On Sun, 06 Jun 2004 12:44:38 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Well, Cecil, so far I haven't been able to follow the logic in the lines above.
Perhaps they are correct for that particular example, but I'm not so sure.

Please pick any example of your choice of matched systems. Dr. Best's equation
13 will be valid for any matched system. VFtotal = V1 + V2 will be valid for
any system, matched or not.

For
example, if 100 w is available only 75 w will enter the 150-ohm line initially,
so initially only 56.25 w is absorbed in the 50-ohm load and 18.75 w is
reflected, which then sees a 3:1 mismatch on return to the 50-ohm line, making
the re-reflected power 4 .69 w . I haven't had time to work through the
remaining steps to the steady state.

When you do, you will get the same values as I.

So before I do I notice that you state that
Eqs 10 thru 15 are valid for any matched system. So let's see if this is so by
using the example Steve used earlier in his Part 3, the one he took from
Reflections and then called it a 'fallacy'.

As I have said before, Steve's equations are correct but he simply drew the
wrong conclusions from them. His "fallacy" is a fallacy but has nothing to
do with his equations. He simply drew the wrong conclusions from valid
equations.

This is that example: 50-ohm lossles line terminated with a 150 + j0 load. 100 w
available from the source at 70.71 v. Matched at the line input, in the steady
state the total forward power Pfwd = 133.33 w and power reflected is Pref =
33.333 w. With these steady state powers the forward voltage is 81.65 v and
reflected voltage is 40.82 v. Due to the integration of the reflected waves the
source voltage 70.71 increased 10.94 v to 81.65 v. Therefore, in the steady
state V1 = 81.65 v and V2 = 40.82 v.

Nope, you simply misunderstood what Steve said. V1 and V2 are *NOT* on the 50 ohm
line. In fact, the 1 WL 50 ohm line is irrelevant and just serves to confuse. V1
and V2 are voltages existing *at the match point* at the INPUT of the tuner. Steve
chose an example that is virtually impossible to explain or understand.

Cecil, Steve's equations 4 thru 8 are correct, valid, and completely GENERAL. In
the text preceding the Eqs he even specifies Zo as 50 ohm, not that it matters.
He correctly defines V1 in Eq 7 and he correctly defines V2 in Eq 8. However, he
makes a vital error in the paragraph preceding these two equations.

He says incorrectly, "When two forward traveling waves add, general
superposition theory and Kirchoff's voltage law require that the total
forward-traveling voltage be the vector sum of the individual forward-traveling
voltages such that VFtotal = V1 + V2."

This statement is TOTALLY FALSE, and this error is the basis for the remainder
of his equations to be invalid. Kirchoff's voltage law does not apply in this
case of transmission line practice. There are times when circuit theory doesn't
hold and transmission line theory is required.

You are still ignoring his Eq 6 in Part 1, which is false and invalid because he
mistook the expression for determining the standing wave for the total forward
wave. Look back at my previous msg where I've shown that the addition of the
forward and reflected waves yields the standing wave, not the forward wave. The
standing wave is NOT the forward wave.

Refer to the text on your CD at the paragraph that begins: "A transmission line
system analysis must be performed with voltage and current, from which the power
is then derived." Read on from this point to where it reads, "If total
re-reflection of power occurs at the T-network, the re-reflected voltage must
have the same magnitude as the reflected voltage."

Please note the values of voltages and currents that appear in that entire
section, because this section is a direct copy of my example he took from
Reflections in an attempt to disprove it. Which he does in the next sentence:

"Therefore, based on the assumption that total power re-reflection and in-phase
forward-wave addition, the total forward-traveling wave of 81.65 v must be the
result of a voltage having a magnitude of 70.711 v adding in phase with a
voltage having a magnitude of 40.825 v. Two in-phase complex voltages having
magnitudes of 70.711 v and 40.825 v cannot add together such that the resulting
voltage has a magnitude 81.65 v."

OF COURSE IT CAN'T, because these two voltages CANNOT BE ADDED TOGETHER TO
DERIVE THE FORWARD VOLTAGE.. This is further evidence that he didn't realize
that Eq 6 in Part 1 was wrong, because it derives the standing wave voltage,
NOT THE FORWARD VOLTAGE.

He then goes on in an unsuccessful attempt to prove my method wrong, in which he
gets himself into trouble with those equations that don't work in general. If
you still don't see the problem, Cecil, please go back and review my analysis in
the earlier post and explain to me why you disagree with my results that show
conclusively that the equations don't work.

To conclude, I have shown you why I have not used his values of V1 and V2
incorrectly, as you say. If you can show that I'm wrong I'll take the time to
study the step-by-step in your example below.

Walt


Let's take it step by step starting with Steve's example:

100W XMTR---50 ohm line---tuner---1WL 50 ohm line---150 ohm load

The 1WL 50 ohm lossless line is irrelevant except for power measurements so
eliminate it.

