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 Transmission lines or T-lines are used to guide propagation of EM waves at high frequencies.  Examples: › Transmitter and antenna › Connections between computers in a network › Interconnects between components of a stereo system › Connection between a cable service provider and aTV set. › Connection between devices on circuit board  Distances between devices are separated by much larger order of wavelength than those in the normal electrical circuits causing time delay. 2

 Properties to address: › time delay › reflections › attenuation › distortion 3

 Types of transmission lines 4

 The differential segment of the transmission line 5 R’ = resistance per unit length L’= inductance per unit length C’= capacitor per unit length G’= conductance per unit length

 General transmission lines equations: 6

 Time-harmonic waves on transmission lines After arranging we have 7 where

 Instantaneous form  Phasor form 8

 lossless when R’ = 0 and G’ = 0 9 and

 low loss when R’ <<  L’ and G’ <<  C’ 10 Expanding in binomial series gives for x << 1

Therefore, we get 11

12 or For lossless line, Characteristic impedance Z 0 is defined as the the ratio of the traveling voltage wave amplitude to the traveling current wave amplitude.

13 Power transmitted over a specific distance is calculated. The instantaneous power in the +z traveling wave at any point along the transmission line can be shown as The time-averaged power can be shown as W.

14 A convenient way to measure power ratios Power gain (dB) Power loss (dB) 1 Np = dB dB

15 Representation of absolute power levels is the dB m scale dB m

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a) what fraction of the input power does it reach the output? b) What fraction of the input power does it reach the midpoint of the line? c) What is the attenuation constant? 17

 To satisfy boundary conditions between two dissimilar lines  If the line is lossy, Z 0 will be complex. 18

 The phasor voltage along the line can be shown as  The phasor voltage and current at the load is the sum of incident and reflected values evaluated at z = 0. 19

 Reflection coefficient  A reflected wave will experience a reduction in amplitude and a phase shift.  Transmission coefficient 20

21 W W W

 The main objective in transmitting power to a load is to configure line/load combination such that there is no reflection, that means. 22

 Incident and reflected waves create “Standing wave”.  Knowing standing waves or the voltage amplitude as a function of position helps determine load and input impedances 23 Voltage standing wave ratio

 If a load is matched then no reflected wave occurs, the voltage will be the same at every point.  If the load is terminated in short or open circuit, the total voltage form becomes a standing wave.  If the reflected voltage is neither 0 nor 100 percent of the incident voltage then the total voltage will compose of both traveling and standing waves. 24

 let a load be position at z = 0 and the input wave amplitude is V 0, 25 where

we can show that 26 traveling wavestanding wave The maximum amplitude occurs when The minimum amplitude occurs when standing waves become null,

 The minimum voltage amplitude occurs when two phase terms have a phase difference of odd multiples of .  The maximum voltage amplitude occurs when two phase terms are the same or have a phase difference of even multiples of . 27

 If  = 0,  is real and positive and  Each z min are separated by multiples of one-half wavelength, the same applies to z max. The distance between z min and z max is a quarter wavelength.  We can show that 28

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