In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings
in Reflections concerning the analysis of stub matching procedures using reflection coefficients are
applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in
what follows I hope to persuade those who agree with Owen's position to reconsider.

To assist in understanding why my use of reflection coefficients in analyzing impedance-matching circuitry, I
find it useful to include the concept of virtual open- and short-circuit conditions. I realize that some of
the posters on this NB deny the existence of virtual open-and short-circuits. Therefore, I hope that my
presentation here will also persuade those posters to reconsider their position.

While working in an antenna lab for more than 50 years I have analyzed, constructed, and measured hundreds of
impedance-matching circuits comprising transmission-line circuitry using reflection coefficients as
parameters. For example, in 1958 my assignment was to develop the antenna system for the World's first weather
satellite, TIROS 1. The system required an antenna that would radiate efficiently on four different
frequencies in two bands that were more than an octave related. It required a coupling circuit that would
allow four transmitters to operate simultaneously on all four frequencies without mutual interference. After
developing the antenna that also required radiating circular polarization, I then developed the coupling
system, which, pardon my English, utilized several virtual open- and short-circuit conditions to accomplish
the required isolation between the individual transmitters. The entire coupling system was fabricated in
printed-circuit stripline transmission line (not microstrip), with no connectors except for transmitter input
ports and output ports feeding the antenna. Remember, this was in 1958.

Initially I had only a slotted line for impedance measurements during the development stage, but soon after
the PRD-219 Reflectometer became available, invented by my bench mate, Woody Woodward. The PRD-219 measured
SWR and the angle of the voltage reflection coefficient. The magnitude rho of the reflection coefficient was
obtained from the SWR measurement using the equation rho = (SWR - 1)/(SWR + 1), thus the PRD actually measured
the complete complex reflection coefficient. Consequently, all measurements from then on were in terms of
reflection coefficient.

Keep in mind that I was working with real transmission lines--not lossless lines. There were several
stub-matching circuits, several occurrences of virtual open- and short-circuits, and the total loss through
the coupler at both the 108 and 235 MHz bands was no greater than 0.2 dB. The input SWR at all four input
ports for a run of 12 manufactured units never exceeded 1.05:1 relative to 50 ohms.

Please let me now explain my understanding of virtual open- and short-circuits. These circuits are developed
by interference between two sets of voltage and current waves having reflection coefficients of equal
magnitude and phase differences of 180°, respectively. Consider these two examples of a virtual short circuit:

1: The input impedance of a lossless half-wave (180°) transmission line terminated in a physical short circuit
is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference
between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to
the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short
terminating the line. The reflected current wave on return to the input encountered no phase change during its
travel, thus the current reflection coefficient is in phase with that of the source current, allowing the
short circuit to occur.

2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open
circuit is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the
interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°)
returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open
circuit terminating the line. The current reflection coefficient occurs in the same manner as with the
half-wave line above.

These two examples can be confirmed by referring to any reputable text concerning transmission line theory.

The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the
current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be
found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both
physical and virtual short or open circuits placed on a transmission line can cause reflections. Proof is in
measurements performed at various points in the antenna coupler developed for the TIROS spacecraft in 1958.

Now let's examine a specific example of impedance matching with a stub using reflection coefficients, with
more details than I used in the previously-mentioned thread. As I said earlier, I have measured hundreds of
stub-matching circuitry, but for this discussion, yesterday I set up an experimental stub-matching circuit for
the purpose of being able to report directly on the results of current measurements taken on the circuit. The
source is an HP-8640A signal generator, an HP-5328A counter to determine the operating frequency, and the
combination of an HP-8405 Vector Voltmeter and an HP-778D dual directional coupler to form a precision RF
network analyzer.

Because using a 3:1 mismatch the resulting numbers are convenient, I paralleled three precision 50-ohm
resistors to form a resistance of 16.667 ohms, resulting in a 3:1 mismatch on the line to be stubbed. On a
line with a 3:1 mismatch the correct positioning of a parallel matching stub is 30° toward the source from a
position of minimum SWR, where the normalized admittance y = 1.0 + 1.1547. Thus, I selected a short piece of
RG-53 coax that measured exactly 30° in length at 16.0 MHz, meaning the stub will be placed 30° rearward of
the load.

