Waveguides and Guided Waves MCQ Quiz - Objective Question with Answer for Waveguides and Guided Waves - Download Free PDF

Last updated on Apr 4, 2025

Latest Waveguides and Guided Waves MCQ Objective Questions

Waveguides and Guided Waves Question 1:

A rectangular waveguide has dimensions 1 cm × 0.5 cm. Its cut off frequency is : 

  1. 10 GHz
  2. 15 GHz
  3. 5 GHz
  4. 2.5 GHz

Answer (Detailed Solution Below)

Option 2 : 15 GHz

Waveguides and Guided Waves Question 1 Detailed Solution

Concept:

The cut-off frequency of a rectangular waveguide in dominant TE10 mode is given by:

\( f_c = \frac{c}{2a} \), where:

c = speed of light = \( 3 \times 10^8~m/s \), and a = broader dimension of the waveguide

Calculation:

Given:

Dimensions of waveguide = 1 cm × 0.5 cm

So, a = 1 cm = 0.01 m

Using the formula, \( f_c = \frac{3 \times 10^8}{2 \times 0.01} \)

\( f_c = \frac{3 \times 10^8}{0.02} = 1.5 \times 10^{10}~Hz = 15~GHz \)

Correct Answer: 2) 15 GHz

Waveguides and Guided Waves Question 2:

__________ number of 3-dB couplers are needed for a 64 × 64 bi-directional star coupler. 

  1. 128 
  2. 648 
  3. 192 
  4. 4096

Answer (Detailed Solution Below)

Option 3 : 192 

Waveguides and Guided Waves Question 2 Detailed Solution

Concept:

In optical communication, a star coupler is used to distribute optical signals among multiple ports. For an \( N \times N \) **bi-directional star coupler**, the number of **3-dB couplers** needed is given by the formula:

\( \frac{N}{2} \times \log_2 N \)

Given:

N = 64

Calculation:

\( \log_2 64 = 6 \)

\( \text{Number of 3-dB couplers} = \frac{64}{2} \times 6 = 32 \times 6 = 192 \)

Correct Answer: 3) 192

Waveguides and Guided Waves Question 3:

The core refractive index and a relative refractive index difference of a multimode step-index fiber are specified as 1.5 and 2%, respectively. At operating wavelength of 1300 nm, the approximate number of propagating modes is 1000. The diameter of the fiber core is :

  1. 10 µm 
  2. 31 µm 
  3. 62 µm
  4. 150 µm

Answer (Detailed Solution Below)

Option 3 : 62 µm

Waveguides and Guided Waves Question 3 Detailed Solution

Concept:

The number of propagating modes in a multimode step-index fiber is approximately given by, \( M = \frac{V^2}{2} \)

Where V is the normalized frequency (V-number), and is given by, \( V = \frac{2\pi a}{\lambda} \cdot NA \)

NA is the numerical aperture and is defined as, \( NA = n_1 \cdot \sqrt{2\Delta} \)

Where, n1 = core refractive index, Δ = relative refractive index difference, λ = operating wavelength, a = core radius

Calculation:

Given:

n1 = 1.5, Δ = 2% = 0.02, λ = 1300 nm = 1.3 × 10-6 m, M = 1000

Calculate NA: \( NA = 1.5 \cdot \sqrt{2 \cdot 0.02} = 1.5 \cdot \sqrt{0.04} = 1.5 \cdot 0.2 = 0.3 \)

Now, \( M = \frac{V^2}{2} \Rightarrow V^2 = 2M = 2000 \Rightarrow V = \sqrt{2000} \approx 44.72 \)

From, \( V = \frac{2\pi a}{\lambda} \cdot NA \)

\( 44.72 = \frac{2\pi a}{1.3 \times 10^{-6}} \cdot 0.3 \Rightarrow a = \frac{44.72 \cdot 1.3 \times 10^{-6}}{2\pi \cdot 0.3} \approx \frac{58.136 \times 10^{-6}}{1.884} \approx 30.85 \times 10^{-6}~m \)

Core diameter = 2a ≈ \( 61.7~\mu m \)

Correct Option:

The closest answer is: 3) 62 µm

Waveguides and Guided Waves Question 4:

The maximum digital transmission rates for unipolar return-to-zero data transmissions over an optical fiber 10-km long with specified pulse-spreading constant of 10 ns/km is : 

  1. 5 Mbps
  2. 10 Mbps
  3. 20 Mbps
  4. 25 Mbps

Answer (Detailed Solution Below)

Option 2 : 10 Mbps

Waveguides and Guided Waves Question 4 Detailed Solution

Concept:

The maximum digital transmission rate over an optical fiber is limited by pulse dispersion, which spreads the signal in time and can cause inter-symbol interference (ISI).

