Plate to Plate load resistance calculations

[skyboltone]

This one is too many for me. Maybe you bright bulbs can help.

Output load impedances:

EL-34 single ended at 265v = 2000 ohms. Push Pull at 450 = 6500 ohms
6L6GC single ended at 350v = 4200 ohms. Push Pull at ab1 350v =5600
6V6GTA single ended at 315v = 8500 ohms. Push Pull at a1 285v =8500
EL-84 single ended at 250v = 4500 ohms. Push Pull at AB1 300V =8000

I'm not getting the trend here. The RCA receiving tube manual is silent on the subject. I want to run a couple of 6CA5s Push Pull at max plate voltage or above. Single ended we show 4500 ohms load resistance at 125V on the plates. I'm gonna run a single stage input. No tone stack. A 12A?7 long tailed pair (maybe) and a post PI high cut. The power supply is likely to be split. A line to line voltage transformer with a bridge rectifier to the Output tube plates and a voltage doubler to the input tube and PI. What's the load impedance of a pair of 6CA5s in PP at say 140 to 160VDC?? (Edit: It's in the manual under the Push Pull AB1 section, sorry)
This may be a waste of time, but I'm curious about that tube.

Thanks in advance gents
Dan H[/b]

[David Root]

The following method works in class A and AB1, with all beam power and pentode power tubes.

Get the plate curves, ideally the one with multiple screen voltage curves. Mark the plate voltage, say 150V, on the x-axis and draw a line from there to the mid-point of the knee of the chosen screen voltage curve. Each curve is at Eg=0. The slope of this line is the effective plate resistance Za. Four times that (in push-pull) is Zaa for maximum power output.

So for the 6CA5, using as example the OTHER type of plate curve which is for a single screen voltage (in this case 125V) with curves for different bias voltages, read back down to the x-axis from the midpoint of the knee of the Eg=0 curve, you find 30V. Subtract that from 150V and divide by the current in amps at the knee midpoint, which is 0.0725. 120/0.0725=1,655,
x 4=6,600.

Similarly, Po max at Zaa 6,600 is 0.5 x 0.0725 (150-30) = 4.4W. NOTE that this is without negative feedback, which of course reduces Po max.

Check Pa (150) squared/6600=3.4W peak. Divide by sq.rt. of 2 (1.414) for RMS=2.4W, divide by 2 for one tube = 1.2W. Compare to Pa max=5W, no problemo! Not really any need to do this at this low Vp, but it's a good habit to get into.

All from Radiotron Designers Handbook, 4th Edn. 1953, Vol. 2, page 584, Fig. 13.43. Explanation is on p. 583.

[PRR]

What David said. (With one quibble.) Plot it.

> I'm not getting the trend here.

Yeah, there's a trend and plenty of wiggle-room.

Single-ended is clear. Sine output is at max 0.5 times plate dissipation. So to make the most of your expensive ($3?) bottles, you aim at Pdmax. For the mighty 6CA5, 5 Watts Design Center.

You can do this with 500V and 10mA, or 50V and 100mA.

Wait: they say 130V max. While I bet you could live at 150V for a very long time, or buy a 10-pack and run 200V without excessive cost, there is some practical up-limit.

Squinting the plate curves, we have a line for Vg2-125V which is essentially the suggested max Vg2. The tube won't do 100mA at any point shown, and is squeezing 75mA just before it falls over the knee and down the shin to zero.

Most likely good-power loadlines will hit near the knee. The goal is to maximize the V*I of the loadline, which is sorta a longest-diagonal problem. And when you jam a flagpole in the closet, you start by putting one end in the corner.

So the peak current will be OTOO 75 (but use 74mA for simple math). For symmetrical waves, the standing current will be 74mA/2= 37mA.

For maximum power we graze Pdmax, 5 Watts. 5W/37mA= 135V. This is trivially above the rating. We could go around again, estimate the rise of plate current when G2 is raised from 125V to 130V (also making both voltages the same, which may or may not be convenient). Might say 80mA peak, idle at 40mA, 5W/40mA= 125V, "too low". But this isn't gem-cutting. Pencil 125V and 40mA, accept that real life will be 115V to 140V, check for disasters.

As a sanity-check, do V/I to ballpark the load. 125V/40mA= 3.1K.

