Re: Average, RMS and Power Factor made easy!

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Terry Fritz" <twftesla-at-uswest-dot-net>

Hi Darren,

Ok, I "think" I have it all figured out *:-)

The scope is indeed correct.  A 0 to 5 volt 50% duty cycle square wave has
an RMS value of SQRT(5^2 x 0.5) = 3.535534...  The HP meter is "AC coupled"
(I had to actually get out and read the manual for that one :-)).  When I
put the scope on AC coupling, it too then read 2.5 volts.  However, that is
not correct since there is a DC offset in the signal the HP meter misses.

So the RMS value of the original 0-5 volt 50% duty square wave is indeed
0.7071... VRMS.  Good catch!!

Also a good demonstration of why this stuff is so tricky let alone the
marketing tricks of the audio amp folks ;-))

Cheers,

	Terry


>Hi Darren,
>
>At 10:17 AM 1/19/2001 +1030, you wrote:
>>
>>
>>On Tue, 16 Jan 2001, Tesla list wrote:
>>
>>> Original poster: "Terry Fritz" <twftesla-at-uswest-dot-net>
>>> 
>>> Hi Darren,
>>> 
>>> I was using 0 to 1 volt 50% duty cycle square waves.  The 0.707 thing only
>>> applies to nice sine waves.
>>> 
>>> Cheers,
>>> 
>>> 	Terry
>>> 
>>
>>
>>Normally I'd say that too since many people abuse the 1/sqrt(2) factor for
>>non-sinewaves. However if you do the calculation on this square wave you
>>will indeed get the RMS value to be 0.707 V for 50% duty..
>>
>>Original wave:  0 V   50% of the time,  1 V 50% of the time
>>
>>Squared wave:   0 V^2 50% of the time,  1 V^2 50% of the time
>>
>>Mean of the squared wave: 0.5 V^2  (fairly obvious)
>>
>>I.e. mean squared value 0.5 V^2
>>
>>Therefore RMS value 0.707 V
>>
>>It's just luck that the 1 V peak sinewave has the same RMS value as a 0 V
>>-> 1 V  50% squarewave.
>>
>>
>>Have fun,
>>Darren Freeman
>>
>
>Gosh!  I hooked up the Tek Scope and the HP meter to measure the 0 to 5 volt 
>square wave calibration signal from the scope and got...  Two different 
>answers!!  
>
>The Tek scope gives 3.51 VRMS (suspiciously close to 0.7071 x 5) while the 
>HP meter gives a value of 2.46775 VRMS (the meter loads the signal a bit)  
>So the scope is following the "rules" to get 3.5355... while the HP is 
>finding the equivalent voltage to generate the same power in a resistor 
>2.500...
>
>http://hot-streamer-dot-com/temp/RMS-Duh.jpg
>
>So just when I thought I had the RMS thing all figured out, I am all lost 
>again :-p
>
>Cheers,
>
>	Terry