I've made a program to help visualize some transmission line phenomena.
With it, you can see the voltage, current, power, and energy on a
transmission line. This is a prototype of a work in progress. I've spent
more time than I should on it already, but will add some features and
increase its flexibility as time permits.

The program, named TLVis1.exe, is available from
http://eznec.com/misc/rraa/. It doesn't require any installation and
should run on most machines. If it complains about missing files, an
easy way to make sure you have the correct run time files is to download
and install the free EZNEC demo program from http://eznec.com.

Here's how to use it:

First, notice the scroll bar at the lower right. It allows you to select
among five different demonstration setups. This selection bar is
disabled while graphs are being run or displayed. Clicking Run will
start the selected demo or, if paused, will resume it. You can pause the
analysis at any time, step time forward or backward one step at a time
with the appropriate button, and resume with the Run button.

For all demos, the transmission line is lossless, open circuited at the
end, and 3 wavelengths long. The display shows various quantities
(voltage, current, power, or energy) as a function of position along the
line -- the source end is to the left and the load end to the right. The
display at different times shows the quantity along the line at diffent
times. Please keep in mind that the horizontal axis is position along
the line, not time.

For demos 1 - 4, the input consists of a perfect voltage source and
series resistance. The resistance value is three times the Z0 of the
transmission line, resulting in a purely real input reflection
cofficient of +0.5.

For demo 5, only, there is no series resistance at the input, so the
input reflection coefficient is -1.0.

DEMO 1

Demo 1 shows the combined forward and combined reverse traveling voltage
and current waves, and the total voltage. Start the program and click
Run. You'll see black sinusoidal waves moving to the right. These are
the initial voltage and current waves. They show as black because the
forward wave is also the total until the wave reaches the far end of the
line.

Pause the display when the reflected waves are about half way back to
the source. Notice that the forward V and I waves (green) are always in
phase, and the reverse V and I waves (red) are always out of phase. Also
note that at any point along the line, the total is the sum of the
forward and reverse waves.

Resume the analysis by clicking Run. As additional waves accumulate, all
the forward waves are combined to be shown as a single forward wave
(green) and the reverse waves are likewise combined (red). Watch the
voltage and current at the input and output ends of the line. At the
output end, the current is zero at all times, and the voltage is at a
maximum there. At the input end, there's initially some current, as
shown by the black line going up and down at the very input of the line.
There's a time-varying voltage at the input at all times, although it
changes in value as various reflections take place. As the analysis
runs, the system slowly approaches steady state. Eventually, you'll see
that the current at the input end has dropped to zero, as it must, since
there can be no power at the line input at steady state because the
output end is open circuited.

Pause the display once steady state is reached and step the time forward
or back a few steps. Notice that there are times when the voltage is
zero everywhere along the line, and other times when the current is zero
everywhere along the line. This is true only when the SWR is infinite,
as it is here.

DEMO 2

Clear the display and click the end of the slider bar to select demo #2.
The lower graph shows the energy per unit distance on the line. This is
an energy density, since it's per unit distance, and the total energy on
any span of line is the integral of the energy density over that span.
But I'll refer to the density as "energy" for simplicity. The energy is
separated into two components, Ee and Eh. Ee is the energy stored in the
line's capacitance as an E field. Eh is the energy stored in the line's
inductance as an H field. The total energy is the sum of these. The
upper graph shows the total V and I at the same time.

During the initial forward transit, you see only a green line for the
voltage and current. This is because they're normalized to the same peak
value (I = V/Z0), so they exactly coincide. The V line is drawn last, so
it's all you see during this time. Unlike V and I, Ee and Eh have the
same units and so are drawn to scale. Ee is exactly the same as Eh
during the initial forward wave (that is, exactly half the energy at
every point along the line is stored in the E field and half as an H
field), so all you see is the Ee trace, and the total which is exactly
twice as much.

When the reflected wave returns, though, the energy is no longer stored
evenly between E and H, but swaps between one and the other. This gets
pretty interesting as steady state is approached. Steady state is
reached, for practical purposes, when the I trace at the input remains
zero at all times. Pause the display when you reach that point, and use
the single step buttons to watch the energy in slow motion. Several
things are notable:

-- There is no place on the line where the energy is always zero.
It's zero momentarily only at particular places only.
-- There are moments when the energy density is the same at all
places along the line.
-- The relationship between Ee and Eh is the same everywhere on the line
at any given time. In other words, the energy swaps between Ee and Eh
everywhere on the line at the same time. So there are times when
all the
energy everywhere on the is stored in the E field and times where it's
all stored in the H field.

The energy seems to form an initial forward wave, then reflect and
re-reflect to form a standing wave. See the comments in the demo 3
description about this.

A word of caution, though -- some or all these wouldn't be true if there
was a finite load rather than an open cicruit at the far end of the line.

DEMO 3

Clear the display and select demo 3.

The top graph is the same as for demo 2, but the bottom graph shows the
power at each point along the line. The power tells us the magnitude and
direction of energy flow -- when the power is positive, energy is
flowing to the right at that point; when negative, to the left; and when
zero there is no energy moving past that point. The amount of energy
being moved is proportional to the magnitude of the power. The power at
any point is the product of V and I at that point; V and I are shown in
the upper graph.

