1

Transmission Lines

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Figure 11.1 Typical transmission lines in cross-sectional view: (a) coaxial line, (b) two-wire line, (c) planar line, (d) wire above conducting plane, (e) microstrip line.

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Figure 11.2 Common transmission lines: (a) coaxial line, (b) two-wire line, (c) planar line.

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Figure 11.3 Distributed parameters of a two-conductor transmission line.

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Figure 11.4 (a) Coaxial line connecting the generator to the load; (b) E and H fields on the coaxial line.

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Figure 11.5 An L-type equivalent circuit model of a two-conductor transmission line of differential length z.

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Figure 11.6 (a) Input impedance due to a line terminated by a load. (b) Equivalent circuit for finding Vo and Io in terms of Zin at the input.

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Figure 11.7 Voltage and current standing wave patterns on a lossless line terminated by a resistive load.

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Figure 11.8 Input impedance of a lossless line: (a) when shorted, (b) when open.

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Figure 11.9 For Practice Exercise 11.3.

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Figure 11.10 Unit circle on which the Smith chart is constructed.

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Figure 11.11 Typical r-circles for r0, 0.5, 1, 2, 5, ∞.

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Figure 11.12 Typical x-circles for x 0, 0.5, 1, 2, 5, ∞.

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Figure 11.13 Illustration of the r-, x-, and s-circles on the Smith chart.

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Figure 11.14 (a) Smith chart illustrating scales around the periphery and movements around the chart. (b) Corresponding movements along thetransmission line.

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Figure 11.15 Smith chart for Example 11.4.

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Figure 11.16 Smith chart for Example 11.5.

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Figure 11.17 Load matching using a 4 transformer.

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Figure 11.18 Voltage standing wave pattern of mismatched load: (a) without a /4 transformer, (b) with a /4 transformer.

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Figure 11.19 Matching with a single-stub tuner.

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Figure 11.20 Using the Smith chart to determine ℓ and d of a shunt-shorted single-stub tuner.

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Figure 11.21 (a) Typical slotted line; (b) Determining the location of the load ZL and Vmin on the line.

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Figure 11.22 Determining the load impedance from the Smith chart by using the data obtained from the slotted line.

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Figure 11.23 Determining ZL by using the slotted line: (a) wave pattern, (b) Smith chart for Example 11.6.

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Figure 11.24 Smith chart for Example 11.7.

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Figure 11.25 Transients on a transmission line: (a) a line driven by a pulse generator, (b) the equivalent circuit at z 0, t 0.

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Figure 11.26 Bounce diagram for (a) a voltage wave and (b) a current wave.

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Figure 11.27 For Example 11.8.

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Figure 11.28 Voltage bounce diagram for Example 11.8.

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Figure 11.29 Voltage (not to scale) for Example 11.8: (a) at the generator end, (b) at the load end.

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Figure 11.30 Equivalent circuits for the line in Figure 11.27 for (a) t 0, and (b) t ∞.

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Figure 11.31 Current bounce diagram for Example 11.8.

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Figure 11.32 Current (not to scale) for Example 11.8: (a) at the generator end, (b) at the load end.

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Figure 11.33 For Practice Exercise 11.8(a).

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Figure 11.34 For Practice Exercise 11.8(b).

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Figure 11.35 For Example 11.9 (not to scale).

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Figure 11.36 Triangular pulse for Practice Exercise 11.9.

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Figure 11.37 Current waves for Practice Exercise 11.9.

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Figure 11.38 Microstrip line.

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Figure 11.39 Pattern of the EM field of a microstrip line. (From D. Roddy, Microwave Technology, 1986, by permission of Prentice-Hall.)

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Figure 11.40 Near-end crosstalk (NEXT) in a paired cable.

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Figure 11.41 Far-end crosstalk (FEXT) in a paired cable.

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Figure 11.42 Smith chart for Review Question 11.6.

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Figure 11.43 Smith chart for Review Question 11.7.

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Figure 11.44 The diode of Problem 11.3.

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Figure 11.45 Equivalent circuits for Problem 11.4: (a) -type, (b) T-type.

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Figure 11.46 For Problem 11.21.

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Figure 11.47 For Problem 11.22.

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Figure 11.48 For Problem 11.26: (a) network, (b) lossy line.

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Figure 11.49 For Problem 11.29.

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Figure 11.50 Double section transformer of Problem 11.41.

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Figure 11.51 For Problems 11.42 and 11.43.

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Figure 11.52 For Problem 11.44.

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Figure 11.53 For Problem 11.45.

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Figure 11.54 For Problem 11.50.

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Figure 11.55 For Problem 11.54.

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Figure 11.56 For Problem 11.55.

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Figure 11.57 For Problem 11.56.

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Figure 11.58 Two rectangular pulses of Problem 11.56.