VALLIAMMAI ENGINEERING COLLEGE

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1 VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK V SEMESTER EC6503 TRANSMISSION LINES AND WAVEGUIDES Regulation 2013 Academic Year Prepared by Dr. N. Rajesh, Assistant Professor/ECE Mr. M. Selvaraj, Assistant Professor/ECE Mr. A. Anbarasan, Assistant Professor/ECE Mr. M. A. Seenivasan, Assistant Professor/ECE

2 VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING QUESTION BANK SUBJECT : EC6503 TRANSMISSION LINES AND WAVEGUIDES SEM / YEAR: V/ III Year B.E. UNIT I -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 Q.No Questions BT Competence Level 1. What is meant by distortion less line? 2. Relate the characteristic impedance and propagation constant of a transmission line. 3. State properties of infinite line? 4. Write about the importance of characteristic impedance in transmission line. 5. Define reflection loss. 6. Outline the need for loading of a line and give different types of loading. 7. Review the expressions for the phase constant and velocity of propagation for telephone cable. 8. Compare the advantages and disadvantages of co-axial cable and open wire transmission line. 9. Summarize the methods to avoid waveform distortion in a transmission line. 10. Give the general equation for the input impedance of a dissipation line. 11. Calculate the standing wave ratio if the reflection co-efficient BTL 3 Applying of a line is Illustrate how practical lines made appear as infinite lines? BTL 3 Applying 13. Sketch the equivalent circuit of a unit length of transmission BTL 3 Applying line. 14. Analyze the expression for reflection co efficient. BTL 4 Analyzing 15. Point out the relation between characteristic impedance and BTL 4 Analyzing primary constants of a transmission line. 16. Explain the definition of reflection factor and give its BTL 4 Analyzing mathematical expression. 17. Prove that 1 Neper=8.686 decibel. BTL 5 Evaluating

3 18. Estimate the reflection coefficient of a 50 Ω transmission line BTL 5 Evaluating when it is terminated by a load impedance of 60+j40Ω. 19. Formulate the equation to find resistance for direct current in BTL 6 Creating open wire. 20. Formulate Campbell s formula for a uniformly loaded line. BTL 6 Creating PART B 1. (i) Describe the general transmission line equation for the voltage and current at any point on a transmission line. (8) 2. (i) Illustrate Delay or phase distortion Summarize the expression for the attenuation and propagation constant of transmission line in constant R, L, G and C. (5) 3. (i) State and explain camp bells equation for the loading cables. Discuss in detail about inductance loading of telephone cables and derive the attenuation constant, phase constant and velocity of signal transmission for the uniformly loaded cable. 4. (i) Enumerate in detail about the reflection on a line not terminated in its characteristic impedance. Discuss the types of loading of lines. 5. (i) Write a short note on reflection factor and reflection loss and give expressions. Elaborately write about the waveform distortion also derive the condition for distortion less line. 6. (i) Derive the expression for open and short circuited impedance. Derive the conditions (α, β) required for a distortion less line. A distortion less transmission line has attenuation constant α= Np/m and capacitance of 0.01nF/m. the characteristic resistance L/C=50Ω find the resistance, inductance and conductance per meter of the line. 7. (i) A transmission line has the following per unit length parameters: L = 0.1μH, R =5 Ω, C = 300 pf and G = 0.01 mho. Calculate the Propagation constant and characteristic impedance at 500 MHz.