For Return-to-Zero (RZ) data transmission, the bit interval must be at least equal to the total pulse spreading to avoid overlap between bits.

Calculation:

Given:

Fiber length = 10 km, Pulse spreading constant = 10 ns/km

Total pulse spread = \(10~\text{km} \times 10~\text{ns/km} = 100~\text{ns}\)

In unipolar RZ transmission, the maximum bit rate is the reciprocal of the bit period.

\( \text{Bit rate} = \frac{1}{\text{Bit interval}} = \frac{1}{100~\text{ns}} = 10~\text{Mbps} \)

 

Waveguides and Guided Waves Question 5:

With the reduction in actual permittivity, the relative permittivity ______.

  1. increases
  2. reduces
  3. becomes zero
  4. remains the same

Answer (Detailed Solution Below)

Option 2 : reduces

Waveguides and Guided Waves Question 5 Detailed Solution

Explanation:

Permittivity and Relative Permittivity

Definition: Permittivity is a measure of how much electric field is 'permitted' to pass through a material. It quantifies the ability of a material to store electrical energy in an electric field. The absolute permittivity (ε) of a material is the product of the relative permittivity (εr) and the permittivity of free space (ε0), where ε0 is a constant value approximately equal to 8.854 × 10^-12 F/m (farads per meter).

Relative permittivity, also known as the dielectric constant, is a dimensionless quantity that represents the ratio of the permittivity of a material to the permittivity of free space. It indicates how much better the material is at storing electrical energy compared to a vacuum. Mathematically, it is expressed as:

εr = ε / ε0

Working Principle: When an electric field is applied to a material, the material's molecules polarize, aligning themselves with the field. This polarization reduces the overall field within the material, allowing it to store more energy. The relative permittivity reflects the extent of this polarization effect. A higher relative permittivity means the material can store more electrical energy, while a lower relative permittivity means it stores less.

Correct Option Analysis:

The correct option is:

Option 2: reduces

When the actual permittivity (ε) of a material decreases, the relative permittivity (εr) also reduces. This relationship can be understood by revisiting the formula for relative permittivity:

εr = ε / ε0

If the absolute permittivity (ε) decreases while the permittivity of free space (ε0) remains constant, the ratio εr will decrease. This means the material's ability to store electrical energy compared to a vacuum diminishes, leading to a reduction in the relative permittivity.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: increases

This option is incorrect because a reduction in actual permittivity would not lead to an increase in relative permittivity. Since relative permittivity is directly proportional to the actual permittivity, a decrease in one leads to a decrease in the other.

Option 3: becomes zero

This option is incorrect because while a reduction in actual permittivity will lower the relative permittivity, it cannot become zero unless the actual permittivity itself becomes zero. Since actual permittivity is a positive value for all materials, relative permittivity will also remain positive and will not reach zero.

Option 4: remains the same

This option is incorrect because relative permittivity is a function of actual permittivity. If actual permittivity changes, relative permittivity will also change. Therefore, it cannot remain the same if actual permittivity is reduced.

Conclusion:

Understanding the relationship between actual permittivity and relative permittivity is crucial for analyzing the dielectric properties of materials. As explained, relative permittivity reduces when actual permittivity decreases because of their direct proportionality. This fundamental concept is essential in various fields of electrical engineering and material science, where the dielectric properties of materials play a significant role in the design and application of electronic components and systems.

Top Waveguides and Guided Waves MCQ Objective Questions

The magnitude of (|E| / |H|) in a uniform plane wave is:

  1. \(\sqrt {\mu \epsilon}\)
  2. Infinity
  3. \(\sqrt {\dfrac{\mu}{ \epsilon}}\)
  4. 1

Answer (Detailed Solution Below)

Option 3 : \(\sqrt {\dfrac{\mu}{ \epsilon}}\)

Waveguides and Guided Waves Question 6 Detailed Solution

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Concept:

  • Electric field \(\left( {\vec E} \right)\) & magnetic field \(\left( {\vec H} \right)\) are both orthogonal/transverse to each other as well as for the direction of propagation, called transverse electromagnetic wave (TEM).
  • E & H combination called uniform plane wave because E & H has some magnitude through any transverse plane.

