hamonics and sidebands in dc-dc converter
First of all, an unmodulated switching waveform is rectangular in nature and, as per any basic analysis of a square wave, it contains harmonics of the fundamental switching frequency: -



So, a square wave contains a series of sinewave harmonics starting at the fundamental switching frequency and extending, theoretically to infinity. Next, look at the top picture in the image below. This is the general case for a rectangular wave with the duty cycle as a variable: -



It tells us that harmonics can arise at all integer multiples of the fundamental switching frequency. As a side note, the special symmetrical case of a square wave happens to only contain odd numbered harmonics.

The question shows a sinusoidal base frequency altering (modulating) the PWM duty cycle in order to generate a PWM sinewave. This will produce sidebands either side of every generated harmonic. The distance in Hz from the centre of the harmonic to the centre of either sideband is twice the modulating frequency.

Analysing the sidebands is the real tricky bit to understand; you have to start by considering the formula for the n\$_{th}\$ harmonic: - 

a\$_n\$ is proportional to \$\dfrac{2}{n} sin(n\pi d)\$ 

And, if d (the duty cycle) approaches zero (or unity) the "sin" term becomes zero i.e. the harmonics greatly reduces in amplitude. This happens at twice the modulating frequency i.e. all the harmonics are amplitude modulated at twice the frequency of the modulating waveform.

Because there are DC terms involved, this boils down to exactly the same analysis as a regular AM broadcast: -



The wiki link above shows the full math behind AM and sidebands but it basically boils down to any one of the following trig identities: -



So, sum and difference frequencies are produced and it is these sum and difference frequencies that create the sidebands.



New section that hopefully demonstrates that a simple PWM circuit (based around an AD8605 op-amp, a 100 kHz triangle wave and a 1 kHz sine wave) produces sidebands at +/- 2 kHz from the harmonics of the basic PWM switching waveform: -



There are wider sidebands too and these are also at intervals of +/- 2 kHz. These are most likely due to my circuit being an imperfect modulator. So, using a much faster op-amp and, band pass filtering the resultant PWM at 100 kHz, it can be clearly seen that it is a classic case of amplitude modulation at twice the modulation frequency: -