# Sawtooth voltage

1. May 28, 2004

### oooride

I'm confused on how to approach this question..

Show that the rms value for the sawtooth voltage shown in Figure 33.54 is Delta V_max / sqrt 3.

All Figure 33.54 shows is a graph of Delta V vs time with amplitudes of +Delta V_max and -Delta V_max with the sawtooth wave going between the amplitudes three times, starting at -Delta V_max and ending at -Delta V_max.

How would I go about starting this question? The only thing I can think of using to start is, Delta V_rms = Delta V_max / sqrt 2 = .707 * Delta V_max. I have no idea how or why I should use this though.. I'm completely stuck..

Any help is greatly appreciated.

2. May 29, 2004

### AKG

$$V_{rms} = \sqrt{\frac{1}{T}\int_0^T [V(t)]^2 dt$$

I believe this is the equation to find the rms (root mean squared) of anything, so you can replace V with f, I, or anything to find rms-frequency, -current, etc. If you look at the equation, it should be clear why it's called root mean squared. T is the period, V(t) is the voltage at t. A sawtooth voltage will just increase linearly over one period, something like V(t) = mt + b (your basic linear relationship). You can easily square this [ V(t) = (mt + b)^2 = (m^2)t^2 + (2mb)t + b^2 ], and integrate from 0 to T, and then divide by T, then take the root. That should be your rms Voltage. I'm pretty sure, at least...

3. May 30, 2004

### turin

This is indeed correct, with one generalization that is probably not important here since there should be a clearly recognizable period, T.

4. Jun 5, 2004

### Gza

Oh man, I remember having to find that rms value in my lab class a few weeks ago. Not fun.