On Tue, 20 Dec 2005 18:28:31 GMT, Cecil Moore wrote:

Ron J wrote:
I was curious. If a matching network was designed to make the SWR at a
band of frequency less than 1.4 to 1, then what would happen if I
inserted a power sensor on the line with a rated SWR of 1.05 to 1 at
this frequency band?

Would that make my overall system SWR 1.4 + .05 = 1.45 to 1?

SWRs, like power, cannot be superposed.

Because the worse case SWR is often the concern, it can in fact be
found, not by addition but by multiplication.

In the case given, the worse case SWR = 1.4 * 1.05 = 1.47:1, an
insignificant change from the original due to the insertion of, what I
believe is an in-line sensor.

Of course, it is equally likely that the insertion of the power sensor
will -improve- the SWR.

Consider both SWRs in terms of their equivalent reflection
coefficients, rho.

swr - 1
rho = -----------
swr + 1

Letting swr = 1.4, rho = 0.1667

With swr = 1.05, rho = 0.0244

Worse case = 0.1667 + 0.0244 = 0.1919

Converting back to SWR = 1.473, as given above.

Best case = 0.1667 - 0.0244 = 0.1423

Converting back to SWR = 1.331

Without Gamma, which has phase info, all we know are the error limits,
the SWR is somewhere between 1.331 and 1.473.

Note: If we could make the swr of the sensor = 1.4 and put it in the
right location in the line, the net swr = 1:1. This is commonly
called a -matching network-. [g]