4 8. (i) A telephone cable 64Km long has a resistance of 13Ω/Km and a capacitance of µf/km.calculate the attenuation constant, velocity and wavelength of the line at 1000Hz. A generator of 1V, 1 khz frequency, supplies power to a 100km open wire line terminated in 200 Ω resistance. The line parameter are R= 10.4Ω/km, L= H/km, G= mho/km. C= μF/km, Z0= , γ= o.calculate the reflection coefficient, Input impedance (Zs), Power and Transmission efficiency. (9) BTL 3 Applying 9. (i) Draw and explain the reflection loss due to mismatch between source and load impedances. The characteristic impedance of a uniform transmission line is Ω at a frequency of 800MHz.at this frequency, the propagation constant is 0.054( j0.99). Solve R and L. (4) BTL 3 Applying 10. (i) Illustrate the Zo and in terms of primary constants. Examine the L-type equivalent circuit model of a two conductor transmission line and derive the transmission line equations. BTL 4 Analyzing 11. (i) Characterize the behavior of attenuation and phase constant of an infinite line. Analyze the expressions for short circuited and open circuited impedance. BTL 4 Analyzing 12. (i) Explain the propagation constant of continuously loaded cable. Explore the performance of a transmission line with insertion of line and calculate insertion loss in nepers. BTL 4 Analyzing 13. (i) Illustrate in detail about input impedance and transfer impedance of transmission lines. Summarize how an infinite line equal to finite line terminated in its characteristic impedance. BTL 5 Evaluating A 2 meter long transmission line with characteristic impedance of 60+j40 is operating at ω =10 6 rad/sec has attenuation constant of Np/m and phase shift constant of 0 rad/m if the line is terminated by a load of 20+j50,find the input impedance of this line.

5 14. (i) The characteristics impedance of a 805meter long transmission line is ⁰Ω, the attenuation constant is ˉ⁶ Np/m. and the phase shift constant is ˉ⁶ rad/m at 5KHz calculate the line parameters R,L,G and C per meter and the phase velocity on the line. BTL 6 Creating The constants of a transmission line are R=6 Ω/km, L=2.2 mh/km, C= ˉ⁶F/km and G= ˉ⁶ mho/km. Calculate at the frequency of 1kHz. (a) The terminating impedance for which no reflection will be setup in the line. (b) The attenuation in db suffered by 1 khz, while travelling a distance of 100 km when the line is properly terminated and the phase velocity with which the signal would travel. PART C 1. A communication line has L=3.67mH/Km, G=0.08*10-6 mhos/km, C=0.0083μF/Km and R=10.4Ω/Km. Determine the characteristic impedance, propagation constant, phase constant, velocity of propagation, sending end current and receiving end current forgiven frequency f=1000hz,sending end voltage is 1 volt and transmission line length is 100 kilometers. 2. A 300m long line has the following constants R=4.5kW, L=0.15 mh, G=60 mho and C=12 nf. Operating frequency f=6mhz. Find propagation constant, characteristic impedance and velocity of propagation. 3. (i) Derive the condition for minimum attenuation in a distortion less line. Formulate Open and short circuit impedance in a symmetrical π network. (15) BTL 5 Evaluating (15) BTL 5 Evaluating (8) BTL 6 Creating

6 4. (i) Develop and derive the relation between primary constants and secondary constants. (8) BTL 6 Creating Determine the characteristic impedance of the T network for given values as follows. Verify characteristic impedance with the help of open circuit and short circuit impedance.z1/2=100ω and Z2=400Ω. UNIT II - HIGH FREQUENCY TRANSMISSION LINES Transmission line equations at radio frequencies - Line of Zero dissipation - Voltage and current on the - 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 Q.No Questions BT Competence Level 1. Outline the assumptions to simplify the analysis of line performance at high frequencies? 2. Identify the method to analyze the performance of the line at radio frequency. 3. List the properties of an infinite line. 4. Define nodes and antinodes on a line. 5. Outline the nature and value of Z0 for the dissipation less line? 6. Show the nature of input impedance of open circuit and short BTL 3 Applying circuit dissipation less lines of different wavelengths. 7. Solve the terminating load for a certain R.F transmission line BTL 3 Applying which has the characteristic impedance of the line 1200 Ω and the reflection co-efficient was observed to be Categorize the transmission lines available for RF signal BTL 3 Applying transmission. 9. Explain the assumptions of open wire at radio frequencies. BTL 4 Analyzing 10. Analyze the line with zero dissipation and find the values of BTL 4 Analyzing attenuation constant and characteristic impedance? 11. Examine the skin effect in co axial cable. BTL 4 Analyzing 12. Measure the VSWR and reflection co efficient of a perfectly BTL 5 Evaluating matched line with no reflection from load. 13. A lossless transmission has a shunt capacitance of 100 pf/m BTL 5 Evaluating and a series inductance of 4μH/m. evaluate the characteristic impedance. 14. Formulate the expression for the ratio of power delivered to BTL 6 Creating the load. 15. Mention the values of SWR for open circuit, short circuits and matched line. 16. Determine the values of VSWR in the case of (a) ZR = 0 and (b) Z R = Z0 BTL 6 Creating

