EC6503 Transmission Lines and Waveguides Question Bank Regulation 2013

EC6503 TRANSMISSION LINES AND WAVEGUIDES QUESTION BANK FRANKLIN VIJAY S ASSISTANT PROFESSOR /ECE ANJALI AMMAL MAHALINGAM ENGG., COLLEGE – KOVILVENNI TIRUVARUR (DT)

REVISED SYLLABUS OF ANNA UNIVERSITY CHENNAI REGULATION 2013

EC6503 - TRANSMISSION LINES AND WAVEGUIDES

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UNIT 1: TRANSMISSION LINE THEORY General theory of Transmission lines - the transmission line - general solution - The infinite line Wavelength, velocity of propagation - Waveform distortion - the distortion-less line - Loading and different methods of loading - Line not terminated in Z0 - Reflection coefficient - calculation of current, voltage, power delivered and efficiency of transmission - Input and transfer impedance Open and short circuited lines - reflection factor and reflection loss. . PART A: 1. Compare the advantages and disadvantages of co-axial and open wire transmission line.  The open wire line is easy to construct. It is comparatively cheaper. Since insulation between the conductors is air, the dielectric loss is very small. This line is balanced to the earth. The main disadvantage of this line is that there is significant energy loss due to radiations. So it is unsuitable at higher frequencies ( ). The main advantage of the co-axial cable is that electromagnetic fields cannot leak into the free space; hence radiation losses are totally absent. Outer conductor provides very effective shielding to the external electromagnetic fields. The co-axial cable transmission line is costlier. The losses in the dielectric increase as the frequency of the signal increases. Hence above this line cannot be used.



2. List the primary and secondary line constants of transmission line. 1. Resistance 3. Capacitance 2. Inductance 4. Conductance 

These 4 line parameters are constants are called as Primary Constants of the transmission line. These constants are assumed to be independent of frequency for the transmission line.



Apart from impedance (



All these constants are fixed at one particular frequency but change their values as the frequency changes. These are constants are called as Secondary Constants.

other constants related to the transmission line are characteristic ), and p propagation constant ( ).

3. Define characteristic impedance of a line. The ratio of the voltage applied and the current flowing is the input impedance of the line. This input impedance of the infinite line is called characteristic impedance of a line. It is also defined as the impedance looking into an infinite line having same electrical properties. It is denoted as . 4. When does a finite line appear as an infinite line?  Consider an infinite line with , we get:

*



+

When

;

This show that finite line is terminated in its characteristic impedance behaves as an infinite line, to the sending end generator. QUESTION BANK

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5. State properties of the infinite line.  No waves will ever reach receiving end hence there is no reflection.  The at the sending end decides the current flowing when voltage is applied. effect on the sending end current.

has no

6. Draw the equivalent electrical circuit of a unit length of a transmission line.

7. What is wavelength of a line? The distance the wave travels along the line while the phase angle is changing through radians is called a wavelength. where

is phase shift

8. What is distortion? What are its types?  When the received signal is not the exact replica of the transmitted signal then the signal is said to be distorted. There exists some kind of distortion in the signal. 

The types of distortion are: a) Frequency distortion and b) Phase distortion

9. Define distortionless line. State the condition for distortionless line. A line in which there is no phase (or) frequency distortion and also it is correctly terminated, is called a distortionless line. The condition for distortionless line is . 10. Define phase distortion and frequency distortion. Frequency distortion: The attenuation constant is a function of frequency. Hence the different frequencies transmitted along the line will be attenuated to the different extent. For example a voice signal consists of many frequencies. And all these frequencies will not be attenuated equally along the transmission line. Hence received signal will not be exact replica of the input signal at the sending end. Such a distortion is called frequency distortion. Phase distortion (or) delay distortion: The phase constant also varies with frequency. Now the velocity is given by: . Thus the velocity of propagation of waves also varies with frequency. Hence some waves will reach receiving end very fast while some waves will get delayed than the others. Hence all frequencies will not have same transmission time. Thus the output wave at the receiving end will not be exact replica of the input wave at the sending end. Such a distortion is called phase (or) delay distortion.

