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Unformatted text preview: 1 Chapter II Transmission Lines • Transmission Line Equations • Transmission Line Properties • Discussion Of Steady State Regime • Standing Wave Patterns And VSWR • Introduction To Smith Chart • Impedance Matching 1 • Impedance Matching 2 • Impedance Matching 3 2 Transmission Line Equations A typical engineering problem involves the transmission of a signal from a generator to a load . A transmission line is the part of the circuit that provides the direct link between generator and load. Transmission lines can be realized in a number of ways. Common examples are the parallelwire line and the coaxial cable . For simplicity, we use in most diagrams the parallelwire line to represent circuit connections, but the theory applies to all types of transmission lines. 3 4 If you are only familiar with low frequency circuits , you are used to treat all lines connecting the various circuit elements as perfect wires, with no voltage drop and no impedance associated to them (lumped impedance circuits) . This is a reasonable procedure as long as the length of the wires is much smaller than the wavelength of the signal. At any given time, the measured voltage and current are the same for each location on the same wire. 5 8 6 2.999 10 5.0 10 5,000 60 c m km f λ = = = 8 3 9 2.999 10 5.0 10 5.0 60 10 c m mm f λ = = = Let’s look at some examples. The electricity supplied to households consists of high power sinusoidal signals, with frequency of 60Hz or 50Hz , depending on the country. Assuming that the insulator between wires is air ( ε = ε ), the wavelength for 60Hz is: which is the about the distance between S. Francisco and Boston! Let’s compare to a frequency in the microwave range, for instance 60 GHz . The wavelength is given by which is comparable to the size of a microprocessor chip . 6 For sufficiently high frequencies the wavelength is comparable with the length of conductors in a transmission line . The signal propagates as a wave of voltage and current along the line, because it cannot change instantaneously at all locations. Therefore, we cannot neglect the impedance properties of the wires (distributed impedance circuits). 7 Note that the equivalent circuit of a generator consists of an ideal alternating voltage generator in series with its actual internal impedance. When the generator is open ( Z R = ∞ ) we have: I in = 0 and V in = V G If the generator is connected to a load Z R ( 29 ( 29 G G i n G n G R R i R I V Z V V Z Z Z Z = + = + G i n G I V Z = and V in = 0 If the load is a short ( Z R = 0) 8 The simplest circuit problem that we can study consists of a...
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This note was uploaded on 03/09/2012 for the course ECE 450 taught by Professor E.kudeki during the Spring '12 term at Illinois College.
 Spring '12
 E.Kudeki
 Impedance

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