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Unit – I Filters EC6503 Transmission lines and Waveguides Department of ECE 2018 - 2019 EC6503 TRANSMISSION LINES AND WAVEGUIDES UNIT –I TRANSMISSION LINE THEORY PART A - C303.1 1. Distinguish lumped parameters and distributed parameters. Lumped parameters are individually concentrated or lumped at discrete points in the circuit and can be identified definitely as representing a particular parameter. Distributed parameters are distributed along the circuit, each elemental length of the circuit having its own values and concentration of the individual parameters is not possible. 2. What are the different types of transmission lines? The different types of transmission lines are 1.Open wire line 2. Cable 3. Coaxial line 4. Waveguide 3. Describe the different parameters of a transmission line. (1)The parameters include resistance, which is uniformly distributed along the length of the conductors. Since current will be present, the conductors will be surrounded and linked by magnetic flux, and this phenomena will demonstrate its effect in distributed inductance along the line.(2)The conductors are separated by insulating dielectric, so that capacitance will be distributed along the conductor length.(3)The dielectric or the insulators of the open wire line may not be perfect, a leakage current will flow, and leakage conductance will exist between the conductors. 4. Give the general equations of a transmission line. The general equations are, E = ERcosh√ZY s + IRZosinh √ZY s I = IRcosh√ZY s + ( ER / Zo ) sinh √ZY s where Z= R + jωL = series impedance, ohms per unit length of line and Y = G + j ωC = shunt admittance, mhos per unit length of line. 5. What is the advantage in terminating a line with its characteristic impedance? A line of finite length, terminated in a load equivalent to its characteristic impedance, appears to the sending end generator as an infinite line. 6. Define wavelength of the line. (Jan 2016) The distance the wave travels along the line while the phase angle is changing through 2π radians is called a wavelength. 7. What is the relationship between characteristic impedance and propagation constant. R jL Z and R jLG jC . On multiplying Z , characteristic o G jC o impedance and , propagation constant, we get, Z X R jL and G jC o Z o 8. What is meant by distortion less line?&Give the condition for a distortion less line? (Nov 2017). A distortion less line is one which has neither frequency nor delay distortion. The attenuation constant and velocity of propagation cannot be functions of frequency. The condition for a distortion less line is, LG = RC 1 EC6503 Transmission lines and Waveguides Department of ECE 2018 - 2019 9. Find the characteristic impedance of the line at 1600 Hz if Z oc 750 30 and Z sc 600 20 (Nov 2016). Solution: Characteristic impedance, Z Z Z o oc sc = 750 30 X 600 20 = 670.8 25 10. Define frequency distortion. Attenuation constant α is a function of frequency. All frequencies transmitted on a line will then not be attenuated equally. A complex applied voltage, such as a voice voltage containing many frequencies, will not have all frequencies transmitted with equal attenuation, and the received waveform will not be identical with the input waveform at the sending end. This variation is known as frequency distortion. 11. Define delay or phase distortion. All frequencies applied to a transmission line will not have the same time of transmission, some frequencies being delayed more than others. For an applied voice voltage wave the received waveform will not be identical with the input waveform at the sending end, since some frequency components will be delayed more than those of other frequencies. This phenomenon is known as delay or phase distortion. 12. How can you reduce frequency distortion? Frequency distortion is reduced in the transmission of high quality radio broadcast programs over wire lines by use of equalizers at the line terminals. These circuits are networks whose frequency and phase characteristics are adjusted to be inverse to those of the lines, resulting in an over-all uniform frequency response over the desired frequency band. 13. How can you overcome delay distortion? Coaxial cables are used to overcome delay distortion. In such cables, the internal inductance is low at high frequencies because of skin effect, the resistance is small because of the large conductors, and capacitance and leakages are small because of the use of air dielectric with a minimum of spacers. The velocity of propagation is raised and made more nearly equal for all frequencies. 