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11. If a line is to have neither frequency nor delay distortion, how do you relate attenuation constant and velocity of propagation to frequency? (or) How distortion can be reduced in a transmission line?  The condition for distortionless line is .  The phase constant is given by:



Using this condition,

)

√(

√ √

and

√

(

)

. Thus for the condition

,

the velocity of propagation becomes independent of frequency. This eliminates the phase distortion and a direct function of frequency. 

The attenuation constant √



is given by: )

√(

(

Thus for the condition , the value becomes frequency. This eliminates the frequency distortion.

) √

and it is independent of

12. What is meant by loading of a line and loaded line? What are its types?  The process of increasing inductance of a transmission line artificially is called loading of a line, and such a line is called loaded line. 

There are two types of loading a line which are, i. Continuous loading (or) Krarup loading (or) Heavy side loading, ii. Lump loading (or) Pupin loading (or) Coil loading

13. Define reflection coefficient. The ratio of the amplitudes of the reflected and incident voltage waves at the receiving end of the line is called reflection co-efficent.

14. Define reflection loss. The reflection loss is defined as the number of nepers or decibels by which the current in the load under image matched conditions would exceed the current actually flowing in the load. Let is the load current under image matching condition and under image mismatch condition, then reflection loss is given by: |

|

|

|

[

]

(or)

is the actual load current |

|

|

|

[

]

15. Define insertion loss. The insertion loss of a line or network is defined as the number of nepers or decibels by which the current in the load is changed by insertion of a line or a network in between the load and the source. QUESTION BANK

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16. What is return loss? Write its expression. The return loss is defined as the ratio of the power at the receiving end due to incident wave to the power reflected by the load. It is also called Singing point. [| | ] PART B: 1. Obtain the general solution of transmission line and write its physical significance. (or) Derive the expressions for the voltage and current at any point on a transmission line in terms of propagation constant, length and characteristic impedance of the line. (16) *** 2. Explain the waveform distortion in transmission line. Derive the conditions required for a distortionless line. (8) *** 3. Explain the reflection on lines not terminated in characteristic impedance diagrams. (8)***

with phasor

4. Derive the equation of attenuation constant and phase constants of a transmission line in terms of line constants and . (8) *** 5. Give an account on inductance loading of Telephone cables. Derive Campbell’s equation. (8) *** 6. A cable has been uniformly loaded by an inductance such that . Assume leakage conductance to be nil, deduce an expression for attenuation and phase constant without neglecting . (8) 7. Derive the equations for input and transfer impedance of transmission lines. (8) 8. Write a short note on reflection factor and reflection loss. (6) UNIT 2: HIGH FREQUENCY TRANSMISSION LINES Transmission line equations at radio frequencies - Line of Zero dissipation - Voltage and current on the dissipation-less line, Standing Waves, Nodes, Standing Wave Ratio - Input impedance of the dissipation-less line - Open and short circuited lines - Power and impedance measurement on lines - Reflection losses - Measurement of VSWR and wavelength. PART A: 1. What are the standard assumptions made for RF line? When a line, either open-wire or coaxial is used at frequencies of a megahertz or more, some standard assumptions are considered:  At very high frequency, the skin effect is considerable. Hence it is assumed that the currents may flow on the surface of conductor, then the internal inductance becomes zero.  Because of skin effect, resistance increases with √ while the line reactance increases directly with . Hence it is assumed that is .  The lines at radio frequency is constructed such that may be considered zero.

