Reflection coefficient for total re-reflection
 

On Jun 22, 1:49*pm, Cecil Moore wrote:
Let's return to an earlier example and compare a single-port analysis
with a dual-port analysis.

100w
source--50 ohm--+--1/2WL 291.4 ohm--50 ohm load

The 50 ohm Z0-match point is at '+'. The forward power on the 50 ohm
line is 100 watts and the reflected power on the 50 ohm line is zero
watts. The forward power on the 291.4 ohm line is 200 watts and the
reflected power on the 291.4 ohm line is 100 watts. 100 watts is being
sourced and delivered to the 50 ohm load.

The voltage reflection coefficient, rho, at the load is (50-291.4)/
(50+291.4)=0.7071. The power reflection coefficient, rho^2, at the
load is 0.5, i.e. half of the power incident upon the load (200w) is
reflected (100w). Since the load is a single-port, these parameters
are consistent with a single-port analysis. In a single-port analysis,
we cannot tell the difference between a virtual reflection coefficient
and a physical reflection coefficient.

The problem comes when we use a single-port analysis on the Z0-match
point. Since the reflected power on the 50 ohm line is zero, a single-
port analysis would yield rho=0.0 and rho^2=0.0 when viewing the Z0-
match from the source side. When we perform a dual-port analysis, we
get different values for rho and rho^2, i.e. we get the complement of
the reflection coefficients at the load which is a characteristic of
any simple Z0-match similar to the above example.

For a dual-port analysis, rho looking into the Z0-match from the
source side is (291.4-50)/(291.4+50)=0.7071 and rho^2 looking into the
Z0-match from the source side is 0.5, the same as at the load. Looking
back into the Z0-match from the load side, the sign of rho is negative
just as it is at the load with rho^2=0.5, the same as at the load.

Since the two analyses yield different values for the reflection
coefficients, which analysis is correct? The answer gives the clue to
the resolution of this discussion.
--
73, Cecil, w5dxp.com

ok, i'm afraid i'm going to have to ask the simple question... if you
blackbox the load and stub and look at just the one connection to it
and that gives you no reflected power... where do you define the
second port, and why?

Reflection coefficient for total re-reflection
 

On 6/22/2011 3:24 PM, dave wrote:
On Jun 22, 1:49 pm, Cecil wrote:
Let's return to an earlier example and compare a single-port analysis
with a dual-port analysis.

100w
source--50 ohm--+--1/2WL 291.4 ohm--50 ohm load

The 50 ohm Z0-match point is at '+'. The forward power on the 50 ohm
line is 100 watts and the reflected power on the 50 ohm line is zero
watts. The forward power on the 291.4 ohm line is 200 watts and the
reflected power on the 291.4 ohm line is 100 watts. 100 watts is being
sourced and delivered to the 50 ohm load.

The voltage reflection coefficient, rho, at the load is (50-291.4)/
(50+291.4)=0.7071. The power reflection coefficient, rho^2, at the
load is 0.5, i.e. half of the power incident upon the load (200w) is
reflected (100w). Since the load is a single-port, these parameters
are consistent with a single-port analysis. In a single-port analysis,
we cannot tell the difference between a virtual reflection coefficient
and a physical reflection coefficient.

The problem comes when we use a single-port analysis on the Z0-match
point. Since the reflected power on the 50 ohm line is zero, a single-
port analysis would yield rho=0.0 and rho^2=0.0 when viewing the Z0-
match from the source side. When we perform a dual-port analysis, we
get different values for rho and rho^2, i.e. we get the complement of
the reflection coefficients at the load which is a characteristic of
any simple Z0-match similar to the above example.

For a dual-port analysis, rho looking into the Z0-match from the
source side is (291.4-50)/(291.4+50)=0.7071 and rho^2 looking into the
Z0-match from the source side is 0.5, the same as at the load. Looking
back into the Z0-match from the load side, the sign of rho is negative
just as it is at the load with rho^2=0.5, the same as at the load.

Since the two analyses yield different values for the reflection
coefficients, which analysis is correct? The answer gives the clue to
the resolution of this discussion.
--
73, Cecil, w5dxp.com

ok, i'm afraid i'm going to have to ask the simple question... if you
blackbox the load and stub and look at just the one connection to it
and that gives you no reflected power... where do you define the
second port, and why?

Logic, immediately, suggests to me, that varying the frequency and
measuring voltage, amperage, and SWR would begin to immediately point
the answer(s.)