14. Give the expressions for attenuation constant, phase constant and velocity of propagation in a telephone cable. Attenuation constant, α = √ (ωRC) / 2 Phase constant, β = √ (ωRC) / 2 Velocity of propagation, vp = ω/ β = √ (2ω) /RC 15. What is the need for inductance loading of telephone cables? The condition for a distortion less line is, LG = RC. In order to achieve this condition, L/C ratio has to be increased. To increase this ratio, the value of L must be increased which in turn is increased by adding lumped inductors spaced at regular intervals along the telephone cables. 16. What do you mean by reflection factor? 2 EC6503 Transmission lines and Waveguides Department of ECE 2018 - 2019 The change in current in the load due to reflection at the mismatched junction is called 2 Z Z the reflection factor and is given by reflection factor, k = R O Z R Z O 17. Define reflection loss. 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 Z Z 2 the load. Reflection loss, nepers = 10 log R o , Reflection loss, dB = 20 log 4Z Z R O Z Z R o 2 Z R Z O Where ZR = Receiving end impedance, Zo = characteristic impedance 18. Define insertion loss of a line. (May 2015) 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 the insertion. 19. What are the primary&secondary constants of a transmission line? The primary constants of a transmission line are resistance R, ohm/unit length, inductance L, henry/unit length, capacitance C, farad/unit length and conductance G, mho/unit length. The secondary constants of a transmission line are characteristic impedance and propagation constant. 20. A transmission line has Z o 745 12 ohms and is terminated by Z R 100ohms. Calculate the reflection loss in dB and reflection factor. (May 2017) Z Z Solution: Reflection loss, dB = 20 log R o = 3.776 dB 2 Z R ZO 2 Z Z Reflection factor, k = R O = 0.648 Z Z R O 21. When does a finite line appear as an infinite line? A line of finite length, terminated in a load equivalent to its characteristic impedance appears to the sending end generator as an infinite line. 22. Write the equation for the input impedance of a transmission line. The equation for the input impedance of a transmission line is Z R coshl Z o sinhl Zin Z o Z coshl Z sinhl o R 23. A 50 ohms coaxial cable feeds a 75+j20 ohms dipole antenna. Find reflection coefficient and standing wave ratio. Solution: Given Zo = 50 ohms, ZR = 75+j20 ohms Z Z Reflection co-efficient, K = R o Z R Z o 3 EC6503 Transmission lines and Waveguides Department of ECE 2018 - 2019 75 j20 50 25 j20 3238.65 75 j20 50 125 j20 126.589.09 1 K 1 0.25 0.2529.56 SWR, S 1.666 1 K 1 0.25 24. Find the reflection coefficient of a 50 ohm transmission line when it is terminated by a load impedance of 60+j40 ohm.(Nov 2015) Solution: Given Zo = 50 ohms, ZR = 60+j40 ohms Reflection co-efficient, K = 60 j40 50 10 j40 41.2375.9 60 j40 50 110 j40 117.04719.98 0.352355.9169 1 K Standing wave ratio,S 1 K 1 0.3523 2.08 1 0.3523 25.What is the drawback of using ordinary telephone cables?(May 2015) The drawback of using ordinary telephone cables is the attenuation and velocity are functions of frequency and there will be very considerable frequency and delay distortion. 26. Find the attenuation constant and phase constant of a wave propagating along the line Whose 1.048x104 88.8 Solution: Propagation constant, j that is, 1.048x104 88.8 In rectangular form, 2.194x106 j1x104 , Equating the real and imaginary parts, we get, 2.194x106 nepers per unit length and 1x104 rad per unit length. 27. What is characteristic impedance? (Nov 2017) The characteristic impedance of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. 28.A lossless line hasan characteristic impedance of 400Ω. Determine the standing wave ratio if the receiving impedance is 800+j0.0Ω. (May 2017) Reflection co-efficient, K = 800 400 400 1 0.33 800 400 1200 3 1 0.3333 Z R Z1o.999 2 1 0.3333 Z R Z o PART B- C303.1 4 EC6503 Transmission lines and Waveguides Department of ECE 2018 - 2019 1. (i) Derive the transmission line equation and hence obtain the expression for voltage and current on a transmission line. (ii) Prove that an infinite line equal to finite line terminated in its characteristic impedance.(May 2016,Nov 2017 ) 2. A communication link has R = 10.4 ohm/km, L = 3.67 mH/km, G = 0.08 µmho/km and C = 0.0083µF/km.
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