Click Run and notice that there seems to be a power "wave" moving to the
right, although its period is half the period of V or I. And it exhibits
a standing wave just like V or I, except the frequency with which it
oscillates up and down is twice that of V or I. The power is zero
everywhere on the line at those times when either the voltage or current
is zero everywhere.

It's important to note that this power distribution, which can seemingly
be described as a sum of forward and reverse traveling waves, isn't made
up of a forward wave made from the forward voltage and current waves and
a reverse wave from the reverse voltage and current waves. It's
calculated from the total voltage and current, not separate forward and
reverse waves. Nor do the power "waves" represent average power. It's
instantaneous power whose average value over any integral number of V or
I half cycles is zero, and whose average over any half wavelength of
line is zero.

DEMO 4

Clear the display and select demo 4.

This shows power and energy density at the same time, with power as the
top graph and energy as the lower.

Pause the display when the analysis has reached steady state, indicated
by the power at the input end of the line remaining at zero at all
times. Single step until the total energy trace is as flat as you can
get it, meaning that an equal amount of energy is stored in each small
part of the line. The power waveform is at its maximum amplitude at this
time, meaning that energy is moving as rapidly as it ever does. Look at
the first power peak, just to the right of the line input (left side of
graph). At that point along the line, the energy is moving to the right
at its maximum rate. Click the "Single Step " button once. You can see
that the energy just to the right of that maximum-power point has
increased, and to the left it's decreased. (It decreased to the left
even though the power waveform is positive because more energy was
required from the line just to its right than it was being furnished
from the left.) Look carefully as you step and you'll see that the power
graph isn't the derivative of the energy graph (although it looks that
way at some times). That's because these are graphs of position, not
time, and power is the *time*, not position, derivative of energy.

Single step until you reach the time when the power is zero everywhere
along the line. The energy distribution is the most uneven at that time.
Click one step forward or back and notice that the energy graph changes
very little -- zero power means there's no movement of energy at that time.

DEMO 5

This is the same setup as demo 1 except that the source resistor has
been replaced by a short circuit, leaving a perfect voltage source
connected directly to the input end of the line and an input reflection
coefficient of -1. An analysis I did and posted showed the input voltage
oscillating among three values, one of which was zero, and never
reaching a stable steady state. This display shows that behavior.

It's been interesting to develop and work with this program. I hope
you'll learn from it as I have. I'll post notices as I make improvements
to it.

Roy Lewallen, W7EL

"Roy Lewallen" wrote in message
...
I've made a program to help visualize some transmission line phenomena.

(snip program description)

Thanks, Roy. It is very interesting.

I'm having a hard time getting my head around Demo 5. The waves go away
periodically (every 8 wavelengths?), sort of like a squegging oscillator.
(By the way, it appears that the line is two wavelengths long rather than
three.) This was totally unexpected. I will think more about this and try to
picture the reason.

Nice tool.

John

On Mon, 07 Jan 2008 00:14:30 -0800
Roy Lewallen wrote:

I've made a program to help visualize some transmission line phenomena.
With it, you can see the voltage, current, power, and energy on a
transmission line. This is a prototype of a work in progress. I've spent
more time than I should on it already, but will add some features and
increase its flexibility as time permits.

The program, named TLVis1.exe, is available from
http://eznec.com/misc/rraa/. It doesn't require any installation and
should run on most machines. If it complains about missing files, an
easy way to make sure you have the correct run time files is to download
and install the free EZNEC demo program from http://eznec.com.

This is a great program Roy. Thanks for creating it and making it available.

73, Roger, W7WKB

John KD5YI wrote:
"Roy Lewallen" wrote in message
...
I've made a program to help visualize some transmission line phenomena.

(snip program description)

Thanks, Roy. It is very interesting.

I'm having a hard time getting my head around Demo 5. The waves go away
periodically (every 8 wavelengths?), sort of like a squegging oscillator.
(By the way, it appears that the line is two wavelengths long rather than
three.) This was totally unexpected. I will think more about this and try to
picture the reason.

Nice tool.

You'll find a detailed analysis which derives the reason for the
behavior in my posting on Dec. 28 in this thread. You can see it by
going to http://tinyurl.com/ypfshd. I agree it's counter-intuitive. It's
a consequence of the contrived zero-loss system.

Roy Lewallen, W7EL

For those who haven't followed the discussion (which I fully
understand), you'll find a mathematical analysis of the system of demos
1-4 in my postings of Jan. 1 in this thread. The voltage distribution
development from startup is in http://tinyurl.com/27uzrf, and an
analysis of the power at the input and the energy entering the system
was in a second posting also on Jan. 1; you can find it at
http://tinyurl.com/ypo2b4. The system of demo 5 which has the unusual
response was analyzed in my posting of Dec. 28,
http://tinyurl.com/ypfshd. The first and third include links to SPICE
output plots which illustrate the time responses. (Note that they don't
look like the TLVis1 plots because the SPICE plots have time as the
horizontal axis while TLVis1 has position along the line as the
horizontal axis.)

