Subj:	Series resonant PDM trap-from NU2B
Date:	3/6/05 

The problem might be to figure out how you can replace the
last shunt cap in a PDM filter with a series LC resonant circuit
to short out the fundamental frequency of the PDM driver to prevent
spurious stuff from getting out.
This is the case where you may be modulating a 50V at 10 amp CE final.

If you are interested in a formula to work out the details you will find
that you have to solve an equation in two unknowns. The fun part is that
if you solve the equations as a function of frequency ratios the results
are simplified and you have to do none of that J-omega calculation stuff.

The basic idea is to insert an inductor in series with the last cap so
that (ball park values follow...) the high end roll off of a 10 kc LPF
 is unchanged even though a series short to ground exists at 100 kc.
(Don't know what your switching freq really is, but these probably
are reasonably close)

What happens is that the original capacitor (Corig) in the circuit is 
reduced slightly in value (call it Cnew) and then resonated with a new
 series L which does two things

(1) It series resonates at an Nth harmonic ratio of the fundamental.
    That is, Fseries of Cnew and Ls =100kc therefore N=10=100kc/10 KC

(2) The added L raises the effective capacitance of Cnew so that
    at 10 KC the effective capacitance is equal to the old C_orig.
    This is why the filter response is basically unchanged.

Now for the formula:
   K=1-1/(N^2)
   Cnew=K*Corig

Try it for a few harmonic values:
  N=2   K=1-1/(4)  = 0.750
  N=3   K=1-1/(9)  = 0.889
  N=4   K=1-1/(16) = 0.938
  .
  .
  N=10  K=1-1/(100)= 0.990  This is our case, only 1% change
                            which really means no change.

As you can see, this is really easy for the PDM example,
since notching out something 10 times higher in frequency
than the signal of interest is very easy and will not disturb the
basic lowpass filter values at all.

The real fun is applying the same principle to the much tougher
problem of, for example, reducing the second harmonic of your
75 meter xmtr to prevent 40 meter harmonics.

As part of the NU2B ClassE program program I showed how to change the
final shunt cap in a 3-pole LPF such that the 2-harmonic is notched out.
If you run that program, then at start-up (3.8 mhz design):
Press "A" for ALT topologies and the conversion is listed as
(3a)-Tchebychev Filter-Cp out Conversion.
You'll see that the original cap =1081 pf was replaced by a value
of 0.75*1081 pf = 811 pf (See above N=2 where K=0.75))
The 811pf cap was then used with a 0.541 uhy series coil to notch out
the 7.6 mhz second harmonic.
This is an example where the cap was changed 25% but still disturbed
the LPF basic response very little.

Hope this note will help a little with figuring out more about
all this real fun stuff!

Also, when you first fire up and test at the LPF 10 KC bandedge (worsecase), 
remember to start at low audio and monitor the temperature
of the first shunt cap (input side). This is the guy that takes all 
of the stress. Only 0.1 ohms ESR could dissipate 50-100 watts at 1KW out!
But perhaps you are using ten or so 0.5uf high quality caps
in parallel. It would also be good to split the output cap also,
with about 80 % on the modulator and the other 20% as the CE final bypass caps.

Also consider a parallel resonant trap with about 0.02uf (ballpark
guess for 100uhy) on the last series inductor in the LPF. This will give
you a broader notch (about 60kc) at the 80 db level. I better stop,
'cause this is way too much fun and I'll be up all night.

Regards and keep the fire extinguisher close by.
BobbyT NU2B LI, NY