Re: [TowerTalk] Reference plane for FCC power limit

[Chuck Counselman <ccc@space.mit.edu>]

At 11:38 AM -0700 9/3/03, Bill Turner wrote:
> On Wed, 3 Sep 2003 13:05:56 -0400, Chuck Counselman W1HIS wrote:
>
> >  The "forward" power at a reference plane/point along a simple TEM
> >  transmission-line such as coaxial cable or parallel-wire line depends
> >  not only on the voltage across and the current through the line at
> >  said plane, but also on an assumed value, e.g., 50 ohms, of the
> >  characteristic impedance Zo of said line.
>
> I've read that statement a half dozen times and it still makes no
> sense.  The Zo determines the ratio of E/I, but for a given power
> level, Zo has no effect on E*I.  (Assuming the theoretical lossless
> line for discussion purposes, of course).  Where am I wrong?


My statement that you quoted (above) referred specifically to 
"forward" power, which I took care to distinguish (in several 
sentences that you did not quote) from _net_ power.

Your statement refers to "E*I", by which I assume you meant the 
time-average, over an RF cycle, of the complex product of E*, the 
complex conjugate of the complex-amplitude E, and the 
complex-amplitude I.  I would have written <E*I>.  The real part of 
<E*I> is what I called _net_ power or _real_ power, and the imaginary 
part of <E*I> is what I called _imaginary_ power or _reactive_ power, 
in the sentences of my message that you did not quote.

I believe that your confusion is about the difference between forward 
power and net power.  Net power equals forward power minus reverse 
power.  In other words, forward power equals net power plus reverse 
power.

If you have a tiny transmitter and a big mismatch, you can have a 
very big forward power, easily more than ten times the net power.

Relatedly, it is essential to distinguish between the forward and the 
reverse waves on a transmission line when speaking of voltage, 
current, and impedance.  The value of Zo does _not_ completely 
determine the ratio of E/I, whether you  take E and I in this formula 
to be real or complex.  You can easily see that Zo does not determine 
the ratio of E/I by considering a lossless line terminated in a 
short-circuit.  At this termination and every integer half-wavelength 
back from it, the ratio of E/I equals zero, completely independent of 
the value of Zo.  The ratio of E/I equals Zo only when there is no 
reflected wave.

-Chuck, W1HIS

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