characterized by the wave is

Solution:

Because, magnitude is different (0.5, 1) and phase is 90º

QUESTION: 23

The electric field on the surface of a perfect conductor is 2V/m. The conductor is immersed in water with ε = 80 ε_{0}. The surface charge density on the conductor is ((ε_{0} = 10^{-9}/36p)F/m)

Solution:

.

QUESTION: 24

A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls calculate the phase velocity for dominant mode.

Solution:

V_{g} . V_{p} = C^{2}

where .

QUESTION: 25

A plane electromagnetic wave travels in dielectric medium of relative permittivity 9. Relative to free space, the velocity of propagation in the dielectric is

Solution:

.

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