Question re: PJ's formula for parafeed cap sizing

[Deke609]

As set in in various other threads/posts, PJ's formula for parafeed cap sizing is as follows: 2*L/(R*R), where L is the inductance of the plate choke in Henries (H) and R is the primary impedance of the output transformer in Kohms. PJ has indicated that anything 1/2 or 2 times as big will work.  I think I read somewhere that PJ came up with this simplification after crunching a ton of complex relationships.

@PJ - my question is this: does your formula hold for all values of L and R, or only within "reasonable" limits? I ask b/c my SII's and Kaiju sound really great paired with my LCD4 200 ohms headphones.  But that load results in some really high primary impedances. Example: the Kaiju 3K primary impedance at 16 ohms, is way higher with 200 ohms - on paper it looks like north of 30K!  Plugging 40H and 30K your formula suggests I can get away with a 0.1 uF cap! 

I can of course just try it myself and see how it sounds - but the change isn't that easy to make with all the stuff I've packed into my Kaiju and SII's.  So it would great to know whether it's a go or no-go, at least on paper/in theory.

MTIA, Derek

[Paul Birkeland]

IMO you're too far off the range of reasonable values to use that formula with a 40H plate choke and presuming the transformer will reflect 30K (this itself is rather unlikely).

Still, 0.1uF is a very easy value to come by, you could give it a try to establish a datapoint for yourself.

[Paul Joppa]

The formula holds, but it's not useful for what you are doing.

The purpose of the formula is to assure that the tube sees a mostly-resistive impedance in the deep bass that is close to the design impedance. So yes, a 0.1uF cap  with 40H choke will produce a nice resistive load down to  something like 100Hz. Below that, the plate choke doesn't have enough inductance to support flat response, and at 30K ohms, the treble will roll off due to primary self-capacitance somewhere around 3-4kHz. And the tube doesn't care; it's operating point is optimized for efficient power into 4Kohms so can't put much power into such a high impedance, but its plate impedance is so much lower than the load that the load impedance has little effect on the tube.

This gets to the difference between a power amp and a voltage amp. A power amp transfers as much power as it can to a specific load; a voltage amp assumes that the current drawn from the amp is small enough to ignore, i.e. the load impedance is "high" relative to the source impedance. Running a 16-ohm output into 200 ohms  is a load impedance of 12.5 times the optimum for power, so it qualifies as a voltage amp. Preamps are usually treated as voltage amps.

As you can see, the boundary between the two is fuzzy, which invites confusion.

I have not yet done an analysis of parafeed voltage amps that satisfies me. The Mainline parafeed cap was chosen experimentally, and came out to 10uF into the OT-2. That's probably a good starting point for Stereomour as well.

[Deke609]

Many, many thanks PJ. This is very interesting and useful info.

... So yes, a 0.1uF cap  with 40H choke will produce a nice resistive load down to  something like 100Hz. Below that, the plate choke doesn't have enough inductance to support flat response, and at 30K ohms, the treble will roll off due to primary self-capacitance somewhere around 3-4kHz. ...

... The Mainline parafeed cap was chosen experimentally, and came out to 10uF into the OT-2. That's probably a good starting point for Stereomour as well.

This is very interesting. If you will indulge me, I have a couple of follow-up questions:

(1) DO you think the 10uF starting point apply to the Kaiju as well - which by design just happens to have 10uF parafeed caps? 

My SII-45 only has 4.7 uF. When I first posted about my impressions of the Kaiju as compared to my SII-45, one of the things I noted was that the Kaiju was much more treble-weighted. I'm now wondering whether what I was really hearing was rolled-off highs in the SII (which I'd grown accustomed to) and in switching to the Kaiju all I could hear was treble. Having just switched back to listening to the SII-45 with new iron, the lack of treble shimmer is quite noticeable (and I miss it).  I will try some 10ufs - I still have the the ones that came stock with the Kaiju. I'll also try the 6:1 winding, which is notionally a 5K4/150 ohms setup.

(2) Does it follow that the roll-off issue should go away if I place a resistor in parallel with the phones to hit the target load value?

I think it follows, and I'll be testing this myself when some new resistors arrive. But I just want to be sure that I'm following (as best I can) your explanation.

Again, many thanks, Derek

[Paul Joppa]

Rather than that, I'll withdraw the paragraph. I haven't thought it through well enough, and don't have time to do so right now.

[Deke609]

Ok. Thanks PJ. I'll try taking some frequency response measurements with different secondary loads, cap sizes and winding ratios.

cheers, Derek

[Paul Birkeland]

I rather liked what was in that paragraph...

[Deke609]

I think the following quote from PJ in 2009 discussing parafeed cap values for "effectively unloaded secondaries" applies here. I am assuming that a very high load on the secondary is a bit like an open circuit and in this sense is like an unloaded secondary.

... The situation is even worse for preamps with effectively unloaded secondaries. The simplified theory gives L/(R*R) as before, with R being the tube's plate resistance (if the transformer is unloaded) and L being the OPT inductance. This gives enormous capacitors, and the inductance will vary hugely - more than a 10 to 1 range - depending on the frequency and voltage at which it is measured.

This simplified theory ignores the effective resistance in parallel with the OPT inductance. This resistance is a combination of wire resistance, eddy currents in the laminations which appear as resistance, and magnetic hysteresis which is nonlinear but absorbs energy so you can think of it as a kind of resistance.

In practice, these uncertain loss resistances are the critical parameter, so the only reliable approach I know of is to experiment with different capacitor values and make measurements. You'll have to measure the frequency response at a variety of signal levels to be confident of your choice. ...

So measurement and experimentation are the ticket.