We have obtained the following solutions for the steady-state
voltage and current phasors in a transmission line:
Loss-less line
Lossy line
V ( z ) V e j z V e j z
V ( z ) V e z V e z
1 j z j z
1 z
I ( z ) V e V e I ( z ) V e V e z
z0
z0
Since V (z) and
Chapter I
Circuits
Complex numbers, Phasors, and Circuits
Power in Circuits
1
Complex Numbers, Phasors and Circuits
Complex numbers are defined by points or vectors in the complex
plane, and can be represented in Cartesian coordinates
j
z a jb
1
or in p
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
1
Transmiss
Power in Circuits
Consider the input impedance of a transmission line circuit, with an
applied voltage v(t) inducing an input current i(t).
For sinusoidal excitation, we can write
v(t ) V0 cos(t )
i(t ) I 0 cos(t )
/ 2, / 2
where is the phase difference
Standing Wave Patterns
In practical applications it is very convenient to plot the magnitude
of phasor voltage and phasor current along the transmission line.
These are the standing wave patterns:
The standing wave patterns provide the top envelopes that
Smith Chart
The Smith chart is one of the most useful graphical tools for high
frequency circuit applications. The chart provides a clever way to
visualize complex functions and it continues to endure popularity
decades after its original conception.
From
Electromagnetic Waves
For fast-varying phenomena, the displacement current cannot be
neglected, and the full set of Maxwells equations must be used
The two curl equations are analogous to the coupled (first order)
equations for voltage and current used in