 

Intrinsic Impedance \(\left( \eta \right) = \frac{E}{H}\)

And also \(\eta = \sqrt {\frac{{j\omega \mu }}{{\sigma + j\omega \varepsilon }}} \)

But for free space

\( \Rightarrow \eta = \frac{E}{H} = \sqrt {\frac{\mu }{\varepsilon }} \)

Pointing vector is a vector whose direction is the direction of wave propagation pointing vector \( = \vec E \times \vec H\) (Hence it is a direction of wave propagation)

Where,

E = Electric filed

B = magnetic field

H = Magnetic field

μ0 = Permeability of free space = 4π x 10-7 H / m

ϵ0 = Permittivity of free space = 8.85 x 10-12 F/m

Optical fibre works on the phenomenon of _______

  1. total internal reflection
  2. polarization
  3. diffraction
  4. refraction

Answer (Detailed Solution Below)

Option 1 : total internal reflection

Waveguides and Guided Waves Question 7 Detailed Solution

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The correct answer is total internal reflection.

Key Points

  • Optical fiber:
    • The working of an optical fiber is based on total internal reflection. Hence, option 2 is correct. 
    • Optical fibers consist of many long high-quality composite glass/quartz fibers. Each fiber consists of a core and cladding.
    • The refractive index of the core (μ1) material is higher than that of the cladding (μ2).
    • When the light is incident on one end of the fiber at a small angle, the light passes inside, undergoes repeated total internal reflections along with the fiber, and finally comes out.
    • The angle of incidence is always larger than the critical angle of the core material concerning its cladding.
    • Even if the fiber is bent, the light can easily travel through along the fiber.
  • 6192296a9f8a5d183b87bf5a 16388893671021

Which of the following is not a microwave generation source?

  1. Klystron
  2. PIN Diode
  3. TWTA
  4. Magnetron

Answer (Detailed Solution Below)

Option 2 : PIN Diode

Waveguides and Guided Waves Question 8 Detailed Solution

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  • Microwave tubes are used for high power/frequency generation.
  • Tubes generate and amplify high levels of microwave power more cheaply than solid-state devices.


Microwave tubes are classified into two types:

Linear-Beam Tube:

  • Klystrons and Traveling-Wave Tube(TWT) are examples of linear beam tubes with a focused electron beam (as in CRT).


Crossed-Field Tube:

  • In these tubes, both the Magnetic and electric fields are at right angles to each other.

  • The Magnetron is an example of cross-field tubes.

  • Magnetrons are the cross-field tubes in which the electric and magnetic fields cross, i.e. run perpendicular to each other.

26 June 1

Parameters

Klystron

Magnetron

TWTs

Frequency

Few GHz to hundred GHz

1 - 25 GHz

1 to 10 GHz

Output Power

10 MW

Several kW

Order of kW

Efficiency

10 %

30 - 60 %

20 %

Uses

Oscillator and Amplifier

Oscillator

Oscillator and Amplifier

The refractive index of the core is uniform throughout and undergoes an abrupt change at the cladding boundary which is known as ______.

  1. uniform-index fibre
  2. scale-index fibre
  3. graded-index fibre
  4. step-index fibre

Answer (Detailed Solution Below)

Option 4 : step-index fibre

Waveguides and Guided Waves Question 9 Detailed Solution

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Step-index fiber:

1. The refractive index of the core is uniform throughout and undergoes on abrupt change at the core-cladding boundary.

2. The path of light propagation is zig-zag in a manner

Additional Information

Optical fibres are transparent fibres and act as a light pipe to transmit light between its two ends. They are made up of silicon dioxide.

 

F1 J.K Madhu 19.05.20 D13

Refracting index is changing between the cladding and the core in optical fibre

Graded-index fiber:

1. The refractive index of the core is made to vary gradually such that it is maximum at the center of the core.

2. The path of light is helical in manner.

 

F1 Utkarsha.S 24-09-20 Savita D1

This type of fiber optics works when the wavelength is much smaller than the core radius.