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2. What is small and zero dissipation line. i. is small with respect to , then the line is considered as small dissipation line. This concept is useful when lines are employed as circuit elements (or) where resonance properties are involved. ii. is completely neglected, then the line is termed as zero dissipation line. This concept is useful when the line is used for transmission of power at a high frequency and the losses are neglected completely. 3. For the line of zero dissipation what will be the values of characteristic impedance, propagation constant, attenuation constant and phase constant. According to the standard assumptions for line at a high frequency, and .  The value of the characteristic impedance is real and resistive, it is represented by the symbol .

√ 

Similarly the propagation constant

is given by: √(

√

)(

√

) √

Hence at high frequencies: and

√

4. Explain standing waves. When a line is not terminated correctly into its characteristic impedance , then the part of energy transmitted returns back to the source as reflected wave. Then the distribution of voltage along the length of the line is not uniform, but a line consists maximum and minimum values of voltages. The points along the line where magnitude of voltage or current is zero are called Nodes while the points along the line where magnitude of voltage or current is maximum are called Antinodes. 5. Define standing wave ratio. The ratio of the maximum to minimum magnitudes of current or voltage on a line having standing waves is called the standing-wave ratio, . i.e., |

|

|

|

6. Express standing wave ratio in terms of reflection coefficient  The standing-wave ratio then may be defined in terms of the reflection co-efficient as: | | where is reflection coefficient | | 7. Write the relation for reflection coefficient in terms of The reflection coefficient in terms of and as: where

and

.

is load impedance is characteristic impedance QUESTION BANK

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8. Give the minimum and maximum value of SWR and reflection coefficient.  When i.e., when the line is short circuited, , Reflection is maximum 

When

i.e., when the line is open circuited, , Reflection is maximum



ranges in magnitude from

to

and its phase ranges from

to

.

9. Write the expressions for the input impedance of dissipationless line. The input impedance of a dissipationless line is given by:

*

+

10. Write the expressions for the input impedance of open and short circuited dissipationless line. For short-circuited line,

:

For open-circuited line,

:

where

11. Draw the variation of the input impedance of open and short circuited dissipationless line for line.

PART B: 1. Explain the method of power and impedance measurement on the line. (8) *** 2. Explain the following: *** a. Standing waves (3) b. Standing wave ratio (3) c. Relation between SWR and reflection coefficient. (3) d. Nodes and antinodes (3) e. A method to measure SWR (4)

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3. Derive the expressions for the input impedance of the dissipationless line and deduce the expressions for the input impedance of open and short circuited dissipation less line. (8) *** 4. Explain in detail voltages and currents on the dissipationless line. (8) *** 5. Define standing wave ratio and obtain the expressions for VSWR interms of reflection coefficient. (8) 6. Explain in detail reflection losses on the unmatched line and derive the expression for reflection losses as a function of standing wave ratio. (8) UNIT 3: IMPEDANCE MATCHING IN HIGH FREQUENCY LINES Impedance matching: Quarter wave transformer - Impedance matching by stubs - Single stub and double stub matching - Smith chart - Solutions of problems using Smith chart - Single and double stub matching using Smith chart PART A: 1. What is meant by electrical length of a line? The length of the transmission line is expressed in terms of wavelength is called an electrical length of a line. Example line. 2. Why is the Quarter wave line called as copper insulator? As quarter wave line is shorted at ground, its input impedance is very high. So the signal on line passes to the receiving end, without any loss due to this mechanical support. Thus the line acts as an insulator at this point. Hence such line is referred as copper insulator. 3. Mention the application of quarter wave line.  It can transformer a low impendance into a high impendance and vice versa, thus it can be consider as an impendance inverter.  It may be used as a transformer for impedance matching of load.  It may be used to provide mechanical support to the open wire line or center conductor of a coaxial cable. 4. Distinguish between single stub matching and double stub matching. S.No Single stub matching Double stub matching 1. In a single stub matching method only one In a double stub matching, two short stub either open or short circuit is used for circuit stubs are used for impedance impedance matching. Such a stub is located matching. The location of stubs is not at a definite point so as to achieve definite but it is arbitrary. The impedance matching. adjustments for impedance matching are fulfilled with length of the stubs. 2. The single stub matching is useful for one The double stub matching can be used for frequency only, for different frequencies, different frequencies by adjusting stub location of stub must have to be changed. lengths because stub positions are Also it is most suitable for open wire line arbitrary. Also it is most useful and easy and found to be troublesome in case of co- method of impedance matching for the axial line. co-axial line.