7 17. Compute the relation between standing wave ratio and magnitude of reflection co efficient. 18. Express SWR in terms of reflection coefficient. 19. Write the expression for standing wave ratio in terms of reflection co-efficient. 20. Formulate the minimum values and maximum values of SWR and reflection coefficient. PART B 1. (i) Derive the expressions for voltage and current at any point on the radio frequency line terminated in ZR. Obtain the expressions for the same for different receiving end conditions. Support with the graph of voltage and current on a line for all conditions. Enumerate about the power and impedance measurement on lines. 2. (i) Brief notes on Standing waves, nodes, standing wave ratio also make relation between the standing wave ratio S and the magnitude of the reflection coefficient. State the condition for the open wire line at high frequencies and derive the parameters. 3. (i) Review the parameters of open wire line and co axial at RF. Mention the standard assumptions made for radio frequency line. Give condition for dissipation less. 4. (i) Discuss about the Line constants for zero dissipation. Discuss the reflection coefficient of different transmission lines. 5. (i) An ideal loss less quarter wave (s=ƛ/4) transmission line of characteristics impedance 60Ω is terminated in a load impedance ZR. What is value of the input impedance of the line when ZR=0, and 60Ω. Compare the features of open wire and co axial cable at high frequencies. 6. (i) Derive the line constants of zero dissipation less line. Interpret the various parameters of open wire and co axial lines at radio frequency. Discuss in detail about Standing wave ratio.

8 7. (i) 8. (i) Explain in detail about the variation of input impedance along open and short circuit lines with relevant graphs. Sketch the voltages and currents on dissipation less line for the conditions given below. (a) Open circuit (b) Short circuit (c) Rr =R0 The VSWR measured on UHF transmission line at a frequency of 300MHz found to be 2.if the distance between load and voltage minimum is 0.8m, solve the normalized load impedance. BTL 3 Applying 9. (i) A lossless transmission line with Z0 = 75 Ω and of electrical length l = 0.3λ is terminated with load impedance of ZR = (40+j20) Ω. Determine the reflection coefficient at load, SWR of line, input impedance of the line. A low loss transmission line of 100Ω characteristic impedance is connected to a load of 200Ω.calculate the voltage reflection coefficient and the standing wave ratio. BTL 3 Applying 10. (i) Calculate standing wave ratio and reflection coefficient on a line having Z0 =300 Ω and terminated in ZR=300+j400 Ω. A lossless line in air having a characteristic impedance of 300 Ω is terminated in unknown impedance. The first voltage minimum is located at 15cm from the load. The standing wave ratio is 3.3.calculate the wavelength and terminated impedance. BTL 4 Analyzing 11. (i) An antenna as a load on a transmission line produces a standing wave ratio of 2.8 with a voltage minimum 0.12λ from the antenna terminals. Calculate the antenna impedance, reflection factor and reflection loss at the antenna if R0=300 Ω for the line. Express the mathematical expressions for the input impedance of the dissipation less line. Deduce the input impedance of open and short circuited dissipation less line. (8) BTL 4 Analyzing Discuss about Reflection losses on the unmatched line. 12. (i) Obtain the expression for input impedance of OC and SC line at high frequencies and (5) BTL 4 Analyzing

