Walter Maxwell wrote in
:

Summarizing reflection coefficient values at stub point with stub in
place: Line coefficients: voltage 0.5 at +120°, current -60° (y = 1
+ j1.1547) Stub coefficients: voltage 0.5 at -120°, current +60° (y
= 1 - j1.1547) Resultant coefficients: voltage 0.5 at 180°, current
0.5 at 0° WRONG Resultant coefficients: voltage 1.0 at 180°, current
1.0 at 0° CORRECT

Walt,

Though admittance or impedance at a point on the mismatched line are
calculated from the underlying Zo and the reflection coefficient
corrected for line loss, they are easier to work in than the raw
reflection coefficient.

It is easier to explain why the stub is located at a position where Yn'=1
+jB than where Gamma=0.5120 (assuming lossless line). It is relatively
obvious that where Yn'=1+jB, a shunt reactance of -jB from a s/c or o/c
stub will leave Yn=1 which is the matched condition.

Re your worked solution (above), I agree that the normalised admittance
looking into 30deg of line with load 16.667+j0 is about 1-j1.1547 (not
the different sign).

I make the normalised admittance looking into the stub about 0+j1.15 (and
the reflection coefficient about 0.5-98, how do you get 1+j1.15?

The addition of the two normalised admittances 1-j1.15 + 0+j1.15 gives 1
+j0 which is the matched condition.

The design is correct, the stub results in a match at the stub connection
point (irrespective of what is connected on the source side of the
point), but I can't understand your maths above (allowing for the sign
error that I think you have made).

Is the reflection coefficient explanation a clearer explanation than
using admittances?

Owen

BTW, my line loss calculator solutions (http://www.vk1od.net/tl/tllc.php)
for Belden 8262 RG58 (you said RG53, but you probably meant RG58) a

(Note some symbols arent supported by plain ascii and appear as '?'.)

Load to Stub connection:

Parameters
Transmission Line Belden 8262 (RG-58C/U)
Code B8262
Data source Belden
Frequency 16.000 MHz
Length 1.030 metres
Zload 16.67+j0.00 ?
Yload 0.059999+j0.000000 ?
Results
Zo 50.00-j0.54 ?
Velocity Factor 0.660
Length 29.97 ?, 0.083 ?
Line Loss (matched) 0.059 dB
Line Loss 0.149 dB
Efficiency 96.63%
Zin 22.12+j24.55 ?
Yin 0.020258-j0.022480 ?
Gamma, rho, theta, VSWR (source end) -2.44e-1+j4.29e-1, 0.493,
119.6?, 2.950
Gamma, rho, theta, VSWR (load end) -5.00e-1+j4.03e-3, 0.500, 179.5?,
3.000
? 6.54e-3+j5.08e-1
k1, k2 1.30e-5, 2.95e-10
Loss model source data lowest frequency 1.000 MHz
Correlation coefficient (r) 0.999884

Stub:

Parameters
Transmission Line Belden 8262 (RG-58C/U)
Code B8262
Data source Belden
Frequency 16.000 MHz
Length 1.685 metres
Zload 100000000.00+j0.00 ?
Yload 0.000000+j0.000000 ?
Results
Zo 50.00-j0.54 ?
Velocity Factor 0.660
Length 49.02 ?, 0.136 ?
Line Loss (matched) 0.096 dB
Line Loss 40.574 dB
Efficiency 0.01%
Zin 0.50-j43.44 ?
Yin 0.000265+j0.023019 ?
Gamma, rho, theta, VSWR (source end) -1.37e-1-j9.69e-1, 0.978, -
98.0?, 90.720
Gamma, rho, theta, VSWR (load end) 1.00e+0+j1.07e-8, 1.000, 0.0?, inf
? 6.54e-3+j5.08e-1
k1, k2 1.30e-5, 2.95e-10
Loss model source data lowest frequency 1.000 MHz
Correlation coefficient (r) 0.999884

Walt, before digging into your recent posting, I'd really like to get
one issue settled. I think it would be helpful in our discussion. The
issue is:

Can you find even one example of any transmission line problem which
cannot be solved, or a complete analysis done, without making the
assumption that waves reflect from a "virtual short" or "virtual open"?
That is, any example where such an assumption is necessary in order to
find the currents, voltages, and impedances, and the magnitude and phase
of forward and reverse voltage and current waves?