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5. Write the disadvantages of single stub matching.  Single stub impedance matching requires that the stub be located at a definite point on the line. So, it is useful for one frequency only, for different frequencies, location of stub must have to be changed.  For a coaxial line, it is not possible to determine the location of a voltage minimum without a slotted line section, so that placement of a stub at the exact required point is difficult. 6. Why are short circuited stub preferred over open circuited stub?  A short- circuited stub is mainly preferred to an open-circuited stub because of its simpler construction and the inability to maintain high enough insulation resistance at the open circuit point to ensure that the stub is really open-circuited.  A shorted stub has a lower loss of energy due to radiation, since the short circuit can be easily established with a large metal plate compared to open-circuited stub. 7. What is Smith chart? A modified form of circle diagram for the dissipationless line has been developed by P.H. Smith. “Smith chart is a special polar diagram containing constant resistance circles, constant reactance circles, circles of constant standing wave ratio and radius lines representing lineangle loci: used in solving transmission line and waveguide problems”. PART B: 1. What is quarter wave transformer? Discuss the application of quarter wave line in impedance matching. (8) *** 2. Obtain the expression for the length and location of a short circuited stub for impedance matching on a transmission line. (8) *** 3. Draw and explain the principle of double stub matching. (8) *** 4. Explain the applications of smith chart. UNIT 4: PASSIVE FILTERS Characteristic impedance of symmetrical networks - filter fundamentals, Design of filters: Constant K - Low Pass, High Pass, Band Pass, Band Elimination, m- derived sections - low pass, high pass composite filters. PART A: 1. What is symmetrical and asymmetrical network? Write its properties. When the electrical properties of the network are unaffected even after interchanging input and output terminals, the network is called symmetrical network. When the electrical properties of the network are affected even after interchanging input and output terminals, the network is called asymmetrical network.  

The electrical properties of symmetrical network are given as: i. Characteristic impedance ii. Propagation constant The electrical properties of asymmetrical network are given as: i. Iterative impedance ii. Image impedance iii. Image transfer constant QUESTION BANK

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2. For a symmetrical network, define propagation constant and characteristic impedance.  The characteristic impedance of a symmetrical network is the impedance measured at the input terminals of the first network in the chain of infinite networks in cascade and it is represented as .  Under the assumption of equal input and output impedances for a symmetrical T network terminated by its characteristic impedance , the ratio of the input current (sending end) to output current (receiving end) was defined as an exponential function, referred by the name propagation constant ( ). 3. What is the significance of propagation constant in symmetrical network?  The ratio of the input current (sending end) to output current (receiving end) was defined as an exponential function, referred by the name propagation constant ( ).

| |

where

is a complex number and it is given by,

| |  The term is called as the attenuation constant, since it determines the magnitude ratio between input and output quantities, or the attenuation produced in passing through the network. The units of are nepers.  The exponent is the phase constant as it determines the phase angle between input and output quantities, or the shift in phase introduced by the network. The units of are radians. 4. Define pass band, stop band and cut –off frequency in relation with a filter?  The range of frequencies over which attenuation by filter is zero is called pass band.  The range of frequencies over which attenuation is infinite is called stop band.  The frequencies at which the network changes from a pass network to a stop network, or vice versa, are called cut-off frequencies. 5. What are called constant-K filters and what are the demerits. A T or section in which series and shunt arm impedances and satisfy the relationship  where is a real constant is called as constant-k section. Drawbacks in prototype filter section:  Ideally the attenuation should change sharply in the stop band. But in all prototype filter section, the attenuation changes gradually in the stop band. Hence frequencies near cut-off frequency are passed through the filter.  In the pass band, output of the filter should remain constant. This indicates that the remain constant. But the varies with frequency from value , i.e., design impedance value, throughout the passband. Hence, filter cannot be terminated properly. 6. Why constant-K filters are called prototype filters? The constant-k sections either T or , of any type of filter are known as prototype sections, because other complex network can be derived from it.

