[Amps] RMS-PEP & 2x8877

[wl fuqua]

I had to fire up my old computer to locate this but here it is from a year 
and a half ago.
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 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
                                                         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               .5                      .01
Square Root of average                  .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 
     .0012
average of 
totals               .5                      .01                     .00015
Square Root of 
average                  .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


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