I just discovered that the way I phrased the first problem of in the Fourier Series series of 3 problems on this list was incorrectly stated. I had said the 3-phase AC system was wye-connected and full wave rectified with a half-dozen diode rectifiers. The only way to full wave rectify it with 6 diodes is to leave the central neutral untapped and not connected to any of the diodes. The central neutral could conceivably be connected up using a couple of more diodes on it, but in that case neither of those diodes would ever conduct at any part of the 3-phase cycle anyway (assuming all 3 branches were truly voltage-balanced). Effectively the 6 diodes on the effective delta vertices are the only relevant ones. Also, the answer I was looking for would be off by a factor of √(3 from the correct answer, as I had stated the problem. So here is a corrected statement of problem that fixes the generating details by using an actually relevant *delta*-connected 3-phase AC sine wave power source.
1) Consider a *delta*-connected 3-phase AC ideal sine wave voltage source, (say from a power company or an alternator) Suppose each AC vertex of the 3-phase system's delta has an RMS voltage, V relative to each of the other 2 vertices. The voltage from all 3 vertices is full-wave rectified (using a half-dozen ideal diode rectifiers) and superimposed to make a DC voltage source (such as for the charging system for a car's lead-acid battery & electrical system, or for a high power DC supercharging system for an e-vehicle). This means the DC output voltage is the instantaneous maximum of the 3 absolute values of the 3 vertices' individual relative AC voltage differences. A consequence of this is that the resulting "DC" voltage has a relatively small AC ripple on it whose fundamental frequency is 6 times that of the original AC source. The DC output is unfiltered.
A) What is the mean output DC voltage in terms of V?
B) What is the AC ripple factor for this DC voltage source? The ripple factor is the quotient (often expressed as a percentage) of the RMS AC ripple voltage difference between the instantaneous voltage and its DC background mean value, divided by the mean voltage value.
C) Extra credit: What is the Fourier series for the AC ripple in terms of V and the original 3-phase AC source? And how much of the AC power is in the ripple's fundamental frequency mode?
(Fortunately, the way I phrased the above problem on the hallway white board last year did not have the error because then I didn't go into any details about how the rectified waveform was generated, and only just presented 'DC' waveform in terms of the instantaneous maximum of the absolute values of the 3 mutually phase-shifted sine waves.)