Question 1

1. Write the name of all primary parameters of a transmission line.

Accepted Answer

(a) Above ~60 GHz, waveguide dimensions shrink to impractically small, hard-to-manufacture sizes while microstrip remains easy to fabricate photolithographically and integrates directly with active devices, so microstrip is preferred; (b) between 1-30 GHz, waveguides handle far higher power with much lower loss than microstrip, so waveguides are preferred for high-power, low-loss links in that range.

Question 2

2. Find the value of ∇·D at (0, 1, 0) when D = x²y âx + xy² âz.

Accepted Answer

In a conducting (lossy) medium the propagation constant γ = α+jβ is complex; solving the wave equation with a general complex permittivity gives frequency-dependent α, β, and hence phase velocity vp = ω/β and group velocity vg = dω/dβ, both differing from the lossless free-space value c and from each other, showing the medium is dispersive.

Question 3

3. Write the expression of characteristic impedance of free space.

Accepted Answer

Solving the inhomogeneous wave equation for the magnetic vector potential A with a time-varying source at position r' and observation point r (retarded time t−R/c) gives the retarded potential A(r,t) = (μ/4π)∫[J(r',t−R/c)/R]dv', from which the radiated E and H fields of any antenna are derived by differentiation.

Question 4

4. If electric potential φ = x² + y² + z², then find its electric field.

Accepted Answer

Common waveguide types are rectangular waveguide (TE/TM modes, most widely used), circular waveguide (TE/TM modes with Bessel-function field patterns, used for rotary joints and low-loss circular polarization), ridge waveguide (wider single-mode bandwidth), and elliptical waveguide (flexible, used for long antenna feeder runs).

Question 5

5. Calculate the reflection coefficient of a wave from medium (2) Z2 = 1+j to…

Accepted Answer

The Smith chart is a polar plot of the normalized impedance/admittance (constant-r and constant-x circles) mapped onto the unit reflection-coefficient circle; it is used graphically to convert between Γ and Z, find VSWR, and design impedance-matching networks (single/double-stub, quarter-wave) without complex-number arithmetic.

Question 6

6. What is the use of a stub in a transmission line?

Accepted Answer

Maxwell's equations exist in differential (point) form, integral form, phasor (time-harmonic) form, and free-space/source-free form, each expressing the same four physical laws (Gauss's electric/magnetic law, Faraday's law, Ampere-Maxwell law) in a different mathematically convenient representation.

Question 7

7. If VSWR = 200 then find the reflection coefficient magnitude.

Accepted Answer

A transmission line is a distributed-parameter conductor pair (coaxial cable, twin-lead, microstrip, etc.) that guides electromagnetic energy with characteristic impedance Z0, used in power transmission, telecommunication signal routing, RF/microwave interconnects, matching networks, and as circuit elements (stubs, resonators, delay lines).

Question 8

8. Write the condition of (i) free space and (ii) lossy medium.

Accepted Answer

Two common impedance matching techniques for transmission lines are single-stub matching and quarter-wave transformer matching (double-stub matching and lumped L-network matching are also widely used).

Question 9

9. Write one equation of Maxwell for the dynamic electric field.

Accepted Answer

On a Smith chart, the centre point (Γ = 0) is the common centre of all constant-VSWR circles; it represents a perfectly matched load (Z = Z0), and each constant-VSWR circle is centred there with radius |Γ| = (VSWR−1)/(VSWR+1).

Question 10

10. Find the length of a dipole antenna working at 30 MHz.

Accepted Answer

The Poynting vector S = E×H represents power flow per unit area and has SI unit watt per square metre (W/m²).

Question 11

1. Derive the expression of intrinsic impedance of free space.

Accepted Answer

(a) Above ~60 GHz, waveguide dimensions shrink to impractically small, hard-to-manufacture sizes while microstrip remains easy to fabricate photolithographically and integrates directly with active devices, so microstrip is preferred; (b) between 1-30 GHz, waveguides handle far higher power with much lower loss than microstrip, so waveguides are preferred for high-power, low-loss links in that range.

Question 12

2. Explain the following: (i) Constant VSWR circle on Smith chart. (ii) Singl…

Accepted Answer

In a conducting (lossy) medium the propagation constant γ = α+jβ is complex; solving the wave equation with a general complex permittivity gives frequency-dependent α, β, and hence phase velocity vp = ω/β and group velocity vg = dω/dβ, both differing from the lossless free-space value c and from each other, showing the medium is dispersive.

