Tough maths problem for power convertor

[bodger]

You guys seem to know a bit about maths so I thought I'd ask you for some help with a problem with a power convertor I am designing.

As a one liner the question is: -

What periodic waveform when subtracted from its 180 degree phase shifted self produces a sinewave. The initial waveform has to have the lowest rms value possible.

In effect how can I get a sinewave with only a small dc offset - the signal is push/pulled into a transformer.

The best results I have had have been with a fully rectified sinewave thats inverted - this however produces a triangle wave but  the initial waveform has a very low rms value.

Rog.

[hartiberlin]

Are you sure you meant 180 degrees phase shifted and not 90 degrees phase shifted ?
At 180 degrees phase shifted all waveforms cancel out each other !
Regards, Stefan.

[bodger]

No definately 180 degrees - I forgot to mention the initial waveform is positive going only - the waveform and its 180 phase shifted counter part are fed into opposite ends of a transformer so they push/pull.
As maths isn't my real strong point, today I gonna hack together a bit of C code to brute force a solution ie: run through a couple of million different waveforms until I find the best solution (dirfference being sinusoid and waveform with low rms) - it will be interesting how this compares to a maths solution (should one be found).
Rog.

[gyulasun]

Hi,

If your initial signal is positive going only, and you really phase shift it by 180 degree, then you still get a positive going signal, right?  You have to invert this 180 degree phase shifted signal to get a real  push-pull drive into the opposite ends of a transformer coil (whose coil is really a double coil with a grounded center tap).

What do you all think?

Gyula

[bodger]

Yes and no,
Centre tap is at 0v, but what I am trying to do is lets say a one point in time have one tap at +ve rail, other at 0v so current flows in that direction, next point in time the other tap is at +ve rail so current flows other way, for the times in between there is ramp up/down (on taps)  in such a fashion as to produce a sinewave on the secondary. The inputs (to the taps) should be of the form to produce little (average) dc  through the transformer hence the low rms requirement.
Maybe this is impossible and maybe I do need a negative rail, but I am hoping not to have to have one as it compicates the sourcing voltage(s).
Rog.