UNIT I TRANSMISSION LINE THEORY A line of cascaded T sections & Transmission lines General Solution, Physicasignificance of the equations 1. Derive the two useful forms of equations for voltage and current at any point on a line. (16) [N/D 11, M/J 12] 2. Deduce the expressions for characteristic impedance and propagation constant of a line having cascaded, identical and symmetrical T sections. (8)[N/D 11] 3. If Z=R + jωl and Y = G + jωc, find the velocity of propagation for an ideal line in terms of line parameters. (8)[N/D 11] 4. A distortionless transmission line has attenuation constant (α) of 1.15x10 3 Np/m and capacitance of 0.1x10 9 Farad per meter. The characteristic resistance the resistance, inductance and conductance per meter of the line. (6) = 50 Ω. Find The infinite line, wavelength, velocity, propagation &distortion bus line, the telephone cable 5. Explain the condition for distortionless line. Characteristic impedance of a transmission line at 8 MHz is 40 j2 Ω and the propagation constant is 0.01+j0.18 per meter. Find the primary constants. (16) [N/D 2011] 6. A line has the following primary constants: R = 100 Ω/km, L = 0.001 H/km, G = 1.5 µmho/km, C = 0.062 µf/km. Find the characteristic impedance, propagation constant, velocity of propagation and wavelength. (16) 7. The characteristic impedance of a 805 m long transmission line is 94 23.2 o Ω, the attenuation constant is 74.5 x 10 6 Np/m and the phase shift constant is 174 x 10 6 rad/m at 5 khz. Calculate the line parameters R, L, G and C per meter and the phase velocity of the line. (16) Department of Electronics and Communication Engineering1
Reflection on a line not terminated in Zo, Reflection Coefficient, Open and short circuited lines & Insertion loss 8. Explain the following: [N/D 11] a) Reflection on a line not terminated in Z 0 (8) b) Open and short circuited lines (8) 9. A low loss transmission line of 100 Ω characteristic impedance is connected to a load of 200 Ω. Calculate the voltage reflection co efficient and the standing wave ratio. (6)[M/J 12] 10. Explain the theory of open and short circuited lines with voltage and current distribution diagrams and also derive all expressions for input impedance. (10)[M/J 12] 11. A generator of 1V, 1 khz supplies power to a 100 km open wire line terminated in 200 Ω resistance. The line parameters are R = 10 Ω/km, L = 3.8 mh/km, G = 1x10 6 mho/km, C = 0.0085 µf/km. Calculate the input impedance, reflection coefficient, the input power, output power and transmission efficiency. (16) Department of Electronics and Communication Engineering2
UNIT II HIGH FREQUENCY TRANSMISSION LINES Parameters of open wire line and coaxial cable at RF & Line constants for dissipation voltages and currents on the lossless dissipation line 1. Derive the equations that permit easy measurements of power flow on a line of negligible losses. (10) [N/D 11] 2. Derive the expressions for input impedance of open and short circuited lines. ` (6)[N/D 11] 3. Explain the parameters of open-wire and co-axial lines at radio frequency. (16)[N/D 11] Standing waves nodes standing wave ratio, Input impedance of open and short circuited lines Power and impedance measurement on lines λ / 4 line 4. A 30 m long lossless transmission line with Z 0 = 50 Ω operating at 2 MHz is terminated with a load of Z L = 60 + j 40 Ω. If U = 0.6 C on the line calculate, a) Reflection coefficient (5) b) Standing wave ratio (5) c) Input impedance (6) [N/D 12] Department of Electronics and Communication Engineering3
UNIT III IMPEDANCE MATCHING IN HIGH FREQUENCY LINES Impedance matching single and double stub matching circle diagram, Smith chart and its applications & Problem solving using Smith chart 1. Write short notes on the following : a) Impedance matching (8) b) Single and double stub matching. (8) [N/D 12] 2. An ideal lossless quarter wave transmission line of characteristic impedance 60 Ω is terminated in a load impedance Z L. Determine the value of the input impedance of the line when Z L = 0, and 60 Ω. (6) [M/J 12] 3. Write the concepts of single and double stub matching. (10) [M/J 12] 4. A 100 Ω, 200 m long lossless transmission line operates at 10 MHz and is terminated into an impedance of 50 j 200 Ω. The transit time of the line is 1μs. Determine the length and location of a short circuited stub line. (8) [M/J 12] 5. What are the concepts of quarter wave length line and half wave length line? (8) [M/J 12] 6. Explain the method of single stub matching using smith chart. (8) 7. Draw and explain the principles of double stub matching. (16) 8. A lossless line has a characteristic impedance of 400 Ω. Determine the standing wave ratio if the receiving end impedance is 800 + j0.0 Ω.(8) 9. A UHF lossless transmission line working at 1 GHz is connected to an unmatched line producing a voltage reflection coefficient of (0.866 + j 0.5). Calculate the length and position of the stub to match the line. (8) Department of Electronics and Communication Engineering4
10. Consider a 30 m long lossless transmission line with a characteristic impedance of 50 Ω operating at 2 MHz. The line is terminated in a load impedance of (60 + j40) Ω. Calculate the reflection coefficient, the standing wave ratio and the input impedance, if the velocity on the lineis v= 0.6c (c =line is terminated in a load impedance of Z L = (25 + j50) Ω. Use the smith chart to find a) Voltage reflection coefficient b) VSWR c) Input impedance of the line, given that the line is 3.3λ long d) Input admittance of the line (16) Department of Electronics and Communication Engineering5
