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

Walter Maxwell wrote:
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.

I'm sorry, Walt,
Your belief that V2 is a reflected wave is the root of the misunderstanding.
V2 is a re-reflected wave and is therefore forward-traveling toward the load.
V2 is equal to the reflected wave voltage multiplied by the reflection
coefficient. V1 and V2 are traveling in the same direction, toward the load.

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?

(1-rho^2) is the POWER transmission coefficient. For a single impedance
discontinuity situation, 1+rho is the VOLTAGE transmission coefficient.
From the IEEE Dictionary: "transmission coefficient, ... Note 2, An interface
is a special case of a network where the reference planes associated with
the incident and transmitted waves become coincident; in this case the
voltage transmission coefficient is equal to one plus the voltage
reflection coefficient."
--
73, Cecil http://www.qsl.net/w5dxp



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