All measurements obtained during the experiment were less than 2 percent in error compared to a perfect
text-book setup. Consequently, rather than bore you with the exact measured values, I'm going to use the
text-book values for easier understanding.

At the 16.667 + j0 load the measured voltage reflection coefficient = 0.5 at 180°, current 0.5 at 0°.
At the stub point voltage reflection coefficient of the line impedance = 0.5 at +120°, current 0.5 at -60°.
Open-circuited stub 49° in length measured separately in parallel with 50 ohms yields voltage reflection
coefficient 0.5 at -120°, current 0.5 at +60°. (Keep in mind that in operation the stub is in parallel with
the 50-ohm line resistance at the stub point.)
With stub connected in parallel with the line the voltage reflection coefficient at the stub point is 0.04 at
0°, current 0.04 at 180°. (Equivalent SWR = 1.083, and impedance = 54.16 + j0 ohms.)

Summarizing reflection coefficient values at stub point with stub in place:
Line coefficients: voltage 0.5 at +120°, current -60°
Stub coefficients: voltage 0.5 at -120°, current +60°
Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0°

These two resultant reflection coefficients resulting from the interference between the load-reflected wave at
the stub point and the reflected wave produced by the stub define a virtual short circuit established at the
stub point.

Let's now consider what occurs when a wave encounters a short circuit. We know that the voltage wave
encounters a phase change of 180°, while the current wave encounters zero change in phase. Note that the
resultant voltage is at 180°, so the voltage phase changes to 0° on reflection at the short circuit, and is
now in phase with the source voltage wave. In addition, the resultant current is already at 0°, and because
the current phase does not change on reflection at the short circuit, it remains at 0° and in phase with
source current wave. Consequently, the reflected waves add in phase with the source waves, thus increasing the
forward power in the line section between the stub and the load.

So how do we know that the virtual short circuit resulting from the interference is really performing as a
short circuit?

First, an insignificant portion of the reflected wave appears on the source side of the stub point, thus, from
a practical viewpoint, indicating total re-reflection of the reflected waves at the stub point.

Second, the voltage in the line section between the stub and load that has a 3:1 SWR has increased relative to
that on the source line by the factor 1.1547, the amount expected on a line having a 3:1 SWR after total
re-reflection at an open or short circuit. This increase factor is determined from the equation for the
increase in forward power on a line with a specific value of SWR, where rho is the corresponding value of
reflection coefficient. The power increase factor equation is power increase = 1/(1 - rho^2). Thus the voltage
increase factor is the square root of the power increase factor. With rho = 0.5, as in the case of the above
experiment, the power increase factor is 1.3333..., the square root of which is 1.1547.

We have thus proved that the virtual short circuit established at the stub point is actually performing as a
real short circuit.

I believe it is remarkable that the maximum deviation of the measured values obtained during the experiment is
less than 2 percent of the text-book values that would appear with lossless elements, and ignoring measurement
errors and tolerances of the measuring equipment. The recognized sources of error a
1. Tolerance in readings from the Vector Voltmeter
2. Ripple in the coupling factor in the directional coupler
3. Attenuation in the coax
4. The fact that the nomional Zo of the RG-53 coax is 53.5 ohms, not 50, as used as the reference in the
measurements.

My final comment is that I hope I have assisted in appreciating the practical use of virtual open and short
circuits, and that matching procedures can be analyzed using reflection coefficients that are not restricted
to lossless or distortionless transmission lines.

Walt, W2DU

On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote:

Hi Walt,

1: The input impedance of a lossless half-wave (180°) transmission line
There are two parts to the following statement:
terminated in a physical short circuit is zero ohms, a short circuit,
which is the causal relationship;
but a VIRTUAL short circuit because it was achieved only by the interference
between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to
the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short
terminating the line.
this is the correlationship.

Without the cause, there is no correlation.

There is nothing to be disputed beyond that.

