[Amps] RMS-PEP & 2x8877

[Bill Fuqua]

When this came back the columns were messed up. I hope this is better.

OK enough...
RMS has one meaning, definition or procedure if you want to call it that.
R take square root
of
M the average (mean)
of
S the square of a number of data points
It may look complicated as an equation or an integral expression (calculus)
but it is SIMPLE!!!!
For example...

Take one cycle of a 1 volt peak sine wave and divide into at least 8 
equally spaced points starting at zero degrees.
Calculate instantaneous voltage, voltage squared and power into 50 ohms 
load at each point.
Do not use 360 degrees because it is the same point as 0 degrees. You may 
do this for any number
of full cycles and you may want to do this on a spread sheet for each 
degree (ie 360 points) or what ever.
Phase         Voltage           Voltage Squared           Power into 50 ohms
Degrees                                                                Watts
0                     0                        0 
       0
45                  .7071                   .5 
   .01
90                   1                         1 
      .02
135                 .7071                  .5 
   .01
180                  0                        0 
      0
225                 -.7071                 .5 
   .01
270                  -1                       1 
      .02
335                 -.7071 
.                5                                 .01
totals                    0                    4 
      .08

average of 
totals     0                   .5                                 .01

Square Root of average of
the voltage squared                   .7071

The RMS value of the signal is .7071 times the peak (1 Volt)= .7071 volts 
GEE look at above bold and underlined.
What is the power of this signal into a 50 ohm load?
.7071 volts squared divided by 50 ohms= .01 watts Look again above at the 
average power bold.
It is all very consistent with calculations using RMS voltage or Current 
and resistance and power.
Now what happens when we take RMS of the Power??

Phase       Voltage      Voltage Squared         Power into 50 
ohms            Power Squared
										Watts
0                 0                         0                            0 
                                         0
45               .7071                  .5                           .01 
                                     .0001
90                1                        1                           .02 
                                       .0004
135              .7071                 .5                           .01 
                                    .0001
180               0                       0                             0 
                                        0
225               -.7071               .5                            .01 
                                    .0001
270               -1                       1                           .02 
                                       .0004
335               -.7071                .5                           .01 
                                     .0001
totals               0                     4                            .08 
                                        .001

average of
totals              0                      .5                           .01 
                                        .00015

Square Root
of 
average        0                     .7071 
                                  0.01225                 RMS power ?????
OK above is your RMS power for what ever good it is....
And it does not relate to any of the other numbers you may use such as 
voltage, current. resistance or power. But does give you 22.5% bigger 
number in this example.
73
Bill wa4lav