Low pass filters do work a lot like, but not exactly as Grumpy_Mike sayd.

Cuttoff frequency means the amplitude is -3dB

-3dB means half the power (relative power is measured in 10log) but usally we measure voltage and then -3dB means 0.71 of the amplitude (relative amplitude is measured in 20log)

http://en.wikipedia.org/wiki/Low-pass_filterA single-pole low-pass filter has a rolloff of 6dB/octave which is the same as a rolloff of 20dB/decade.

So 100Hz measured at the output of a simple 10Hz RC lowwpass filter (first order filter) will be 20dB reduced at the output. In voltage -20dB means 1/10th of the amplitude.

For a PWM signal of 100Hz 50-50 duty cycle into a simple 10Hz low-pass filter we will measure a DC output of half the amplitude of the squarewave. On top of this DC there will be 100 Hz and a lot of uneven harmonics like 300Hz, 500Hz, 700Hz and more uneven harmonics at an ever decreasing amplitude.

It is all mathematics. Fourier analyse of a 50-50 square wave of 100 Hz, tells us there will be a 100Hz component of amplitude 4/pi + 300Hz component of 4/(3*pi) amplitude + 500Hz of amplitude 4/(5*pi) etc etc

the 100Hz component will be -20dB so [1/10 of 4/pi] about 0.127 of the amplitude of the square wave

the 300Hz component will be -30dB so [1/30 of 4/(3*pi)] about 0.014 (1.4%) of the square wave amplitude.

the 500Hz component will be -34dB s0 [1/50 of 4/(5*pi)] about 0.005 (0.5%) of the square wave amplitude.

(

http://www.allaboutcircuits.com/vol_2/chpt_7/2.html)Higher order components are lower because fourier analyse says the amplitude is lower combined with the effect of the higher attenuation in the low-pass filter.

So higher order like 7th and 9th harmonics can sometimes be neglected because there amplitude is less than 0.25% of the original square wave amplitude.

When the PWM input signal has not an exact 50-50 duty cycle or varies in duty-cycle then the mathematics really get complicated.

So a long answer for a quick question. I hope my explanation was clear and sorry for the boring mathematics, but electronics aint easy.