9 measure the power. Explore the standing waves with neat diagram. 13. (i) 14. (i) Summarize the relation between standing wave ratio (S) and magnitude of relation co efficient. A line with zero dissipation has R=0.006 Ω / m, C=4.45/ m, L=2.5 µh / m,if the line is operated at 10MHz find R0, α,β,λ, v. Determine the reflection coefficient and voltage standing wave ratio of a line having Ro= 100 Ω and ZR=100-j100 Ω A radio frequency line with Z0=70Ω is terminated by ZL=115-j80 Ω at λ=2.5m. Find the VSWR and the maximum, minimum line impedances (5) (8) BTL 5 BTL 6 Evaluating Creating PART C 1. (i) 2. (i) A lossless transmission line in air has a characteristic impedance of 300Ω and is terminated by an unknown impedance. When the frequency is 200MHz, the standing wave ratio is 4.48 and first voltage minima are situated at 6cm from the load. Evaluate the complex reflection coefficient Terminating impedance of the line. Describe an experimental setup for the determination of VSWR of an RF transmission. A certain low loss line has a characteristic impedance of 400Ω.estimate the standing wave ratio with the following receiving end impedance. ZR=70+ j0.0ω ZR=800+j0.0Ω ZR=660+j475Ω (8) (8) BTL 5 BTL 6 Evaluating Creating Conclude why a quarter wave line is considered as an impedance inverter. Justify your answer. 3. Formulate the Standing wave pattern for open and short circuited load for the following cases: (a) Long line open circuited at the receiving end. (b) Long line short circuited at the receiving end. 4. (i) An UHF transmission line of ZO= is terminated at an unknown load. The VSWR measured in the line is 3 and the position of current maxima nearest to the load is one the fifth wavelength. Evaluate the value of the load impedance. (15) BTL 5 Evaluating (8) BTL 6 Creating

10 Deduce an expression for the input impedance of a dissipation less line and also find the input impedance is maximum and minimum at a distance S. UNIT III 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 Q.No Questions BT Level Competence 1. Define standing wave ratio in terms of reflection coefficient. 2. List the application of a quarter wave line. 3. What is the procedure to find the impedance from the given admittance using smith chart. 4. Calculate the standing wave ratio if the reflection co-efficient of a line is Give the minimum and maximum value of SWR and reflection coefficient. 6. Why is the Quarter wave line called as copper insulator? 7. Compare single stub matching and double stub matching. 8. A 50 line is terminated in load ZR = 90 + j60. Show the reflection coefficient. 9. Explain the VSWR and reflection coefficient of a perfectly matched line with no reflection from load? 10. A 75 lossless transmission line is to be matched to a resistive load impedance of ZL =100 via a quarter wave section. Find the characteristic impedance of the quarter wave transformer 11. Why do standing waves exist on transmission lines? BTL 3 Applying 12. How would you use smith chart for various applications? BTL 3 Applying 13. Why short circuited stub is preferred to open circuited stub? BTL 3 Applying 14. Examine the applications of Half - wave matching line? BTL 4 Analyzing 15. Conclude advantages of double stub matching over single stub BTL 4 Analyzing matching? 16. Can you identify the need for stub matching in transmission BTL 4 Analyzing lines? 17. Determine why it is essential to have impedance matching. BTL 5 Evaluating

11 18. A lossless line has a characteristic impedance of 400. BTL 5 Evaluating Determine the standing wave ratio if the receiving end impedance is 800+j0 19. Formulate for finding the position and length of a stub? BTL 6 Creating 20. A 50 co-axial cable feeds a 75+j20 dipole antenna. Estimate BTL 6 Creating reflection coefficient and standing wave ratio. PART B (13 Marks) 1. (i) Name the procedure for double stub matching on a transmission line with an example. Write notes on Eight wave line and half wave line. 2. Can you recall the technique of single stub matching and find the stub location and stub length equations. (13) 3. (i) Consider a line of RO = 55 ohms terminated in 115+j75 ohms. If the total length of the line is 1.183λ, find the VSWR, input impedance and admittance Find the input impedance and admittance of a co-axial line having RO = 95 ohms and the line is 20m long short circuited at far end operated at 10MHz. 4. (i) Enumerate the operation of quarter wave transformer and mention its applications. Write notes on Eight wave line and half wave line. 5. Explain the transmission line circle diagram by deriving the expression for constant S and constant βs circle. (13) 6. (i) It is required to match a 200 ohms load to a 300 ohms transmission line to reduce the SWR along the line to 1. What must be the characteristic impedance and length of the quarter wave transformer used for this purpose if it is directly connected to the load? The operating frequency is 200 MHz (5) A UHF lossless transmission line working at 1 GHz is connected to an unmatched line producing a voltage reflection coefficient of 0.5(0.866+j 0.5). Calculate the length and position of the stub to match the line using corresponding equations (8) 7. A transmission line is terminated in ZL. Measurements indicate that the standing wave minima are 102 cm apart and that the last minimum is 35 cm from the load end of the line. The value of standing wave ratio is 2.4 and R0 = 250. Determine frequency, wavelength, Real and reactive components of the terminating impedance. Also Verify the results obtained from equations using the smith chart (13) 8. VSWR of a lossless line is found to be 5 and successive voltage minima are 40cm apart. The first voltage minima is observed to be 15cm from the load. The length of the line is 160cm and Zo is 300 Ω. Apply the values in smith chart to find the load BTL 3 Applying