The reflected current wave on return to the input encountered no phase change during its
travel, thus the current reflection coefficient is in phase with that of the source current, allowing the
short circuit to occur.

Allowing, as a verb, suggests causality. The cause is established in
the short. All intermediary apparatus merely maintain the
correlation. There is nothing to be disputed beyond that.

2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open
circuit
which is the causal relationship;
is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the
interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°)
returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open
circuit terminating the line.
this is the correlationship.

The current reflection coefficient occurs in the same manner as with the
half-wave line above.

It is merely the correlation to an existing, physical open without
which the VIRTUAL short circuit would disappear. All intermediary
apparatus merely maintain the correlation. There is nothing to be
disputed beyond that.

These two examples can be confirmed by referring to any reputable text concerning transmission line theory.
There is nothing to be disputed beyond that.

The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the
current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be
found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both
physical and virtual short or open circuits placed on a transmission line can cause reflections.

And here we get to the nut of the matter - causality. It is already
established that either the physical short, or physical open, whose
absence would render any correlation invalid, dominates the action.
The proof follows the quality of the physical open or the physical
short. A poor physical open or poor physical short will never be
improved by ANY transmission line mechanics. On the other hand, poor
transmission line mechanics will never deliver the action of the best
physical short or the best physical open.

We have thus proved that the virtual short circuit established at the stub point is actually performing as a
real short circuit.

There is nothing to be disputed beyond that. This is not, however, a
proof that the VIRTUAL short (or open) is the cause.

This may appear to be a criticism of semantics (English to some).
However, engineering relies on a far stricter degree of meaning than
most endeavors. Correlation is not Causality is one particular
admonition that comes to mind from the field of logic. It applies
here too.

Walt, it seems to me that you have a need to distinguish VIRTUAL from
physical for reasons other than the transmission line mechanics of
combining loads (or as I distinguished in other threads, routing
energies). A VIRTUAL short or open is metaphor, and it is an useful
metaphor for describing systems. What I see beyond these examples you
have provided are statements (in other discussions) that tend to
confer a reality to the VIRTUAL which is obviously a contradiction on
the face of it. Other than that, there is absolutely nothing in your
published work that is in dispute.

73's
Richard Clark, KB7QHC

On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote:

My final comment is that I hope I have assisted in appreciating the practical use of virtual open and short
circuits, and that matching procedures can be analyzed using reflection coefficients that are not restricted
to lossless or distortionless transmission lines.

Hi Walt,

You have tackled a job that some would shrug off as being impossible
to accomplish. You have performed an admirable job of bench work
demonstrating the lessons of the best text books. Few here go to
those lengths, or with such precision and accuracy.

Your tight writing also reveals a mind that still sees the "big
picture" and can describe it with sufficient detail for those who
would otherwise dismiss the topic as being too vast and complex to
comprehend.

73's
Richard Clark, KB7QHC

On Fri, 13 Apr 2007 12:08:10 -0700, Richard Clark wrote:

On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote:

My final comment is that I hope I have assisted in appreciating the practical use of virtual open and short
circuits, and that matching procedures can be analyzed using reflection coefficients that are not restricted
to lossless or distortionless transmission lines.

Hi Walt,

You have tackled a job that some would shrug off as being impossible
to accomplish. You have performed an admirable job of bench work
demonstrating the lessons of the best text books. Few here go to
those lengths, or with such precision and accuracy.

Your tight writing also reveals a mind that still sees the "big
picture" and can describe it with sufficient detail for those who
would otherwise dismiss the topic as being too vast and complex to
comprehend.

73's
Richard Clark, KB7QHC

Richard, thank you for your comments and kind words. Coming from you it's hard to express my true appreciation
for what you've said.

Sincerely, Walt

Walter Maxwell wrote in
:

In the thread 'Constructive Interference and Radiowave Propagation',
Owen, on 4-8-07 asserted that my writings in Reflections concerning
the analysis of stub matching procedures using reflection coefficients
are applicable only in cases where the transmission line is either
lossless, or distortionless. I disagree, and in what follows I hope to
persuade those who agree with Owen's position to reconsider.