The analyses, SPICE results, and TLVis1 outputs should all agree.

Roy Lewallen, W7EL

On Mon, 07 Jan 2008 16:00:33 GMT
"John KD5YI" wrote:

"Roy Lewallen" wrote in message
...
I've made a program to help visualize some transmission line phenomena.

(snip program description)

Thanks, Roy. It is very interesting.

I'm having a hard time getting my head around Demo 5. The waves go away
periodically (every 8 wavelengths?), sort of like a squegging oscillator.
(By the way, it appears that the line is two wavelengths long rather than
three.) This was totally unexpected. I will think more about this and try to
picture the reason.

Nice tool.

John



Demo 5 is a demonstration of the pitfalls of dealing with discontinuities. The demonstration portrays equal periods of sequential open circuit conditions and short circuit conditions.

The discontinuity here is that a reflection factor of 1 is used if the returning voltage is less than the initial voltage, but a reflection factor of -1 is used for any returning voltage exceeding the initial voltage.

Demo 5 is a demonstration of why a Thevenin voltage source is much to be prefered over a simple ideal voltage source for continuous running circuits.

Another way of illustrating the problem is to say that the ideal voltage source overwhelms any voltage from a returning wave. If an external voltage less than the initial voltage is applied to the ideal voltage source, vr = 0, vf = videal. If the external voltage exceeds the initial voltage, then vr = 0, vf = 0 This is a discontinuity, which shows up in Demo 5.

A third way of illustrating the discontinuity problem is to say that you can not apply a voltage to two wires that are short circuited at the input. In Demo 5, the reflected wave returns to find the circuit short circuited. On the other hand, the ideal voltage source applied voltage to an open circuit. We can not have it both ways.

73, Roger, W7?WKB

Correction:

Roy Lewallen wrote:
. . .
For all demos, the transmission line is lossless, open circuited at the
end, and 3 wavelengths long. . .

The line is 2, not 3, wavelengths long.

I apologize for the error.

Roy Lewallen, W7EL

John KD5YI wrote:

(By the way, it appears that the line is two wavelengths long rather than
three.) . .

You're right, thanks for pointing it out. My apology. I've posted a
correction.

Roy Lewallen, W7EL

Roger Sparks wrote:

Demo 5 is a demonstration of the pitfalls of dealing with discontinuities. The demonstration portrays equal periods of sequential open circuit conditions and short circuit conditions.

The discontinuity here is that a reflection factor of 1 is used if the returning voltage is less than the initial voltage, but a reflection factor of -1 is used for any returning voltage exceeding the initial voltage.

That's not correct. A voltage source reflection factor of -1 is always
used for the perfect source case, both in my analysis and in the
program. See my analysis of Dec. 28 http://tinyurl.com/ypfshd.

Demo 5 is a demonstration of why a Thevenin voltage source is much to be prefered over a simple ideal voltage source for continuous running circuits.

Ideal voltage sources are routinely and properly used in a great deal of
circuit analysis. The problem with this transmission line setup isn't
the use of perfect voltage source, it's that the entire system has no
loss. Putting a finite resistance at the far end of the line, for
example, results in a well-behaved system.

It sounds like you're confusing a Thevenin equivalent circuit with a
voltage source in series with an impedance. All Thevenin equivalent
circuits fit this description, but not all voltage sources in series
with a resistance are Thevenin equivalents. I haven't used a Thevenin
equivalent circuit in any of my analyses.

Another way of illustrating the problem is to say that the ideal voltage source overwhelms any voltage from a returning wave. If an external voltage less than the initial voltage is applied to the ideal voltage source, vr = 0, vf = videal. If the external voltage exceeds the initial voltage, then vr = 0, vf = 0 This is a discontinuity, which shows up in Demo 5.

There are no discontinuites in the mathematical analysis. The forward
and reverse waves always have a finite value or zero, and they always
sum to the source voltage. No infinite currents or voltages occur. You
can see from the program that the input voltage stays constant. (That
is, it generates a sine wave of constant amplitude.) The only
consequence is the oscillatory behavior of the line voltage and current.

A third way of illustrating the discontinuity problem is to say that you can not apply a voltage to two wires that are short circuited at the input. In Demo 5, the reflected wave returns to find the circuit short circuited. On the other hand, the ideal voltage source applied voltage to an open circuit. We can not have it both ways.

Again, there is no discontinuity.

The demo 5 system doesn't represent anything that can be built in real
life, and is basically just a curiosity. It was included mainly to
verify that the program works properly under this limiting-case
condition. It certainly has spurred some people to think about the
meaning of perfect sources and reflection coefficients and revealed a
lot of misunderstanding in the process, and I imagine it'll continue to
do so.

Roy Lewallen, W7EL

Roy Lewallen wrote:
There are no discontinuites in the mathematical analysis.

Maybe this is the source of a lot of confusion. If the Z0
of a transmission line changes from 50 ohms to 300 ohms,
that *IS* an impedance discontinuity. Any change in Z0
*IS* an impedance discontinuity, i.e. not a constant Z0.
Only a constant Z0 is not an impedance discontinuity.
--
73, Cecil http://www.w5dxp.com