So, the refractive index of the core remains constant for step-index fiber.

Difference between step-index and graded-index fiber.

Step Index

Graded Index

The Refractive index profile is uniform within the core

inside the core

Refractive index profile is variable within the core

Light signal propagate in a zig-zag manner

Light signal propagate in the skewed form inside the core

It supports single-mode

It supports only multi-mode fiber

Low bandwidth

High bandwidth

The type of interconnection cable that has the highest bandwidth is the

  1. Twisted-pair cable
  2. Co-axial cable
  3. Open-wire cable
  4. Fibre-optic cable

Answer (Detailed Solution Below)

Option 4 : Fibre-optic cable

Waveguides and Guided Waves Question 10 Detailed Solution

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The data rate for optical fiber is 1 Gbps.

Twisted pair

Co-axial Cable

Optical Fibre

Transmission of signals in electrical form over metallic conducting wires

Transmission of signals takes place in electrical form over the inner conductor

Signal transmission takes place in an optical form over glass fibre

Low noise immunity

Higher noise immunity than twisted pair

Highest noise immunity

Affected by external magnetic fields

Less affected by external magnetic fields

Not affected by external magnetic fields

cheapest

Moderate-expensive

Expensive

Low bandwidth

Moderate-high bandwidth

Very high bandwidth

High attenuation

Low attenuation

Very low attenuation

Easy installation

Fairly easy installation

Difficult installation

26 June 1

  • In an optical fiber, the information is passed through light, which must not escape outside of it.
  • This phenomenon of confining the light inside the optical fiber is termed as Total internal reflection.
  • For this, the construction and material used to ensure that the total internal reflection of light takes place to prevent the escape of it.

OFC

The data rate of different communication systems is:

Twisted wire

300 bps – 10 Mbps

Microwave

256 Kbps – 100 Mbps

Satellites

256 Kbps – 100 Mbps

Coaxial Cables

56 Kbps – 200 Mbps

Fiber optic cable

500 Kbps – 10 Gbps

The dominant mode in rectangular waveguide is

  1. TE11
  2. TEM
  3. TE01
  4. TE10

Answer (Detailed Solution Below)

Option 4 : TE10

Waveguides and Guided Waves Question 11 Detailed Solution

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Concept:

The dominant mode in a particular waveguide is the mode having the lowest cut-off frequency.

The cut-off frequency for a rectangular waveguide with dimension ‘a (length)’ and ‘b (width)’ is given as:

\(\Rightarrow {{f}_{c\left( mn \right)}}=\frac{c}{2}\sqrt{{{\left( \frac{m}{a} \right)}^{2}}+{{\left( \frac{n}{b} \right)}^{2}}}\)

'm' and 'n' represents the possible modes.

Application:

For a standard rectangular waveguide a > b;

The minimum frequency is obtained when m = 1 and n = 0,

\(i.e.~{{f}_{c\left( 10 \right)}}=\frac{c}{2}\sqrt{\frac{{{m}^{2}}}{{{a}^{2}}}}=\frac{c}{2a}\)

26 June 1

  • For a rectangular waveguide with b > a, TE01 will be the dominant mode with the lowest cut-off frequency.
  • TEM mode cannot exist in Hollow conductor waveguide
  • Circular and rectangular are hollow waveguides hence there is no TEM mode in them, they can support only TE or TM but not TEM mode
  • The transmission line, parallel plate waveguide, coaxial cable can have TEM mode

The waveguide can be considered as

  1. high pass filter
  2. low pass filter
  3. band pass filter
  4. none of these

Answer (Detailed Solution Below)

Option 1 : high pass filter

Waveguides and Guided Waves Question 12 Detailed Solution

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Waveguides only allow frequencies above cut-off frequency and do not pass below the cut-off frequencies.

Hence it acts as a high pass filter.

The cut off frequency is given as:

\({{\rm{\lambda }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{m}}}{{\rm{a}}}} \right)}^2} + {{\left( {\frac{{\rm{n}}}{{\rm{b}}}} \right)}^2}} }}\)

Where a and b are the dimensions of the waveguide (a>b)

m and n are mode numbers TEmn

Which fiber is preferred for long distance communication?

