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the difference between avg and rms?

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liuyonggen_1

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when using "measure" demand avg and rms in hspice ,respectively, to simulate the current with many hamonics, what's difference between the two results?

thanks a lot!
 

The average means simply taking values, summing them, and then dividing the results by the number of total values you consider. Actually, this measure doesn't give any information about the size of values: if they are both positive and negative the average will be similar to zero! Therefore, if you are interested on size of values without regard for positive or negative, a different approach must be used. You can think of taking values, without considering their sign, and then doing the above mentioned average. That can be a kind of measure, but actually it is not the best in terms of statistics. In statistical terms, the mean is done by squaring the considered values, and then by squaring root the average (the above mentioned one) of them.
The average is better called "arithmetic mean", the rms is called "quadratic mean" instead. Their is a relationship between those kind of measures, i.e. QUADRATIC MEAN^2 = ARITHMETIC MEAN^2 + VARIANCE, where VARIANCE is the variance of that particular population of considered values.

N.S.
 

McShamrock said:
The average means simply taking values, summing them, and then dividing the results by the number of total values you consider. Actually, this measure doesn't give any information about the size of values: if they are both positive and negative the average will be similar to zero! Therefore, if you are interested on size of values without regard for positive or negative, a different approach must be used. You can think of taking values, without considering their sign, and then doing the above mentioned average. That can be a kind of measure, but actually it is not the best in terms of statistics. In statistical terms, the mean is done by squaring the considered values, and then by squaring root the average (the above mentioned one) of them.
The average is better called "arithmetic mean", the rms is called "quadratic mean" instead. Their is a relationship between those kind of measures, i.e. QUADRATIC MEAN^2 = ARITHMETIC MEAN^2 + VARIANCE, where VARIANCE is the variance of that particular population of considered values.


thank you very much!
i have another question, when i would like to calculate the power (a constant voltage times a current with many harmonic frequencies), should i use "rms".
that's to say,how to include the power of harmonic frequencies of the non-ideal current.
thanks a lot!
Click to expand...
 

liuyonggen_1,
An RMS voltage, when connected to a resistive load will produce the same amount of power as A DC voltage of the same value.
.
Consider a square wave with a 1V "peak" value, a 0V "valley" value, and a 0.5 (50%) duty cycle. The average value is 0.5. The RMS value is 1/SQRT(2). The power dissipated in a 1 Ohm load = [Pveak^2/R] X Duty Cycle = [1^2/1] X 0.5 = 0.5w. The power generated by the [1/sqrt(2)]RMS Voltage = Vrms^2/R = [1/SQRT(2)^2]/R = .5/1 = 0.5 (Same answer).
.
The RMS value of a voltage consisting of multiple frequencies (not necessarily harmonics) is equal to the Square root of (the sum of squares of the RMS values of each frequency).
.
You can get the frequency components using a spectrum analyzer, or by doing an FFT of the waveform.
Regards,
Kral
 

Kral said:
liuyonggen_1,
An RMS voltage, when connected to a resistive load will produce the same amount of power as A DC voltage of the same value.
.
Consider a square wave with a 1V "peak" value, a 0V "valley" value, and a 0.5 (50%) duty cycle. The average value is 0.5. The RMS value is 1/SQRT(2). The power dissipated in a 1 Ohm load = [Pveak^2/R] X Duty Cycle = [1^2/1] X 0.5 = 0.5w. The power generated by the [1/sqrt(2)]RMS Voltage = Vrms^2/R = [1/SQRT(2)^2]/R = .5/1 = 0.5 (Same answer).
.
The RMS value of a voltage consisting of multiple frequencies (not necessarily harmonics) is equal to the Square root of (the sum of squares of the RMS values of each frequency).
.
You can get the frequency components using a spectrum analyzer, or by doing an FFT of the waveform.
Regards,
Kral
Click to expand...



thanks for your reply.
but i still don't understand how to get "The RMS value is 1/SQRT(2)", could you explain it in detail? thanks !
 

The RMS voltage value is the one, which cause energy dissipation, while the average is the value, which you see, when measure with analog voltmeter.
 

liuyonggen_1,
The hard way is to do an FFT on the square wave and then use the "square root of sum of squares" method. This is not realyy practical because an ideal Fourier transform yields an infinite series.
.
The next most difficult method is to derive it directly from the mathematical definition of RMS. Vrms = ∫(V^2/T )dt where the integral is evaluated from 0 to the T where T is the period. In the case of a square wave, V is a constant = 1.
.
The easy way is to work backwards from the fact that the power (with a 1 Ohm load) = .5W. We know that P = Vrms^2/R. Then Vrms^2 = PR. Vrms = Sqrt(PR) = Sqrt(.5 X 1) = Sqrt(.5) = 1/Sqrt(1/2) = 1/Sqrt(2).
.
Incidentally, I apologize for an error in my earlier post for calculating the RMS value from the squares of the frequency components. There should b a 1/n term under the radical, where n is the number of terms.
Regards,
Kral
 

RMS= 1/sqrt(2) is only valid for pure sinusoidal.
RMS of a square wave is actually equals to the mid point of the square pulse.
 

Hi, kral, thanks for your help!
according to your post, if i would like to get the RMS, i have to know the power dissipation,right?
if we don't know the power, it's difficult to know the RMS,right?

Added after 4 minutes:

sengyee88 said:
RMS= 1/sqrt(2) is only valid for pure sinusoidal.
RMS of a square wave is actually equals to the mid point of the square pulse.
Click to expand...

could you say something about the different between avg and rms?
thanks a lot!
 

liuyonggen_1,
You don't necessarily have to know the power. Using the power was convenient in the square wave example. If you know the exact voltage waveform, you can alway calculate the RMS value using the definition of RMS given in the 2nd paragraph of my previous post.
.
True RMS voltmeters are available that give you the RMS value directly. They have some limitations that must be considered. Many True RMS meters have crest factor limitations. Crest factor is the ratio of Vpeak to Vrms. They also have frequency limitations.
.
Regarding the post from sengyee88, it is true that the RMS value of a sine wave with a peak voltage of 1 is (1/SQRT(2)). However, the value of .5 for the square wave example is not correct. If it were true, then the power dissipated in a 1 Ohm load would be = Vrms^2/R = .5^2/1 = 0.25 Watts, which is incorrect. You can verify this result by generating the square wave, and measuring its value with a True RMS voltmeter, and an ordinary run-of-the-mill average sensing AC voltmeter.
Regards,
Kral
 

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