Impedance transformation / Waveguides

Chapter 14.7 Impedance transformation

Lessons In Electric Circuits Volume II – AC Book
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Lessons In Electric Circuits Volume II – AC Book

  • 512CHAPTER 14. TRANSMISSION LINES• The lowest-frequency resonant point on a transmission line is where the line is one quarter-wavelength long. Resonant points exist at every harmonic (integer-multiple) frequency of thefundamental (quarter-wavelength).• Standing wave ratio, or SWR, is the ratio of maximum standing wave amplitude to minimumstanding wave amplitude. It may also be calculated by dividing termination impedance bycharacteristic impedance, or vice versa, which ever yields the greatest quotient. A line withno standing waves (perfectly matched: Zload to Z0) has an SWR equal to 1.• Transmission lines may be damaged by the high maximum amplitudes of standing waves.Voltage antinodes may break down insulation between conductors, and current antinodes mayoverheat conductors.14.7Impedance transformationStanding waves at the resonant frequency points of an open- or short-circuited transmission lineproduce unusual effects. When the signal frequency is such that exactly 1/2 wave or some multiplethereof matches the line’s length, the source “sees” the load impedance as it is. The followingpair of illustrations shows an open-circuited line operating at 1/2 (Figure 521,14.53) and 1 wavelength(Figure 522,14.54) frequencies:ZsourceEsource75 ΩMaximum IMaximum EZero I500 kHzMaximum EZero IZero EFigure 14.53: Source sees open, same as end of half wavelength line.In either case, the line has voltage antinodes at both ends, and current nodes at both ends.That is to say, there is maximum voltage and minimum current at either end of the line, whichcorresponds to the condition of an open circuit. The fact that this condition exists at both ends ofthe line tells us that the line faithfully reproduces its terminating impedance at the source end, sothat the source “sees” an open circuit where it connects to the transmission line, just as if it weredirectly open-circuited.The same is true if the transmission line is terminated by a short: at signal frequencies corre-sponding to 1/2 wavelength (Figure 522,14.55 below) or some multiple (Figure 522,14.56 below) thereof, thesource “sees” a short circuit, with minimum voltage and maximum current present at the connectionpoints between source and transmission line: