# Check my calculations: Shunt feedback input impedance

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#### hpasternack

[See schematic image in post #3 below.]

I will probably regret this, but...

I'm having a debate with another hobbyist and I was wondering if someone would check my calculations. The image is a simplified schematic of part of a push-pull pentode amplifier. There is a 470K shunt feedback resistor from the plate of the output tube V2 to the input of the source follower. I would like to determine the effective load resistance seen by the plate of the driver tube V1.

1) I assume the gain of the source follower is unity.
2) I assume the gain of the output tube is 10.
3) The feedback resistor is bootstrapped by the gain from the MOSFET gate to the V2 plate, giving an effective resistance of 470k / (10 + 1) = 42.7K.
4) The effective plate load on V1 is the parallel combination of the plate resistor, the bias resistor, and the bootstrapped feedback resistor, 220K || 1M || 42.7K = 34.5K.

To throw some more numbers at this, assuming the amplifier is driven to full output with 20VRMS on the grid, giving 200VRMS on the plate:

Feedback resistor current = 220V / 470K = 0.47mA
Plate resistor current = 20V / 220K = 0.09mA
Bias resistor current = 20V / 1M = 0.02mA

So, the total AC current in V1 is 0.58mA. With a 20V swing, the load line resistance is 20V / 0.58mA = 34.5K, the same result.

The bottom diagram is a more basic model. The signal source is the Thevenin equivalent of V1's internal generator voltage, uVgk, and the parallel combination of its plate resistance (~44K assumed) the 220K plate resistor, and the 1M bias resistor. This gives Rs = ~35K.

Rs in series with Rf forms a voltage divider having a ratio of Rs / (Rs + Rf). This gives a feedback factor of 0.07, a little lower than Schade's recommended 10%. Using the feedback equation, the resulting closed-loop gain is 10 / (1 + 10 * 0.07) = 5.9. The resulting reduction in gain is -4.6dB.

In the real world there will be some cathode resistance on V1 which will increase its effective plate resistance, giving more feedback. Also, the value of plate resistance may be higher depending on the tube's operating point. So the actual gain reduction may easily be set to Schade's -6.95dB.

Note that the gain reduction is from the V1 internal voltage generator, not its plate. This is an abstraction, as uVgk cannot be measured directly in the circuit.

This example is based on a schematic floating around the forum. The real-world amplifier uses a 6SL7 differential driver with a tail current of 1.15mA, or 0.575mA per tube. Since we calculated above that we need an input current of 0.58mA RMS = 0.82mA peak, it follows that the circuit as designed will be unable to drive the amplifier to peak output. Nonetheless, the designer has built and tested the amplifier, hence the debate and the conundrum.

FWIW I have put the full amplifier schematic into SPICE and confirmed the values I obtained by calculation. I know SPICE sometimes lies or gives misleading results but the fact that the simulation yields the same result increases my confidence in my math.

Assuming the value of 34.5K for the plate load is correct, this would seem to be far too low a value for a high-mu tube like the 6SL7 to drive, even at levels below the clipping point.

Since a number of people have built the amplifier and it seems to work I'm at a loss to explain the apparent contradiction. It would seem that I've made a mistake. If so I would be very appreciative if someone would show me what I've done wrong.

Thanks.

-Henry

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#### PRR

Paid Member
I don't see the image.

There is no low-load a tube *can't* drive. It may be weak and nonlinear, sure. Without seeing the circuit I would expect gain above 30 with 34k load and THD like 5%. "Works".

#### hpasternack

Sorry. I have images on Google Photos but I cannot comprehend the nonsense scheme they have for making links public. I see it here even when I sign out of Google. I'll try to make it visible. Thanks and stand by.

...

Changed to an attachment, should be more reliable.

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• Amp-Schematic.jpg
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#### Bandersnatch

"the designer has built and tested the amplifier"

That and a nickel will get you a 5-cent cigar. Just like:

"a number of people have built the amplifier and it seems to work"

Hooking up a few differential probes, as well as SE ones would tell much more of the tale...aka support the argument. Plate-to-grid makes for a more difficult load. Plan for it.

I don't see any errors, math or theory with a quick exam. And yes, I see the schematic in the second post.
cheers,
Douglas

#### hpasternack

PakProtector, I presume?

I think the designer and I have made some progress toward understanding my question. I hope he'll jump in at some point especially if he can figure out the cause of the discrepancy between his measurements and what the theory seems to be saying.

Once a year or so I make another tiny bit of progress toward building amps around a pair of 5K plate-to-plate 80W transformers I've been sitting on for thirty years. I'm not going to live forever and I don't want my kids to toss these parts in the trash so one of these days I need to finish this project. Where the heck does the time go?

Douglas, you probably know what transformers I'm talking about, LOL.

I have power iron good for 525V B+. The original plan was to build something like KT88 ultralinear amps. But I have a stash of NOS 807s that I'd like to use. With 300V on the screens I should be able to get sixty or seventy watts out of a pair in this application.

The required output tube grid drive is 90V peak-to-peak. Playing around with 6SL7 load lines I could maybe just barely get that to work, but it's not a pretty operating point. Thinking it through, I believe a better approach is to use a low-mu driver and build out the required source impedance with a series resistor. The source resistance is the same either way so this approach shouldn't impact frequency response. In fact, this probably improves linearity by reducing the effect of driver tube nonlinear plate resistance on gain.

A 6SN7 seems to do the trick biased at 4-5mA per side and has some headroom. I prefer my driver to be able to swing at least twice the required signal voltage. The resulting gain of that stage is pretty low, around 7.5 from one grid to plate. So the gain has to be made up in the input stage. A 6SL7 does the trick here.

Anyway, we'll see what happens. I have a few more days of vacation left so maybe I'll get to the point of ordering parts before I have to go back to work.

#### GoatGuy

Yah, they're expensive, but KT–120's are the way to go.

Shoot for a “500 volt, regulated power supply” amplifier.
Class-A mostly, until getting close to 50% of full output power…
Then OK to transition to Class B.
By the time the music is that loud,
… no one will take umbrage at the A-B transition cross-over.

And pretty-please, go for 6SN7s as the front-end-to-phase-inverter stages. They're such remarkably precious linear triodes.

Just go and revel in the 'flavor' of 6SN7.

If you have rack of low-output devices, (but why would you?), take the time to separate the pre-amplifier from the pair of monoblocks that you are (are>) going to build.

I — for one — would look very forward to keeping current on this thread.

-= GoatGuy =-

#### Chris Hornbeck

[See schematic image in post #3 below.]

1) I assume the gain of the source follower is unity.
2) I assume the gain of the output tube is 10.
3) The feedback resistor is bootstrapped by the gain from the MOSFET gate to the V2 plate, giving an effective resistance of 470k / (10 + 1) = 42.7K.
4) The effective plate load on V1 is the parallel combination of the plate resistor, the bias resistor, and the bootstrapped feedback resistor, 220K || 1M || 42.7K = 34.5K.

I'm not smart enough to be able to parse a much smarter person's thinking, but maybe could add some common gotchas.

The gain of the output stage can't really be "defined" a priori. It'll fall out at the end of your calculation. Maybe start with an estimated open-loop gain, 30?, or something in that range, from an estimate of gm times R-load.

The first stage valve might be more usefully modeled as a current source when studying the current summing node. And of course the MOSFET can be ignored.

So, the interesting part is the current summing node, with the first valve's current contribution, some parasitic R losses, not too bad, and the fedback current from the output valves. All sum to zero, but what's fair in your zero-sum game?

All good fortune,
Chris

#### Bandersnatch

henry, I have a pair of the same. Different manufacture, but just as yours are, missing the stack of 49% Ni lams in the middle. I am going to run 26HU5 in mine.

Not decided on the B+ yet; but likely just about 350V. I have enough heater current on those power Irons to heat up as many damper diodes it takes( well, as many as I need to soak up 10A ).

In the mean time, distracting myself with a 1983 Daisy 777. Down to 'minute of doorknob' at 10meters one handed, standing.

On tube choice, to heck with 6SN7, get a pair of 12A4. Now for a plate-to-grid amp, go pentodes anyway. Lots of good ones. With a good bit of signal voltage, you don't need to worry about a 3rd stage, or a low current/high gain tube. I want to try 6DT5 for the E-Linear LTP. It is a cute little, 5687-sized bottle and a 9W plate, and a 1.2A heater. Either that or the EL84...
cheers,
Douglas

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#### hpasternack

I have two power transformers rated 380V @ 800mA and 6.3VCT @ 7A. I was intending to build monoblocks but I don't have space in my rack. One power transformer would be sufficient to run a stereo 807 amplifier. Monoblocks are not out of the question, but simpler is better.

The outputs are Peerless S-271As from Magnequest Mike. They are supposed to be superb transformers. The main reason I never built an amplifier around them is that I was always waiting to do a no-holds-barred design. The complexity and challenge put me off and I never got around to it. Setting an achievable goal increases the probability I will actually do the project.

KT-120s would require separate chassis on account of the increased filament draw. I have some nice screen regulators I built last year but I think UL would be better in this case. I don't want to rely wholly on global feedback for low output impedance. Because the grid drive requirement is double for KT-120s versus 807s, designing a driver stage for shunt feedback would be much harder.

I guess a good way to motivate myself is to get other people interested in my project. I would hate to disappoint folks, though.

If I design the amp for KT-120s I can also run KT-88s. So let's suppose the two options are 807s in Class AB2 with shunt feedback or KT-88/120s in UL mode. I would use the source followers in either case. I'm leaning toward 807s but I am willing to be convinced otherwise, so have at it.

I've never used SPICE in any serious fashion until now. I understand the pitfalls but it seems useful for trying out general design ideas. So I threw this circuit together (attached). I put in a differential input stage to get the benefit of the extra gain in the second stage. As shown this design has 30dB closed-loop gain and 6dB global feedback. I'm not wedded to anything at this point.

FWIW and YMMV.

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• Amplifier-SPICE.PNG
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#### hpasternack

I'm not smart enough to be able to parse a much smarter person's thinking, but maybe could add some common gotchas.

You and me both, hah.

The gain of the output stage can't really be "defined" a priori. It'll fall out at the end of your calculation. Maybe start with an estimated open-loop gain, 30?, or something in that range, from an estimate of gm times R-load.

I'm reading the output stage gain directly off the 807 plate curves with a 1250 Ohm load line (correct for a 5000 Ohm push-pull primary in Class B). With 525V on the plates, 300V on the screens, and -30V on the grids the voltage gain is actually less than ten. I just used that number because it was convenient for working out my original question.

You probably realize the speaker impedance varies all over the place so the load line is at best a crude approximation. Because there isn't enough feedback to make the closed-loop gain independent of open-loop gain the whole thing is a continuously-varying nonlinear mess. It makes my head hurt so I try not to think about it.

The first stage valve might be more usefully modeled as a current source when studying the current summing node. And of course the MOSFET can be ignored.

This whole thing gets much easier if you use a pentode driver which actually comes a lot closer to being a controlled current source than a triode. I probably should use a pentode but I have an irrational fear of them even though they make more sense in this application. You can convert the tube model to the Norton equivalent, which uses a current source. The math is slightly different but the result is same, which is why it's "equivalent."

So, the interesting part is the current summing node, with the first valve's current contribution, some parasitic R losses, not too bad, and the fedback current from the output valves. All sum to zero, but what's fair in your zero-sum game?

Miller's Theorem tells us when we have a floating network driven by voltage sources at either end, we can compute the total current as the sum of the currents due to the the individual sources, as if the opposite ends were grounded. Though there's only, say, 20V on the input end of the feedback resistor, the -200V on the other end adds another factor of ten to the current, hence the dramatic reduction of apparent resistance.

#### hpasternack

henry, I have a pair of the same. Different manufacture, but just as yours are, missing the stack of 49% Ni lams in the middle.

I remember the saga. Where does the time go, Douglas?

On tube choice, to heck with 6SN7, get a pair of 12A4. Now for a plate-to-grid amp, go pentodes anyway. Lots of good ones. With a good bit of signal voltage, you don't need to worry about a 3rd stage, or a low current/high gain tube. I want to try 6DT5 for the E-Linear LTP. It is a cute little, 5687-sized bottle and a 9W plate, and a 1.2A heater. Either that or the EL84...

Hmmm. 12A4 looks like a nice tube. As I said above, I realize pentodes make more sense here. They just scare me because they're not audiophile-fashionable.

#### Bandersnatch

Henry, I do remember Mike. He said he 'improved' those transformers by building without Ni, instead of just admitting he could not get the stuff in that size any more. Mine are just built on 2x2 stacks of M4 SuPerOrthoSil because that is the best I could do at the time. Had to destroy an S-271-S to get it. I expect decent performance. I got it from the S265Q...

Fashionable my...nevermind. Besides, you are running them as finals, so how about that? If you are going to worry about what somebody else thinks, you are never going to get anything worth listening to.

The EL84 is pretty fine in a first cut I made at this amp, running S258Q outputs from the same source. 50% tap used to deliver plate voltage to the EL84. Now the 6DT5 is the first pentode I have run across set out for vertical deflection amp service *AS A PENTODE*. It has a big cathode. It is cheap, and likely plentiful( I know I got some, but I cant find that particular part in my stash ).
cheers,
Douglas

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#### PRR

Paid Member
Nevermind the Googie troubles or the fancy math.

Your plan works Rf against.... what? Actually rk of the driver. If rk is swamped with a large RK this can be very linear; is the basis of several video amps. But if you swamp a tube the gain goes away.

Taking NFB around *one* gain stage, a stage that *also* must deliver large output, is always a compromise. Maybe the only one possible? Well, you can always NFB from output plate to opposite driver cathode. Now you have a forward gain near 150, something to work with.

Is this amp for your brain or your ears? Your brain can keep improving it another 30 years. If you propped-up your good OTs with a guitar amp PT and a quad of 6V6 you'd give your ears a treat real soon.

#### Bandersnatch

To elaborate on PRR, a quad of 6V6, built on the RCA SP20 schematic would be interesting. I'd get rid ov the 12AU7 stage in favour of a 6SN7 LTP at least. The 6S3p-EV would probably get that duty though. IOW, I suggest building on the SP20 topology, but with a higher bandwidth front end. There is no global loop of NFB on that one either.
cheers,
Douglas

you have 5 days of vacation left now Henry...LOL

#### hpasternack

I have a nice solid-state amplifier. The last two tube amps I built I sold and I don't have any others at the moment. This project is mostly for my head.

I considered adding a cathode resistor to the 6SL7 so I can raise Rf. This works after a fashion, but in the end you need a certain amount of gain and current swing, and the tube is a fixed quantity.

The EL84 looks like it would work well, if a bit of overkill.

A quad of 6V6s would protest if I hit them with 525V.

I built this line amp last year. It's the chassis work that's such a bloody pain. Hopefully the image will show up.

I feel bad that I used Broskie's boards instead of rolling my own but I wanted a relatively quick and easy build. I only post the image to demonstrate that I do have some modest building skills. It works pretty well. More gain than I need. The main problem is the crappy Chinese power transformers buzz. One day I will replace them, and pay through the nose for a professionally-made front panel.

I've just about convinced myself the version with the 6SN7 LTP will work. If I don't run out of enthusiasm I may build it that way. I would design the amp so I can swap out driver boards easily.

#### Bandersnatch

Just examining the parts bins and space claims for the 26HU5 amp. I have a few choices for front end tubes. The 6DT5 has my interest, the EL84 and 6V6 are proven good, but I re-discovered the original plan, the type 8233. Now that puppy is quite a beast... I doubt I will realize half its published gm, probably more like a third.

I have about 420V to feed a Graetz bridge. Half SiC Schottky, Half 6DN3. There goes half my on-board supply of 6.3. Power Iron is salvaged from a Beckman something. Choke is a UTC S37. Output is of course the S-271-S. And I just remember I will likely want a split-CT grid choke. A Triad 25.2V at 2A will run the 600 mA cathode heaters of the finals.

Your pre is quite fine Henry. 300V will be fine for a quad of 6V6's. Hammond power Iron is easy to find. Chokes that will do input service are available on ebay. To heck wid the 6V6's then. Run a quad of EL84, and drive them with another pair of EL84. Simplify the tube shopping...

Start cutting Henry!
cheers,
Douglas

I am trying a new amp building theory: the amps are for my wire's 'upstairs' system. She is going to do some soldering. They have a decent chance to get built...

#### hpasternack

The goal here is to grind up existing parts so there is less for the children to throw away when I die. Hence, we will work with what we have in the attic.

I have a lot of NOS 5687s. Turns out switching the 6SN7 to a 5687 works much better driving the shunt feedback. So I will do it that way. And a 6SL7 differential pair input. I have some of those, too: NOS Tung Sol. Tung Sol good, right? Gives me 41dB open-loop gain and 6dB gain reduction across the 807. I'm satisfied with this formula. I have no bloody idea if this is accurate but I found a THD plug-in for LTSpice and the numbers look good up to 70W or so.

So this is the design. I will not let you try to convince me to change it. I will move on to considering parts purchases tomorrow.

Check out my funky voltage regulators. Shamelessly reverse-engineered from a commercial product that was promoted for years on the non-commercial part of this forum:

Do not be surprised if I don't actually follow through on this. But one can always hope.

#### Bandersnatch

You will discover that a 5687 is not as good as a pentode for driving the shunt FB. I resisted pentodes for signal amplification too...LOL

Also, why are you contemplating an 'amp within an amp' in form of regulators?
cheers,
Douglas

#### hpasternack

If I don't use the screen regulators then my kids will have to throw them away. Same for the 5687s. This logic makes design choices much easier.

#### Bandersnatch

Alright then, keep the 5687... Cascode them with a low current, high voltage MOSFET. The old 'build a pentode'. At the current you're considering, you won't need to put its gate at very high voltage at all.

For an amp I built, I ran FQP1N60, and a 6H6Pi...B+ of 600V. No failures in a dozen years of use.
cheers,
Douglas

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