Digital Signal Processing Reference
In-Depth Information
IDEAL TRANSMISSION-LINE
FUNDAMENTALS
3.1 Transmission-line structures
66
3.2 Wave propagation on loss-free transmission lines
67
3.2.1 Electric and magnetic fields on a transmission line
68
3.2.2 Telegrapher's equations
73
3.2.3 Equivalent circuit for the loss-free case
76
3.2.4 Wave equation in terms of
LC
80
3.3 Transmission-line properties
82
3.3.1 Transmission-line phase velocity
82
3.3.2 Transmission-line characteristic impedance
82
3.3.3 Effective dielectric permittivity
83
3.3.4 Simple formulas for calculating the characteristic impedance
85
3.3.5 Validity of the TEM approximation
86
3.4 Transmission-line parameters for the loss-free case
90
3.4.1 Laplace and poisson equations
91
3.4.2 Transmission-line parameters for a coaxial line
91
3.4.3 Transmission-line parameters for a microstrip
94
3.4.4 Charge distribution near a conductor edge
100
3.4.5 Charge distribution and transmission-line parameters
104
3.4.6 Field mapping
107
3.5 Transmission-line reflections
113
3.5.1 Transmission-line reflection and transmission coefficient
113
3.5.2 Launching an initial wave
116
3.5.3 Multiple reflections
116
3.5.4 Lattice diagrams and over- or underdriven transmission lines
118
3.5.5 Lattice diagrams for nonideal topologies
121
3.5.6 Effect of rise and fall times on reflections
129
3.5.7 Reflections from reactive loads
129
3.6 Time-domain reflectometry
134
3.6.1 Measuring the characteristic impedance and delay of a transmission
line
134
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