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7. What is m-derived filter? A m-derived filter is a new filter section derived from a prototype constant K-section. It has cutoff frequency same as that of a prototype section. The attenuation characteristics of such filter are much improved in the stop band. 8. What are the advantages of m-derived filters?  A sharper cut-off characteristics with steeper rise at , the slope of the rise being adjustable by fixing the distance between and .  of the filter will be more uniform within the passband when m- derived half section having are connected at the ends.  m- derived filters make it possible to construct “composite filters” to have any desired attenuation/frequency characteristics. 9. What is the drawback of m-derived filter? How can it be overcome?  It is observed that in the stop band attenuation drastically reduces after in low pass section and before in high pass section.  This drawback of m- derived filter can be overcome by connecting number of sections including prototype sections and m- derived sections with terminating half sections. Such a combination of different sections is called “composite filters”. 10. Why m-derived filter of L-sections are used as terminations of composite filters? To have proper impedance matching and constant characteristic impedance throughout the pass band, we must connect the terminating sections with . So m-derived filter of L-sections are used as terminations of composite filters. 11. Draw the general block diagram of composite filter.

PART B: 1. Derive the equations for the characteristic impedance of symmetrical T and networks. (8) *** 2. With suitable filter sections, design constant K low pass and high pass filters. (16) *** 3. Draw a constant –K T-section band elimination filter and explain the operation with necessary design equations. (8) *** 4. Construct a band pass constant –K filter. (8) *** 5. Derive the relevant equations of m derived low pass filter and high pass filter. (8) UNIT 5: WAVE GUIDES AND CAVITY RESONATORS General Wave behaviors along uniform Guiding structures, Transverse Electromagnetic waves, Transverse Magnetic waves, Transverse Electric waves, TM and TE waves between parallel plates, TM and TE waves in Rectangular wave guides, Bessel’s differential equation and Bessel function, TM and TE waves in Circular wave guides, Rectangular and circular cavity Resonators. QUESTION BANK

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PART A: Guided Waves Between Parallel Planes: 1. What is principal wave? Write its characteristics. The wave is a special case of guided wave propagation. It is called principal wave. Some of the properties for as follows. 1.

The fields are entirely transverse.

2. 3.

The propagation constant for transmission is given by: Cut-off frequency for transmission is given by:

4.

The velocity of propagation

is given by:

1. Compare and mode. S.No mode 1. The Transverse Electric ( ) wave has the magnetic field in the direction of propagation, but no component of the electric field in the same direction. 2. The waves are also called - waves. 3. In this mode, the wave impedance is given as: (

√

√ mode ) wave has The Transverse Magnetic ( the electric field in the direction of propagation, but no component of the electric field in the same direction. The waves are also called - waves. In this mode, the wave impedance is given as:

)

√

(

)

√

2. Define the cut off frequency for the guided waves. Cut-off frequency is the operating frequency below which attenuation occurs and above which propagation takes place. 3. Define the term phase and group velocity. Phase velocity: It is defined as the rate at which wave changes its phase as the wave propagates inside the region between two parallel planes. Group velocity: It is defined as the actual velocity with which the wave propagates inside the region between two parallel planes. 4. Write down the relationship between group velocity, phase velocity and free space velocity. The product of group velocity and phase velocity is the square of free space velocity.

where

;

;

5. Define wave impedance. The characteristic impedance or wave impedance is defined as the ratio of the amplitudes of and between the parallel planes.

