400 Hz

[Paul Koning]

> On May 5, 2021, at 11:07 AM, Grant Taylor via cctalk <cctalk at classiccmp.org> wrote:
> 
> I have found the Motor Generator thread to be fascinating and enlightening.  But it has made many a reference to the 400 Hz or other frequency much higher than mains line frequency.  Despite the comments about the frequency, I'm still confused as to why the higher than mains frequency was used.
> 
> Were the higher frequencies used because it directly effected the amount of time / duration in (fractions of) seconds between peaks of rectified (but not yet smoothed) power?
> 
> I ask because it seems to me like the percentage of time / duty cycle of raw rectified but not yet smoothed) power would be the same at any and all frequencies.  Is this assumption / understanding correct or completely off the mark?
> 
> A few different people made references to the amount of capacitance needed at 400 Hz et al. vs 50/60 Hz mains frequency.  Someone even spoke about high power DC being produced by polyphase converters and the possibility to tweak tweak winding voltages in order to possibly do away with the need for capacitors.

There are a couple of considerations: transformers, filter capacitors, and ripple amplitude.

Ripple amplitude is affected by the number of phases and by whether you use half wave or (the normal) full wave rectifiers.  For example, a full wave single phase rectifier produces a abs(sin(2pi * f * t)) waveform.  A multi-phase full wave rectifier produces the max of these waveforms offset by the phase angles -- in other words, the "valleys" are filled in by the "peaks" of some of the other phases.  The ripple filter then smooths that out into DC, or more precisely, makes the ripples a lot smaller.  What exactly those waveforms then look like depend on the filter used.

So rectifying 3 phase power produces much smaller ripple than rectifying single phase.  For exotic applications where you can afford to deal with more than 3 phases you can make the amplitude smaller still.

The above is independent of frequency.

Now for transformers.  As the operating frequency increases, the amount of iron or other core material needed goes down.  So a 400 Hz transformer for a given amount of power can be much smaller than a 60 Hz transformer for the same job.  This is why modern power supplies are "switching supplies": they convert the mains voltage into high frequency power -- sometimes as high as a megahertz or so -- which allows the power transformer to be tiny.

Finally, capacitors.  The ripple attenuation of a filter depends on the impedance of the filter elements.  The most common is a capacitor filter, so the filter capacitors (their AC impedance) is in parallel with the load impedance.  The ripple attentuation is basically the ratio of filter capacitor impedance to load impedance.  Capacitor impedance is inversely proportional to frequency, so the use of a higher frequency allows the use of smaller capacitors.  This too is used in modern switching regulators, where the capacitors are often just a few microfarads and are generally ceramic, not electrolytic.  

In all this there are limits on how far you can usefully go.  Motor generators above a few hundred hertz are hard to build, though there exist alternators that produce multiple-kilohertz output (look up Alexanderson machines).  Switching regulators can to into the MHz range, but if you go too high your benefits stop because the transformers and capacitors are no longer close enough to "ideal components".  For example, the impedance of a capacitor stops dropping at some frequency that depends on its design, this is the ESR (effective series resistance) of the part.  Near or above that frequency is is no longer a good filter capacitor, or for that matter a good capacitor for many other purposes.

	paul