Hi Walt,

I did not say that, or in my view, imply that, it is your own
interpretation of what I did say. I did make comment limited to Chapter 3
of Reflections II, and I stand by that comment.

Chapter 3 does not discuss stub matching at all, though you may apply
principles that you develop in Chapter 3 to your discussion / analysis in
later chapters, including to stub matching.

Owen

I have to agree with what Richard and some others have said.

First, that you've done a tremendous job of sharing your extensive
knowledge and experience, and explaining transmission line phenomena in
such a clear and understandable manner. We all owe you a great debt for
this.

But second, that there's something which you do state that I and some
others can't accept. And that is that a "virtual" short (or open)
circuit causes reflections, or that waves reflect from it. I maintain
that for either to happen requires that traveling waves interact with
each other. The "virtual" short or open is only the result of the sum --
superposition -- of traveling waves. Those traveling waves, and hence
their sum, cannot cause a reflection of other waves, or alter those
other waves in any way. Only a physical change in the (assumed linear)
propagating medium can alter the fields in a traveling wave and cause a
reflection. A real short circuit is in this category; a virtual short
circuit is not. It doesn't matter if the waves are coherent or not, or
even what their waveshapes are or whether or not they're periodic -- as
long as the medium is linear, the waves cannot interact.

You have clearly shown, and there is no doubt, that waves behave *just
as though* a virtual short or open circuit were a real one, and this is
certainly a valuable insight and very useful analysis tool, just like
the "virtual ground" at the summing junction of an op amp. But I feel
it's very important to separate analytical tools and concepts from
physical reality. If we don't, we're led deeper and deeper into the
virtual world. Sooner or later, we reach conclusions which are plainly
wrong.

There are many other examples of useful alternative ways of looking at
things, for example differential and common mode currents in place of
the reality of two individual currents, or replacing the actual
exponentially depth-decaying RF current in a conductor with an imaginary
one which is uniform down to the skin depth and zero below. But we have
to always keep in mind that these are merely mathematical tools and that
they don't really correspond to the physical reality.

Unless I've incorrectly read what you've written, you're saying that
you've proved that virtual shorts and opens reflect waves. But in every
example you can present, it can be shown that all waves and reflections
in the system can be explained solely by reflections from real impedance
changes, and without considering or even noticing those points at which
the waves superpose to become virtual short or open circuits. That, I
believe, would disprove the conjecture that virtual shorts or opens
cause reflections. Can you present any example which does require
virtual shorts or opens to explain the wave behavior in either a
transient or steady state condition?

If I've misinterpreted what you've said, I share that misinterpretation
with some of the others who have commented here. And if that's the case,
I respectfully suggest that you review what you've written and see how
it could be reworded to reduce the misunderstanding.

Once again, we all owe you a great deal of thanks for all you've done.
And personally, I owe you thanks for many other things, including
setting such an example of courtesy, civility and professionalism here
in this group (as well in everything else you touch). It's one I strive
for, but continually fall far short of.

Roy Lewallen, W7EL

Richard Clark wrote:

On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote:

The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the
current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be
found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both
physical and virtual short or open circuits placed on a transmission line can cause reflections.


And here we get to the nut of the matter - causality. It is already
established that either the physical short, or physical open, whose
absence would render any correlation invalid, dominates the action.
The proof follows the quality of the physical open or the physical
short. A poor physical open or poor physical short will never be
improved by ANY transmission line mechanics. On the other hand, poor
transmission line mechanics will never deliver the action of the best
physical short or the best physical open.

I agree that this is the problem in Walt's otherwise brilliant work.
Reflections are only caused by the direct interaction between
electromagnetic waves and matter. It is nevertheless valid to say
that systems behave as though virtual impedances cause reflections.
Virtual reflection coefficients are a clever tool and methodology for
systems analysis. But it must be remembered that the propagation of
electromagnetic waves is effected only by certain physical properties
of matter, as described eloquently by James C. Maxwell and others.
Those fundamentals of wave behavior are not different in the steady
state than at other times.

