Multiple reflections on a mismatched
transmission line
Introduction
This applet visually demonstrates multiple reflections of a transmitted
ramp or pulse on a transmission line in the time domain. The reflections
are due to a mismatched load and/or source resistance and not an impedance.
Due to the limitations of space and patience, the number of reflections
that the applet shows are three from the mismatched load and three from
the mismatched source. This should be sufficient to be able to imagine
what would be happening to the amplitudes of the reflected pulses and the
voltages on the line as more reflections occur. A document, reflections.doc,
that describes the theory the reflections on a transmission line is provided
if required.
Figure 1 Applet input controls
As shown in Figure 1, the inputs required by the applet are, in order
of entry:
-
Load, Source or Distribution. These three radio buttons comprise set 1.
Only one of these radio buttons can be selected. Whatever the selection
made, a graph that indicates the cumulative voltage history at the various
points on the line will be displayed. If the "Load" radio button is selected,
only the voltages that appear at the load will be displayed for the total
duration of the applet run. Similarly, if the "Source" button is selected,
the cumulative history at the source only is displayed. This allows one
to see what happens at the source due to the various reflected voltages
adding and subtracting. The "Distribution" button, allows the cumulative
voltage history to be displayed as the voltage that one would see if sitting
on the front of the wave as it travels back and forth down the line.
-
The Text field default values. This single button comprises set 2 of the
radio buttons. If this button is selected, as shown in Figure 1, then the
text fields are filled with the default values provided by the applet.
If this button is not selected, then manual insertion of each parameter
must be completed. All text fields must contain numerical values. If this
is not done, a message will remind you that it is necessary to do so. If
the default values are entered, the value in any text box can be manually
varied after completing a selection from each of the three sets of radio
buttons. If the text box is changed before all radio button selections
are made, on making the final selection, the text fields will revert to
the default values.
-
A pulse or a ramp signal to be used as the input to the line. This is set
3 of the radio buttons. Only one of the two in this set can be chosen.
That is, either the pulse or the ramp.
The text fields:
-
The line parameters, that is, the distributed capacitance (pF/m) and distributed
inductance (
). These line parameters
are used to determine the characteristic impedance of the line 
and the velocity of propagation u, of the signal down the line . The default
distributed parameter values provided, (100 pF/m and 0.25
) give the line characteristic impedance as 50W
and the velocity of propagation as 2/3 the speed of light.
-
The line length in metres. As this length is varied, the time for the pulse
or ramp to propagated down the line varies. Increasing the line length
allows the drawing of the coaxial cable to be lengthened, as shown in Figure
2.
-
The pulse width in microseconds. This provides flexibility to the applet
and permits investigation into what happens when a sending signal and its
reflections exist on the line at the same time. By extending the pulse
length and shortening the line multiple reflections can exist on the line
simultaneously.
-
The applet speed. This is the video rate of the applet. For the case of
a pulse input the pulses move too quickly for the mind to absorb all that
is going on. By increasing the rate to 50 or 75 this will slow the pulse
travelling down the line so that the process of reflection can be observed
in more detail. However, due to the additional code required for the ramp
input waveform, the applet works slow enough at an applet speed of zero.
Above 20, it becomes intolerably slow. The applet speed is related to the
number of milliseconds delay introduced into the main loop of the code
to slow the code loop down.
-
The source resistance. The applet signal appears after the source resistance,
no matter what the resistive divider effect is. The source resistance will
produce a reflection coefficient if different from the characteristic impedance
of the line. If the source impedance is greater than the characteristic
impedance of the line this reflection coefficient will be positive, and
if less, then the reflection coefficient will be negative.
-
The load resistance. Again, the load resistance will produce a reflection
coefficient if different from the characteristic impedance of the line.
If the load impedance is greater than the characteristic impedance of the
line this reflection coefficient will be positive, and if less, then the
reflection coefficient will be negative.
The source and load resistance if each is different from the characteristic
impedance of the line, together produce two reflection coefficients that
can be both positive, negative or one positive and the other negative.
The effect of these reflection coefficients are produce an inverted or
non-inverted reflected pulse or ramp voltage on the line. The voltage sum
history permits the cumulative voltage at the load, at the source or on
the line to be observed for the duration of the six reflections that occur
on the line.
The screen text output (in blue) provides information on the derived
quantities which are also characteristics of the line. From the capacitance
and inductance inputs (per unit length), the characteristic impedance and
velocity of the signal is derived, which in this case is 50 Ohms and 2/3
speed of light, respectively. From the source resistance input and the
characteristic impedance of the line, the source reflection coefficient
is derived. Similarly, from the load resistance and the characteristic
impedance of the line the load reflection coefficient is found. From the
velocity of the signal and the line length, the time it takes for a pulse
to travel down the line is also found. This is given as the "Line Length
in us". Again, from the velocity of the signal, the pulse with can be expressed
in terms of length, that is the distance travelled in so many microseconds.
This is shown as the "Pulse Width in metres."
Figure 2, shows a screen shot of a reflected ramp at the load and a
partial voltage history of the distribution with time.
Figure 2 A reflected ramp at the load
Figure 3 shows a screen shot where all reflections have finished
and the complete voltage sum history is displayed for the time duration
of the original ramp entering the line to the final reflection exiting
the line.
Figure 3 Voltage sum history for the distribution mode (Sitting
on the front of the wave as it travels down the line)
A document, reflections.doc, that describes
the theory the reflections on a transmission line is provided if required.
The source code
(version Rev.1 99/12/17) is available according to the GNU
Public License.
Tony Townsend,
tonyart@ieee.org