Multigap Debunchers

The performance of two and three gap debunchers was investigated by computing how well a straight line between the ordinates +1 and -1 and of abscissa length Tr radians can be approximated by a two and three term harmonic series. What is desired is a series that will minimize the maximum deviations between the straight line and the series approximation to that line. The usual Fourier series, or least squares fit which is equivalent to it, does not satisfy this desideratum. The series coefficients were obtained by means of a computer program written for the CDC-6600. For a two term series, the minimized maximum difference is 0.017. A three term least squares fit gives a maximum difference of 0.0058; this is small enough for our purpose, so no calculations were done to minimize it. The calculations were repeated for a straight line of extension 4 radians along the abscissa. The results are minimized maximum differences of 0.057 and 0.014, for two and three term series respectively.