A VIRTUAL short or open is metaphor, and it is an useful
metaphor for describing systems. What I see beyond these examples you
have provided are statements (in other discussions) that tend to
confer a reality to the VIRTUAL which is obviously a contradiction on
the face of it. Other than that, there is absolutely nothing in your
published work that is in dispute.

I completely agree. I think if we got past this one issue, the
newsgroup might actually find itself devoted more to discussions of
antennas.

73, Jim AC6XG

On Apr 13, 9:37 am, Walter Maxwell wrote:
In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings
in Reflections concerning the analysis of stub matching procedures using reflection coefficients are
applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in
what follows I hope to persuade those who agree with Owen's position to reconsider.

To assist in understanding why my use of reflection coefficients in analyzing impedance-matching circuitry, I
find it useful to include the concept of virtual open- and short-circuit conditions. I realize that some of
the posters on this NB deny the existence of virtual open-and short-circuits. Therefore, I hope that my
presentation here will also persuade those posters to reconsider their position.

While working in an antenna lab for more than 50 years I have analyzed, constructed, and measured hundreds of
impedance-matching circuits comprising transmission-line circuitry using reflection coefficients as
parameters. For example, in 1958 my assignment was to develop the antenna system for the World's first weather
satellite, TIROS 1. The system required an antenna that would radiate efficiently on four different
frequencies in two bands that were more than an octave related. It required a coupling circuit that would
allow four transmitters to operate simultaneously on all four frequencies without mutual interference. After
developing the antenna that also required radiating circular polarization, I then developed the coupling
system, which, pardon my English, utilized several virtual open- and short-circuit conditions to accomplish
the required isolation between the individual transmitters. The entire coupling system was fabricated in
printed-circuit stripline transmission line (not microstrip), with no connectors except for transmitter input
ports and output ports feeding the antenna. Remember, this was in 1958.

Initially I had only a slotted line for impedance measurements during the development stage, but soon after
the PRD-219 Reflectometer became available, invented by my bench mate, Woody Woodward. The PRD-219 measured
SWR and the angle of the voltage reflection coefficient. The magnitude rho of the reflection coefficient was
obtained from the SWR measurement using the equation rho = (SWR - 1)/(SWR + 1), thus the PRD actually measured
the complete complex reflection coefficient. Consequently, all measurements from then on were in terms of
reflection coefficient.

Keep in mind that I was working with real transmission lines--not lossless lines. There were several
stub-matching circuits, several occurrences of virtual open- and short-circuits, and the total loss through
the coupler at both the 108 and 235 MHz bands was no greater than 0.2 dB. The input SWR at all four input
ports for a run of 12 manufactured units never exceeded 1.05:1 relative to 50 ohms.

Please let me now explain my understanding of virtual open- and short-circuits. These circuits are developed
by interference between two sets of voltage and current waves having reflection coefficients of equal
magnitude and phase differences of 180°, respectively. Consider these two examples of a virtual short circuit:

1: The input impedance of a lossless half-wave (180°) transmission line terminated in a physical short circuit
is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference
between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to
the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short
terminating the line. The reflected current wave on return to the input encountered no phase change during its
travel, thus the current reflection coefficient is in phase with that of the source current, allowing the
short circuit to occur.

2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open
circuit is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the
interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°)
returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open
circuit terminating the line. The current reflection coefficient occurs in the same manner as with the
half-wave line above.

These two examples can be confirmed by referring to any reputable text concerning transmission line theory.

The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the
current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be
found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both
physical and virtual short or open circuits placed on a transmission line can cause reflections. Proof is in
measurements performed at various points in the antenna coupler developed for the TIROS spacecraft in 1958.

Now let's examine a specific example of impedance matching with a stub using reflection coefficients, with
more details than I used in the previously-mentioned thread. As I said earlier, I have measured hundreds of
stub-matching circuitry, but for this discussion, yesterday I set up an experimental stub-matching circuit for
the purpose of being able to report directly on the results of current measurements taken on the circuit. The
source is an HP-8640A signal generator, an HP-5328A counter to determine the operating frequency, and the
combination of an HP-8405 Vector Voltmeter and an HP-778D dual directional coupler to form a precision RF
network analyzer.

