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Old January 27th 08, 09:45 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Suzy wrote:
"JOHN PASSANEAU" wrote in message
...
There is no such thing as DC! How's that you say? You have to turn it on
sometime and someday you may turn it off. There for, DC is just very low
frequency AC.


John Passaneau W3JXP


That's false reasoning OM! Alternating current is not the same as
discontinuous current. In the example you provide, a DC supply is either off
or on; it does not reverse polarity! You do not make AC by switching on and
off DC, even at 50 Hz (or your 60 Hz)


But through the techniques of linear circuit analysis, we can split the
pulsed DC into two components, a pure steady DC component and a
symmetrical AC component. We can do two separate analyses with the two
(AC and DC) excitations, and sum the results. The answer will be exactly
the same as if we had done the calculations directly. One can then
reasonably claim that the switched DC is the sum of an AC waveform and a
pure DC component.

Roy Lewallen, W7EL
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Old January 28th 08, 12:26 AM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Arrgh! I did it again!

Roy Lewallen wrote:

Ah is a unit of charge, not energy. The battery, making the simplifying
(and invalid) assumption of constant voltage during discharge, contains
2.16 Mj of energy.


That's 2.16 MJ, not Mj.

It'll sink in eventually . . .I hope.

Roy Lewallen, W7EL
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Old January 28th 08, 08:05 AM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Roy Lewallen wrote:
"Ah is a unit of charge, not energy."

The most common 12-volt battery is the lead-acid storage battery used in
automobiles. It should not be allowed to become completely discharged
nor to remain less than fully charged for a long time. The battery`s
capacity is rated in amperes x hours. The discharge rate is assumed to
be 8 hours. Slower discharges can be supported for more ampere-hours and
faster discharges likely won`t meet the rated ampere-hour product.

A 50 Ah battery would be expected to deliver about 6.25 A for a period
of 8 hours provided its electrolyte does not rise to more than 110
degrees F. 2-volt cells can be discharged down to 1.75 volts per cell
or a voltage of 10.5 volts for the 6 cells of a 12-volt battery.

Best regards, Richard Harrison, KB5WZI

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Old January 28th 08, 08:31 AM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Roy Lewallen wrote:
"So the rate at which a transmission line transfers energy depends on
its length?"

No, it depends on the power fed into the line.

Storage in the line depends on its length, plus the incident and
reflected energies per unit length of the line. Velocity is fixed by
construction of the line so a slow velocity factor allows more energy
storage as the source energy output is constant and independent of the
line`s velocity factor.

Best regards, Richard Harrison, KB5WZI

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Old January 28th 08, 01:31 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

On Jan 27, 9:45*am, Cecil Moore wrote:
Keith Dysart wrote:
Not at all. The equations don't just stop working at 0 frequency.


As a matter of fact, EM waves cannot exist without
photons. There is zero wave activity at DC. Therefore,
the forward power and reflected power is zero at DC
steady-state.


And yet all the circuit theory derivations of reflection
coefficient, power, voltage and current distributions
work just fine for DC (or, if you prefer, low rate pulses).

Digital designers use exactly that for solving real world
problems. They do not refuse to solve problems when the
conditions approach DC. The equations all work.

You really should try to stop thinking about photons
for just a short while.


Yep, you guys would like to sweep the technical knowledge
from the field of optical physics and quantum electro-
dynamics under the rug. One wonders why.


An intriguing accusation. Transmission lines can be
understood well, and real world problems solved without
reference to photons and EM waves. Just use the well
known circuit theory based equations. And they extend
all the way to DC.

For those who like EM waves and photons... Why do you
want to limit yourselves? Why won't you use the circuit
theory bases equations to solve problems for which they
work? Just because EM waves and photons do not?

Think of it as a long pulse. That should satisfy your
need to have 'waves'.


No, only photons will satisfy the definition of EM
waves. There are no photons. There are no waves. There
are no forward and reflected powers. There are no
changing E-fields or H-fields. There is not even any
movement of electrons associated with the source
voltage.


May be true. But why do you want to use that as an excuse
not to solve solveable problems?

...Keith


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Old January 28th 08, 01:45 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

On Jan 27, 10:26*am, Cecil Moore wrote:
Keith Dysart wrote:
When the generator is matched to the line so that
the reflected wave does not encounter an impedance
discontinuity when it arrives back at the generator
(and therefore is not reflected), ...


On the contrary, it is redistributed back toward
the load in the process of destructive interference
and becomes constructive interference associated
with the forward wave. Whether you call that a
reflection or not, the fact that the forward
power equals the source power plus the reflected
power tells us that reflected power being dissipated
in the source would violate the conservation of
energy principle.


Unfortunately, this is quite wrong. And I continue to
be surprised that you argue that there is a reflection
where there is not an impedance discontinuity.

Some parts of the rest of your post are correct by
coincidence, but since the underlying premise of
reflections where there is no discontinuity is
incorrect, I have snipped it.

But this debate has been had before. You do not want
to understand how the output impedance of a generator
affects a returning signal. I have offerred references
and you have refused to look. I have offerred spice
simulations, and you have refused to look. When the
discussion moves to simpler generators so that the
behaviour can be studied, you will declare them
uninteresting because they do not represent "real
ham transmitters". You will make jokes about 10 cent
resistors, not realizing that is how real test
equipment prevents re-reflection. (How well would
a TDR work, if any substantial amount of the return
was reflected?)

