I appreciate the input but bear in mind my math/science is mid high school level (work in progress). I'm having great deal of trouble understanding how a signal that is 490Hz has a DC component and this occurs at 0Hz.

When is the signal 0Hz? Are we simply taking a snapshot of the PWM signal when it is high (5V)? If this is the case then the capacitive reactance will be infinite? I feel I'm missing some key concept.

@septillion

I don't understand what a pure sine wave is?

I can understand the confusion. At high school, I only knew what a sinewave was. But probably didn't know what frequency was... I think haha.

Anyway..... you know what a sinusoidal signal is, right? In maths....

y(t) = sin(t) defines ONE particular sinusoidal signal from a family of sinusoidal signals. This one happens to be a 'sine' wave. The wavey pattern of y(t) plotted versus time will repeat itself every (2.pi) seconds. This is known, because....in maths.... the sinusoidal expression is generally written with 1 more parameter... ie y(t) = sin(w.t) where w = 2.pi.f

'w' is called 'angular frequency', units of radians per second. I can't type greek symbols...but 'w' is actually supposed to be like a running-writing 'w'.

Yep.... pi is 3.14159 etc. And 'f' is the 'cyclic frequency'.

So, for y(t) = sin(t)...which is sin( 1.t ), you can see that the angular frequency 'w' is equal to 1 for this particular case. So w = 1. But, w is defined as 2.pi.f.

So w = 2.pi.f = 1

Rearranging the above gives cyclic frequency, f = 1/(2.pi), in units of Hertz, or 'cycles per second'. It means a cyclic frequency of 1 radian per second corresponds to a cyclic frequency of 1/(2.pi) Hertz. A 'cycle' means one single repetition of a portion of the waveform. If measured in units of 'seconds', 1 cycle will take a certain amount of time. And that certain amount of time (labelled capital "T") is called a 'period', or 'the period'.

The relation between the period T and the cyclic frequency f is simple..... it is: f = 1/T, or T = 1/f.

So, when angular frequency w (for this particular case) is equal to 1 radian per second, then we can easily figure out that the corresponding cyclic frequency f is equal to 1/(2.pi) Hertz. And the period T is 1/f, which is 2.pi seconds.

So, if you have a 50 Hertz sinusoidal signal that happens to be a 'sine' wave, then you could mathetically write it as y(t) = sin(2.pi.50.t)

And if you want to make this sine wave larger....just put a multiplying factor on the front of it... like...

y(t) = 3sin(2.pi.50.t), or 3sin(100.pi.t) .... or 3sin(314.159t)

One more thing. The 'sine' wave has a value of zero at time t = 0. And, as time increases, the 'sine' wave value gets larger and larger and will eventually reach a value of '1', before dropping back to zero again.... just google 'sine' wave, and you'll see. If you don't want a 'sine' wave, then you can always modify it.... by adding an offset to it.... like

y(t) = sin(w.t - 2.pi.b) ....'b' is a fractional number....and you could limit 'b' to a value between -1 and +1. For example... if 'b' is one-quarter, ie. b = 0.25, then

y(t) = sin( w.t - pi/2 )

The above is just some starting details for you about sinusoidal signals. Work towards understanding that first.