12 impedance and input impedance. (13) 9. A RF transmission line with Zo=300 0 Ω is terminated in an impedance of Ω. This load is to be matched to the transmission line by using a short circuited stub. With the help of smith chart, Find the length and location of the stub (13) 10. A 50 transmission line feeds an inductive load 35+j35. Analyze and design a double stub tuner to match this load to the line using smith chart. Spacing between the two stubs is λ/4 (13) 11. (i) Derive the expression of radius and center for constant R and X circles in Smith Chart. The terminating load of UHF transmission line working at 300MHz is 50+50j ohms. Calculate VSWR and the position of the voltage minimum nearest to the load if the characteristics impedance of the line is 50 ohms. 12. (i) Consider a line with a load of ZR/RO =2.6+j, which is 28 long. Find the input impedance Examine the operation and application of quarter wave transformer. 13. Determine the length and location of the stub to produce an impedance match on a line of 600 ohms terminated in 200 ohms. The stub is short circuited at the other end. Determine the length and location of the stub. (13) 14. (i) A load 50+j100 ohms is connected across a 50 ohms line. Design a short circuited stub to provide matching between the two at a single frequency of 30MHz. Construct the procedure for double stub matching on a transmission line with an example. BTL 3 Applying BTL 4 Analyzing BTL 4 Analyzing BTL 4 Analyzing BTL 5 Evaluating BTL 6 Creating PART C(15 Marks) 1. (i) Determine length and location of a single short circuited stub to produce an impedance match on a transmission line with characteristic impedance of 600 ohm and terminated in 1800ohm. (8) A 300 Ω transmission line is connected to a load impedance of (450-j600) Ω at 10MHz.Evaluate the position and length of a short circuited stub required to match the line using smith chart. 2. (i) The input impedance of a λ/8 long, 50Ω transmission line are Z1=25+j100 Ω Z2=10-j50 Ω Z3=100+j0 Ω and Z4=0+j50 Ω, when various load impedances are connected at the other end. In each case, estimate the load impedance and the reflection coefficient at the input and load ends (11) Explain the applications of quarter wave transformer. (4) BTL 5 Evaluating BTL 6 Creating

13 3. (i) A line having characteristic impedance of 50 Ω is terminated in load impedance [75+j75] Ω. Determine the reflection coefficient and voltage standard wave ratio. (10) Mention the significance of smith chart and its application in transmission lines. (5) 4. (i)develop the expression for the input impedance of the dissipation less line and thus obtain the expression for the input impedance of the quarter wave line. Also discuss the application of the quarter wave line (10) Design a single stub match for a load of 150+j225 Ω for a 75 Ω line a 500 MHz using smith chart. (5) BTL 5 Evaluating BTL 6 Creating UNIT IV 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 Q.No Questions BT Level Write down the expression for design impedance and cut-off 1. frequency of low pass filter. Competence State the characteristics of an ideal filter? Describe the advantages of m-derived filters? Define cutoff frequency. A constant K T-section high pass filter has fc = 1.5KHz and design impedance 500Ω. Find L. What is constant-k filters? Compare constant k and m-derived filters. Explain composite filter. Classify different types of filter on the basis of operation. Draw a simple High-pass filter section and show the values of circuit elements. 11. Solve the value of L and C of a constant-k filter having a cutoff frequency of 3KHz and load of 600 Ω. BTL 3 Applying

