Tom Bruhns wrote:
Now can you children quit bickering?

Does it really hurt anything to remind everyone that +1 at 180 degrees
equals -1 at zero degrees?
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote in message ...

Does it really hurt anything to remind everyone that +1 at 180 degrees
equals -1 at zero degrees?

No, and I already agreed with that in another posting in this thread.
Perhaps you missed it. But it's just flat wrong to claim that the
negative value for sqrt(x^2) can be correct when you know that the the
original value of x is not negative: x in this case is the magnitude
of a complex number, and that magnitude is real and never negative.

Not only is that wrong, but it's also potentially confusing to lurkers
who may read into it that the only two values of rho which can result
in |rho|=1 are rho=+1 and rho=-1, and that's wrong. Just do it right
and say that your square root = |rho| = +1 and not -1, because it's a
magnitude, and that rho then can be magnitude 1 at ANY phase angle,
not just 0 and 180.

None of which has anything to do with the two of you continuing to
squabble like a couple of young children.

Cheers,
Tom

Tom Bruhns wrote:

Cecil Moore wrote:
Does it really hurt anything to remind everyone that +1 at 180 degrees
equals -1 at zero degrees?

No, and I already agreed with that in another posting in this thread.

When a piece of coax is shorted, we can calculate:

rho = (Z1-Z0)/(Z1+Z0) = (0-50)/(0+50) = -1

After that, we can say it really means +1 at 180 degrees but it is
mathematically consistent in either case.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote:

Tom Bruhns wrote:

Cecil Moore wrote:
Does it really hurt anything to remind everyone that +1 at 180 degrees
equals -1 at zero degrees?

No, and I already agreed with that in another posting in this thread.

When a piece of coax is shorted, we can calculate:

rho = (Z1-Z0)/(Z1+Z0) = (0-50)/(0+50) = -1

After that, we can say it really means +1 at 180 degrees but it is
mathematically consistent in either case.

This has been repeated so frequently of late, without qualification,
that readers may begin to believe that it is true in general.

It is only true for the special case of single frequency sinusoidal
waveforms.

For more complex waveforms (consider square, sawtooth, step, for
example), negation and 180 degree phase shift are not the same
operation.

Since reflection coefficients (at least for lines with approximately
real Z0) work perfectly fine for these more complex waveforms, it
seems unwise to be thinking that negation and 180 degree phase
shift are the same.

For the example above, stick with rho = -1. It will help you solve
more problems that way.

....Keith

wrote:
It is only true for the special case of single frequency sinusoidal
waveforms.

Which is the general case for a key-down ham transmitter.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote:

wrote:
It is only true for the special case of single frequency sinusoidal
waveforms.

Which is the general case for a key-down ham transmitter.

It is indeed the usual case, but limiting your thinking to the
usual case reduces your opportunity for understanding.

Believing too strongly in the usual case will inhibit your
ability to understand when you begin to explore more
general cases. First you will have to unlearn your beliefs.
If you have repeated them to yourself for too long without
understanding their limitations, you can find it very difficult
to let go of them even when they no longer serve.

It is therefore useful to occasionally remind yourself of
the limitations applicable to your assertions.

....Keith