> Wollcott describes, in as obscure and unreadable manner as he can
It is actually quite readable, if you read white-on-black, and if you don't try to understand. If you try to wrap your brain around each statement, you will be frustrated.
It is, of course, NOT a rigorous technical paper but a Sales Pitch. So it is a little unfair to critique it on technical accuracy.
First, for handy reference: Wollcott's 1963/1967 patent drawing #6:
Van Scoyoc was mentioned; here is part of his Radio News article from 1948:
The tubes with red dots I put on Wollcott do about the same as the four tubes in Van Scoyoc.
What differentiates the White cathode follower from a simple cathode follower with a tube constant current source is the connection between the plate of the cathode follower and the grid of the bottom tube, which brings the current source under feedback control and provides for a very constant impedance when sinking or sourcing current. Theoretically the impedance of the lower tube approaches zero, actually equaling a few ohms.
The output impedance of a WCF is just 1/2Gm. For 6DJ8 this will tend to be around a hundred ohms. I suppose for most tube-work, that "approaches zero" near-enuff. It is quite constant even for fairly large swings, and very-constant for the small signals here. (It better be near-constant, because the left-lower or signal-input stage has no other feedback and drives a fairly low-Z load: R88, U86's cathode, and the feedback nest.)
within our topology, cathode drive provides yet another advantage. When the tube whose cathode is driven takes it’s input from a cathode follower, an almost complete cancellation of distortion occurs as a result of the antiphase relationship of the two tubes,
I would not argue that. However what he is selling today does NOT use a simple cathode-follower against a cathode-input stage. It uses the very linear WCF. Where is the cancellation? (This passage may have been written for an earlier version without WCF, and not excised from this revision.)
The extremely low noise of our amplifier is largely due to...
Someone shoveled the wrong words into this passage. It can be low-noise because 6DJ8 is high-Gm and thus low thermal noise voltage, and impedances after that are small. Yes, it has buzz-cancellation; when I pay more than $99 for an amp it BETTER have buzz-rejection. Many ways to do that.
Normally Driving a tube’s cathode produces little or no signal gain
Amusing passage but really meaningless.
we cannot claim absolute priority in the use of vacuum tubes in a non-inventing mode,...
"non-inventing mode"??? ah, well....
...nor even in the use of crosscoupled tube circuits with opposite grid and cathode drive and separate mirror image cathode follower inputs for signal and negative feedback.
See Van Scoyoc 1948 above; preserved in Radiotron Designers Manual 4th edition pg 663.
...positive feedback from cathode of the bottom pentode driving the cathode of the bottom gain triode and grid of the top gain triode. The effects of this arrangement are several. First, the gain of the triode gain stage rises toward infinity before the application of negative feedback, which essentially eliminates the imbalance between the cathode and grid driven tubes and which instead makes for almost perfectly symmetrical drive.
This is not utter BS. Positive feedback inside a negative feedback loop is a powerful lever to reduce errors in tube op-amps. You also find it in some of the Dynaco tube amps, particularly to get enough gain to feed-back the RIAA curve. Such schemes are tricky but can be designed for mass production (and certainly at Wollcott's level of quality control).
When this “infinite” gain is subsequently reduced by the application of negative feedback, the noise floor of the circuit drops dramatically.
Well, when gain drops, output noise drops. But the PFB isn't affecting the noise. Perhaps the writer mis-heard the designer.
I'm not going to think too much about odd-order cancellation. The bootstrapping sure will reduce classic resistor-loaded nonlinearity (read-up on ramp-wave generation with tubes). I mis-trust sand-state CCSes, anyway Wollcott seems to be making a pure-vacuum amp.
the open loop bandwidth of our main gain circuit extends out into the megahertz.
Yeah? An hour before this, I'd happened to throw a small pentode and 100K resistor on a simulator and got 40MHz unity-gain bandwidth, gain~120 up to 300KHz or ~20 up to 2MHz. This level of performance is well described in the MIT Radiation Labs (RADAR) book series that came out after WWII, and extended much further by oscilloscope designers through the 50s and 60s. Keep Gm high, C low.
the effect that it has on clipping.
There may be a glimmer here. Recall that transistor power amps were invariably bootstrapped until the price of a CCS came down below the price of the cap. And the clipping DID change about that time. When the output gives up, its input won't be overdriven if the driver depends on bootstrapping. Like when you literally lift yourself by your bootstraps, you rise; but when you hit the ceiling your shoulders drop, bootstrap-pull is reduced, you stop rising.
Between Wollcott's sales literature and this talk of bootstrapping into the ceiling, I'm getting an Excedrin Headache
It is actually quite readable, if you read white-on-black, and if you don't try to understand. If you try to wrap your brain around each statement, you will be frustrated.
It is, of course, NOT a rigorous technical paper but a Sales Pitch. So it is a little unfair to critique it on technical accuracy.
First, for handy reference: Wollcott's 1963/1967 patent drawing #6:
An externally hosted image should be here but it was not working when we last tested it.
Van Scoyoc was mentioned; here is part of his Radio News article from 1948:
An externally hosted image should be here but it was not working when we last tested it.
The tubes with red dots I put on Wollcott do about the same as the four tubes in Van Scoyoc.
What differentiates the White cathode follower from a simple cathode follower with a tube constant current source is the connection between the plate of the cathode follower and the grid of the bottom tube, which brings the current source under feedback control and provides for a very constant impedance when sinking or sourcing current. Theoretically the impedance of the lower tube approaches zero, actually equaling a few ohms.
The output impedance of a WCF is just 1/2Gm. For 6DJ8 this will tend to be around a hundred ohms. I suppose for most tube-work, that "approaches zero" near-enuff. It is quite constant even for fairly large swings, and very-constant for the small signals here. (It better be near-constant, because the left-lower or signal-input stage has no other feedback and drives a fairly low-Z load: R88, U86's cathode, and the feedback nest.)
within our topology, cathode drive provides yet another advantage. When the tube whose cathode is driven takes it’s input from a cathode follower, an almost complete cancellation of distortion occurs as a result of the antiphase relationship of the two tubes,
I would not argue that. However what he is selling today does NOT use a simple cathode-follower against a cathode-input stage. It uses the very linear WCF. Where is the cancellation? (This passage may have been written for an earlier version without WCF, and not excised from this revision.)
The extremely low noise of our amplifier is largely due to...
Someone shoveled the wrong words into this passage. It can be low-noise because 6DJ8 is high-Gm and thus low thermal noise voltage, and impedances after that are small. Yes, it has buzz-cancellation; when I pay more than $99 for an amp it BETTER have buzz-rejection. Many ways to do that.
Normally Driving a tube’s cathode produces little or no signal gain
Amusing passage but really meaningless.
we cannot claim absolute priority in the use of vacuum tubes in a non-inventing mode,...
"non-inventing mode"??? ah, well....
...nor even in the use of crosscoupled tube circuits with opposite grid and cathode drive and separate mirror image cathode follower inputs for signal and negative feedback.
See Van Scoyoc 1948 above; preserved in Radiotron Designers Manual 4th edition pg 663.
...positive feedback from cathode of the bottom pentode driving the cathode of the bottom gain triode and grid of the top gain triode. The effects of this arrangement are several. First, the gain of the triode gain stage rises toward infinity before the application of negative feedback, which essentially eliminates the imbalance between the cathode and grid driven tubes and which instead makes for almost perfectly symmetrical drive.
This is not utter BS. Positive feedback inside a negative feedback loop is a powerful lever to reduce errors in tube op-amps. You also find it in some of the Dynaco tube amps, particularly to get enough gain to feed-back the RIAA curve. Such schemes are tricky but can be designed for mass production (and certainly at Wollcott's level of quality control).
When this “infinite” gain is subsequently reduced by the application of negative feedback, the noise floor of the circuit drops dramatically.
Well, when gain drops, output noise drops. But the PFB isn't affecting the noise. Perhaps the writer mis-heard the designer.
I'm not going to think too much about odd-order cancellation. The bootstrapping sure will reduce classic resistor-loaded nonlinearity (read-up on ramp-wave generation with tubes). I mis-trust sand-state CCSes, anyway Wollcott seems to be making a pure-vacuum amp.
the open loop bandwidth of our main gain circuit extends out into the megahertz.
Yeah? An hour before this, I'd happened to throw a small pentode and 100K resistor on a simulator and got 40MHz unity-gain bandwidth, gain~120 up to 300KHz or ~20 up to 2MHz. This level of performance is well described in the MIT Radiation Labs (RADAR) book series that came out after WWII, and extended much further by oscilloscope designers through the 50s and 60s. Keep Gm high, C low.
the effect that it has on clipping.
There may be a glimmer here. Recall that transistor power amps were invariably bootstrapped until the price of a CCS came down below the price of the cap. And the clipping DID change about that time. When the output gives up, its input won't be overdriven if the driver depends on bootstrapping. Like when you literally lift yourself by your bootstraps, you rise; but when you hit the ceiling your shoulders drop, bootstrap-pull is reduced, you stop rising.
Between Wollcott's sales literature and this talk of bootstrapping into the ceiling, I'm getting an Excedrin Headache
I couldn't figure out what the heck he was on about regarding complementary-symmetry circuits. I still can't. My own version of the cross-coupled inverter (SYclotron) actually IS a comp-sym, but I had to resort to pFETs to pull that one off. And, of course, unless the circuit is driven from a balanced source, it suffers from the same defect as all similar cross-coupled circuits- a balance error of mu/(mu + 1).
Hmm, I drive tube cathodes quite routinely and seem to get gain. What do I know that he doesn't?
Hmm, I drive tube cathodes quite routinely and seem to get gain. What do I know that he doesn't?
PRR - thanks for posting the schematics - a picture is worth a thousand words.
Reading thru' all the above there are a couple of things which stood out - to me at least.
1st as Don stated the positive feedback, bootstrapped load on the high gain triode stage is NOT the best way to do this today. A Solid State Current Source load for the triode stage will easily achieve the same level of performance (or better).
There is one note of caution here; I have amongst my many amps, just one drop dead gorgeous solid state amp. One of its "secrets" to achieving stunning and "tubelike" sound is a bootstrapped VAS. I'm not going to identify the amp as Hugh would have me shot for giving away his intellectual property.
Also I simply don't believe the bit about the bootstrap influencing clipping. Again Don pointed out that the boostrap is from the cathode follower output (that is: from the output tube grid drive). The postive feedback (bootstrap) will not be affected at all by the output stage going into clipping. What will be affected is the negative feedback loop around the bootstrapped stage. I would say that not only would clipping be harder BUT stabiltywill be compromised (less negative feedback to counteract the positive feedback loop inside it) - OR am I missing something??
Another little thing buried in the "White Paper" text is that the Cathode Followers are Current Source loaded (it actually says current mirror but ..) and that the output tube grids are direct coupled from the cathode follower.
Thinking about this suggests to me that it should be simple to design an output tube bias servo system where measure of the output tube current can be fed back to the current source reference (perhaps by means of a current mirror to handle DC level shifting). More output tube current => less cathode follower current source load current => more negative output tube grid bias. It may need some resistive as well as current source loading on the cathode follower BUT shoud be workable.
Cheers,
Ian
Reading thru' all the above there are a couple of things which stood out - to me at least.
1st as Don stated the positive feedback, bootstrapped load on the high gain triode stage is NOT the best way to do this today. A Solid State Current Source load for the triode stage will easily achieve the same level of performance (or better).
There is one note of caution here; I have amongst my many amps, just one drop dead gorgeous solid state amp. One of its "secrets" to achieving stunning and "tubelike" sound is a bootstrapped VAS. I'm not going to identify the amp as Hugh would have me shot for giving away his intellectual property.
Also I simply don't believe the bit about the bootstrap influencing clipping. Again Don pointed out that the boostrap is from the cathode follower output (that is: from the output tube grid drive). The postive feedback (bootstrap) will not be affected at all by the output stage going into clipping. What will be affected is the negative feedback loop around the bootstrapped stage. I would say that not only would clipping be harder BUT stabiltywill be compromised (less negative feedback to counteract the positive feedback loop inside it) - OR am I missing something??
Another little thing buried in the "White Paper" text is that the Cathode Followers are Current Source loaded (it actually says current mirror but ..) and that the output tube grids are direct coupled from the cathode follower.
Thinking about this suggests to me that it should be simple to design an output tube bias servo system where measure of the output tube current can be fed back to the current source reference (perhaps by means of a current mirror to handle DC level shifting). More output tube current => less cathode follower current source load current => more negative output tube grid bias. It may need some resistive as well as current source loading on the cathode follower BUT shoud be workable.
Cheers,
Ian
First principles/algebra help wanted.
Monday morning Oz time.
On the wekend I waded thru' the 2 patent papers. It clicked that the positive feedback loop Wolcott is talking about is NOT the bootstrap but separate balance positive feedback loops spanning 2 stages.
Patent 3,11,680 derives from first principles an expression for the gain of a 2 stage amp with nested feedback. I worked thru' this and agreed with his expression (EQUATION 1).
EQUATION 1:
A = {A1.A2}/N
where N = 1-A1.B1-A1.A2.B2
Then he just states (without support) the total distortion is given by:
EQUATION 2:
D={1/N}.D1+{(1-A1.B1)/N}D2+{(1-A1.B1)/N}D1.D2
Where
A1, A2 are the gains of 1st stage and 2nd stage, B1, B2 are the feedback factors and D1, D2 are the distortions
His whole theory then depends upon the special case when A1.B1 is made equal to 1. when this equation would reduce to:
D={1/N}.D1
That is the distortion of the 2nd stage drops out of the equation and doesn't contribute to the total distortion at all.
I can't seem to derive that distortion formulae (EQUATION 2) from 1st principles and am not sure its correct. If its not correct then his whole premise is not correct either.
Can anyone assist?
Thanks,
Ian
Monday morning Oz time.
On the wekend I waded thru' the 2 patent papers. It clicked that the positive feedback loop Wolcott is talking about is NOT the bootstrap but separate balance positive feedback loops spanning 2 stages.
Patent 3,11,680 derives from first principles an expression for the gain of a 2 stage amp with nested feedback. I worked thru' this and agreed with his expression (EQUATION 1).
EQUATION 1:
A = {A1.A2}/N
where N = 1-A1.B1-A1.A2.B2
Then he just states (without support) the total distortion is given by:
EQUATION 2:
D={1/N}.D1+{(1-A1.B1)/N}D2+{(1-A1.B1)/N}D1.D2
Where
A1, A2 are the gains of 1st stage and 2nd stage, B1, B2 are the feedback factors and D1, D2 are the distortions
His whole theory then depends upon the special case when A1.B1 is made equal to 1. when this equation would reduce to:
D={1/N}.D1
That is the distortion of the 2nd stage drops out of the equation and doesn't contribute to the total distortion at all.
I can't seem to derive that distortion formulae (EQUATION 2) from 1st principles and am not sure its correct. If its not correct then his whole premise is not correct either.
Can anyone assist?
Thanks,
Ian
Distortion formula
I arrived at the same gain formula also. I then derived a distortion formula using the standard distortion term added to the output of each stage.
V1 = (1+B1*V1 + B2*V0)*A1 +D1
V0 = A2*V1+D2
(Vin is set equal to 1, V0 is Vout)
then derive:
V1 = (A1 + A1*B2*D2 + D1) / (1 - A1*B1 - A1*A2*B2)
V0 = (A1 + A1*B2*D2 + D1) * A2 /(1 - A1*B1 - A1*A2*B2) + D2
which if A1*B1 = 1, then gives:
V0 = D1/(A1*B2)
not quite the same as the D = D1/N mentioned above, but close. Maybe can re-check my results.
The cancellation of D2 is as expected, due to the A1,B1 stage having infinite gain when the A1*B1 = 1 condition is given (unity gain around the A1,B1 loop). This whole scheme is just conventional NFB with huge loop gain in stage A1. Practically speaking, the A1*B1 = 1 condition is more likely adjusted to just slightly less than one so as to avoid oscillation in the first stage, particularly when output clipping cuts out the B2 negative feedback function.
The use of bootstrapping in the A1 gain stage was just to get linear gain with the equivalent of an active load. (its operation is not included in the formulas) But since an active load mostly gets rid of the 2nd harmonic and not the higher harmonics from a stage, it really doesn't do much for the resulting sound of the amplifier.
One might be tempted to use a vacuum tube current mirror gain stage in place of the A1 gain stage (still using the B1 positive feedback loop to get very high resultant gain), should do a little better at reducing some of the higher harmonics. But still won't get rid of the highest, most annoying harmonics. One could then add error correction to the current mirror stage to eliminate the higher harmonics, but the complexity would be getting very out of hand by then. I think just using error correction on the A2 stage alone makes better sense, but then its not really the same amp.
Don
I arrived at the same gain formula also. I then derived a distortion formula using the standard distortion term added to the output of each stage.
V1 = (1+B1*V1 + B2*V0)*A1 +D1
V0 = A2*V1+D2
(Vin is set equal to 1, V0 is Vout)
then derive:
V1 = (A1 + A1*B2*D2 + D1) / (1 - A1*B1 - A1*A2*B2)
V0 = (A1 + A1*B2*D2 + D1) * A2 /(1 - A1*B1 - A1*A2*B2) + D2
which if A1*B1 = 1, then gives:
V0 = D1/(A1*B2)
not quite the same as the D = D1/N mentioned above, but close. Maybe can re-check my results.
The cancellation of D2 is as expected, due to the A1,B1 stage having infinite gain when the A1*B1 = 1 condition is given (unity gain around the A1,B1 loop). This whole scheme is just conventional NFB with huge loop gain in stage A1. Practically speaking, the A1*B1 = 1 condition is more likely adjusted to just slightly less than one so as to avoid oscillation in the first stage, particularly when output clipping cuts out the B2 negative feedback function.
The use of bootstrapping in the A1 gain stage was just to get linear gain with the equivalent of an active load. (its operation is not included in the formulas) But since an active load mostly gets rid of the 2nd harmonic and not the higher harmonics from a stage, it really doesn't do much for the resulting sound of the amplifier.
One might be tempted to use a vacuum tube current mirror gain stage in place of the A1 gain stage (still using the B1 positive feedback loop to get very high resultant gain), should do a little better at reducing some of the higher harmonics. But still won't get rid of the highest, most annoying harmonics. One could then add error correction to the current mirror stage to eliminate the higher harmonics, but the complexity would be getting very out of hand by then. I think just using error correction on the A2 stage alone makes better sense, but then its not really the same amp.
Don
> It clicked that the positive feedback loop Wolcott is talking about is NOT the bootstrap
No, in those days we knew bootstrapping was positive feedback but rarely called it that.
One particular reason: bootstrapping is "almost always" stable and safe, since several simple topologies give a gain that is known to be less than unity. Other forms of PFB get away from you a little too easy for simple design.
Positive feedback for gain: nearest example is the resistor between the cathodes on some Dynaco preamps. Some tube opamps used PFB to good effect; MIT Radar Labs series has some good discussion.
Dyna-type PFB between two cascaded single-ended stages will increase 2nd-order nonlinearity. But taken across a push-pull system it decreases it. 2nd-order nonlinearity can be considered as "gain is higher on negative half-cycles than on positive half-cycles". So when the top side is swing low with high gain, the PFB is pushing harder on the bottom side which is swung high with low gain. It increases gain when gain is low, and vice-versa too. I don't know if this extends to higher harmonics. I suspect that in many real tubes, the higher harmonics do not follow the simple quadratic law, but are artifacts of grid-winding tolerances. In that case then it generally won't cancel, unless you are exceptionally lucky to find a box of tubes all wound on the same day by the same person who happened to be very consistent with her work.
> bootstrapped load on the high gain triode stage is NOT the best way to do this {today}
I'm inclined to question any such dogmatic statement as that. Aside from religious debate about "all tube" and the cost of a CSS (negligible today), there can be advantages to bootstrapping.
For one: the signal-node can rise to or above the supply voltage. We used to do that in transistor power amps. While CSS affairs became common, we still find bootstrapping in some 12V car-amps, where the top output transistor Base should be swung as far up as possible, closer than a good CSS can swing, sometimes a little beyond the supply rail. This makes the difference between an "18W" rating and a "25W" rating. Not big to the ear, but fools buyers. In a tube amp with beam/pentode outputs, we should not have to swing above a lightly decoupled B+, but with regulators in the picture, maybe it is a little shy of plate-swing.
And there is an advantage in overload. It is not true, as you once asserted, that "The positive feedback (bootstrap) will not be affected at all by the output stage going into clipping". The bootstrap comes from a cathode follower, which also drives the output grids. If we used a CSS and global negative feedback with high gain, when the output clips the NFB will increase the drive, throw the drivers to extreme swings far larger than needed to saturate the output tubes. This gives long post-overload recovery times, especially if there is a coupling capacitor in the path. If we get our high gain with bootstrapping and PFB, taken from the cathode driving the grids, consider: the cathode output impedance is around 1K. The grids are 100K when linear or cutoff, but almost any clipping condition (low plate voltage or high plate current) puts us in a positive-grid range. Here the grid impedance drops to about 1K. The cathode-follower gain drops from about 0.95 to 0.5. If the voltage-amp stage gain is proportional to its effective plate load, gain falls. Say he uses a 50K plate resistor. When cathode follower is working at 0.95, the effective load is 1,000K. When strained against a clipping output stage, CF gain is 0.5, volt-amp effective load is 100K. Gain has fallen-off 10:1. That ignores the added PFB loops, which will also collapse fast when the CF strains into clipped-grids. The volt-amp pushed by NFB is not going to over-react so badly.
No, in those days we knew bootstrapping was positive feedback but rarely called it that.
One particular reason: bootstrapping is "almost always" stable and safe, since several simple topologies give a gain that is known to be less than unity. Other forms of PFB get away from you a little too easy for simple design.
Positive feedback for gain: nearest example is the resistor between the cathodes on some Dynaco preamps. Some tube opamps used PFB to good effect; MIT Radar Labs series has some good discussion.
Dyna-type PFB between two cascaded single-ended stages will increase 2nd-order nonlinearity. But taken across a push-pull system it decreases it. 2nd-order nonlinearity can be considered as "gain is higher on negative half-cycles than on positive half-cycles". So when the top side is swing low with high gain, the PFB is pushing harder on the bottom side which is swung high with low gain. It increases gain when gain is low, and vice-versa too. I don't know if this extends to higher harmonics. I suspect that in many real tubes, the higher harmonics do not follow the simple quadratic law, but are artifacts of grid-winding tolerances. In that case then it generally won't cancel, unless you are exceptionally lucky to find a box of tubes all wound on the same day by the same person who happened to be very consistent with her work.
> bootstrapped load on the high gain triode stage is NOT the best way to do this {today}
I'm inclined to question any such dogmatic statement as that. Aside from religious debate about "all tube" and the cost of a CSS (negligible today), there can be advantages to bootstrapping.
For one: the signal-node can rise to or above the supply voltage. We used to do that in transistor power amps. While CSS affairs became common, we still find bootstrapping in some 12V car-amps, where the top output transistor Base should be swung as far up as possible, closer than a good CSS can swing, sometimes a little beyond the supply rail. This makes the difference between an "18W" rating and a "25W" rating. Not big to the ear, but fools buyers. In a tube amp with beam/pentode outputs, we should not have to swing above a lightly decoupled B+, but with regulators in the picture, maybe it is a little shy of plate-swing.
And there is an advantage in overload. It is not true, as you once asserted, that "The positive feedback (bootstrap) will not be affected at all by the output stage going into clipping". The bootstrap comes from a cathode follower, which also drives the output grids. If we used a CSS and global negative feedback with high gain, when the output clips the NFB will increase the drive, throw the drivers to extreme swings far larger than needed to saturate the output tubes. This gives long post-overload recovery times, especially if there is a coupling capacitor in the path. If we get our high gain with bootstrapping and PFB, taken from the cathode driving the grids, consider: the cathode output impedance is around 1K. The grids are 100K when linear or cutoff, but almost any clipping condition (low plate voltage or high plate current) puts us in a positive-grid range. Here the grid impedance drops to about 1K. The cathode-follower gain drops from about 0.95 to 0.5. If the voltage-amp stage gain is proportional to its effective plate load, gain falls. Say he uses a 50K plate resistor. When cathode follower is working at 0.95, the effective load is 1,000K. When strained against a clipping output stage, CF gain is 0.5, volt-amp effective load is 100K. Gain has fallen-off 10:1. That ignores the added PFB loops, which will also collapse fast when the CF strains into clipped-grids. The volt-amp pushed by NFB is not going to over-react so badly.
Hi PRR,
You make a good point about the gain falling off significantly during clipping due to CF loading from grid current, the bootstrapping does appear have a utilitarian side here as far as recovery is concerned. One might consider putting a clamping diode on the grid to cathode of the output tube to strengthen this effect.
However, the distortion formula above (if I am correct, hope someone will check the derivation) Dist = D1/(A1*B2)
is not very good and one may well wish for a little cleaner active load instead of a bootstrap load on the gain stage. (I would suggest using a current source powered by the bootstrap signal so as to get the advantages of both. This is something I have thought McIntosh could benefit from too.)
The B2 NFB term may well be comparable (but inverse) to the A1 gain term, so one is very dependent on a good tube (low D1) in the gain stage. If the Dist = D1/N formula in the patent is correct, then one has Dist = D1/(A1*A2*B2) which would look a lot better for linearity. Some ACCURATE mathematicians out there?
(V1 = (1+B1*V1 + B2*V0)*A1 +D1
V0 = A2*V1+D2 solve for V0 when A1*B1 = 1 )
Don
You make a good point about the gain falling off significantly during clipping due to CF loading from grid current, the bootstrapping does appear have a utilitarian side here as far as recovery is concerned. One might consider putting a clamping diode on the grid to cathode of the output tube to strengthen this effect.
However, the distortion formula above (if I am correct, hope someone will check the derivation) Dist = D1/(A1*B2)
is not very good and one may well wish for a little cleaner active load instead of a bootstrap load on the gain stage. (I would suggest using a current source powered by the bootstrap signal so as to get the advantages of both. This is something I have thought McIntosh could benefit from too.)
The B2 NFB term may well be comparable (but inverse) to the A1 gain term, so one is very dependent on a good tube (low D1) in the gain stage. If the Dist = D1/N formula in the patent is correct, then one has Dist = D1/(A1*A2*B2) which would look a lot better for linearity. Some ACCURATE mathematicians out there?
(V1 = (1+B1*V1 + B2*V0)*A1 +D1
V0 = A2*V1+D2 solve for V0 when A1*B1 = 1 )
Don
alternative version of Wolcott amp
I was recently looking thru the 3rd ed. of Morgan Jones's "Valve Amplifiers" book and noticed Fig. 2.49 on page 136. This uses active loads (with a common reference V) on a triode LTP (with a current source in the tail too).
Triodes are used, so the plate Ra's set the operating levels stably if adjusted carefully. As mentioned, getting the currents correct is a bit touchy.
This reminded me of a solid state design that I have seen that gets very high gain using SS devices with their high output impedance devices in the same configuration. Substituting pentodes in would arrive at the same result. So, envision Fig. 2.49 with pentodes in place of triodes.
Manually setting currents for the operating levels now becomes impossible, but is readily fixed. Just use a set of high value resistors from the plates to control the voltage reference level for the common referenced active loads. (A resistive divider to the B+ rail from the tied together plate connected resistors, and a cap across the top "reference" resistor sets the operating voltage "reference" for the current loads; use P Mosfets for the active devices .) This makes for a common mode servo to set the plate operating levels. The active current loads adjust themselves to match the tail current source requirement. The pentode gains are now free to approach their Rp * gm level, ie huge.
With this circuit in mind, one could substitute into the Wolcott design and eliminate the positive feedback stage. This would be keeping in the same spirit as the Wolcott design by providing a massive gain stage, but should be easier for the Diyer as far as stability is concerned. Putting grid to cathode clamp diodes across the subsequent cathode followers should minimize hard clipping problems.
Don
I was recently looking thru the 3rd ed. of Morgan Jones's "Valve Amplifiers" book and noticed Fig. 2.49 on page 136. This uses active loads (with a common reference V) on a triode LTP (with a current source in the tail too).
Triodes are used, so the plate Ra's set the operating levels stably if adjusted carefully. As mentioned, getting the currents correct is a bit touchy.
This reminded me of a solid state design that I have seen that gets very high gain using SS devices with their high output impedance devices in the same configuration. Substituting pentodes in would arrive at the same result. So, envision Fig. 2.49 with pentodes in place of triodes.