When you decide that you do not want to argue that
reflections occur where there is no impedance
discontinuity, and are willing to study output
immpedance, the learning can begin.

...Keith
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Old January 28th 08, 04:56 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Keith Dysart wrote:
Transmission lines can be
understood well, and real world problems solved without
reference to photons and EM waves.


If that were true, we would not be having this
argument. The real world problem is - where does
the reflected EM energy go? Since you have not "solved
that real world problem", your methods are suspect.

OTOH, optical physicists solved that same problem
long before any of us were born.

Why won't you use the circuit
theory bases equations to solve problems for which they
work?


The main reason not to use your methods is that you use
them to arrive at wrong concepts. EM waves cannot exist
without energy. If there exists no EM wave energy, there
are no EM waves. If EM waves exist, they are necessarily
associated with energy and momentum, both of which must
be conserved. The amount of that energy flowing past a
measurement point/plane in a unit-time is the power
(density) associated with the reflected wave. Even the
energy and momentum of a single photon can be calculated.

Any length of transmission line with reflections contains
exactly the amount of energy necessary to support the
forward and reflected waves. That amount of energy exists
in the transmission line and is not delivered to the load
during steady-state.

Because your model doesn't tell you where the reflected
energy goes, you assume there is zero energy in reflected
waves. Again, I challenge you to use your fingers to
replace the reflected power circulator load in a system
with a KW source driving an open-circuit. That shock therapy
will, no doubt, change your mind about the non-existence of
reflected power.
--
73, Cecil http://www.w5dxp.com
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Old January 28th 08, 05:30 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Keith Dysart wrote:
Unfortunately, this is quite wrong. And I continue to
be surprised that you argue that there is a reflection
where there is not an impedance discontinuity.


Since an absence of reflections violates the conservation
of energy principle, there is something wrong with your
assertion and your earlier example was proved to contain
a contradiction.

Psource = Pfor - Pref = Pload

Pfor = Psource + Pref = Pload + Pref

Those equations are true only if reflected energy
does not flow back into the source. I suspect that,
contrary to your assertions, the actual real-world
source presents an infinite impedance to reflected
waves.

When you decide that you do not want to argue that
reflections occur where there is no impedance
discontinuity, ...


You simply fail to recognize the impedance
discontinuity.

Please perform the following experiment to prove
there is no impedance discontinuity and no distortion
and get back to us.

zero ohm
TV RCVR--+--TV source--+--Z0 stub----------open
|
Z0 source impedance resistor
|
GND

The source output goes into the stub. Reflections
occur at the open end of the stub and flow back
through the zero impedance source to be dissipated
in the Z0 source resistor and displayed without
distortion on the TV RCVR. If what you say is true,
it should be duck soup for you to prove.
--
73, Cecil http://www.w5dxp.com
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Old January 28th 08, 06:45 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Keith Dysert wrote:
"(How well would a TDR worh, if any substantial amount of return was
reflected?)"

A properly terminated line does not make reflections. I would imagine
multiple reflections on an oscilloscope produce the same smear as as
they do on TV.

TDR is suggested for monitoring bridge integrity and performance. Where
was it when we needed it? TDRs are likely cheaper than replacing all the
questionable bridges.

TDR is used to determine the characteristics of electrical lines by
observing reflected waveforms.Tektronnix is a leader with its "I
Connect" software. Roy can likely describe it. Agilent suggests TDR is
the most general approach to evaluating the time domain response of any
electromagnetic system is to solve Maxwell`s equations in the time
domain. The foregoing is courtesy of Wikipedia. The incoherent structure
of the last sentence was theirs too.

Best regards, Richard Harrison, KB5WZI

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Old January 28th 08, 11:18 PM posted to rec.radio.amateur.antenna
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Default Derivation of Reflection Coefficient vs SWR

Roger Sparks wrote:
"It is not too hard to use the concept of traveling waves to derive the
familiar reflection coefficient to SWR relationship."

Yes. Terman has done it for us in his 1955 opus. He just uses the letter
S to represent SWR.

On page 86:
"The voltage and current of the incident wave at the load must satisfy
Eq. (4-8) =
Eprime / Iprime = Zo."

And at the top of page 86:
"The reflected wave.----is identical with the incident wave except that
it is traveling toward the generator. Eq. (4-11) =
Edouble prime / Idouble prime = -Zo."

"The load voltage is the sum of the voltages of the incident and
reflected waves at the load,....
The load current is the sum of the currents of the incident and
reflected waves at the load,....
The vector ratio EL / IL must equal the load impedance ZL."

"The vector ratio E2 / E1 of the voltage of the reflected wave to the
voltage of the incident wave at the load is termed the reflection
coefficient of the load.

Reflection coefficient = rho = E2/E1 =
(ZL/Zo)-1 / (ZL/Zo)+1."

And on page 97:
"Standing-wave ratio = S = Emax/Emin, Eq.(4-20)
And: S= [E1] + [E2] / [E1] - [E2], Eq. (4-21)"

The standing-wave ratio S is one means of expressing the magnitude of
the reflection coefficient; the exact relation between the two is S =
1+[rho] / 1- [rho]

or [rho] = S-1 / S +1
This relationship is illustrated graphically in Fig. 4-9.

Best regards, Richard Harrrison, KB5WZI

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