Circuit to remove dc and extract AC signal

I built a very durable steam vapouriser using a standard electric kettle, and a way of supplying it with a reduced power. This has the advantage that the vapouriser is cheap, readily available, is run well below its normal power rating so should last forever, and can be plugged in directly at first to heat the water quickly, before going to reduced power for long term steam generation.

Being an engineer, I happened to have an auto-transformer to hand. However, it is easy enough to buy fairly cheaply fixed transformers, or variable power controllers for heaters like this. Don't use a conventional lighting controller triac dimmer, it won't have the current capacity, unless you use a very low power kettle like a tiny 'travel kettle'. Choosing the amount of reduced power going to the kettle gives you a choice of the rate of steam production.

If you are happy with wiring mains components yourself and doing it safely, then wiring a light bulb or a motor-run capacitor in series will reduce power to the kettle.

To complement Andy aka...

The quote in question.

sinusoidal PWM output's instantaneous average (over one time period of carrier wave) is same as the fundamental frequency component in the signal

Take a 10V pk sine wave and take a PWM signal that toggles between +15V and -15V.

At zero degrees (or the equivalent timebase): a sinwave will have an amplitude of ... 0. Now take an associated PWM that would be used to synthesis a sinewave at this point in time. At this point the PWM duty will be 50% -> 0V

Now take 90deg (or the equivalent timebase) the sinewave would be at its peak, a peak of +10V. At this instance, the PWM (concidering one period) duty would be 83.333...% and this would have an average of +10V