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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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OK enough...<br>
<br>
RMS has one meaning, definition or procedure if you want to call it
that.<br>
<br>
R take square <b>root <br>
</b><x-tab> </x-tab>of<br>
M the average (<b>mean</b>) <br>
<x-tab> </x-tab>of<br>
S the <b>square</b> of a number of data points<br>
<br>
It may look complicated as an equation or an integral
expression (calculus)<br>
but it is SIMPLE!!!!<br>
<br>
For example...<br>
<br>
<br>
Take one cycle of a 1 volt sine wave and divide into at least 8 equally
spaced points starting at zero degrees.<br>
Calculate instantaneous voltage, voltage squared and power into 50 ohms
load at each point.<br>
Do not use 360 degrees because it is the same point as 0 degrees. You may
do this for any number<br>
of full cycles and you may want to do this on a spread sheet for
each degree (ie 360 points) or what ever.<br>
<br>
Phase
<x-tab> </x-tab>Voltage<x-tab> </x-tab><x-tab> </x-tab>Voltage
Squared<x-tab> </x-tab>Power into 50 ohms<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>Watts<br>
0<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>0<br>
45<x-tab> </x-tab><x-tab> </x-tab>.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<br>
90<x-tab> </x-tab><x-tab> </x-tab>1<x-tab> </x-tab><x-tab> </x-tab>1<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.02<br>
135<x-tab> </x-tab><x-tab> </x-tab>.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<br>
180<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><br>
225<x-tab> </x-tab><x-tab> </x-tab>-.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<br>
270<x-tab> </x-tab><x-tab> </x-tab>-1<x-tab> </x-tab><x-tab> </x-tab>1<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.02<br>
335<x-tab> </x-tab><x-tab> </x-tab>-.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<br>
<br>
totals<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab>4<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.08<br>
average of
totals<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><b>.01<br>
</b>Square Root of
average
<x-tab> </x-tab><b><u>.7071<br>
<br>
<br>
</u></b>The RMS value of the signal is .7071 times the peak (1
Volt)= .7071 volts GEE look at above <b><u>bold and
underlined</u></b>.<br>
<br>
What is the power of this signal into a 50 ohm load?<br>
.7071 volts squared divided by 50 ohms= .01 watts Look
again above at the average power <b>bold</b>.<br>
<br>
It is all very <b>consistent</b> with calculations using RMS voltage or
Current and resistance and power.<br>
<br>
Now what happens when we take RMS of the Power??<br>
<br>
<br>
Phase
<x-tab> </x-tab>Voltage<x-tab> </x-tab><x-tab> </x-tab>Voltage
Squared<x-tab> </x-tab>Power into 50
ohms<x-tab> </x-tab>Power
Squared<br>
<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>Watts<br>
0<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>0<br>
45<x-tab> </x-tab><x-tab> </x-tab>.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0001<br>
90<x-tab> </x-tab><x-tab> </x-tab>1<x-tab> </x-tab><x-tab> </x-tab>1<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.02<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0004<br>
135<x-tab> </x-tab><x-tab> </x-tab>.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0001<br>
180<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0<br>
225<x-tab> </x-tab><x-tab> </x-tab>-.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0001<br>
270<x-tab> </x-tab><x-tab> </x-tab>-1<x-tab> </x-tab><x-tab> </x-tab>1<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.02<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0004<br>
335<x-tab> </x-tab><x-tab> </x-tab>-.7071<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0001<br>
totals<x-tab> </x-tab><x-tab> </x-tab>0<x-tab> </x-tab><x-tab> </x-tab>4<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.08<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.0012<br>
average of
totals<x-tab> </x-tab><x-tab> </x-tab>.5<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.01<b><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab>.00015<br>
</b>Square Root of
average
<x-tab> </x-tab>.7071<x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><x-tab> </x-tab><b><u>0.01225</u>
RMS power ?????<br>
<br>
OK above is your <u>RMS power</u> for what ever good it
is....<br>
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.<br>
73<br>
Bill wa4lav<br>
<br>
<br>
<br>
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<tr><td width=79></td></tr>
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