Need help understanding plate load of parafeed output tube

[Deke609]

All - I'm struggling to make sense of the load that a parafeed output tube "sees".  Here's how I *understand* things:

An amplified AC signal appears at the plate of the output tube. The AC signal is referenced to signal ground (e.g., the chassis) which we treat as 0V. Accordingly, there is a voltage potential difference between plate and signal ground -- and if these two points (plate and ground) are connected with a conductor, current will flow. In a choke-loaded parafeed setup, there are 2 paths to signal ground: (1) plate -> parafeed cap -> output transformer (OT) -> cathode bypass cap -> ground; and (2) plate -> plate choke (PC) -> last PSU cap -> ground.

To make things simpler, we can assume that all caps in the above two paths allow AC to pass freely, and so we can ignore them. That leaves two simplified paths to ground: (1) through the OT; and (2) through the PC.  Both the OT and the PC have impedance, which for the sake of this thought experiment we can think of simply as resistance. So we have 2 parallel resistors to ground.

Let's suppose the PC has fixed 100 "resistance units" (the actual units don't matter for this thought experiment - all that matters is the ratio of units of one path to the other). The OT primary's "resistance units" (impedance) are variable and depend on the load put on the OT secondary. Let's suppose that the OT is loaded so that its primary also has 100 "resistance units". So we then have two parallel paths to ground, each of 100 units. This means that the tube "sees" an effective resistance of 50 units to ground.

This suggests that, unlike in a non-parafeed setup where there is only one path to ground via the non-parafeed OT, the presence of the PC in parallel with the OT in a parafeed setup limits the plate loading effect (the load that the tube "sees") of changes to the OT primary impedance. Example: OT primary "resistance units" are increased from 100 to 10K. In a non-parafeed setup, the tube now "sees" a 10K load. But in a parafeed setup with a PC having 100 "resistance units", the tube "sees" 100 units in parallel with 10K units, which works out to about 99 units -- i.e., at really high primary impedances, plate load = PC impedance.

Is this correct? Or am I way out to left field (again)?

MTIA, Derek

[Paul Birkeland]

I would suggest that you do the analysis for something like a Stereomour at 1kHz.  You can calculate the reactance of all of the components (including the parallel feed cap, it's important), then you'll get a datapoint for what each component is doing.

Then you can repeat the AC analysis at 100Hz to see how things are changing.

[Paul Joppa]

PB's suggestion is good.

Your analysis is good, but the plate choke "resistance unit" is the inductive reactance of the plate choke - 40 henries for Kaiju, which is 25,000 ohms at 100Hz. At 12Hz it's 3000 ohms, same as the OPT. The parafeed capacitor in conjunction with the plate choke keeps the load resistive and around 3000 ohms to somewhat below 12Hz  but you must take into account the reactances to get a useful analysis. (I used a SPICE simulation rather than working out the math...)

[Deke609]

Many thanks PB and PJ.

I will do the calculations that PB suggests - maybe 20Hz, 100Hz, 1kHz and 20kHz - to get a sense of what is going on.

cheers, Derek

[Deke609]

I finally got around to doing some basic calculations using 70H as the plate choke inductance (the value of the new Lundahl choke) and 5K as the primary impedance of the output transformer, with various parafeed cap values.

Things I think I figured out:

If maintaining a relatively constant plate load of around 5K were the only goal then a parafeed cap of somewhere between 1 uF and 1.5 uF would work best.

BUT the parafeed cap value also determines the low frequency roll-off because the parafeed cap in series with the primary of the OT acts like a frequency dependent dropping resistor. At 20 Hz, a 1 uF cap has a capacitive reactance (Xc) of approx 8.1K, which is more than 1.5 times the 5K primary impedance - so more than 60% of the signal voltage is dropped across the cap and not the transformer. Whereas at 1 KHz, a 1 uF cap has an Xc of only 160R, and so nearly all the signal voltage is dropped across the primary.

There also appears to be a practical limit on how high of a constant plate load one can achieve. 5K is totally doable. But at 10K, to get a relatively constant load one would have to have an enormous plate choke. 

BUT a really high primary impedance (e.g., 30K) paired with a high value parafeed cap value (e.g., 10 uF) pretty much eliminates the low end voltage-divider/roll-off issue, but at the price of reintroducing a frequency dependent plate load from about 1 KHz down.

So it's a balancing act of compromises.

In my listening tests so far, I mostly prefer high a plate load  - its sounds tighter.   I think my preference has something to do the fact that my planar headphones have a ruler flat impedance across audible frequencies and consequently reflect a constant load on the primary.  I also wonder whether there is some law of diminishing returns re maintaining a constant plate load - specifically, if you maintain a minimum plate load of say 10K at 20 Hz, whether fluctuations above that value at higher frequencies would result in less distortion than the same fluctuations where the plate load dips to 5K instead of 10K.  I guess that's something load lines would tell me.  But any input/guidance from the experts on this or other relevant variables of which I am unaware would be most appreciated.

cheers and thanks, Derek

[Paul Birkeland]

At 20 Hz, a 1 uF cap has a capacitive reactance (Xc) of approx 8.1K, which is more than 1.5 times the 5K primary impedance - so more than 60% of the signal voltage is dropped across the cap and not the transformer. Whereas at 1 KHz, a 1 uF cap has an Xc of only 160R, and so nearly all the signal voltage is dropped across the primary.

You need to convert the inductance of the plate choke and output transformer into resistances at 20Hz in order to make the comparison at 20Hz. 

