[Amps] Resonant Choke Filters

[RFlabnotes at aol.com]

I have never (yet) actually built one of these power supplies. However, the 
various comments I have read here over the last year have really piqued my 
interest, so I decided to do some analysis of potential designs. I think the 
results of that analysis would be useful to anyone interested in resonant 
choke power supplies.

I analyzed some power supply models using a new program which I am just 
finishing, which does a precise job of modelling a power supply based upon 
all of the component specs, including the power transformer resistances. I 
just enhanced it to allow a resonant choke input and the results are 
interesting and useful.

 The final power output, voltage, ripple, etc are all a complicated result of 
the interaction of all of these parameters. However, I have been able to 
deduce a few basic approximations for the resonant choke/capacitor values, 
which I will post here for reference.

For review, the primary function of the resonating capacitor is to reduce the 
no-load voltage. The standard choke input filter allows the output to rise 
almost to the peak transformer voltage with no loading, possibly causing 
trouble in other areas. It turns out that the primary parameter which 
controls the amount of output peaking (at light load) is L/Rload. 

I make two assumptions for purposes of trying to derive some general purpose 
approximations (i.e. "design rules"). The first: The target is to limit the 
peaking to 5%. For a 2000V supply, this would be 100V. So, in evaluating the 
effect of any component parameter, we consider its effect to be "significant" 
depending on whether or not it limits the peaking to 5%. That seems like a 
reasonable approx. to me, but it is somewhat conservative. The second is that 
a minimum load current is specified. It is usually set by the HV bleeder.

There are several different ways of expressing the results, and I have chosen 
the following because it is simple and easy to remember (it also has a 
definite meaning in the context of the circuit, but it is complicated to 
prove here). My choice is an old friend, loaded-Q. In this case we define the 
loaded-Q of the inductor to be Rload/X(sub)L. We choose an Rload which 
represents the minimum load current via I(load)=V/Rload. (A firm example is 
below.)

What I have found is that the desirable range for this number is Q<10. If 
that is satisfied, the peaking will be limited to 5%. If you follow the 
arithmetic backwards, that dirrectly leads to a value of minimum L. Q from 
10-20 produces slightly more peaking (6-8%) but may cause problems with 
trying to satisfy minimum L requirements at FULL load current.

Another consideration is the accuracy of the components, L and C. Here is 
what my calculations have shown about this. The nominal component values are 
given by the standard parallel resonance formula, with L subject to 
limitation as above. In practice, most designers will have a specific value 
of L to work with, maybe one of several. Hence, there is a target value of C. 
The required accuracy of L and C is also a function of Q(loaded) as follows. 
For Q of 5, the permissible error in L or C is about 40%, for Q=10 it is 
about 25% and for Q=20 it is about 10% (all errors are +/-). So you can see 
that precision is really not much needed here, unless you want to push the Q 
way up in attempt to get by with the smallest possible choke. 

As far as the direction of the error is concerned, I found no significant 
difference having the resonance above 120Hz or below. The only thing I did 
see was that as you err on the side of too high C (resonant frequency is LOW) 
it is slightly more tolerant of the error. That is, the peaking deteriorates 
more with C that is too small (higher freq.) If you have to choose between a 
cap that is 15% high and one that is 15% low, use the first one (lower 
frequency). 

Colin provided me with the values used in the 30S-1, right out of the manual. 
For the HV supply:  8H/.15uFD/54K  and screen supply 3.5H/.5/5K.  For these 
values the Q(loaded) as described above is 8.9 (HV) and 1.9(Screen). One of 
the capacitors is spec'd somewhat below resonance of 120Hz and the other is a 
little above. These numbers all agree well my stated 'rules'.

I think this gives anyone contemplating one of these things enough to go on 
for a final design.

73
Eric von Valtier

P.S. If you have trouble figuring out your choke inductance, and don't have a 
bridge, I can supply you with several tips on measuring it with just a 
voltmeter and a resistor.