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6. Define guide wavelength. The wavelength is defined as the distance travelled for the phase shift through given by:

radians. It is

This is the wavelength in the direction of propagation of a guide. Hence it is also called as guide wavelength.

7. Plot the frequency Vs wave impedance curve for the waves between parallel conducting planes.

8. What is meant by dominant mode? What is the dominant mode for parallel plate wave guides? The dominant mode is the mode with lowest cut-off frequency (or longest cut-off wavelength). For parallel plate wave guide the dominant modes are mode and mode. Waveguides: 9. What is the need for guide termination? A wave guide is a form of transmission line and must be properly terminated at the receiving end to avoid reflections. The termination should provide a wave impedance equal to the impedance of the transmitted mode in the guide. 10. Discuss the impossibility of waves in hollow wave guide. The TEM wave cannot propagate through the wave guide, because, it needs either axial current or an axial displacement current to support transverse magnetic field. Both these conditions are not possible in wave guide. Hence it can not exist in rectangular waveguide. 11. Write the expression for phase velocity and group velocity for a rectangular wave guide? Phase velocity √ Group velocity

√

( (

)

where

is free space velocity.

)

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12. Which is the dominant mode of rectangular wave guide? Why? The dominant mode is the mode with lowest cut-off frequency (or longest cut-off wavelength). 

mode is called as dominant mode in



mode is called as dominant mode in

wave: wave:

is :

√

is : 2a

From the above , it is clearly noted that . Hence out of these two dominant modes, the most dominant mode is mode in rectangular wave guide. 13. A hollow wave guide behaves like a high pass filter. Why?  The propagation constant for / transmission is given by: √( 

At lower frequencies, (

)

(

)

)

( )

. Thus

becomes real with value equal

)

( )

. Thus

becomes imaginary with value

to attenuation constant .  

At higher frequencies, (

equal to phase constant . Thus the lower frequencies are attenuated completely, with no propagation; while the higher frequencies are allowed to propagate with appropriate phase shift only, so the system acts as High Pass Filter.

14. Write the advantages and disadvantages of circular wave guide? Advantages of circular wave guides:  mode in circular wave guide has the lowest attenuation per unit length of wave guide, hence suitable for long distance wave guide transmission.  In circular wave guide, and modes are rotationally symmetrical and hence rotation of polarization could be overcome.  The circular wave guides are easier to manufacture and join than rectangular wave guides. Disadvantages of circular wave guides:  Propagation in rectangular wave guide is easier compared to circular wave guide.  Circular wave guide occupies more space compared to rectangular wave guide system.  Due to infinite number of modes existing in a circular wave guide, it becomes very difficult to separate these modes.  Angle of polarization of wave changes because of discontinuities and even small irregularities, as a result of which coupling energy out of wave guide at receiving end becomes difficult.  Fabrication of certain type of components is more difficult for circular wave guide. 15. Write the applications of circular wave guide?  Short and medium distance broadband communication.  mode is suitable for long distance wave guide transmission above .  Rotating joints in radars to connect the horn antenna feeding a paraboloid reflector.

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16. Which mode is called as dominant mode in the circular wave guide? 

mode is called as dominant mode in



mode is called as dominant mode in

wave: wave:

From the above , it is clearly noted that . Hence out of these two dominant modes, the dominant mode is mode in cylindrical wave guide. 17. What is Bessel function? Write Bessel’s function of first kind of order zero. The analysis of field components within the hollow, perfectly conducting cylinder with uniform cross section is carried out using the cylindrical coordinate system. The resulting differential equation is called Bessel’s equation. The solution of such equation is called Bessel function. Bessel’s function of first kind of order zero: ∑(

)

(

)

( )