14 12. Draw a simple Band-pass filter network and identify the values of circuit elements. BTL 3 Applying 13. For an m-derived low pass filter, obtain the relationship between cut-off frequency, frequency of infinite attenuation and m? BTL 3 Applying Examine the demerits of constant k filters. BTL 4 Analyzing Calculate the value of C required by a prototype high pass T- section filter having a cutoff frequency of 1KHz to work into a 600Ω load resistance. BTL 4 Analyzing Distinguish between active filters and passive filters. BTL 4 Analyzing Deduce the expression for attenuation constant and phase constant for a constant k low pass filter. BTL 5 Evaluating 18. A T section low pass filter has series inductance of 80mH and shunt capacitance of F. Evaluate the cutoff frequency and the design impedance. BTL 5 Evaluating 19. Design a prototype low pass filter T section of design impedance Ro =500Ω and cutoff frequency fc=2000hz. BTL 6 Creating 20. A constant-k T-section high pass filter has a cutoff frequency of 10 KHz. The design impedance is 600 Ω. Estimate the value of L. BTL 6 Creating PART B (13 Marks) 1. (i) Define the characteristic impedance of symmetrical T and Π section networks. (5) How would you explain the properties of symmetrical network in terms of characteristic impedance and propagation constant? (5) (iii) Find out the expression of attenuation in Neper and Decibel. (3) 2. (i) Give the fundamentals of the Pass band and Stop band Filter. (5) Describe the operating principle of crystal filters along with its applications. (8) 3. (i) Write notes on m derived low pass filter with necessary equations and diagrams. Recall the operation of m derived high pass filter with necessary equations and diagrams.

15 4. Outline the design equations for m-derived band pass and band elimination filters. (13) 5. (i) What do you mean by composite filter? Discuss its construction, design and characteristics briefly Find the characteristics impedance and propagation constant of the symmetrical T network whose series arm is 50 ohms and shunt arm is 5000Ω 6. Explain and derive characteristic impedance, inductance, capacitance and cut-off frequency for constant k low pass and constant k high pass filter, also draw their reactance curves. (13) 7. (i) With a neat diagram explain the operation of a constant-k band pass filter. Derive the equation of resonance. Develop expression for the circuit elements used in the series and shunt arms of the filter. Consider a T-section. (9) Demonstrate a symmetrical T section with ZO = 600 ohms and γ=0+jπ/4. (4) 8. Develop a T section and π section constant k high pass filter and Low pass filter having cutoff frequency of 12 KHz and nominal impedance R0 =500Ω Also find Z0, Phase constant at 24KHz and Attenuation at 4KHz. (13) 9. (i) Construct a low pass filter (both π and T-sections) having a cutoff frequency of 2KHz to operate with a terminated load resistance of 500Ω. Identify and explain the operation of constant-k band elimination filter with necessary equations and diagrams. 10. (i) How would you design a high pass filter having a cutoff frequency of 1 KHz with a load resistance of 600Ω? (5) Examine and design an m-derived low pass filter to work into load of 400Ω with cut off frequency at 1KHz and resonant frequency 1100Hz (8) 11. (i) Analyze and design a Band pass filter to operate into input and output resistance of 100Ω and have a pass band between 4.8KHz and 5.2KHz. (5) The series arm Z1 of a filter consists of a 0.5µF capacitor in series with an inductor of 0.35H. If Ro =500Ω, determine the elements in the shunt arm and the manner in which they may be connected. Find the frequency of resonance of and pass band. (8) 12. (i) Given that the cutoff frequency of 5000 Hz and a design impedance of 600 ohms. The frequency of infinite attenuation is f =1.25 fc. Design an m-derived T-section low pass filter. BTL 3 BTL 3 BTL 4 BTL 4 BTL 4 Applying Applying Analyzing Analyzing Analyzing