Because using a 3:1 mismatch the resulting numbers are convenient, I paralleled three precision 50-ohm
resistors to form a resistance of 16.667 ohms, resulting in a 3:1 mismatch on the line to be stubbed. On a
line with a 3:1 mismatch the correct positioning of a parallel matching stub is 30° toward the source from a
position of minimum SWR, where the normalized admittance y = 1.0 + 1.1547. Thus, I selected a short piece of
RG-53 coax that measured exactly 30° in length at 16.0 MHz, meaning the stub will be placed 30° rearward of
the load.

All measurements obtained during the experiment were less than 2 percent in error compared to a perfect
text-book setup. Consequently, rather than bore you with the exact measured values, I'm going to use the
text-book values for easier understanding.

At the 16.667 + j0 load the measured voltage reflection coefficient = 0..5 at 180°, current 0.5 at 0°.
At the stub point voltage reflection coefficient of the line impedance = 0.5 at +120°, current 0.5 at -60°.
Open-circuited stub 49° in length measured separately in parallel with 50 ohms yields voltage reflection
coefficient 0.5 at -120°, current 0.5 at +60°. (Keep in mind that in operation the stub is in parallel with
the 50-ohm line resistance at the stub point.)
With stub connected in parallel with the line the voltage reflection coefficient at the stub point is 0.04 at
0°, current 0.04 at 180°. (Equivalent SWR = 1.083, and impedance = 54.16 + j0 ohms.)

Summarizing reflection coefficient values at stub point with stub in place:
Line coefficients: voltage 0.5 at +120°, current -60°
Stub coefficients: voltage 0.5 at -120°, current +60°
Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0°

These two resultant reflection coefficients resulting from the interference between the load-reflected wave at
the stub point and the reflected wave produced by the stub define a virtual short circuit established at the
stub point.

Let's now consider what occurs when a wave encounters a short circuit. We know that the voltage wave
encounters a phase change of 180°, while the current wave encounters zero change in phase. Note that the
resultant voltage is at 180°, so the voltage phase changes to 0° on reflection at the short circuit, and is
now in phase with the source voltage wave. In addition, the resultant current is already at 0°, and because
the current phase does not change on reflection at the short circuit, it remains at 0° and in phase with
source current wave. Consequently, the reflected waves add in phase with the source waves, thus increasing the
forward power in the line section between the stub and the load.

So how do we know that the virtual short circuit resulting from the interference is really performing as a
short circuit?

First, an insignificant portion of the reflected wave appears on the source side of the stub point, thus, from
a practical viewpoint, indicating total re-reflection of the reflected waves at the stub point.

Second, the voltage in the line section between the stub and load that has a 3:1 SWR has increased relative to
that on the source line by the factor 1.1547, the amount expected on a line having a 3:1 SWR after total
re-reflection at an open or short circuit. This increase factor is determined from the equation for the
increase in forward power on a line with a specific value of SWR, where rho is the corresponding value of
reflection coefficient. The power increase factor equation is power increase = 1/(1 - rho^2). Thus the voltage
increase factor is the square root of the power increase factor. With rho = 0.5, as in the case of the above
experiment, the power increase factor is 1.3333..., the square root of which is 1.1547.

We have thus proved that the virtual short circuit established at the stub point is actually performing as a
real short circuit.

I believe it is remarkable that the maximum deviation of the measured values obtained during the experiment is
less than 2 percent of the text-book values that would appear with lossless elements, and ignoring measurement
errors and tolerances of the measuring equipment. The recognized sources of error a
1. Tolerance in readings...

read more »



Grrr...thought I had posted a followup but it seems to have not shown
up. I'll try to capture the essence of it here...

I think the idea of a virtual short and a virtual open is fine. I use
similar things all the time in my work with op amps, with AGC
controlled levels, and even with ratiometric measurements. However,
in all these cases, including the transmission line virtual short and
open, it's important to understand that it IS only an approximation to
the real thing. There are times when the approximation is fine, as in
Walt's posted example. However, there are times when the
approximation fails, and it's important to somehow be aware of those
times. One way to do that is to simply use the tools that are
available on modern computers to keep track of line loss, and then the
times when the approximation isn't good become obvious. For
example...