UNIT IVFILTERS The neper the decibel Characteristic impedance of Symmetrical Networks & Current and voltage ratios Propagation constant Properties of Symmetrical Networks 1. Derive the equations for the characteristic impedance of symmetrical T and π networks. (8)[N/D 11] 2. Explain the properties of symmetrical network in terms of characteristic impedance and propagationconstant. (8)[N/D 11] 3. Discuss the characteristics of symmetrical network. (6) 4. Explain the properties and characteristic impedance of symmetrical networks. (6) [N/D 12] Filter fundamentals Pass and Stop bands & Constant K Filters Low pass, High pass band pass, band elimination filters 5. Design constant-k low pass and high pass filters with suitable filter sections. (16) [N/D 11] 6. Design T and π section low pass filter which has series inductance 80 mh and shunt capacitance 0.022µf. Find the cutoff frequency and design impedance. (10)[N/D 12] 7. Calculate the values of the inductor and capacitors of a prototype constant-k low pass filter composed of π section to operate with a terminating load of 600 Ω and to have a cutoff frequencyof 3 khz. (6)[M/J 12] 8. Construct a band stop constant-k filter. (10)[M/J 12] m derived sections, Filter circuit design Filter performance Crystal Filters 9. Design a m-derived T-section low pass filter having cutoff frequency f c = 1000 Hz, design impedance R k = 600 Ω and frequency of infinite attenuation f = 1050 Hz. (10) 10. Design am-derived T type low pass filter with a load of 500 Ω with cut-off frequency of 4 khz and peak attenuation of 4.15 khz. (8) 11. What are the advantages of m-derived filter? Design a m-derived Low Pass Filter (T and π sections) having design resistance R 0 = 500 Ω, cutoff frequency f c = 1500 Hz and infinite attenuation frequency f =2000 Hz. (16)[N/D 12] Department of Electronics and Communication Engineering6
UNIT V WAVE GUIDES AND CAVITY RESONATORS Transmission of TM waves between Parallel planes & Transmission of TEwaves between Parallel planes 1. Derive the field equations of TE waves between parallel planes. (8)[N/D 11] 2. Explain the transmission of TM waves between parallel planes. (8)[M/J 12] 3. Write the instantaneous field expressions for TM 1 mode in a parallel plane waveguide. (8)[M/J 12] 4. Explain the transmission of TE waves between parallel planes. (8) [M/J 12] 5. Sketch the field lines of TE 1 mode in parallel plane waveguides. (8)[M/J 12] Transmission of TEM waves between Parallel planes 6. Explain TEM and TM for attenuation with planes of finite conductivity. (16)[N/D 11] 7. Explain the concept of transmission of TM waves and TEM waves between parallel planes. (16) [N/D 11] Manner of wave travel, Velocities of the waves & Characteristic impedance Attenuators 8. Derive the relation among phase velocity, group velocity and free space velocity. (8)[N/D 11] 9. Design a T and π type attenuators to produce attenuation of 20 db and to work in a line of 600 Ω. (8) [N/D 11] Department of Electronics and Communication Engineering7
10. For a frequency of 5 GHz and plane separation of 8 cm in air, find the following for TM 1 mode: a) Cutoff Wavelength b) Characteristic Impedance c) Phase Constant (8) 11. For a frequency of 10 GHz and plane separation of 5 cm in air, find the following for TE 1 : a) Cutoff Wavelength b) Phase Velocity c) Group Velocity (8) 12. For a frequency of 6 GHz and plane separation of 3cm, find the group and phase velocities for the dominant mode. (8) TM waves in Rectangular guide & TE waves in Rectangular waveguide 13. A rectangular air filled copper waveguide with dimension 0.9 inch x 0.4 inch cross section and 12 inch length is operated at 9.2 GHz with a dominant mode. Find its cutoff frequency, guide wavelength, phase velocity and characteristic impedance. (16) [N/D 11] 14. Find the resonant frequencies of first five lowest modes of an air filled rectangular cavity of dimensions 5 cm x 4 cm x 2.5 cm. List them in ascending order. (8) [N/D 11] 15. A rectangular waveguide with dimensions a = 2.5 cm and b = 1 cm, is to operate below 15.1 GHz. How many TE and TM modes can the waveguide transmit, if the guide is filled with a medium characterized by σ = 0, ε 1 = 4ε 0 and µ r = 1? Calculate cutoff frequencies of the modes. (8) Department of Electronics and Communication Engineering8
Cylindrical waveguides 16. Explain the transmission of TM waves in a circular waveguide with relevant expression for the field components. (10)[M/J 12] 17. A 10 GHz signal is to be transmitted inside a hollow circular conducting pipe. Determine the inside diameter of the pipe such that its lowest cutoff frequency is 20% belowsignal frequency. (6) [M/J 12] 18. Derive the field expression for TM wave propagation in rectangular waveguide stating the necessary assumptions. (16)[N/D 12] 19. An air filled circular waveguide having an inner radius of 1 cm is excited in dominant mode at 10 GHz. Find the cutoff frequency, guide wavelength, wave impedance and the bandwidth for operation in dominant mode only. (Given X 11 =1.84, X 01 =2.40) (8) [N/D 11] The TEM wave in coaxial lines, Excitation of wave guides 20. Explain the concept of excitation of waveguides. (8)[N/D 12] Guide termination and resonant cavities 21. Explain the principle of rectangular cavity resonator. (8)[M/J 12] 22. Explain the structure, advantages and disadvantages of resonant cavities. (8) [N/D 12] 23. What is meant by quality factor of the cavity resonator? Derive the expression for the quality factor of rectangular and circular cavity resonator. (16) Department of Electronics and Communication Engineering9