# DC to AC conversion and filter wave shaping

My question refers to checking concepts.It's a scientific one,so I am not looking for a way to make a DC to AC power supply for a device because its charger broke or something similar.

The goal is to convert the output of an astable multivibrator into a sine wave that can drive a transformer in a decent way.

The way to do this:connect two low pass filters one to another.One will have a square wave at the input and convert it into a triangle wave.The other will receive it and convert into a sine wave.

simulate this circuit – Schematic created using CircuitLab

I know that for each filter to work as an integrator,the time period of the incoming wave has to be smaller or equal to the RC time constant of the filter.I will calculate these accordingly.This is not the issue.

The problem starts with the square wave.I'm not sure if it should go below 0 or if it's ok to let it vary between 0 and +5V for example.The same is available to the triangle wave.I'm not sure if it will produce the desired sine wave if it won't oscillate between a negative and a positive voltage.

The question is:What kind of square and triangle waves should be generated so that a circuit such as the one described by the schematic will work as explained?Will a square wave (from the multivibrator) input which oscillates between 0 and +V make it work or should it shift from -V to +V?

The problem starts with the square wave.I'm not sure if it should go below 0 or if it's ok to let it vary between 0 and +5V for example.

Obviously, a DC offset in the input wave doesn't matter to the output – it won't pass through the transformer.

So you can use pretty much any periodic function. Since you said yours is a scientific question:

make yourself a plot of the spectrum of the periodic function you apply to the input (spectrum = Fourier transform!). You know that all periodic function have line spectra. The zero-mean square wave has lines in its spectrum spaced every 1/period – that's pretty handy, because that means that you can put your low pass somewhere betweeen 1/period and 2/period, which implies it can have pretty relaxed transition between pass- and stopband.

The triangle is just a square wave convoluted with itself. That's awesome – because convolution in time domain is multiplication in frequency domain, which means that the triangle wave's spectrum is just the squared spectrum of the square wave, so the same filter can be used. However, for practical reasons: It's a lot harder to produce a good triangle wave than a good square wave, and especially if you consider switching losses, fully switched semiconductors are usually much more efficient.

Also, from a practical point of view: your transformer already is an inductive device – and you might very well get away by adding a capacitor in series instead of having RC lowpasses on the input, which would give you a resonant circuit around the frequency you feed in, with (virtually) no power lost, solving the DC offset problems at the same time.

• No the DC component won't pass through, but it may saturate the transformer destroying its performance. – Brian Drummond Aug 14 '16 at 10:25
• @Brian true! Yet you barely find someone inverting the input to his DC/AC converter first – simply because the generation of the inverse voltage would pretty much need the same field energy in a separate inductance as you'd need the transformer to withstand additionally. – Marcus Müller Aug 14 '16 at 10:43
• Also, I tried to hint at that in my last sentence; @BrianDrummond if you have a nice way of explaining magnetics non-linearity, please do add it to my answer (or as an answer of your own; I'd definitely appreciate (read: upvote) that). – Marcus Müller Aug 14 '16 at 10:44
• Note also that if you feed in a signal with a spectral component at $f=0$ and get out one without... well, the energy has to go somewhere :) – Marcus Müller Aug 14 '16 at 10:45
• About the alternative:I think I see how that works.I can add a transistor that will be switched on and off and the LC will oscillate when the multivibrator output is off.I can't really see it working without the BJT. – Daniel Tork Aug 14 '16 at 13:21

If you filter a square wave it will become triangular if its amplitude is much smaller than the square at the input. Not good if your goal is to convert power. Then further filtering the triangle will round it out, mixing it look more like a sine, but not completely. In a mathematical sense the difference in each step is exactly the same.