RMS Voltage of triangle wave

1. Oct 17, 2006

Nothing000

What the RMS voltage is of a triangle wave?

I am supposed to derive it. I am coming up with $$\frac{2}{T}\sqrt{V_{m}$$

Last edited: Oct 17, 2006
2. Oct 17, 2006

Nothing000

Here is the derivation I did. Where it says $$\{n | n \in Z \}$$ I meant to say "for some integer n", I was just trying to be fancy, but I guess that's the incorrect notation.

I am attempting to upload a better image. Hopefully this is better:

Attached Files:

• Vrms Derivation.gif
File size:
70.8 KB
Views:
531
Last edited: Oct 17, 2006
3. Oct 17, 2006

Nothing000

Crap, I didn't square $$v(t)$$ in the radical.
Damn it!

Does anyone see anything else wrong?

4. Oct 17, 2006

Integral

Staff Emeritus
I am uncomfortable with your definition of the triangle waveform. I would define the function and express your limits of integration in terms of the period. To be more general you may need to avoid using 0 as one extreme of the waveform.

So for example the first part would be :
$$v = \frac {4(v_m - v_0)t} T + v_0$$
With
$$0 \leq t \leq \frac T 4$$

I based this on the coordindate pair
$$(v_0, 0) ; (v_m , \frac T 4)$$

So this waveform would have miminums of $v_0$ at 0 , $\frac T 2$ and $T$

and maxs of $v_m$ at $\frac T 4$ and $\frac {3T} 4$

5. Oct 17, 2006

Nothing000

When you say definition of triangle waveform are you refering to the definition of v(t) at the top of the page?
Because this information is given to us just like that, except it says "for integer n" instead of the notation $$\{n | n \in Z \}$$ which I incorectly used.

6. Oct 17, 2006

Integral

Staff Emeritus
Ok, so that is a definition of a specific triangle wave, under that definiton, isn't T=1 ?

Given that that the problem is simple, square each part of the function and integrate.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?