Roy Lewallen, W7EL

Walter Maxwell wrote:

Consider my two explanations, or definitions of what I consider a virtual short--perhaps it should have a
different name, because of course 'virtual' implies non-existence. The short circuit evident at the input of
the two line examples I presented---do you agree that short circuits appear at the input of the two lines? If
so, what would you call them?

I'd call them "virtual shorts". If they were short circuits, we should
be able to connect a wire across the transmission line at that point
with no change in transmission line operation. But we can't. While
things will look the same on the generator side, they won't be the same
beyond the real short. So they aren't short circuits.

Roy, I'd like for you to take another, but perhaps closer look at the summarizing of the reflection
coefficients below. I originally typed in the wrong value for the magnitude of the resultant coefficients.
With the corrected magnitudes in place, the two paragraphs following the summarization now make more sense,
because the short circuit established at the stub point leads correctly to the wave action that occurs there.

Summarizing reflection coefficient values at stub point with stub in place:
Line coefficients: voltage 0.5 at +120°, current -60° (y = 1 + j1.1547)
Stub coefficients: voltage 0.5 at -120°, current +60° (y = 1 - j1.1547)
Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° WRONG
Resultant coefficients: voltage 1.0 at 180°, current 1.0 at 0° CORRECT

Repeating from my original post for emphasis:
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.

There's no need to repeat this. I'm well acquainted with transmission
line phenomena, and understand fully what's happening. I have no
disagreement with this analysis. I would draw attention to the fact that
the "virtual short" is, as you say, simply the superposition
(interference) of traveling waves. So there is nothing at that point
except the traveling waves which pass through that point.

The following paragraph shows how the phases of the reflected waves become in phase with the source waves so
that the reflected waves add directly to the source waves, establishing the forward power, which we know
exceed the source power when the reflected power is re-reflected. The same concept applies to antena tuners.

Sorry, I'm not going to divert onto the topic of propagating power,
either instantaneous or average. If that concept is required in order to
show that waves interact with each other, then it simply shows that the
concept is invalid. Let's stick to voltages and currents. If that's not
adequate, then I'll exit at this point, and turn the discussion over to
Cecil. That's his domain, not mine.

Again repeating for emphasis:
Let's now consider what occurs when a wave encounters a short circuit.

Ok.

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,

Ok so far. . .

thus increasing the
forward power in the line section between the stub and the load.

Again, let's leave power out of it, ok?

Keep in mind that the short at the stub point is a one-way short, diode like, as you say, because in the
forward direction the voltage reflection coefficient rho is 0.0 at 0°, while in the reverse direction, rho at
the stub point is 1.0 at 180°, which is why it's a one-way short.

The voltages, currents, waves, and impedances impedances on the line are
just the same as if there were a diode-short at that point. Which is why
it's a useful analytical tool. But all there really is at that point are
some interfering waves, traveling through that point unhindered.

You say that no total re-reflection occurs at the stub point. However, with a perfect match the power rearward
of the stub is zero, and all the source power goes to the load in the forward direction. Is that not total
reflection?

Not from the "virtual short" -- it only looks like it. The re-reflection
is actually occurring from the end of the stub and from the load, not
from the "virtual short". If, for example, you suddenly increased the
source voltage, there would be no reflection as that change propagated
through that "virtual short". (That is, after a delay equal to the
round-trip time to the "virtual short", you'd see no change.) The
apparent reflection from that point wouldn't appear until the change
propagated to the end of the stub and to the load (going right through
the "virtual short" unhindered), reflected from them, and arrived back
at the "virtual short" point. This is one of the ways you can tell that
a "virtual short" isn't a real short. Under steady state conditions, it
looks just like a real one. But it isn't. Waves which seem to be
reflecting from it are really reflecting from the end of the stub and
from the load -- they're passing right through the "virtual short", in
both directions.