Regards,
JS

Reflection coefficient for total re-reflection
 

On 6/22/2011 5:50 PM, John Smith wrote:
On 6/22/2011 3:24 PM, dave wrote:
On Jun 22, 1:49 pm, Cecil wrote:
Let's return to an earlier example and compare a single-port analysis
with a dual-port analysis.

100w
source--50 ohm--+--1/2WL 291.4 ohm--50 ohm load

The 50 ohm Z0-match point is at '+'. The forward power on the 50 ohm
line is 100 watts and the reflected power on the 50 ohm line is zero
watts. The forward power on the 291.4 ohm line is 200 watts and the
reflected power on the 291.4 ohm line is 100 watts. 100 watts is being
sourced and delivered to the 50 ohm load.

The voltage reflection coefficient, rho, at the load is (50-291.4)/
(50+291.4)=0.7071. The power reflection coefficient, rho^2, at the
load is 0.5, i.e. half of the power incident upon the load (200w) is
reflected (100w). Since the load is a single-port, these parameters
are consistent with a single-port analysis. In a single-port analysis,
we cannot tell the difference between a virtual reflection coefficient
and a physical reflection coefficient.

The problem comes when we use a single-port analysis on the Z0-match
point. Since the reflected power on the 50 ohm line is zero, a single-
port analysis would yield rho=0.0 and rho^2=0.0 when viewing the Z0-
match from the source side. When we perform a dual-port analysis, we
get different values for rho and rho^2, i.e. we get the complement of
the reflection coefficients at the load which is a characteristic of
any simple Z0-match similar to the above example.

For a dual-port analysis, rho looking into the Z0-match from the
source side is (291.4-50)/(291.4+50)=0.7071 and rho^2 looking into the
Z0-match from the source side is 0.5, the same as at the load. Looking
back into the Z0-match from the load side, the sign of rho is negative
just as it is at the load with rho^2=0.5, the same as at the load.

Since the two analyses yield different values for the reflection
coefficients, which analysis is correct? The answer gives the clue to
the resolution of this discussion.
--
73, Cecil, w5dxp.com

ok, i'm afraid i'm going to have to ask the simple question... if you
blackbox the load and stub and look at just the one connection to it
and that gives you no reflected power... where do you define the
second port, and why?

Logic, immediately, suggests to me, that varying the frequency and
measuring voltage, amperage, and SWR would begin to immediately point
the answer(s.)

Regards,
JS


A 50 ohm, non-reactive/carbon load would complicate matters, so
naturally, I am assuming that is NOT the case ...

Regards,
JS

Reflection coefficient for total re-reflection
 

On Jun 22, 5:24*pm, dave wrote:
ok, i'm afraid i'm going to have to ask the simple question... if you
blackbox the load and stub and look at just the one connection to it
and that gives you no reflected power... where do you define the
second port, and why?

For the two-port analysis, only the impedance discontinuity at point
'x' is in the black box. One port is the source side of the impedance
discontinuity. The second port is the load side of the impedance
discontinuity. It allows the standard s-parameters to be measured and
the standard s-parameter equations to be used.

On the source side of the impedance discontinuity:

b1 = s11(a1) + s12(a2)

On the load side of the impedance discontinuity:

b2 = s21(a1) + s22(a2)

Those are the normalized voltage equations. Squaring those equations
shows what happens to the component powers including interference
components. Reference:

http://www.sss-mag.com/pdf/an-95-1.pdf
--
73, Cecil, w5dxp.com

Reflection coefficient for total re-reflection
 

On Jun 22, 7:52*pm, John Smith wrote:
A 50 ohm, non-reactive/carbon load would complicate matters, so
naturally, I am assuming that is NOT the case ...

IMO, the resistor load simplifies things as a single-port analysis can
be used on a resistor because there is only one component of power
accepted by the resistor. What would complicate things, IMO, is a 50
ohm antenna feedpoint impedance which is a virtual impedance.
Analyzing the antenna as a multiple port device shows where the
multiple energy components go which is a complication of the present
point I am trying to make about the Z0-match point 'x'.

However, the single-port vs dual-port analysis differences at the
impedance discontinuity 'x' also apply to the analysis at the load
resistor vs an antenna AND at the source where Walt seems to be using
a single-port analysis involving a virtual source impedance which
depends for its very existence upon forward and reflected energy
components flowing in opposite directions at the source impedance
point which necessarily causes interference accompanied by a
redistribution, not a reflection, of energy components.
--
73, Cecil, w5dxp.com

Reflection coefficient for total re-reflection
 

On 6/23/2011 5:59 AM, Cecil Moore wrote:
On Jun 22, 7:52 pm, John wrote:
A 50 ohm, non-reactive/carbon load would complicate matters, so
naturally, I am assuming that is NOT the case ...

