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

wrote:

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.

Can you give me an example of a key-down CW transmitter that is not
single frequency sinusoidal waveforms?
--
73, Cecil http://www.qsl.net/w5dxp



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