Chapter 2. Transmission Line Theory. Sept. 29 th , 2008. 2.1 Transmission Lines. A transmission line is a distributed-parameter network, where voltages and currents can vary in magnitude and phase over the length of the line. Lumped Element Model for a Transmission Line
Sept. 29th, 2008
Lumped Element Model for a Transmission Line
Figure 2.1 Voltage and current definitions and equivalent circuit for an incremental length of transmission line. (a) Voltage and current definitions. (b) Lumped-element equivalent circuit.
Time-domain form of the transmission line, or telegrapher, equation.
where the complex propagation constant. (α = attenuation constant, β = phase constant)
Wave propagation in +z directon
Wave propagation in -z directon
Figure 2.2 (p. 53)Field lines on an arbitrary TEM transmission line.
(H || S)
ə/əφ = 0
From the B.C., Eφ = 0 at ρ = a, b Eφ = 0 everywhere
The total current on the inner conductor at ρ = a
The total voltage and current on the line
RL = -20 log|Γ| dB
Transmission line impedance equation
ZL = 0 Γ= -1
Figure 2.6 (a) Voltage, (b) current, and (c) impedance (Rin = 0 or ) variation along a short-circuited transmission line.
ZL = ∞ Γ= 1
Figure 2.8 (a) Voltage, (b) current, and (c) impedance (Rin = 0 or ) variation along an open-circuited transmission line.
Figure 2.9 (p. 63)Reflection and transmission at the junction of two transmission lines with different characteristic impedances.
Derivation of the Smith Chart
Figure 2.11 (p. 67)Smith chart for Example 2.2.
Figure 2.12 (p. 69)ZY Smith chart with solution for Example 2.3.
Figure 2.14 (p. 71)Voltage standing wave patterns for Example 2.4. (a) Standing wave for short-circuit load. (b) Standing wave for unknown load.
Figure 2.17 (p. 74)Reflection coefficient versus normalized frequency for the quarter-wave transformer of Example 2.5.
Figure 2.18 (p. 75)Multiple reflection analysis of the quarter-wave transformer.
Figure 2.19 (p. 77)Transmission line circuit for mismatched load and generator.
By (2.67) &