IMO, the resistor load simplifies things as a single-port analysis can
be used on a resistor because there is only one component of power
accepted by the resistor. What would complicate things, IMO, is a 50
ohm antenna feedpoint impedance which is a virtual impedance.
Analyzing the antenna as a multiple port device shows where the
multiple energy components go which is a complication of the present
point I am trying to make about the Z0-match point 'x'.

However, the single-port vs dual-port analysis differences at the
impedance discontinuity 'x' also apply to the analysis at the load
resistor vs an antenna AND at the source where Walt seems to be using
a single-port analysis involving a virtual source impedance which
depends for its very existence upon forward and reflected energy
components flowing in opposite directions at the source impedance
point which necessarily causes interference accompanied by a
redistribution, not a reflection, of energy components.
--
73, Cecil, w5dxp.com

But cecil, with a 50 ohm NON-inductive load (not inductive over all
freqs of concern), fed by 50 ohm line, from a 50 ohm source ... would
find a stub a bit of a problem ... indeed, a shorted stub more so --
choice of proper line length and placement of the stub would allow its'
use, on very limited frequencies, with excellent dummy load results, but
the need, ever, escapes me!

Anyway, I just commented to **** old dave off ... :-) I admit it!

Regards,
JS

Reflection coefficient for total re-reflection
 

On Jun 23, 12:43*pm, Cecil Moore wrote:
On Jun 22, 5:24*pm, dave wrote:

ok, i'm afraid i'm going to have to ask the simple question... if you
blackbox the load and stub and look at just the one connection to it
and that gives you no reflected power... where do you define the
second port, and why?

For the two-port analysis, only the impedance discontinuity at point
'x' is in the black box. One port is the source side of the impedance
discontinuity. The second port is the load side of the impedance
discontinuity. It allows the standard s-parameters to be measured and
the standard s-parameter equations to be used.

On the source side of the impedance discontinuity:

b1 = s11(a1) + s12(a2)

On the load side of the impedance discontinuity:

b2 = s21(a1) + s22(a2)

Those are the normalized voltage equations. Squaring those equations
shows what happens to the component powers including interference
components. Reference:

http://www.sss-mag.com/pdf/an-95-1.pdf
--
73, Cecil, w5dxp.com

but what is your second source? you can always represent the second
source in that case in terms of the transmitter output so the second
input can be eliminated giving you a single port model.

Reflection coefficient for total re-reflection
 

On Jun 23, 12:43*pm, Cecil Moore wrote:
On Jun 22, 5:24*pm, dave wrote:

ok, i'm afraid i'm going to have to ask the simple question... if you
blackbox the load and stub and look at just the one connection to it
and that gives you no reflected power... where do you define the
second port, and why?

For the two-port analysis, only the impedance discontinuity at point
'x' is in the black box. One port is the source side of the impedance
discontinuity. The second port is the load side of the impedance
discontinuity. It allows the standard s-parameters to be measured and
the standard s-parameter equations to be used.

On the source side of the impedance discontinuity:

b1 = s11(a1) + s12(a2)

On the load side of the impedance discontinuity:

b2 = s21(a1) + s22(a2)

Those are the normalized voltage equations. Squaring those equations
shows what happens to the component powers including interference
components. Reference:

http://www.sss-mag.com/pdf/an-95-1.pdf
--
73, Cecil, w5dxp.com

p.s. if the separation between the two ports is just the discontinuity
connection 'point' then the voltages must be the same and the currents
are exact opposites only because of the direction convention defined,
there can be no difference measuring on one side of a point to the
other.

Reflection coefficient for total re-reflection
 

On Jun 23, 4:41*pm, dave wrote:
but what is your second source? *you can always represent the second
source in that case in terms of the transmitter output so the second
input can be eliminated giving you a single port model.

a1 is the normalized forward voltage on the 50 ohm feedline from the
source. a2 is the normalized reflected voltage on the 291.4 ohm
feedline from the load. Those are the two sources associated with the
impedance discontinuity inside the black box. a2 could just as easily
be from a second generator instead of a reflection.

