On Mar 31, 2:22*pm, Roger Sparks wrote:
On Mon, 31 Mar 2008 10:03:52 -0700
Roger Sparks wrote:
On Sun, 30 Mar 2008 07:43:59 -0700 (PDT)
Keith Dysart wrote:
On Mar 29, 7:18 pm, Roger Sparks wrote:
On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)
Keith Dysart wrote:
On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.
clip
http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf
clip
I doubt that this will satisfy your power location concerns because the spread sheet shows more power being delivered to the resistor than is present in the voltage. *This is because the impedance of the power equation has changed due to the contribution of the current component. Consider that for columns B and C, the same current flows whether the voltage in B is applied or the voltage in C is applied. *This can only happen if the impedance seen by each respective voltage is different. *This is interference at work *
--
73, Roger, W7WKB
After posting previosly, I got to thinking that interference here is wrecking the analysis of Column D. *The traveling wave analysis is correct (Column H). *Only one current is flowing through Rs, and the current is not enough to supply the power suggested in column D. *While it is logical to add the voltages from Column B and Column C, the two voltages are often in opposition so they are not "seen" by Rs. *As a result, we must have a reflection from Rs that I am not taking into account. *
Column B is correct; this being the voltage produced by the source
divided by two.
It is also the forward voltage on the line.
Vrs.source(t) = Vf(t) = 70.7 sin(wt)
Column C is the reflected voltage (not the reflected voltage impressed
across the
source resistor). The reflection coefficient is -1, and the delay is
90 degrees
so the reflected voltage at the generator is
Vr(t) = -1 * Vf(t - 90 degrees)
= - 70.7 sin(wt-90)
= 70.7 sin(wt+90)
But Vr is impressed across the resistor in the opposite direction to
that of
Vrs.source, so the equation for total Vrs is
Vrs.total(t) = Vrs.source(t) - Vr(t)
thus column D should be B31-C31.
Alternatively,
Vrs.reflect(t) = -Vr(t)
and then
Vrs.total(t) = Vrs.source(t) + Vrs.reflect(t)
Column E is correctly computing the instantaneous power from Column D
since
P(t) = V(t) * I(t)
= V(t) * V(t) / R
= V(t) * V(t) / 50 (in this example)
but has the wrong data because of the error in Column D.
Column F is integrating the power to yield either the energy in a
cycle or
the average power per cycle (though presented in unusual units).
I agree G is erroneous and I am not sure what H is computing.
...Keith