Making sense of self-resonance of plate choke in parafeed use

[Deke609]

I'm having trouble making sense of self-resonance of plate chokes and getting a bit freaked out - I hope needlessly and out of ignorance .  As Iv'e mentioned elsewhere, I've ordered some nanocrystalline core plate chokes for my Kaiju rebuild to pair with my nano OPTs.

I've heard back from the builder about some final measured specs: 69H and parasitic capacitance of <75 pF - which the builder says is actually quite good for such a large choke. But here's where the freakout comes. Plugging those two values into the self-resonance formula, we get a self resonance frequency ("SRF") of 2.2 kHz.  Which, if I understand things correctly, means that the only impedance that the choke presents at 2.2 kHz is its winding DC resistance, and above that freq. it is increasingly more capacitive than inductive. That doesn't sound too good to me.

I haven't been able to find much online about this issue - lots of stuff about RF chokes, but not a lot about tube audio plate chokes. But I have found a few passing references to the SRF typically being mid-band of the desired frequency response - 2.2 kHz is pretty much mid-band, so this suggests that things are OK. But if so, I don;t understand why.

What I'm hoping is that the SRF of the entire plate load comprised of plate-choke/parafeed-cap/OPT must be calculated as a bundle -- i.e., and most importantly, with the capacitance of the parafeed cap in parallel with parasitic capacitance of the plate choke -- in which case the parallel capacitance is effectively the parafeed cap, and that's 10 uF in my rebuilt Kaiju headphone amp.  That gives me a self-resonance < 7Hz.  Increasing the parafeed cap to 15 uF would knock it below 5 Hz.

Based on my very shaky understanding of circuit theory, the above "parallel" calculation makes some sense since (1) plate-choke/last-PSU-cap and (2) parafeed-cap/OPT are, in conventional-flow terms, parallel paths to 0V for AC signal appearing at the plate - and so, I think, could be represented as an equivalent circuit comprising a single path to 0V.

But, for reasons that will be obvious to anyone who has read even a small sample of my past questions/musings on this forum, I don't really trust my understanding of these things.

In brief, my question is: am I SOL or am I ok?

MTIA, Derek

[Deke609]

Hmm ... true to form, it looks like i screwed up my thinking about self-resonance. I had it my head that at self-resonance, inductance and capacitance cancel each other, leaving only DCR. But taking a second run at things, I'm reading that it is the opposite: at resonance, impedance is effectively infinite -- i.e., impedance peaks, not collapses, at self resonance. J.H.C.! I'm pretty sure I learned that earlier this year, but completely forgot it.

So I'm good?

MTIA, Derek

[Paul Joppa]

You're good. You have just been mixing up a parallel resonance with a series resonance.

The plate choke self-capacitance is in parallel with its inductance; at resonance the impedance approximates infinity. (At high frequencies, the capacitance is also in parallel with the OPT self-capacitance, which is usually several hundreds of pF.)

An inductance and capacitance go to zero impedance at resonance if they are in series instead of parallel.

Incidentally, the middle of the audio band is around 800Hz, based on balancing the perceived loss of musical information at the frequency extremes. As long as the plate choke self-resonance is above 800Hz, the treble is better than the bass.

[Deke609]

Much appreciated, as always, PJ.  Freakout has now passed.   

You have just been mixing up a parallel resonance with a series resonance.

Yup! I see that now. Thank you for pointing this out.

... As long as the plate choke self-resonance is above 800Hz, the treble is better than the bass.

That's interesting. And is that something that can be shifted a bit by playing with the parafeed cap value? Your formula/rule-of-thumb is 2L/R-squared, with room to go half or twice as big.  Does going bigger, and thus reducing capacitive reactance, shift things more towards the bass, and vice versa?

Many thanks again, Derek

[Paul Joppa]

Sorry, I did not mean to apply that comment to any specific treble or bass design. I just meant that in your case, the effect of plate choke self-capacitance can be pretty much ignored.

[Deke609]

Oh, OK. Many thanks again.

Derek

[trobbins]

Derek, if you were keen you can measure the impedance magnitude (and phase) with frequency and that can show a few interesting aspects including:
- the inductance value change with frequency below the resonance frequency (due to core material permeability)
- the capacitance value calculated above the resonance
- the peak impedance at the resonance

I've done that recently using a soundcard and REW software and the REW impedance measurement setup.  However that is a 'no DC current' measurement and at the Vrms excitation level provided by the soundcard (unless you add an interposing amplifier).  The choke inductance with DC current can be measured by another fairly simple technique that effectively tests at twice the mains frequency and can be set for specific ac excitation voltage and DC current levels.

Both those forms of measurement can add a little more awareness of the performance of the choke in a parafeed.