Using the numbers of my bench experiment, assuming a source power of 1 watt, and with the
magnitude rho of 0.04, power going rearward of the stub is 0.0016 w, while the power absorbed by the load is
0.9984 w, the sum of which is 1 w. The SWR seen by the source is 1.083:1, and the return loss in this
experiment is 27.96 dB, while the power lost to the load is 0.0070 dB. From a ham's practical viewpoint the
reflected power is totally re-reflected.

Sorry, you're going to have to do this without propagating waves of
average power, or I'm outta here.

In my example using the 49° stub the capacitive reactance it established at its input is Xc = -57.52 ohms.
Thus its inductive susceptance B = 0.0174 mhos, which cancels the capacitive line susceptance B = -0.0174 mhos
appearing at the stub point.

My point is that the 49° stub can be replaced with a lumped capacitance Xc = -57.52 ohms directly on the line
with the same results as with the stub--with the same reflection coefficients.

That's fine, I agree.

In this case one cannot say
that the re-reflection results from the physical open circuit terminating the stub line.

I most certainly can! And do. I don't see how your example furnishes any
proof or even evidence of wave interaction. I can come to the same
conclusion without any assumption of wave interaction, and you have
agreed (in your response to my question about finding an example that
requires interaction for analysis) that this can always be done.

Various posters have termed my approach as a 'short cut'. I disagree. I prefer to consider it as the wave
analysis to the stub-matching procedure, in contrast to the traditional method of simply saying that the stub
reactance cancels the line reactance at the point on the line where the line resistance R = Zo. In my mind the
wave analysis presents a more detailed view of what's actually happening to the pertinent waves while the
impedance match is being established.

I'm sorry, I disagree. It's a less detailed view, and it conceals what's
really going on.

Roy Lewallen, W7EL

Roy Lewallen, W7EL wrote:
"Those traveling waves, and hence their sum, cannot cause a reflection
of other waves, or alter those waves in any way."

Let`s reason together on the situation in a quarter-wavelength
short-circuited transmission line stub. I maintain it has a hard short
on its far end and a high impedance on its near end.

A high impedance means just what it says. You can put a high voltage on
it and the resulting current is small.

Reflection from a short-circuit results in a 180-degree voltage phase
reversal at the short.

A round-trip on a 1/4-wave stub produces an additional 180-degree phase
reversal.

This means thats volts returning to the open-circuit end of the stub are
about of the same phase and magnitude as when they started out.

Nearly identical voltages appear at the same pair of terminals from
opposite directions. Significant current flows in either direction? I
think it does not.

Where voltage causes insignificant current flow, we have a high
impedance.

That is why King, Mimno, and Wing on page 30 of Transmission Lines,
Antennas and Wave Guides say:
"Since the input impedance of a short-circuited quarter-wavelength
section of transmission line is a very high resistance, short-circuited
stubs may be used to support the line."

Best regards, Richard Harrison, KB5WZI

On Sat, 14 Apr 2007 10:59:17 -0500, (Richard
Harrison) wrote:

That is why King, Mimno, and Wing on page 30 of Transmission Lines,
Antennas and Wave Guides say:
"Since the input impedance of a short-circuited quarter-wavelength
section of transmission line is a very high resistance, short-circuited
stubs may be used to support the line."

Hi Richard,

One example begs another, symmetrical one; and here is the example of
my asking you why you would struggle through building an open line
reflected as a short (the quarterwave section).

For argument's sake, let's amend KM&W to say:
"Since the input impedance of a open-circuited quarter-wavelength
section of transmission line is a very low resistance, open-circuited
stubs connected in series with the line elements may be used to
support the line."

This statement is equivalent in the transmission line mechanic's tool
kit, certainly. However, it brings with it the difficulties of
maintaining a "good" open (especially when that open is in close
proximity to earth, or at least to the press of humanity). Casting
those problems into the line obviously presents loss issues of a poor
virtual short.

This conforms to my experience with many plumbing designs on the
microwave bench. The absence of open quarterwave sections was nearly
universal due to the problems of their implementation. It takes
little effort to realize why KM&W did not offer this alternative. If
you browse Terman, he also avoids such constructions.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
"This conforms to my experience with many plumbing designs on the
microwave bench."