16 Design an m-derived high pass filter π sections with a cut off frequency of 1000/π KHz to work into load of 600Ω 13. Design a low pass composite filter for the following specifications. Cut-off frequency fc =2 khz. Frequency of infinite attenuation f = 2200 Hz Load impedance of 600Ω.Use π section to develop composite filter. (13) 14. Develop a composite High pass filter to operate into the load of 600Ω and have a cutoff frequency of 1.2 KHz. The filter is have one constant k section, one m derived section with f =1.1 KHz and suitably terminated half section (13) PART-C (15 Marks) 1. (i) Evaluate an m-derived T section low pass filter having cutoff frequency of 1KHz.Design impedance is 400 Ω and the resonant frequency is 1100 Hz. (3) Justify the equations for the characteristic impedance of symmetrical T and π networks. (iii) Recommend the properties of symmetrical network in terms of characteristic impedance and propagation constant. 2. Design a constant K bandpass filter deriving expressions for the circuit components. A constant K high pass filter cuts off at a frequency of 2300 Hz. The load resistance is 500 Ω. Calculate the values of components used in the filter. (15) 3. (i) Explain &draw the m-derived T- section high pass filter.(10 Summarize composite filter and design a constant K-low pass filter and having cut-off at which 2.5KHz and design resistance Ro is 700Ω. (5) 4. (i) Discuss the operation and design of constant-k T section band elimination filter with necessary equations & diagrams. (8) Build a constant K bandpass filter (both T and π sections)having a design impedance of 600 Ω and cut-off frequencies of 1KHz. and 4KHz BTL 5 BTL 6 BTL 5 BTL 6 BTL 5 BTL 6 Evaluating Creating Evaluating Creating Evaluating Creating UNIT V - 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. PART A

17 Q.No Questions BT Competence Level 1. Define the quality factor of cavity resonator? 2. Write Bessel s functions of first kind of order zero? 3. Mention about the dominant mode of a rectangular waveguide. 4. TM01 and TM10 modes are not exists in a rectangular Waveguide Justify. 5. Define cutoff frequency of a waveguide? 6. Compare TE and TM mode BTL 3 Applying 7. What are commonly used guide terminations? BTL 3 Applying 8. Mention the application of cavity resonators BTL 3 Applying 9. How cavity resonator is formed? BTL 4 Analyzing 10. Characterize the velocity as Group velocity and Phase BTL 4 Analyzing velocity in a transmission Line. 11. List out the characteristics of TEM waves. BTL 4 Analyzing 12. Discuss about the dominant mode and degenerate modes BTL 5 Evaluating in rectangular waveguide. 13. Compare between waveguide and cavity resonator. BTL 5 Evaluating 14. A wave is propagated in the dominant mode in a parallel BTL 6 Creating plane waveguide frequency is 6GHz and the plane separation is 4cm. Calculate the cutoff wavelength and the wavelength in the waveguide. 15. A wave is propagated in a parallel plane waveguide. The frequency is 6GHz and the plane separation is 3cm. Determine the group and phase velocity for the dominant Mode. 16. Determine the size of the circular waveguide required to BTL 6 Creating propagate TE11 mode if λc=8cm and ρ11= An air filled rectangular waveguide of cross section 5cm x 2 cm is used to propagate TM11 mode at 10 GHz. Determine cut-off wavelength and guide wavelength. 18. Assess the features of Transverse Electro Magnetic (TEM) waves. 19. An air filled rectangular waveguide of inner dimension x in centimeters operates in the dominant TE10 modes. Calculate the cut-off frequency and phase velocity of a wave in the guide at a frequency of 7GHz TEM wave is not possible through hollow rectangular waveguide - Justify. PART B 1. (i) Describe the principle of operation and applications of resonant cavities. Explain the excitation of various modes in Rectangular cavities.