100W XMTR---50 ohm line---tuner---150 ohm load

The tuner can now be replaced by 1/4WL of 86.6 ohm feedline.

100W XMTR---50 ohm line---x---1/4WL 86.6 ohm line---150 ohm load
100W-- 107.76W--
--0W --7.76W
V1--
V2--

Now we have an example that is understandable and we haven't changed
any of the conditions.

The magnitude of the reflection coefficient is 0.268. That makes the magnitude
of the transmission coefficient equal to 1.268 (Rule of thumb for matched
systems with single step-function impedance discontinuities)

So V1 = 70.7 * 1.268 = 89.6V V2 = VF2 * 0.268 = 6.95V

VFtotal = V1 + V2 = 89.6V + 6.95V = 96.6V

PFtotal = 96.6V^2/86.6 = 107.76W

So, Cecil, do you still believe these equations are valid for every matched
situation?

Yes, they are, Walt, once one understands them. I don't blame you for being
confused about Steve's example. He chose the worst example possible and
didn't explain it very well at all.

I still maintain that you two are two inches apart and neither one of you
will budge an inch.

Cecil, I've shown where we're apart. It's a lot more than 2 inches.

Walter Maxwell wrote:
To conclude, I have shown you why I have not used his values of V1 and V2
incorrectly, as you say. If you can show that I'm wrong I'll take the time to
study the step-by-step in your example below.

Steve is essentially doing an S-parameter analysis without the (square
root of Z0) normalization. Since we know that an S-parameter analysis of a
match point is indeed valid, a lot of Steve's equations are valid by
association.

Assuming the S-parameter equation is valid, we can use it to prove that

VFtotal = V1 + V2

V1/SQRT(Z0) = s21(a1) in the S-parameter analysis.

V2/SQRT(Z0) = s22(a2) in the S-parameter analysis.

VFtotal/SQRT(Z0) = b2 in the S-parameter analysis.

Given: b2 = s21(a1) + s22(a2) is a valid S-parameter equation.

Therefore, VFtotal/SQRT(Z0) = V1/SQRT(Z0) + V2/SQRT(Z0) is a valid equation
because there is an EXACT one-to-one correspondence to the S-parameter equation.

Therefore, if we multiply both sides by SQRT(Z0) we get VFtotal = V1 + V2

The only way for the above equation to be wrong is if the S-parameter equation
is wrong. The only difference in the S-parameter equation and Dr. Best's equation
is the normalization by [SQRT(Z0)].

Given a generalized matched system:

XMTR---Z01---x---1/4WL Z02---load
VF1-- VF2--
--VR1 --VR2

VF2 = VF1(TAU) + VR2(RHO) = V1 + V2 Dr. Best's equation

b2 = s21(a1) + s22(a2) S-parameter equation

Dr. Best is essentially quoting an S-parameter analysis
--
73, Cecil http://www.qsl.net/w5dxp





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On Sun, 06 Jun 2004 17:32:24 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
To conclude, I have shown you why I have not used his values of V1 and V2
incorrectly, as you say. If you can show that I'm wrong I'll take the time to
study the step-by-step in your example below.

Steve is essentially doing an S-parameter analysis without the (square
root of Z0) normalization. Since we know that an S-parameter analysis of a
match point is indeed valid, a lot of Steve's equations are valid by
association.

snip

Dr. Best is essentially quoting an S-parameter analysis

Cecil, if the S-parameteri analysis is applied correctly the results of the
S-parameter analysis should agree with the results of mine that appears in my
earlier posts. You have not responded to the results of my analysis that proves
Steve's use of the equations 9 thru 15 is incorrect. I've proved that these
equations do not work in general. Referring to my analysis, please show me
where I went wrong, if that's your position.

Walt

Walter Maxwell wrote:
Cecil, if the S-parameteri analysis is applied correctly the results of the
S-parameter analysis should agree with the results of mine that appears in my
earlier posts. You have not responded to the results of my analysis that proves
Steve's use of the equations 9 thru 15 is incorrect. I've proved that these
equations do not work in general. Referring to my analysis, please show me
where I went wrong, if that's your position.

I thought I did that, Walt. Your V1 and Dr. Best's V1 are NOT the same quantity.
Your V2 and Dr. Best's V2 are NOT the same quantity. It is no wonder that you
didn't get the same results. The 1WL 50 ohm line in Dr. Best's example is
absolutely irrelevant. Calculating anything on that line is a waste of effort.

Please center your calculations around the match point.

Plug any values into the following generalized matched system:

Z0-match
XMTR-----Z01-----x-----1/4WL Z02-----load
VF1-- VF2--
--0V --VR2

VF2 = VFtotal in Dr. Best's article traveling toward the load

VF1(TAU) = V1 in Dr. Best's article traveling toward the load

VR2(RHO) = V2 in Dr. Best's article traveling toward the load

VR2 will always equal VF1(TAU) + VR2(RHO) = V1 + V2

just like b2 will always equal s21(a1) + s22(a2)
--
73, Cecil http://www.qsl.net/w5dxp



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On Sun, 06 Jun 2004 18:03:31 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Cecil, if the S-parameteri analysis is applied correctly the results of the
S-parameter analysis should agree with the results of mine that appears in my
earlier posts. You have not responded to the results of my analysis that proves
Steve's use of the equations 9 thru 15 is incorrect. I've proved that these
equations do not work in general. Referring to my analysis, please show me
where I went wrong, if that's your position.

