> *where does the 6.28 come from?*

Basic trigonometry. Converts radius to circumference. Nevermind why.

> *this little calculator (3 pole is smallest)*

Cute. Actually gives "correct" answers if you can convert pF to uF in your head. Correct but wrong because it ignores the relative costs of chokes and caps (for 50 years, caps have been MUCH cheaper than chokes for the same filtering effect). In fact we want very low impedances in and out, which suggest big caps. An "optimum" wave-filter is not necessarily the best power filter.

Your first cap off the rectifier must be sized to catch energy from the input sine peaks. 1,000uFd per Amp is a good trial value **for low-volt work**. More is better, up to somewhere past 10,000uFd/Amp where rectifier surge current can be insane. This rule comes from 60Hz work but is VERY rough and will still give you a place to start for 50Hz work.

Two channels of 7591 will eat ~200mA or 0.2A. 0.2*1,000= 200uFd.

200uFd, especially at over 450V, is rather costly. And with a vacuum rectifier, we may be over the peak current*time limit for the bottle (often 10uFd-40uFd for the bottles used in hi-fi).

Duncan's Power Supply Calculator shows why. At 400V 200mA we have only 6V peak-peak ripple, which is "small" compared to 400V. If money is a problem (it always is), a better rule of thumb is to start from 5% RMS ripple. For 60Hz this suggests that the load resistance times the capacitor should be about 40,000ΩuFd. For our 400V/200mA= 2,000 ohm load: 40,000/2,000= 20uFd. For 50Hz, use a constant of 48,000: 48,000/2,000= 24uFd.

This is good commercial practice. It may not be good audio practice. Guitar amps sometimes use "small" caps for dynamic effect (pluck is modulated by droop, sustain is brought out as power falls). Hi-fi often likes more solid rails with lower ripple (and crosstalk). Given the low price of Japanese bulk uFd, 40uFd to 100uFd is reasonable, 470uFd not incredibly insane for silicon rectifiers.

Mojo's 2*80uFd= 40uFd is a reasonable value. It will show about 2.5% RMS ripple. 2.5%*400V= 10V RMS, about 30V peak-peak. This is actually 30V dips from the 400V maximum available, so it means the output wave will show ripple-clipping at about 80% of the power possible with a perfect 400V supply. Even when not clipping, the 10V RMS ripple may cause buzz in the output. Push-pull pentodes are fairly resistant to power rail buzz: we know many classic amps worked with the values Mojo has.

Buzz-reduction for small volt-amp stages is usually done with resistor-capacitor dropping.

If we need lower ripple on the output, we can try an R-C, but the R wastes power. An ideal L-C filter won't waste power.

Pick an L and C value from thin air. Say 10H and 40uFd.

The frequency we want to reduce is the ripple frequency. For 50Hz, it is 100Hz.

Compute the reactance of the L and C at 100Hz:

10H*100Hz*6.28= 6,280Ω ~= 6K

1/(40uFd*6.28*100Hz)= 39.8Ω ~= 40Ω

Since the difference in reactance is large, we can use the approximate result:

Reduction in 100Hz buzz = 40/6K = 0.0067 or 1/150

So for 400V, 200mA, 40uFd -> 10H -> 40uFd:

10V/150= 0.066V RMS buzz

(Duncan's PSD gives 0.019V p-p, about 0.067V RMS, using low-R parts.)

We have computed only the first partial of the ripple, the 100Hz. "Buzz" includes higher partials. At the first cap they are all strong. But after an L-C filter, they fall off at 12dB per octave. This usually makes higher partials negligible: if the 100Hz is too low to hear, and higher falls off fast, the higher partials are too low to hear even with Fletcher-Munson.