18 2. (i) Recall the field component of a Transverse Electric wave in rectangular wave guides. 3. (i) Determine the expression of wave impedance of TE, TM and TEM wave between a pair of Perfectly conducting planes. A rectangular cavity resonator excited by TE101 mode at 20GHz has dimensions a = 2cm, b=1cm. Calculate the length of the cavity. Unterstanding Illustrate the attenuation of TE and TM waves between parallel planes with an appropriate Graph. 4. Obtain the expression for the transmission of TM waves between parallel perfectly conducting planes with necessary expressions for the field components and compare its characteristics with TE and TEM waves. 5. (i) For a frequency of 6 GHz and plane separation of 3cm in air, find the cut off frequency, cut off wavelength, phase velocity and group velocity of the wave. A circular air filed copper cavity is excited in the TM₀₁₀ mode at 9.375GHz. The cavity has length of 6cm and radius 4cm. Find the Resonant frequency and Q-factor. 6. Discuss the transmission of TM waves between parallel perfectly conducting planes with necessary. (13) BTL 3 Applying (13) 7. (i) 8. Interpret the propagation of TM waves in a rectangular waveguide with necessary expressions for the field components. Summarize the characteristics of TE and TM waves and also derive the cutoff frequency and phase velocity from propagation constant. Using Bessel differential equation derive the TM field components in circular waveguides. (13) Unterstanding 9. A rectangular air filled copper waveguide with dimension 0.9inch x 0.4inch cross section and 12inch length is propagated at 9.2GHz with a dominant mode. Find the cutoff frequency, Guide wavelength, Phase velocity, characteristic impedance and the loss. 10. (i) Examine salient features of circular cavity resonator and mention its applications. (13) BTL 5 Evaluating BTL 4 Analyzing

19 A TE11 wave is propagating through a circular Waveguide. The diameter of the guide is 10cm and the guide is air-filled. Given X11=1.842 (a)find the cut off frequency (b)find the wavelength λg in the guide for a frequency of 3GHz. (c)determine the wave impedance in the guide. 11. What is quality factor of a resonator and derive an expression for the quality factor of rectangular and circular cavity resonators. 12. A pair of perfectly conducting plates is separated by 10cm in air and carries a signal frequency of 6GHz in TE1 mode. Find Cut-off frequency, Angle of incidence on planes, Phase velocity, group velocity, Phase constant, Cut-off wavelength, characteristic wave impedance, and wavelength along guiding Walls. Is it possible to propagate TE3 mode. 13. (i) Analyze the expressions for the transmissions of TE waves between parallel perfectly conducting planes for the field components. (3) (2) (2) (13) BTL 6 Creating (13) BTL 3 Applying (13) BTL 4 Analyzing 14. (i) Explain about Bessel functions of first and Second kind and state its properties. (8) BTL 4 Analyzing Calculate the resonant frequency of an air filled rectangular resonator of dimensions a=2cm, b=4cm and d=6cm operating in TE101 Mode. (5) PART C 1. (i) A hollow rectangular waveguide is to be used to transmit signals at a carrier frequency of 6GHz. Choose its dimensions so that the cut off frequency of the dominant TE mode is lower than the carier by 25 % and that of the next mode is atleast 25 % higher than the carrier. (8) BTL 6 Creating Evaluate the ratio of the area of a circular waveguide to that of a rectangular one if both are to have the same cut off frequency for dominant mode..

20 2. (i) A cubical cavity resonator made of copper σ = 5.8 x 107 mho / m is to be operated at 15GHz. Find the dimensions of the cavity, its quality factor and the bandwidth if it is operated in the dominant mode. (8) BTL 5 Evaluating A circular air filled copper cavity is excited in the TM010 mode. The cavity has a length of 6 cam and radius 4 cm with a bandwidth of 3MHz. Find the resonant frequency and quality factor 3. Determine the cut off frequencies of the first two propagating modes of a circular waveguide with a=0.5cm and εr = 2.25 the guide is 50cm in length operating at f = 13GHz. Determine the attenuation. 4. (i) A TE wave propagating in a dielectric filled waveguide of unknown permittivity has dimensions a=5 cm and b = 3cm. If the x components of the electric field is given by Ex=36cos(40πx)sin(100πy)sin(2.4π 1010t 52.9π z (V/m).impedance is maximum and minimum at a distance S. (15) BTL 5 Evaluating (15) BTL 6 Creating