Question 13

3. A rectangular waveguide with dimensions a = 2.5 cm, b = 1 cm is to operate…

Accepted Answer

Solving the inhomogeneous wave equation for the magnetic vector potential A with a time-varying source at position r' and observation point r (retarded time t−R/c) gives the retarded potential A(r,t) = (μ/4π)∫[J(r',t−R/c)/R]dv', from which the radiated E and H fields of any antenna are derived by differentiation.

Question 14

4. Define and derive the boundary conditions for the electric field.

Accepted Answer

Common waveguide types are rectangular waveguide (TE/TM modes, most widely used), circular waveguide (TE/TM modes with Bessel-function field patterns, used for rotary joints and low-loss circular polarization), ridge waveguide (wider single-mode bandwidth), and elliptical waveguide (flexible, used for long antenna feeder runs).

Question 15

5. Define the near and far field of an antenna.

Accepted Answer

The Smith chart is a polar plot of the normalized impedance/admittance (constant-r and constant-x circles) mapped onto the unit reflection-coefficient circle; it is used graphically to convert between Γ and Z, find VSWR, and design impedance-matching networks (single/double-stub, quarter-wave) without complex-number arithmetic.

Question 16

6. If the electric field of a uniform plane wave is E = 0.5 exp(−z/3) sin(10⁸…

Accepted Answer

Maxwell's equations exist in differential (point) form, integral form, phasor (time-harmonic) form, and free-space/source-free form, each expressing the same four physical laws (Gauss's electric/magnetic law, Faraday's law, Ampere-Maxwell law) in a different mathematically convenient representation.

Question 17

7. Define: (i) Divergence theorem and (ii) Stoke's theorem. Derive the EM wav…

Accepted Answer

A transmission line is a distributed-parameter conductor pair (coaxial cable, twin-lead, microstrip, etc.) that guides electromagnetic energy with characteristic impedance Z0, used in power transmission, telecommunication signal routing, RF/microwave interconnects, matching networks, and as circuit elements (stubs, resonators, delay lines).

Question 18

1. Determine the values of β, λg, vp and η for TE10 mode in a 7.2 cm × 3.4 cm…

Accepted Answer

(a) Above ~60 GHz, waveguide dimensions shrink to impractically small, hard-to-manufacture sizes while microstrip remains easy to fabricate photolithographically and integrates directly with active devices, so microstrip is preferred; (b) between 1-30 GHz, waveguides handle far higher power with much lower loss than microstrip, so waveguides are preferred for high-power, low-loss links in that range.

Question 19

2. What is the Poynting vector? Find its expression.

Accepted Answer

In a conducting (lossy) medium the propagation constant γ = α+jβ is complex; solving the wave equation with a general complex permittivity gives frequency-dependent α, β, and hence phase velocity vp = ω/β and group velocity vg = dω/dβ, both differing from the lossless free-space value c and from each other, showing the medium is dispersive.

Question 20

3. Draw the voltage and current variation across a transmission line in the f…

Accepted Answer

Solving the inhomogeneous wave equation for the magnetic vector potential A with a time-varying source at position r' and observation point r (retarded time t−R/c) gives the retarded potential A(r,t) = (μ/4π)∫[J(r',t−R/c)/R]dv', from which the radiated E and H fields of any antenna are derived by differentiation.

Question 21

4. Draw and define the following antenna parameters: (i) Dipole radiation pat…

Accepted Answer

Common waveguide types are rectangular waveguide (TE/TM modes, most widely used), circular waveguide (TE/TM modes with Bessel-function field patterns, used for rotary joints and low-loss circular polarization), ridge waveguide (wider single-mode bandwidth), and elliptical waveguide (flexible, used for long antenna feeder runs).

Question 22

5. Prove Stokes' theorem and discuss its applications.

Accepted Answer

The Smith chart is a polar plot of the normalized impedance/admittance (constant-r and constant-x circles) mapped onto the unit reflection-coefficient circle; it is used graphically to convert between Γ and Z, find VSWR, and design impedance-matching networks (single/double-stub, quarter-wave) without complex-number arithmetic.

Electromagnetics Waves