Now squint the curve. Starting from 125V 40mA, we can maybe swing to 35V and 75mA, and to 215V and 5mA. Grid swing is asymmetrical but not horribly so. We have 215V-35V= 180V p-p, 70mA p-p. The ideal load is 180V/70mA= 2.57K, a bit less than the ruff-guess because we can swing current but voltage swing bumps into the knee. We will (try to) buy a 2.5K OT. We rounded the load down, so we see what the current does. RMS of 70mA p-p is 25mA, and 2,500*0.025A^2 is 1.56 Watts sine rms output.

Huh. The book gets a similar bias point (isn't much choice) but a higher load. Looking back at the grid spacing, my 2K5 load is challenging and may run over 10% THD. Looking at the curve for varying load, distortion does seem to be the issue, and they were ordered to show a condition near 5%.

Also: this tube has a very soft knee. Like a rounded corner, the length of flagpole is only slightly affected by whether you get right into the corner or just near it.

OK, now run two tubes push-pull.

First: all this 13% THD cancels. SE amps will usually be mis-loaded or under-rated so they don't have embarrassing specs. Naked push-pull amps usually have acceptable numbers even when driven to the edge of clipping.

For exact class B, we can swing the tube from zero mA to say 74mA, and again 125V to 35V. The load per side is 1K2. The way P-P OTs are specified, the total load is 4 times that or 4k8. Power output is 3.3 Watts. Raising idle current from zero to ~35mA will make no real difference on power (huge difference in low-power distortion and in battery life).

The simple trend is: compute an SE load ignoring THD, double it, buy a P-P OT.

And in this particular case, the wiggle-room I mentioned does not exist. If you respect the tube ratings, and want good power, 125V 5Kct 3W is about where you have to be.

With a less stingy-rating tube, you start jacking the plate voltage and current. (To jack current you must jack G2 voltage.)

When you do both about the same, the load stays about the same. But sometimes we go high Plate and less-high G2: load Z should rise. Other times, we raise G2 so much that Child's Law raises current faster than voltage, so we find lower impedance.

With these tricks in pure Class A you would over-dissipate, but pure-B is 7 times more sine signal power for the same plate power. Since true cut-off is much too hard, we always compromise somewhere in between. (In this case the push-pull AB compromise is not very different from two SE Class A stages, except lower THD and OT DC.)

> divide by 2 for one tube = 1.2W. Compare to Pa max=5W, no problemo!

I don't follow this part. It seems to have a hidden assumption which I'm too tired to tease apart tonight. Looks to me like it could be biased Pure A, 5W per tube, and you DO have to watch dissipation. With self-bias, it can't idle much cooler than pure A or bias-shift will be a problem. With fixbias we could idle cold and get 78% efficiency at full power sine, except we are only using 90V of the total 125V, 35V is total loss. So 3.3W*(0.22/0.78) is 0.93W in the plates and 3.3W+0.93W= 4.23W total in the 125V-35V range (125V/90V), times 125V/90V= 5.88W total at 3.3W output or 2.58W in plates or 1.3W per plate. So it appears you have the pure B case covered but neglected idle current?

> without negative feedback, which of course reduces Po max.

Well, no and yes.

In SE, THD rises enough that a "good spec" design is well below the bent-wave power it can make. If you have a 2% spec, this tube might be 0.3W no-NFB yet hit 1.5W with good NFB.

We often ignore THD in no-NFB amps but obsess it when we bother to NFB. In that case we might spec it 1W at 1% w/NFB, but boast 1.9W no-NFB (at 13% THD).

NFB won't (shouldn't) reduce power. But when we play THD games with ourselves, it can do funny things.

{EDIT: have to use "Disable Smilies in this post" when you have an "8" next to a ")".}

[PRR]

> A line to line voltage transformer with a bridge rectifier to the Output tube plates and a voltage doubler to the input tube and PI.

I don't see how you can get both on one winding. In fact I know you can't, or I would know how. I just went to too much trouble building a 300V/600V supply. The 600V is doubled, but the 300V works half-wave. In this case that is fine, the 300V load is small. In your case it is reversed.

Why do you need 300V on the little tubes?

