RMS and average value of a sawtooth wave

[JeanTech]

Hi there

How do I calculate the RMS and average value of a sawtooth wave with a period of 1 second and a maximum and minimum value of 0.5 V and -1.5 V respectively?

Thanks in advance
JeanTech

 

[Ratchit]

Hi there

How do I calculate the RMS and average value of a sawtooth wave with a period of 1 second and a maximum and minimum value of 0.5 V and -1.5 V respectively?

Thanks in advance
JeanTech

What is the definition of those two quantities? If you know that, did you try to calculate them?

Ratch

 

[JeanTech]

Sorry I forgot to mention, it is the RMS voltage and average voltage.

I calculated RMS as the sqrt(1/T*(integral of sawtooth wave from o to T)^2). The average value was calculated as 1/T*(integral of sawtooth wave from o to T).

Is this calculation correct?

Thanks
JeanTech

 

[Ratchit]

Sorry I forgot to mention, it is the RMS voltage and average voltage.

I calculated RMS as the sqrt(1/T*(integral of sawtooth wave from o to T)^2). The average value was calculated as 1/T*(integral of sawtooth wave from o to T).

Is this calculation correct?

Thanks
JeanTech

The method is correct, but without knowing the equation of the sawtooth you used, and the results you obtained, I cannot determine if your calculations are correct.

Ratch

 

[MrAl]

Hi,

If the period of the sawtooth (triangle) wave takes the whole period then a simplification is:
Rms=sqrt(b^2+a*b+(a^2)/3)

where
'a' is the peak to peak amplitude of the triangular part alone, and
'b' is the level of the minimum part of the wave.

So for a wave that goes from -1.5v to +0.5v then a=2 and b=-1.5.

This formula works for waves that are basically triangular like a sawtooth but may also have a DC offset.

As another example, if the wave went from 1v to 1.5v then a=0.5 and b=1.

The question of how to calculate the average value however brings up a question of how the wave is going to be used in the application. For many purposes the average is just the average of the wave over time regardless of polarity, but for some purposes the average is the average of the absolute value of the wave over time. The main deciding factor is how the energy is going to be used in the application.