[Deke609]

Good point . Thanks PB. I did calculate and take into account the inductance of the choke at 20/100/1K/20K Hz - 8K-something at 20, 40K-something at 100, and then at 1K and above the inductive reactance of the choke is high enough that the plate load is effectively the primary impedance of the OT. But I forgot to add the inductance of the OT in series with the cap and primary impedance.  Guessing that will nudge the numbers a bit, but not as much as the Xc of the parafeed cap.  [Edit: I was totally wrong about that. I was expecting the Lundahl OT to have low inductance - but it is high, and so will change the calculations considerably] Will add that in the mix now.

cheers and thanks, Derek

[Paul Joppa]

* You can't really ignore the reactive impedance of caps and choke/transformers, if you want to see what's going on. The reactive components exhibit resonances that seriously deviate from resistive behavior. You must analyze the whole circuit from tube to load as a single system

* Usually you can ignore the output transformer inductance (with interleaaved laminations) because the reflected load resistor swamps it. But if you are looking for the lightly-loaded transformer case, you'll have to include it. That's a pain since it is not constant with frequency or signal level, and it is only partially inductive, partly resistive. Its impedance has a phase angle between 0 and 90 degrees - I have used 45 degrees for lack of better information on occasion but I don't trust that very far. In that case, both resistance and inductive reactance are proportional to the square root of frequency. That still ignores the substantial sensitivity to signal level

[Deke609]

Many thanks PJ.

* You can't really ignore the reactive impedance of caps and choke/transformers, if you want to see what's going on. The reactive components exhibit resonances that seriously deviate from resistive behavior. You must analyze the whole circuit from tube to load as a single system

Yes, I tried to do that, but mistakenly omitted the primary inductance. I took into account the "choke path" that terminates via parallel ground paths (a) 300K to ground via the C4S, (b) 100 uf PSU cap to ground, and (c) 130R + 100 uF to ground; with all of that being in parallel with the "parafeed/OT path" -- all at various frequencies and parafeed cap values. But looking back over my calculations, I see that I mucked up the PSU cap calculations b/c I didn't convert uF to F and so ignored them b/c, based on my miscalculation, they didn't contribute anything (they were the first caps I calculated). I will go over it again.

* Usually you can ignore the output transformer inductance (with interleaaved laminations) because the reflected load resistor swamps it. But if you are looking for the lightly-loaded transformer case, you'll have to include it. That's a pain since it is not constant with frequency or signal level, and it is only partially inductive, partly resistive. Its impedance has a phase angle between 0 and 90 degrees - I have used 45 degrees for lack of better information on occasion but I don't trust that very far. In that case, both resistance and inductive reactance are proportional to the square root of frequency. That still ignores the substantial sensitivity to signal level

This is very helpful b/c I couldn't find much about the primary inductance of an OT other than the -3dB cutoff calculation. I hadn't even considered phase. Using your 45 deg. simplification/assumption, do I sum the primary reflected load and inductive reactance like finding a resultant vector (stretching now to remember high school algebra!)?  Or can I ignore the phase part and calculate the resistance component of the reactance and add it to the resistance of the primary reflected load? I don't have a clue what to do with phase information.  I'm probably being unclear, so here's a really simplified example: if we imagine the 45 deg. inductive reactance has having a "phase displacement" (I don't know what it's properly called) on the y-axis, and resistance on the x-axis, my idea is to ignore the y-axis and simply add the x-axis value of resistance to the 5K reflected load. Simple 1/1/sqrt(2) triangle example: 45 deg vector of sqrt(2), with height (y-displacement) of 1 and length (x-resistance) of 1. Do I only need to deal with the 1 value of resistance on the x-axis? Or is something more complicated involved. Hope that kinda makes sense.

many thanks, Derek

[Deke609]

* You can't really ignore the reactive impedance of caps and choke/transformers, if you want to see what's going on. The reactive components exhibit resonances that seriously deviate from resistive behavior. You must analyze the whole circuit from tube to load as a single system

I'm finally returning to this after learning a bit about working with complex numbers. I'd never understood phase, but see now that the phase interactions in a simple LC circuit can have big and surprising effects (well, surprising to me) - e.g. voltages across a capacitor that are greater than the source voltage!  So I will take my time and try to work out a mathematical estimation of what's going on at various frequencies.  Many thanks to PJ and PB for your earlier guidance and suggestions about all of this -- I often don't understand what you mean the first time 'round (even, it turns out, when I think I do), but after lots of mulling and reading up it starts to make sense. Much appreciated.

* Usually you can ignore the output transformer inductance (with interleaaved laminations) because the reflected load resistor swamps it. But if you are looking for the lightly-loaded transformer case, you'll have to include it. That's a pain since it is not constant with frequency or signal level, and it is only partially inductive, partly resistive. Its impedance has a phase angle between 0 and 90 degrees - I have used 45 degrees for lack of better information on occasion but I don't trust that very far. In that case, both resistance and inductive reactance are proportional to the square root of frequency. That still ignores the substantial sensitivity to signal level

I've ordered some custom opts wired as 3K3:16,32,64.  Using a 3K3:64 config, would you consider a 200 ohm load "light loading" - or is it close enough to ignore the inductance of the OPT?

many thanks again, Derek

[Paul Joppa]

Yes, it's borderline  :^)

[Deke609]

Hmm. Thanks PJ.  I'll stick to modelling a "properly" loaded output stage then.  that's challenging enough for me.

cheers and thanks, Derek