  1. Step index single mode fiber
  2. Graded index multimode fiber
  3. Step index multimode fiber
  4. Graded index fiber

Answer (Detailed Solution Below)

Option 1 : Step index single mode fiber

Waveguides and Guided Waves Question 13 Detailed Solution

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  • Single-mode step indexed fibers are widely used for wideband communications are preferred for long-distance communication.
  • Single-mode step-index fiber is used to eliminate modal dispersion during optical communication.
  • In this fiber, a light ray can travel on only one path so minimum refraction takes place hence, no pulse spreading permits high pulse repetition rates.

 

Advantages of single-mode fiber:

1) Low signal loss

2) No modal dispersion

3) Does not suffer from modal dispersion

4) Can be used for higher bandwidth applications

5) Long-distance applications

6) Cable TV ends

7) High speed local and wide area network

26 June 1

Single-mode means the fiber enables one type of light mode to be propagated at a time. This is explained with the help of the following diagram:

F1 S.B 17.6.20 Pallavi D 6

Single-mode fiber core diameter is much smaller than multimode fiber.

F1 S.B 17.6.20 Pallavi D 7

2) For single-mode fiber, the B.W ranges from 50 to 100 GHz/km

Multimode fibers:

Fibers that carry more than one mode are called multimode fibers. There are two types of multimode fibers:

1) Step Index

2) Graded Index

F2 S.B Madhu 09.04.20 D4

The comparison of the refractive index profile for step and graded fibers are respectively shown as:

 

F2 S.B Madhu 09.04.20 D5

 

The multimode step-index multimode fiber suffers from Modal dispersion.

 

F2 S.B Madhu 09.04.20 D6

 

  • Rays of light enter the fiber with different angles to the fiber axis. The limit is the fiber’s acceptance angle.
  • Rays that enter with a shallow angle travel a more direct path and arrive sooner than those that enter at steeper angles.
  • This arrival of different modes of light at different times is called modal dispersion.

What is the relation between the refractive index of core n1 and cladding n2?

  1. n2 is less than n1
  2. n1 is equal to n2
  3. n1 is less than n2
  4. No relation between n1 and n2

Answer (Detailed Solution Below)

Option 1 : n2 is less than n1

Waveguides and Guided Waves Question 14 Detailed Solution

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  • Optical fibers are cylindrical solid glass material acting as waveguides made of two concentric layers of very pure glass.
  • The core (the interior layer) with refractive index n1 serves as the medium for light propagation, while the cladding (the exterior layer) has a lower refractive index n2 where n1 > n2 assuring that light rays are reflected the core.
  • Since the cladding does not absorb any light from the core, the light wave can travel great distances.

OFC

Explanation:

  • The working principle of optical fibers is Total Internal Reflection.
  • Optical fiber mostly used for communication purposes with negligible loss of energy.
  • The “Total Internal Reflection” of light is the boundary between transparent media of two different refractive indices.
  • At present, Optical fiber cables are used for communication like sending images, voice messages, etc.
  • The designing of this cable is done with Plastic or glass so that data can be transmitted effectively and quickly than other modes of communications

In an optical fiber, the refractive index of the cladding material should be

  1. Nearly unity
  2. Very low
  3. Less than that of the core
  4. More than that of the core

Answer (Detailed Solution Below)

Option 3 : Less than that of the core

Waveguides and Guided Waves Question 15 Detailed Solution

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Optical Fiber:

  • In an optical fiber, the information is passed through light, which must not escape outside of it.
  • This phenomenon of confining the light inside the optical fiber is termed Total internal reflection.
  • For this, the construction and material used to ensure that the total internal reflection of light takes place to prevent the escape of it.
  • In any type of optical fiber, the refractive index of the core is always greater than the refractive index of the cladding.
  • It is this property of core and cladding which makes light propagate inside the fiber. 
  • Thus, In a step-index optical fiber refractive index of the core is higher than the cladding

OFC

Principle:

  • When light travels from a high refractive index medium to a low-refractive-index medium, it is refracted away from the normal as shown:

          ISRO 2014 (1-14) Rishi D6

  • At a certain angle θi, there is no refracted wave and the wave is totally internally reflected  (θr = 90°).
  • This angle is called a critical angle.
  • Inside an optical fiber, we have a high refractive index core (n1) and low refractive index cladding (n2).
  • This results in the propagation of waves inside a fiber through total internal reflection phenomenon.
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