I thought I did that, Walt. Your V1 and Dr. Best's V1 are NOT the same quantity.
Your V2 and Dr. Best's V2 are NOT the same quantity. It is no wonder that you
didn't get the same results. The 1WL 50 ohm line in Dr. Best's example is
absolutely irrelevant. Calculating anything on that line is a waste of effort.

Cecil, it seems like we're going around in cirles.

If Steve's equations are valid they should work in general. It doesn't matter
whether we use the values from his T network section that comes later, or the
values in my example that he attempts to prove incorrect.

What does matter is that the equations must deliver the correct answers
regardless of the values used in the equations. I have proved that valid values
plugged into his equations don't yield the correct answers.

Cec;il, why are you avoiding trying to understand the basis for his erroneous
concept of adding forward and reflected voltages to obtain total forward
voltage? You don't even respond to my discussion on this point.

Walt

Walter Maxwell wrote:
Cecil, why are you avoiding trying to understand the basis for his erroneous
concept of adding forward and reflected voltages to obtain total forward
voltage? You don't even respond to my discussion on this point.

I'm not trying to avoid it, Walt. Dr. Best simply doesn't do that. V1 is
a *forward-traveling voltage*. V2 is a *forward-traveling voltage*. Their
sum is VFtotal, the *total forward-traveling voltage*. He does NOT add a
forward voltage to a reflected voltage. V2 is the *forward-traveling* re-
reflected voltage equal to VR2(RHO).

When the reflected voltage is acted upon by the reflection coefficient, it
becomes a forward-traveling voltage. That you think Dr. Best is adding forward
and reflected voltages, is the source the present misunderstanding. The
individual Poynting Vector for V1 points toward the *load*. The individual
Poynting Vector for V2 points toward the *load*. V1 and V2 are coherent
component waves, both flowing toward the load so, of course, they superpose.

Again, consider the following *matched* configuration where RHO is
the reflection coefficient and TAU is the transmission coefficient.

XMTR---Z01---x---1/4WL Z02---load
VF1-- VF2--
--VR1 --VR2

There are four superposition components that occur. Two of them are
traveling toward the load and two of them are traveling toward the
source.

V1 = VF1(TAU) traveling toward the load
V2 = VR2(RHO) traveling toward the load

Adding these two forward-traveling voltages yields VF2 = V1 + V2

V3 = VF1(RHO) traveling toward the source
V4 = VR2(TAU) traveling toward the source

Adding these two rearward-traveling voltages yields VR1 = V3 + V4
which, in a matched case is zero because V3 = -V4.

VF1 breaks up into two components, V1 toward the load and V3
toward the source.

VR2 breaks up into two components, V2 toward the load and V4
toward the source.

Collect and superpose the two forward-traveling terms and you get
the total forward-traveling voltage.

Collect and superpose the two rearward-traveling terms and you get
the total rearward-traveling voltage.
--
73, Cecil http://www.qsl.net/w5dxp



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On Sun, 06 Jun 2004 20:44:46 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Cecil, why are you avoiding trying to understand the basis for his erroneous
concept of adding forward and reflected voltages to obtain total forward
voltage? You don't even respond to my discussion on this point.

I'm not trying to avoid it, Walt. Dr. Best simply doesn't do that. V1 is
a *forward-traveling voltage*. V2 is a *forward-traveling voltage*. Their
sum is VFtotal, the *total forward-traveling voltage*. He does NOT add a
forward voltage to a reflected voltage. V2 is the *forward-traveling* re-
reflected voltage equal to VR2(RHO).

When the reflected voltage is acted upon by the reflection coefficient, it
becomes a forward-traveling voltage. That you think Dr. Best is adding forward
and reflected voltages, is the source the present misunderstanding. The
individual Poynting Vector for V1 points toward the *load*. The individual
Poynting Vector for V2 points toward the *load*. V1 and V2 are coherent
component waves, both flowing toward the load so, of course, they superpose.

Cecil, I know V2 is the re-reflected voltage, but what I'm trying to persuade
you is that they do NOT superpose to form the forward voltage--they superpose
only to form the standing wave. You've go to accept that the standing wave
voltage is NOT the forward voltage. If you can't come to realize this is the key
to the problem I'm going to have to give up.

Incidentally, you say tau is 1+ rho as the transmission coefficient, which when
muliplied by input voltage yields forward voltage. I thought (1 - rho^2) is the
transmission coefficient. These two terms are not equal. Can you explain the
difference?

Walt