First the driver. A glance at the curves shows you can't need 10V peak per grid, and likely under 5V. Grid resistor is 500K (or 100K, but I think you want self-bias), no big deal. A straight volt-amp can make peak audio about 20% of its supply, so you need a 25V supply. Oh, many tubes warp near 50V, but still there's no reason to take more than maybe 50V-70V across the tube, about that or a bit less in its plate R so 30V-50V, 80V-120V total. The long-tail has some waste voltage, but also better linearity, it'll be fine; the cathodyne is much more linear and it can easily do 5V each end with 120V supply.

Assuming the driver (including a volt-amp for the cathodyne) has gain at least as large as interstage loss, the stage before that can also live on this same supply.

You have a volume control somewhere so that whatever strange signal you put in can be scaled to somewhat below (or somewhat above) the level needed to get all 3.3 Watts output.

What you put in may be an electric guitar. Empirical hints suggest that you aim for 0.5V input. Older grid-leak amps with lower input overload levels faded in the late 1950s. Later amps tend to have a gross overload grid level near 1V, and a 2:1 attenuator option. Look-up the RC amp charts for 12AX7 with 1960s Fender values. At 300V, 100K resistor, 220K loading: gain near 50, peak output for 5% THD near 56, so peak grid input near 1.1V. Fender sometimes let the first stage sag to 220V but not lower, so maybe 0.8V overload.

Why take a 0.5V input, gain-up by 50 to 25V swing, when we need a 5V swing?

Run half the supply voltage and half the gain. Just omitting 12AX7 cathode cap will work, though it changes the sound of a naked 12AX7. Putting a loss pad in front of 12AX7 will work. It degrades S/N, but a 3.3W amp does not have a big S so a "poor" S/N ratio may not be a big N. Or find a lower-gain tube. 12AU7 is handy. Gain may be near 15, so a 1Vpk input is a 15Vpk output and needs a 75V supply. Even rounding-up for the 50V warp we don't need no 300V supply.

We have a clue about maximum signal levels. How much gain and where do we control it?

For UN-controlled inputs (not tape/CD which is pre-adjusted), your sensitivity at the volume control wiper should be 50mV to 150mV. you can sometimes violate this, but start here. If sensitivity is higher (as in cheap amps with the Volume in front of the first tube), it hisses all the time. If sensitivity is less and you have uncontrolled inputs (unknown pickup, pick, arm, mood, drugs), anything over a quarter volt at volume wiper tends to imply some horrid-big signals must be delivered to the top of the Volume pot.

A working rule of thumb for large amps is 20mV input at full-up should just make full undistorted power. It may really be that we want a gain of 500-1,000 (into 4 or 8 ohm speaker), which would suggest a lower number for small-amps. We also see a trend from 50mV for older no-fart back-of-band amps to 1mV for modern ego-feeding shredder amps. Say 5mV.

So 5mV into gain of 15 gives 75mV, 1V into 15 gives 15V. Another gain of 15 would give 225V signals on wild gigs, need 1,000V supply, so we have to take a break from gain-up and put in a volume control after the first stage. (You see that 97% of guitar amps do.)

Assuming 100mV or 0.1V at volume wiper, and 5V at power tube grid, and no other losses, we need gain of 50. 12AX7 volt-amp and cathodyne do that neat. 12AX7 longtail gives gain near 25, so we may be short (and it may not matter). 7199 would allow gain over 200 and about 4:1 NFB, more than you maybe want.

So: 6C4 (half a AU7), volume, 12AX7 volt-amp and cathodyne, cupple 6CA5 power bottles. Or do the long-tail, 10mV sensitivity won't suck. Or to justify a higher pricetag, AU7 preamp, Volume, AU7 volt-amp, Fendery tonestack (more knobs is "worth more"), 12AX7 driver etc.

Hammond has some small iron with 6V and ~120V windings. True it may be cheaper to use two generic irons than one for-purpose iron.

[David Root]

Thank you once again, PRR. You really should publish what's in your head.

For those of you following this closely, I hope you noticed the very clear, concise and readily understood practical guide to gain architecture design he has presented in the immediately preceeding paragraphs. I for one have not seen it put so understandably. There is lots of meat in his previous post too.

I have found in reading that this is one area that others (i.e. not PRR) who also really do know how it all fits together, tend to obfuscate and/or omit essential parts of the complete story.
For example, KOC does this to some extent in his discussions of the subject. Whether this be done out of fear of competition from the great unwashed, or simply a belief that this understanding should be earned thru years of striving yet NOT understanding, it has held me back, I know that.

