RadioBanter - View Single Post - Rho = (Zload-Zo*)/(Zload+Zo), for complex Zo

September 8th 03, 10:38 AM

wrote in message ...

You can say that a short is always at zero
volts, but that doesn't mean that there isn't a forward and reflected
voltage moving through it.

True. But if the voltage is always 0, then the sum of the forward
and reflected voltage is always 0.

Well, there is no phasor notation in your overly simplistic
example. So we don't see the forward and reflected waves.

Where does circuit theory predict
Vr = 0.5 * 8.062/_ -97.125 = 4.031/_ -97.125?

This isn't circuit theory, it is from the definition of reflection
coefficient: Vr = Vi * rho.

Right, but if you are going to compare...how does circuit
theory give you Vr = 0.5 * 8.062/_ -97.125 = 4.031/_ -97.125?

Circuit theory gives the voltage across the capacitor as
.02 * (0-j200) = 4/_ -90 (current time impedance)
Reflection theory (can I call it that) using classic rho
gives the voltage across the capacitor as Vr + Vi
0.5 + 4.031/_ -97.125 = 4/_ -90
So both provide the same voltage across the capacitor.

Right, but if you are going to compare...how does circuit
theory give you Vr = 0.5 * 8.062/_ -97.125 = 4.031/_ -97.125?

This would convince me quite a bit, if you could derive this
with circuit theory.

Yes, errrr no! I think that power reflection coefficient as normally
defined has no utility with lossy lines since it can not be used
to make any useful predictions.

Not too sure, are we! And when i say we, i mean WE. "Yes, errrr
no!"
is very much like "maybe" and "sometimes", which a lot of people use
for
fear of making an absolute statement which they may have to (God
Forbid!) retract later, as everything you type is recorded FOREVER.

("FOREVER" used for scary effect for those who are terrified to
admit they were WRONG!)

I find, in practice, that the answer to many apparently simple
questions is 'yes and no'. This simply means the question was
incompletely specified.

Or not understood.

If you define power reflection coeffecient as voltage reflection
coefficient squared then it is indeed around 64.

If you define power reflection coefficient as the actual reflected
power divided by the actual incident power (assuming such real
powers exist), then, indeed, it can not be 64 since that would
violate some generally accepted rules about conservation of energy.

So we have quite a contrast between the meaning implied by the name
and the resulting value. So the value IS 64, but the meaning is
NOT 'power reflection coefficient', though the name may be.

Very nice dancing around the point, Keith!

You're more confused than me!

I disagree with you completely, because a Bird or Daiwa meter will
do exactly that, measure Pfwd and Prev, and then with two cross
needles,
you read off the VSWR! That stands for "VOLTAGE stand wave ratio".

Since directional wattmeters simply compute Vf and Vi and square
the scalar, they will show that factor of 64 mentioned earlier.
This strongly suggests they are not doing a good job of computing
real powers.

I'll agree that power meters recitify the signal, and actually get
a DC voltage from the line. In a certain sense, they are more like
RMS voltmeters than power meters.

I'd like to see ANY power RC over 1 for a passive network,

please show us the circuit to build on the bench!

In practice, none of this matters (for RF -- to keep Peter quiet),
since the line losses are sufficiently low that the line impedance
is sufficiently close to 50 ohms, that the Daiwa gives sufficiently
useful information to allow matching.

Despite this, the examples we are using here have far from real Z0
and are interesting to further our understanding.

Or lack of understanding...

I'd like to know the answer to this question too!
If we are talking about only DISSIPATED power, do we have
to say P=Vrms**2/Re(Zo)? Taking only the real part of the Zo?
And if phase doesn't mean anything for power, how can we use a
complex Zo in the denominator?

And if the Pfrd originates in Zo, Prev is loaded by Zo,
then even if Zo is complex, can you still not say:

[rho]**2 = power RC? Because the Zo cancels out anyways
(a ratio)?

Yup, its a puzzler all right.

And the escape?

Ha! As if you knew! Should we say P=Vrms**2/Re(Zo)? Taking
only the real part of the Zo?

-- Stick to incident and reflected voltage (or current) waves for
analysis. They work.

You don't do this in your circuit theory example. How does
circuit
theory give you Vr = 0.5 * 8.062/_ -97.125 = 4.031/_ -97.125?

-- Don't bother trying to compute the incident and reflected powers.
-- They have no meaning in the general case.
-- Only instantaneous and time averaged power really exist and
they CAN be computed in all cases.

You can't compute average incident and reflected powers when
Zo is complex? Your proof or references, please?

-- Forget power reflection coefficient for it only misleads.
-- And never forget that all a 'directional watt' meter does is
compute and respond to Vf and Vr.

...Keith

I'll agree that power meters recitify the signal, and actually
get
a DC voltage from the line. In a certain sense, they are more like
RMS voltmeters than power meters.

I'd like to see ANY power RC over 1 for a passive network,

please show us the circuit to build on the bench!

Slick