| | 0 0.5 1 -j2-j4-j1-j0.5j0.5j1 j4j2 j0 0 0.5 1 2 4 45 0 135 90
180 225 270 315D C B EAFG
Sheet1
zLGLoad
ReImMagAngle
A010Open
B201/30Resistive = 2Z0
C1000Matched load
D0.501/3180Resistive = Z0/2
E001180Short
F01190Inductive = jZ0
G0-11-90Capacitive = -jZ0
Waves can travel in any direction. In a transmission line waves
can travel in the forward (red) or reverse (blue) directions. These
waves are called traveling waves since energy is transmitted from
one end of the line to the other end.
Another type of waves are called standing waves.Standing waves
only oscillates locally and no energy is transmitted.When two
traveling waves of equal amplitudes traveling in opposite
directions result a standing wave. The following animations show
the resulting standing wave due to the incident wave and the
reflective wave. Since the two waves have the same amplitude, no
energy is transferred from the generator to the load.For a
short-circuited load, the polarities of the incident wave and the
reflective wave at the load are opposite. This slide summaries the
wave interactions for a short-circuited load. Red indicates the
incident wave, which moves from left to right.Red indicates the
incident wave, which moves from left to right.Blue indicates the
reflective wave, which moves from right to left.Green indicates the
resulting wave, which is a standing wave.The following animations
show the standing wave pattern that would be observed in an actual
circuit.
The envelop of the standing wave is shown here. Notice that the
amplitude of the maxima, or the peaks, are twice the amplitude of
the incident wave.Also, the amplitude of the minima, or the nulls,
are zero. A null appears at the load because of the complete
cancellation between the incident and the reflective waves at a
short-circuited load.The following animations show the resulting
standing wave due to the incident wave and the reflective wave.
Since the two waves have the same amplitude, no energy is
transferred from the generator to the load.For an open-circuited
load, the polarities of the incident wave and the reflective wave
at the load are the same.
This slide summaries the wave interactions for an open-circuited
load. Red indicates the incident wave, which moves from left to
right.Red indicates the incident wave, which moves from left to
right.Blue indicates the reflective wave, which moves from right to
left.Green indicates the resulting wave, which is a standing
wave.The following animations show the standing wave pattern that
would be observed in an actual circuit.
The envelop of the standing wave is shown here. Notice that the
amplitude of the maxima, or the peaks, are twice the amplitude of
the incident wave.Also, the amplitude of the minima, or the nulls,
are zero. A peak appears at the load because the incident and the
reflective waves have the same polarity at an open-circuited
load.
For a resistive load equal to the characteristic impedance of
the transmission line, it is called a matched load.For a matched
load, there is no reflective wave. As a result, it is a pure
traveling wave.The next animation shows the traveling wave pattern
for a matched load.
The envelop of the traveling wave is shown here. Notice that the
amplitude of the wave is constant.
The following animations show the resulting standing wave due to
the incident wave and the reflective wave. Since the two waves have
different amplitudes, some energy is transferred from the generator
to the load.If the load is less resistive than the line, the
polarities of the incident wave and the reflective wave at the load
are different.
This slide summaries the wave interactions for a resistive load
that is less than the lines characteristic impedance. Red indicates
the incident wave, which moves from left to right.Red indicates the
incident wave, which moves from left to right.Blue indicates the
reflective wave, which moves from right to left.Green indicates the
resulting wave.The following animations show the wave pattern that
would be observed in an actual circuit.
The envelop of the composite wave is shown here. Notice that the
amplitude of the maxima, or the peaks, are less than the peaks for
the open- and short-circuited cases.Also, the amplitude of the
minima, or the nulls, are greater than zero. A null appears at the
load because the incident and the reflective waves have different
polarities at the load.
The following animations show the resulting standing wave due to
the incident wave and the reflective wave. Since the two waves have
different amplitudes, some energy is transferred from the generator
to the load.If the load is more resistive than the line, the
polarities of the incident wave and the reflective wave at the load
are the same.