Good. Then, Richard Clark must also be familiar with the grooved
circular flange used in conjunction with a smooth flange to join
waveguide segments. This groove isn`t just used to hold a neoprene
gasket. It is also used as an electrical choke to keep the microwaves
within the pipe. It is approximately a 1/4-wave choke and its high
impedance across its open-circuit helps foil the wave escape. If virtual
open-circuits didn`t work, the "choke-flange wouldn`t work either.

Best regards, Richard Harrison, KB5WZI

On Sat, 14 Apr 2007 16:36:11 -0500, (Richard
Harrison) wrote:

Richard Clark wrote:
"This conforms to my experience with many plumbing designs on the
microwave bench."

Good. Then, Richard Clark must also be familiar with the grooved
circular flange used in conjunction with a smooth flange to join
waveguide segments. This groove isn`t just used to hold a neoprene
gasket. It is also used as an electrical choke to keep the microwaves
within the pipe. It is approximately a 1/4-wave choke and its high
impedance across its open-circuit helps foil the wave escape. If virtual
open-circuits didn`t work, the "choke-flange wouldn`t work either.

Hi Richard,

You got the dimensions wrong for the wrong reason. It is a halfwave
shorted cavity (or transmission line sub-section). The cut channel is
quarterwave, but the distance from the middle of the longest side of
the waveguide is another quarterwave. The virtual short bridges the
joined, but non-contacting faces of the two waveguide sections. There
is no high Z action involved.

Further, there are two grooves, the outer one is for the neoprene
gasket.

For others, when two sections of waveguide are joined, there is always
the possibility that the two faces of the ends will not see a machined
match (like an engine head to the engine block - which even there has
problems of warp); hence the possibility of a break in continuity with
an open circuit. Rather than burn money as a solution, engineers
simply forced the problem by having the two faces separated and never
in contact!

What they did to offset this deliberate open is they machined a
circular groove around the flange of one section that was a
quarterwave deep, and a quarterwave away from the voltage node for the
waveguide's TE10 mode of transmission. The geometry of the groove and
its distance from the node was very simple to control in comparison to
guaranteeing fully flush mating faces (especially under the torsion of
ship's movement, or simple heat expansion). This is a hallmark of
engineering where the problem becomes the solution.

As always, a short is vastly more preferred than an open when casting
back into the transmission line and the design engineers went to the
additional length to see it incorporated into the solution.

Dare I call the choke joint a virtual gasket?

73's
Richard Clark, KB7QHC

I'm not sure I understand the point you're trying to make. Nothing I've
said disputes in any way that the input impedance of a shorted quarter
wave stub is high. I'm quite able to make transmission line calculations
and arrive at correct results.

You're certainly correct that there's very little net current at the
open end of the stub. Yet there are waves traveling in both directions
right through that point. Don't believe it? Then check the current
anywhere else along the stub. How did it get there without going through
the "open" at the input end?

Roy Lewallen, W7EL

Richard Harrison wrote:
Roy Lewallen, W7EL wrote:
"Those traveling waves, and hence their sum, cannot cause a reflection
of other waves, or alter those waves in any way."

Let`s reason together on the situation in a quarter-wavelength
short-circuited transmission line stub. I maintain it has a hard short
on its far end and a high impedance on its near end.

A high impedance means just what it says. You can put a high voltage on
it and the resulting current is small.

Reflection from a short-circuit results in a 180-degree voltage phase
reversal at the short.

A round-trip on a 1/4-wave stub produces an additional 180-degree phase
reversal.

This means thats volts returning to the open-circuit end of the stub are
about of the same phase and magnitude as when they started out.

Nearly identical voltages appear at the same pair of terminals from
opposite directions. Significant current flows in either direction? I
think it does not.

Where voltage causes insignificant current flow, we have a high
impedance.

That is why King, Mimno, and Wing on page 30 of Transmission Lines,
Antennas and Wave Guides say:
"Since the input impedance of a short-circuited quarter-wavelength
section of transmission line is a very high resistance, short-circuited
stubs may be used to support the line."

Best regards, Richard Harrison, KB5WZI

Roy Lewallen wrote in
:

anywhere else along the stub. How did it get there without going through
the "open" at the input end?

Ah, a total re-reflector!

Owen

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