On Tue, 08 Jun 2004 13:29:02 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
I'll make it a little easier for you, Cecil. I' ll give you two ways to
determine Vfwd.

OK, here's the example:

100W XMTR---50 ohm line---x----1/2WL 150 ohm line---50 ohm load
PF1=100W-- PF2=133.33W--
--PR1=0W --PR2=33.33W

Way 1. Vfwd = sqrt(Power fwd x Zo)

So Vfwd = sqrt(133.33W x 150ohms) = 141.4 volts (that's what I said)

Way 2. Vfwd = Vsource x sqrt[1/(1- rho^2)]
Now plug rho = 0.5 into the expression for Way 2 and see what comes up.

OK, Vfwd = 70.7V x sqrt[1/0.75] = 81.6 volts (something wrong there)
We know Vfwd has to be 141.4V as calculated above using Ohm's law.

Walt, your two ways don't yield the same value. Perhaps that is the
source of your confusion about what Dr. Best said. Your Way 2 appears
to be a calculation of the voltage delivered to a mismatched load.

Cecil, you've hit the problem on the nose. Until a few posts past I didn't
realize you were using a 150-ohm line. I've been using 50 ohms for the line Zo
terminated with 150 ohms, and you'll find my numbers are correct for that Zo.
Vfwd = 81.6 v is correct for 100 w on a matched 50 ohm line with 3:1 mismatched
load. You'll also get 81.6 using my Way 1.

However, on a 50-ohm line with a 3:1 mismatch and Vfwd = 81.6v (actually it's
81.65 v), the reflected wave is 40.83 v. When the system is matched the phase of
the re-reflected wave is 0° and is also 40.83 v. Therefore, V1 = 81.65 v and V2
= 40.83,v, which means V1 + V2 cannot equal Vfwd. Yet, in the paragraph
preceding Steve's Eq 13 he says that when the phase is 0° Eq. 13 derives
PFtotal. It does not.

Using his Eq 7 V1 yields P1 = 133.33 w, and using his Eq 8 V2 P2 = = 33.33 w.
Using these values of P1 and P2 in his Eq. 12 yields PFtotal = 238 watts, which
is also what we get when plugging V1 and V2 into his Eq 9. We know 238 watts is
incorrect, because it need to be 133.33 w. It makes no sense to plug P1 from Eq
7 into Eq 12 to find PFtotal, because P1 is already PF total.

This clearly proves that Eq 12 is invalid, because Eq 7 and 8 are valid.

I am studying your case with the 150-ohm line, but I haven't yet corralled it.

Walt




re-reflected voltage is also 40.83 v.