I want to receive signals on 4.00MHz, but there's a very strong
station on 4.30MHz. Knowing a little about transmission lines and
stubs, I think, "I can build a resonator from a half wave of line
shorted at both ends, and tune it to 4MHz. Then I can tap my 50 ohm
through line from the antenna to the receiver onto that resonator, and
it won't affect the 4.00MHz signal since it looks like an open
circuit. If I position the tap point so that at 4.300MHz it's half a
wave away from the short at the end of the line, it will see a
4.300MHz virtual short there, and it will eliminate the strong signal
that's giving me trouble."

So I figure out that the line, using solid polyethylene dielectric
line, needs to be about 81 feet long, and the tap point will be 75.53
feet from one end, 5.67 feet from the other. 81 feet of line could
get pretty big, so I'll use RG-174 line. I build the resonator--you
can look at it as two shorted stubs--and try it out. It doesn't seem
to work very well, and I measure it and discover to my horror that the
attenuation at 4.3MHz is only about 12dB, and the attenuation at
4.00MHz is over 8dB. I've gained less than 4dB net on my problem.

Realizing now that the problem is that the stubs I assumed were
lossless really do have some loss, I try larger coax. Well, I've
smartened up a bit by now and I first do some calculations and find
that with RG-58 (about 0.6dB/100ft at 4MHz), I can get 18.6dB loss at
4.300MHz and only 4.8dB loss at 4.000MHz. That's better, but still
not wonderful by any stretch of the imagination.

With RG-8, at only about .19dB/100 feet loss at 4MHz, it improves to
28dB loss at 4.300MHz and only about 1.9dB at 4.00MHz. That wouldn't
be bad, except that it's an awfully big pile of coax on the floor. At
that point I go off and design a good LC filter to do the job, and
find I can get less than a dB loss at 4.00MHz and fully 45dB loss at
4.300MHz, with modest size coils (smaller even than the coil of RG174,
and much smaller than the RG8), and I can use a trimmer cap to fine-
tune the notch to get the most benefit. (BTW--you can also use
trimmer caps to tune stubs...which can save lots of cutting.)

You can develop a feel for when approximations like the virtual short
and the virtual open actually work, but I think you need to go through
several scenarios that show the good, but also the bad and the ugly,
before you jump into blindly using an approximation. Given how easy
it is for me to just include the loss of line in calculations, I'm
unlikely to drop that in favor of the approximation. It's practically
as easy for me to put loss into my calculations as it is to leave it
off, and putting it in makes it immediately obvious when the
approximations fail.

Cheers,
Tom

On Apr 13, 11:40 am, Richard Clark wrote:


[lotsa good stuff snipped]

A poor physical open or poor physical short will never be
improved by ANY transmission line mechanics.

Well, I dunno about that. Try this experiment:

Take a "poor" short, say 1 ohm, and transform it through a lossless
1/4 wavelength line of Zo=200 ohm. The result will be 40,000 ohm.
Now transform this 40K ohm load through another lossless 1/4
wavelength line of Zo=10 ohm. The result of this transformation will
be a "virtual" 0.003 ohm.

Is that an improvement? [g]

Regards,

Wes

On 13 Apr 2007 15:56:26 -0700, "Wes" wrote:

On Apr 13, 11:40 am, Richard Clark wrote:


[lotsa good stuff snipped]

A poor physical open or poor physical short will never be
improved by ANY transmission line mechanics.

Well, I dunno about that. Try this experiment:

Take a "poor" short, say 1 ohm, and transform it through a lossless
1/4 wavelength line of Zo=200 ohm. The result will be 40,000 ohm.
Now transform this 40K ohm load through another lossless 1/4
wavelength line of Zo=10 ohm. The result of this transformation will
be a "virtual" 0.003 ohm.

Is that an improvement? [g]

Hi Wes,

There is always a rational example to deflate absolutisms. Thanx for
the interesting twist of transmission line.

However, I wouldn't want to be the wallet that pays for this.

73's
Richard Clark, KB7QHC