18. Compare transmission line and wave guide. S.No Transmission line Wave guide 1. It supports the transverse It supports many possible configurations. electromagnetic wave (TEM) wave. 2. Due to the skin effect and higher Wave guides can be used efficiently at this dielectric losses, especially in frequency range. Also, these give a lower signal frequency range 3-300 GHz, the attenuation and a larger bandwidth in this transmission line becomes frequency range. inefficient 3. Transmission lines operate from Dc Wave guides can operate only above a specific to a very high frequency. frequency. This frequency is called the cut-off frequency. Thus, a wave guide is a kind of high pass filter. A wave guide cannot be used in DC applications. Below microwave frequencies, a wave guide becomes too large. Cavity resonator: 19. What is meant by cavity resonator? A metallic structure with all of its boundaries forming an enclosed set of conducting walls, inside which electromagnetic waves are confined forming standing wave pattern, is called cavity resonator or resonant cavity. 20. Define the term Quality factor of a resonator? The quality factor of a resonant circuit is the measure of efficiency with which the energy storing elements can store maximum energy. In other words, it is the measure of frequency selectivity of a resonant circuit.

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21. Give the applications of cavity resonators.  The cavity resonators are most widely used in the microwave generation and amplification field. The cavity resonators are used in Klystron amplifier for amplifying microwave signal. The microwave signal is generated with cavity resonator used in Reflex Klystron Oscillator.  The cavity resonators are extensively used in the light house tube. It is a special tube used for VHF range of frequencies.  The cavity resonator plays important role in microwave signal generation when used in cavity magnetron.  The cavity resonators can be used in duplexers in the RADAR system as resonant cavity in Transmit-Receive (TR) tubes and Anti- Transmit-Receive (ATR) tubes.  The cavity resonators are most widely used for the measurement of the microwave signals with the help of cavity wavemeters. 22. Distinguish between wave guide and resonator. S.No Wave guide 1. A wave guide is a hollow metallic tube of any arbitrary but uniform cross section, through which waves can be transmitted. 2. The wave guide is used for transmitting an waves through it at microwave frequencies.

Resonator A cavity resonator is a metallic enclosure with all the sides are closed and conducting. Typically cavity resonator is used for storing energy.

23. List out the parameters describing the performance of a resonator. 1. Quality factor 2. Dimensions of the resonator cavity 3. Skin depth of the conducting walls of resonator. PART B: Guided Waves Between Parallel Planes: 1. Explain the transmission of waves between parallel perfectly conducting planes with necessary expressions and diagrams for the field components. Sketch the field lines of mode in a parallel plate waveguide. (8) *** 2. Discuss the transmission of waves between parallel planes. Sketch the field lines of mode in a parallel plate waveguide. (8) *** 3. Derive the relation among group velocity, phase velocity and free space velocity. (8) *** 4. Explain the concept of transmission of waves and waves between parallel plates. (8) *** Waveguides: 5. Derive the field expression for wave propagation in rectangular waveguide with relavant expressions and diagrams for the field components. (8) *** 6. Derive the field expression for wave propagation in rectangular waveguide with relavant expressions and diagrams for the field components. (8) *** 7. Explain the propagation of electromagnetic waves in cylindrical waveguide with suitable expressions. Deduce the expressions for and waves in cylindrical waveguide. (16) *** 8. Discuss the characteristics of and waves in circular wave guides. (8) 9. Discuss the characteristics of and waves in rectangular waveguide wave guides. (8) QUESTION BANK

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16

wave cannot exist in hollow wave guide. Justify the statement using Maxwell’s equations. (6)

Cavity resonators: 11. Discuss the principle of rectangular cavity resonator. Derive the expression for the resonant frequency of the rectangular cavity resonator. (8) *** 12. Derive the Q factor of a rectangular cavity resonator for mode. (16) *** 13. Determine the dominant modes and their frequencies in an air filled rectangular cavity resonator for , and where , and are the dimensions in the , and respectively. (8) 14. Give brief notes on resonant cavities and its applications. (8)

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