Yes, I agree. I think it's a good idea to ameliorate the situation twice, since the cost of implementing both is so low: Use better diodes AND implement a snubber.
Good diodes reduce the magnitude of oscillation, and then the snubber kills it.
An under-appreciated result in Hagerman's paper is that the snubber's R and C values are 90% determined by the characteristics of the transformer -- with a small dependence on the rectifier capacitance. You can easily squash this dependence, making the snubber values 100.00% determined by the transformer, just by using Hagerman's 2C+1R snubber in Figure 7 (p.8). If Cx >> (Ctransfo + Crectifier) then the oscillation frequency is set exclusively by Ltrasnfo and Cx. It's not dependent on the rectifier capacitance, so you can use the same snubber design for this transformer, and ANY choice of rectifier. Sweet!
Better yet, you can implement Rsnubber as a trimpot. Install crummy diodes (1N4004?), monitor the oscillatory ringing of the secondary, and dial the trimpot until you've damped the ringing to whatever Zeta (waveshape) you like. Now remove the crummy diodes, install the good diodes, and boom! you're done. This same snubber design works equally well for this transformer, whether you use crummy diodes or good diodes! So optimize the snubber with crummy diodes, then use it with good ones. Also note: you get an optimum snubber without ever having to measure the leakage inductance of the transformer's secondary.
Probably the high-reliability way to implement this is to use a 25-turn trimpot that plugs into a 3-pin socket. Power up, attach scope, and dial in the optimum damping. Now remove & measure the trimpot R, and solder in a fixed resistor of that same resistance. Something like the Bourns 3296W would work nicely in a 3-pin SIP socket.
This post may suggest similar ideas.
Be careful with simulations using capacitors. ESR is not constant with frequency so most models are suspect. Simulations aside, an old fashioned transistor radio can be tuned between AM stations and the antenna waved over the DUT. If you hear a buzz you probably have an RF problem. IMO, RF injected into audio circuits can change operating points and have unexpected and audible consequences. Even if it doesn't, I like to play it safe and kill it at the source- the place to deal with all RF problems, never downstream where corrective measures are much less effective. 
I agree, and I must admit that I was leaning towards that experimental method!
Simulations are there to provide a rough idea, some expectations and a first plan to begin with.So, why are fast diodes really better? As I read in Merlin Blencowe's "Designing Power Supplies for Tube Amplifiers", the momentary change of current polarity until the turn-off is - given leakage and stray capacitance - responsible for the ringing.
My thought for this: for slow diodes, current switches from load current to zero and is even reversed during the transition time, compared to fast diodes where it practically becomes zero instantly. So, the dI/dt transient is even bigger with slow diodes - which in turn means a higher voltage spike across the leakage, thus bigger ringing amplitude. The energy stored previously inside the leakage magnetic field flows into the LC circuit, giving a ring that is damped eventually, as expected.
Of course, these could be far from accurate.
Please give me your thoughts!
Oscillatory ringing occurs when the flyback voltage (L x dI/dt) exceeds the diode's Vfwd. Obviously the choice of diode doesn't affect L, but it does affect dI/dt and Vfwd.
Since your simulations have shown big differences in the oscillatory behavior of 1N diodes versus UF diodes, why don't you run those same simulations and this time plot the diodes' dI/dt? Maybe diodes with big dI/dt also oscillate big? It's a worthwhile hypothesis to explore.
In LTSPICE the Waveform Arithmetic function to take the derivative is d( ) ; see image below. Thus to view dI/dt in diode D6 you would plot the expression "d(I(D6))" . I assume other simulators offer similar features.
I think you will be shocked and delighted to compare the dI/dt of your 1N4007 circuit, versus the dI/dt of your UF4007 circuit. One will have (kiloamperes per second) of dI/dt, and the other will have (megaamperes per second) of dI/dt. Really.
By the way, Bob Cordell's diode test circuit (Figure 16.10, p.353) shows one way to measure diode voltage and current in a real power supply with a real transformer and a real filter capacitor bank and a load. If your oscilloscope is a digital model with FFT and waveform arithmetic features, you can tell the scope to directly display the derivative of the current waveform. If your scope won't display waveform derivatives, you can simply capture the current waveform and then afterwards, take the derivative by graphical methods.
Since your simulations have shown big differences in the oscillatory behavior of 1N diodes versus UF diodes, why don't you run those same simulations and this time plot the diodes' dI/dt? Maybe diodes with big dI/dt also oscillate big? It's a worthwhile hypothesis to explore.
In LTSPICE the Waveform Arithmetic function to take the derivative is d( ) ; see image below. Thus to view dI/dt in diode D6 you would plot the expression "d(I(D6))" . I assume other simulators offer similar features.
I think you will be shocked and delighted to compare the dI/dt of your 1N4007 circuit, versus the dI/dt of your UF4007 circuit. One will have (kiloamperes per second) of dI/dt, and the other will have (megaamperes per second) of dI/dt. Really.
By the way, Bob Cordell's diode test circuit (Figure 16.10, p.353) shows one way to measure diode voltage and current in a real power supply with a real transformer and a real filter capacitor bank and a load. If your oscilloscope is a digital model with FFT and waveform arithmetic features, you can tell the scope to directly display the derivative of the current waveform. If your scope won't display waveform derivatives, you can simply capture the current waveform and then afterwards, take the derivative by graphical methods.
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Thanks for the promts! I will give them a chance when I have time to do so.
So, why a faster diode could lead to a lower dI/dt? You mentioned Vfwd, so you mean that until Vfwd reaches 0, it has become momentary lower that L(dI/dt), so we have ringing? So for a fast diode, this would happen so fast, that it could barely be "detected"?
And if so, what is the relevance of Blencowe's point about reverse conduction during transition time? Still a bit confused on that one.
That alone should call into question the simulation, while it is possible to coax high dI/dt's out of diodes in reverse recovery, some attention needs to be paid to reducing inductance and maximising dV/dt.
There is not enough voltage available at the point of recovery to produce that sort of dI/dt with the inductances present in this type of circuit.
Even if the diode switched at the zero crossing, the dV/dt would be just over 0.005V/us for a 1us switching delay that is 5mV over voltage, to achieve 1A/us dI/dt would need an inductance of 5nH. The diode is not switching at zero crossing so the dV/dt will be less. In a real life application a fast recovery diode will see dV/dt's of tens of volts per microsecond, yet we do not see the associated kA/us dI/dt's that this simulation would suggest.
Some members in another thread proposed I go on with that choice, instead of using multiple secondaries. Out of cost considerations, I am thinking of doing it.
But I don't understand what the problem is. The grounds are not connected together at any point if I don't choose so - grounds = the common points for each DC power supply.
Saying almost always, do you have personal experience with such an occasion?
Would it be better to employ a single big bridge and one big reservoir? In that case, every power supply would have the same ground either way, electrically connected.
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