When the single-port model is used, if the impedance is not an
impedor, i.e. if the impedance is virtual, the reflection coefficients
are virtual reflection coefficients that do not reflect anything and
do not absorb power. I will repeat an earlier assertion:

Since a virtual impedance is result of the superposition of a forward
wave and a reflected wave, a virtual impedance cannot re-reflect the
reflected wave, i.e. one cannot re-reflect the reflected wave while at
the same time the reflected wave is being used to generate an
impedance. It has to be one or the other. Otherwise, there is a
violation of the conservation of energy principle. RF EM ExH energy
cannot be used simultaneously to generate a virtual impedance while at
the same time being re-reflected.

If the reflected wave is re-reflected, it must be by an impedance
other than the virtual impedance generated by the reflected wave
itself. If the reflected wave is being used to generate a virtual
impedance, it cannot at the same time be being re-reflected.

On Jun 24, 6:27 am, dave wrote:
p.s. if the separation between the two ports is just the discontinuity
connection 'point' then the voltages must be the same and the currents
are exact opposites only because of the direction convention defined,
there can be no difference measuring on one side of a point to the
other.

The total voltage and total current on both sides of the impedance
discontinuity must be equal. But the superposition components do not
have to be equal and, in fact, cannot be equal. In the case of the Z0-
matched example, the forward voltage on the 50 ohm side is 70.7 volts
while the forward voltage on the 291.4 ohm side is 241.4 volts. In
order for the total voltage to be the same, the reflected voltage on
the 291.4 ohm side, which is 170.7 volts, must be subtracted from the
241.4 volts of forward voltage to yield a total of 70.7 volts. For the
Z0-matched example:

Vfwd1 = Vfwd2 - Vref2

70.7v = 241.4v - 170.7v

Please note that the Z0-match point is at a voltage minimum on the
291.4 ohm feedline. 1/4WL toward the load, the total voltage is
241.4+170.7=412.1 volts (in a lossless system).
--
73, Cecil, w5dxp.com

Reflection coefficient for total re-reflection
 

On Jun 24, 1:52*pm, Cecil Moore wrote:
On Jun 23, 4:41*pm, dave wrote:

but what is your second source? *you can always represent the second
source in that case in terms of the transmitter output so the second
input can be eliminated giving you a single port model.

a1 is the normalized forward voltage on the 50 ohm feedline from the
source. a2 is the normalized reflected voltage on the 291.4 ohm
feedline from the load. Those are the two sources associated with the
impedance discontinuity inside the black box. a2 could just as easily
be from a second generator instead of a reflection.

When the single-port model is used, if the impedance is not an
impedor, i.e. if the impedance is virtual, the reflection coefficients
are virtual reflection coefficients that do not reflect anything and
do not absorb power. I will repeat an earlier assertion:

Since a virtual impedance is result of the superposition of a forward
wave and a reflected wave, a virtual impedance cannot re-reflect the
reflected wave, i.e. one cannot re-reflect the reflected wave while at
the same time the reflected wave is being used to generate an
impedance. It has to be one or the other. Otherwise, there is a
violation of the conservation of energy principle. RF EM ExH energy
cannot be used simultaneously to generate a virtual impedance while at
the same time being re-reflected.

If the reflected wave is re-reflected, it must be by an impedance
other than the virtual impedance generated by the reflected wave
itself. If the reflected wave is being used to generate a virtual
impedance, it cannot at the same time be being re-reflected.

On Jun 24, 6:27 am, dave wrote:

p.s. if the separation between the two ports is just the discontinuity
connection 'point' then the voltages must be the same and the currents
are exact opposites only because of the direction convention defined,
there can be no difference measuring on one side of a point to the
other.

The total voltage and total current on both sides of the impedance
discontinuity must be equal. But the superposition components do not
have to be equal and, in fact, cannot be equal. In the case of the Z0-
matched example, the forward voltage on the 50 ohm side is 70.7 volts
while the forward voltage on the 291.4 ohm side is 241.4 volts. In
order for the total voltage to be the same, the reflected voltage on
the 291.4 ohm side, which is 170.7 volts, must be subtracted from the
241.4 volts of forward voltage to yield a total of 70.7 volts. For the
Z0-matched example:

Vfwd1 = Vfwd2 - Vref2

70.7v = 241.4v - 170.7v

Please note that the Z0-match point is at a voltage minimum on the
291.4 ohm feedline. 1/4WL toward the load, the total voltage is
241.4+170.7=412.1 volts (in a lossless system).
--
73, Cecil, w5dxp.com

meaningless hair splitting. if i put a meter on one side of the stub
connection point i will measure the exact same voltage as on the other
side of the connection point. why don't you guys do something
practical instead of arguing about split hairs and things that can't
be measured?