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

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, 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

Richard Clark, KB7QHC wrote:
"A poor physical open or physical short will never be improved by ANY
transmission line mechanics."

An open-circuit 1/4-wave stub is an open circuit at both ends,
physically. As such, its input is a poor short-circuit until it receives
a reflection from its far end. After the reflection reaches the stub`s
input, it becomes a virtual short-circuit. This occurs at its "poor
physical short" input.

This is a dramatic improvement by transmission line mechanics when this
is the desired effect.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
An open-circuit 1/4-wave stub is an open circuit at both ends,
physically.

Let's look at a 1/4WL open stub.

source ----------------------------------+
|
| 1/4WL
|
|
open

The transmission line and stub are the same Z0 and
both are lossless.

The virtual impedance at point '+' is zero but there
is no physical impedance discontinuity at point '+'.
Are there any reflections originating at point '+'?

If we straighten out the line,

1/4WL
source-----------------------------------+------------open

Are there any reflections originating at point '+'?
--
73, Cecil http://www.w5dxp.com

On Fri, 13 Apr 2007 20:34:56 -0500, (Richard
Harrison) wrote:

This is a dramatic improvement by transmission line mechanics when this
is the desired effect.

Hi Richard,

This kind of drama is found only on the stage.

A poor open is a poor short in reflection. Ever try tuning one that
didn't wander the landscape? Burning money to achieve a working
solution does not render it a dramatic improvement when other methods
(like simply building a good shorted halfwave) are better.

Give me a reason why you suffered to build an open quarterwave, and it
will embrace the issues of quality I already covered.

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