Smith Chart
General Instructions
This spectral simulation is an interactive Java applet. You can
change parameters by clicking on the vertical arrow keys. The five
control buttons at the lower right are used to start (triangle)
and pause (square) the simulation, to skip forward or back one section
at a time (double triangles), and to change speed (+ and -).
After the simulation is complete, the start button takes you back
to the beginning of the simulation. You may experience a delay at
this point.
Theory
In any transmission system, a source sends energy to a load, such
as an antenna. Ideally, we design the transmission network such
that the characteristic impedances of the source, the transmission
line and the load are all identical. Unfortunately, many real-world
situations prevent the match from being perfect.
For example, we might want an antenna (the load) to be useful
over a broad range of frequencies. But the characteristic impedance
of an antenna is unlikely to stay constant with frequency, especially
if the frequency span is great.
When the transmission line impedance does not match that of the
load, part of the transmitted waveform is reflected back towards
the source. The reflected wave, which varies in phase and magnitude,
adds to the incident (transmitted) wave and the sum is called a
Standing Wave.
The reflected wave causes the amplitude to vary as a function
of position along the transmission line. The Standing Wave Ratio
(SWR), which is the ratio between the maximum and minimum amplitudes
of the total waveform, will in this case be greater than one.
If there is no reflected wave, i.e., if the impedance match is
perfect, the amplitude of the total waveform (incident plus reflected
wave) will be the constant, regardless of where we measure it along
the transmission line. The result is a SWR of 1. SWR = 1 indicates
maximum power transfer to the load.
SWR can be inferred by measuring the reflection coefficient of
the circuit. The network analyzer is a tool that enables us to do
just that.
If we know the reflection coefficient, we can determine the characteristic
impedance of the load by using a Smith Chart. The Smith Chart has
circles of constant resistance and arcs of constant reactance. The
relationship between reflection coefficient and characteristic impedance
is shown in the diagram. At first glance, the Smith Chart appears
complicated, but its elegance soon becomes obvious.
The Smith Chart can help us translate the reflection coefficient
into impedance. First, measure the reflection coefficient with a
network analyzer (or invent one of your own choosing). Place the
reflection coefficient, by using either the mouse or the drop-down
input boxes, at the desired value (real + imaginary) on the Smith
Chart. Hit the Play button (triangle), and the program will display
a circle with a radius equal to the reflection coefficient magnitude
(constant VSWR circle). Notice that if you move the reflection coefficient
anywhere on this circle, you can see from the waveform at the left
that the SWR is the same, only its phase changes. (Phase values
are not shown around the chart in this program; however, the phase
is calculated and shown at the left side of the screen.)
In general, only the horizontal line (diameter) is labeled with
(normalized) resistance values and only the unit (outer) circle
is labeled with (normalized) reactance values. To read the desired
values, it is necessary to follow the appropriate circle of constant
resistance to the diameter line, and to follow the appropriate arc
of constant reactance to the unit circle. Hit Play again, and the
program will display the constant-resistance circle and the constant-reactance
arc for you. (The actual values are calculated and shown at the
left side of the screen.)
Experiment with the simulator and see if you can predict the shape
of the standing wave before you move the reflection coefficient.
What is the range of the SWR?
What is the significance of the center of the chart?
What assumptions are made about the transmission line?
What assumptions are made about the source?
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