Two other similar areas I find are interstage impedance/impedance relationships in general, and also the nature of the natural relationships between the DC circuit structure and the AC circuit dynamics. I know that the one informs the other, just as the mind informs the body, and that it's a mutual process in many ways, it's the HOW and the WHY that often eludes me. Forgive me if I sound a little too holistic, that's not my intent.

I need to read some of this stuff from the '20s when it was fresh and new, and is still available. Much of it is indeed lost; I have heard the stories about acres of file cabinets abandoned and trashed when the RCA Harrison operation was closed.

[Noel Grassy]

+You've got a good point. I thankyou PRR for the concise and relatively in depth manner you've explained yourself. I need to re-read this post a few more times perhaps with paper & a pencil in hand too.

[skyboltone]

Oh Lord I do love this stuff:
Thanks PRR and David. I do follow those steps although the "flagpole" allusion made me stop and think for a moment. Yes sir. After I posted this query I ran into a discussion someplace on lower voltage on pre tubes so that was my next tactic. I brought this subject up over a year ago under the heading of headroom and pre-amp design vs pre PI pi network attenuators. Neither of you two fellers had shown up yet and most were advocating big voltage swings in the pre and then squashing them at the PI. Seems like if you're gonna go for grind you'll have more working for it than against it.

I've seen and studied the cathodyne but did not know it had advantages over the LTP. I think I'll go that way. I got a whole mess of NOS 6C4 in the caddy from my Ham radio days so why fool with the 12AU7 though they are abundant as well. I'll think about the tone stack. I've just finished up a spitfire with a "tone" knob, and haven't had enough time to mess with it to see if it's gonna float my boat.

As this project matures (lots of time here) I'll post things as they get thunk up.

Thanks again
Dan

[PRR]

> a belief that this understanding should be earned thru years of striving

Without naming names.... that's BS. People came out of the garden/forest because children learned planting and spear-throwing and grain-grinding from their elders and peers. And even with the best instruction, you don't get good harvest/hunting without years of practice. And the best teachers can always learn more. Sharing is the best policy for everybody. Hogging knowledge may give small short-term benefit (in audio, that rarely works) but ultimately tends to hurt everybody.

You named a name and I'm not aiming at him. He's fairly generous compared to most. The practical problem is: it takes TIME to first digest and then to write-up what you know. (Verbal teaching may go quicker but tends to have a smaller audience... reading/writing and printing technology is yet another example of improved knowledge sharing.) It's rare to find the knowledge, the clarity, and the time/energy to share, all in one person. Someone asked if I had a book.... no, I can toss off a thousand words but I can't find the motivation to do a 100,000-word hunk. (Or to collect and organize the hundreds of small hunks I've banged out in odd moments.)

> Forgive me if I sound a little too holistic, that's not my intent.

It bloody well should be.

An awful lot of people get hung up on minor details. Very few people can see the whole picture.

Years before "holistic" became a common word, I was studying loudspeakers. I was interrupted by a lecture from trumpeter Bill Fielder. He doesn't know a thing about speakers, but I was nominally paid to record events like that so I had to go. He was speaking to trumpet students who think a certain kind of bell or mouthpiece or valve is going to fix all their problems. His sound-byte was "It's just air!" I dunno if the trumpeters got it, but I did. I was obsessing about cones and magnets and hyperbolic flares.... but what I really needed to do was think like the air does. A lot of baffling "speaker" issues fell into focus over the next year.

[David Root]

I couldn't agree more about sharing knowledge and I tried to illustrate that with a specific example I thought many folks would be familiar with. Observation rather than criticism, really, because TUT 1 was a ground breaking book which addressed a real need, especially for me.

The other specific holes in my knowledge I mentioned I'm still working on and I'm not at the point where I can visualize "what the air is doing". That is the goal, however. You have to have an inkling of how much you don't know in order to effectively push out the boundaries of your ignorance.

I made the qualifier about using the word "holistic" only because in recent years it has unfortunately been misused and cheapened by overuse to the point that most people think of it as a sales word for organic supplements and "new age" hype. I do understand and value its original meaning.

Coming back to earth, I would also very much like to see these essential papers from the '20s or so which you referred to, and any other stuff you might feel like recommending for that matter, if you could point us towards them. I am at the practical point now of having three very different amps in build or pre-build at the same time, and I'm sure they would all benefit from any new insights I might gain. "Stop me before I build again!"