This slide summaries the wave interactions for a resistive load
that is greater than the lines characteristic impedance. Red
indicates the incident wave, which moves from left to right.Red
indicates the incident wave, which moves from left to right.Blue
indicates the reflective wave, which moves from right to left.Green
indicates the resulting wave.The following animations show the wave
pattern that would be observed in an actual circuit.
The envelop of the composite wave is shown here. Notice that the
amplitude of the maxima, or the peaks, are less than the peaks for
the open- and short-circuited cases.Also, the amplitude of the
minima, or the nulls, are greater than zero. A peak appears at the
load because the incident and the reflective waves have the same
polarity at the load.
The following animations show the resulting standing wave due to
the incident wave and the reflective wave. Since the two waves have
the same amplitudes, no energy is transferred from the generator to
the load.If the load is inductive, the incident wave lags the
reflective wave by 90 at the load.
This slide summaries the wave interactions for an inductive
load. Red indicates the incident wave, which moves from left to
right.Red indicates the incident wave, which moves from left to
right.Blue indicates the reflective wave, which moves from right to
left.Green indicates the resulting wave, which is a standing
wave.The following animations show the standing wave pattern that
would be observed in an actual circuit.
The envelop of the standing wave is shown here. Notice that the
amplitude of the maxima, or the peaks, are twice the amplitude of
the incident wave.Also, the amplitude of the minima, or the nulls,
are zero. A null appears at a 1/8 wavelength away from the load
because of the phase difference between the incident and the
reflective waves at an inductive load.The following animations show
the resulting standing wave due to the incident wave and the
reflective wave. Since the two waves have the same amplitudes, no
energy is transferred from the generator to the load.If the load is
capacitive, the incident wave leads the reflective wave by 90 at
the load.
This slide summaries the wave interactions for a capacitive
load. Red indicates the incident wave, which moves from left to
right.Red indicates the incident wave, which moves from left to
right.Blue indicates the reflective wave, which moves from right to
left.Green indicates the resulting wave, which is a standing
wave.The following animations show the standing wave pattern that
would be observed in an actual circuit.
The envelop of the standing wave is shown here. Notice that the
amplitude of the maxima, or the peaks, are twice the amplitude of
the incident wave.Also, the amplitude of the minima, or the nulls,
are zero. A peak appears at a 1/8 wavelength away from the load
because of the phase difference between the incident and the
reflective waves at a capacitive load.Smith chart is a graphical
aide for transmission line calculations.Here we will introduce its
basic concepts and use it to perform some simple transmission line
calculations.In an impedance chart, the normalized load impedance
is plotted according to its real and imaginary components.The
normalized load impedance is the ratio between the load impedance
and the lines characteristic impedance. It is in general a complex
number.Blue circles in the chart represent the real impedance.Red
lines in the chart represent the imaginary impedance.The reflection
coefficient is an important parameter for a transmission line
system. It is a complex number and thus can be shown in either
rectangular or polar coordinates.Keep in mind that the magnitude of
the reflection coefficient is less than or equal to 1 since the
amplitude of the reflected wave can not be larger than that of the
incident wave.Thus, to represent the reflection coefficient in a
polar plot we only need to display a unit circle (radius = 1).
The impedance chart and the polar plot of the reflection
coefficient can be overlay to form a basic Smith chart.In this
chart the green concentric circles represent the magnitude of the
reflection coefficient. The dotted black lines represent the phase
of the reflection coefficient. The blue circles represent the real
part of the normalized load impedance. The red lines represent the
imaginary part of the normalized load impedance.The reflection
coefficient and the normalized load impedance can be graphically
determined from each other in this chart.In practice, Smith charts
only display the impedance.The magnitude of the reflection
coefficient are determined using an external magnitude scale. The
phase scale is located on the ring of the chart.The following two
examples show how to determine the reflection coefficient from the
normalized impedance using Smith charts.
Several special cases of load impedance are displayed here.Note
the locations of the normalized impedance in the chart and their
corresponding reflection coefficients shown in he table.