Manually setting currents for the operating levels now becomes impossible, but is readily fixed. Just use a set of high value resistors from the plates to control the voltage reference level for the common referenced active loads. (A resistive divider to the B+ rail from the tied together plate connected resistors, and a cap across the top "reference" resistor sets the operating voltage "reference" for the current loads; use P Mosfets for the active devices .) This makes for a common mode servo to set the plate operating levels. The active current loads adjust themselves to match the tail current source requirement. The pentode gains are now free to approach their Rp * gm level, ie huge.
With this circuit in mind, one could substitute into the Wolcott design and eliminate the positive feedback stage. This would be keeping in the same spirit as the Wolcott design by providing a massive gain stage, but should be easier for the Diyer as far as stability is concerned. Putting grid to cathode clamp diodes across the subsequent cathode followers should minimize hard clipping problems.
Don
Don,
I'm still trying to derive the distortion formulae from first principles.
I liked the way you started (the 2 original formulas) BUT I have a problem with the way you have arbitrarily asigned a value of 1 to Vin. My algebra has been known to be a bit "dodgy" BUT that is even too "dodgy" for me. Still on it when I'm bored with nothing better to do - so sorry - can't confirm your final equation. Hopefully something soon.
Cheers,
Ian
I'm still trying to derive the distortion formulae from first principles.
I liked the way you started (the 2 original formulas) BUT I have a problem with the way you have arbitrarily asigned a value of 1 to Vin. My algebra has been known to be a bit "dodgy" BUT that is even too "dodgy" for me. Still on it when I'm bored with nothing better to do - so sorry - can't confirm your final equation. Hopefully something soon.
Cheers,
Ian
minor card trick
Hi Ian,
I don't think there is anything dodgy about the Vin = 1 trick really. If you prefer, just put Vin back in the formula in place of the 1. Since Vin gets divided out later, when you want Vout/Vin for the final result, I just saved a little time that way.
Basic formulas:
V1 = (Vin+B1*V1 + B2*V0)*A1 +D1
Vout = A2*V1+D2
then solve for Vout/Vin when A1*B1 = 1
I got: Vout/Vin = 1/B2 + D1/( A1*B2)
Don
Hi Ian,
I don't think there is anything dodgy about the Vin = 1 trick really. If you prefer, just put Vin back in the formula in place of the 1. Since Vin gets divided out later, when you want Vout/Vin for the final result, I just saved a little time that way.
Basic formulas:
V1 = (Vin+B1*V1 + B2*V0)*A1 +D1
Vout = A2*V1+D2
then solve for Vout/Vin when A1*B1 = 1
I got: Vout/Vin = 1/B2 + D1/( A1*B2)
Don
Thanks for the caution. I don't have the same Norton Internet Security Suite that you have and have seen no warnings. I have downloaded a number of patents using www.pat2pdf.org and have experienced no problems, although you never know what's lurking out there. Had I seen warnings I would have mentioned it in my recommendation. There is another site, www.pat2pdf.com/, that charges dearly for the same service.
USPTO was the reason for my original post! I had been using the one-image-at-a-time Alternatiff nonsense with USPTO for years until I came across www.pat2pdf.com. This site grabs the images from USPTO one at a time (automatically!) and converts them into one single PDF file for downloading. Free Give it a whirl.
> consider putting a clamping diode on the grid to cathode of the output tube to strengthen this effect.
??? The grid-cathode port IS a diode.
Oh, you mean a sand-diode? Extra part with nonlinear capacitance? Sure! Only: why? In my rough-analysis, G-K conduction in the vacuum drops CF gain to half which drops volt-amp gain to 1/10th or so. We don't want gain to vanish, just not go crazy. Instead of adding a 30-ohm diode to the 1,000-ohm diode, pad-out the cathode follower output with a few K. Such a resistor is shown, though no value given. This too exposes the nonlinear capacitance of the G-K diode, but a vacuum diode's capacitance is much less non-linear than a silicon on the edge of conduction.
> Just use a set of high value resistors from the plates to control the voltage reference level for the common referenced active loads.
I don't have M-J fig 2.49 handy, but if I picture this: you could wind up with one tube saturated and the other cut-off. i.e.: the correct total current but no control of current-split. This gets worse as gain increases.
A way to get high AC gain and DC level is to feed each pentode's screen from its plate, via an R-C decoupling network. This leads to a low value of R, so put in a buffer. A simple emitter-follower will work. The exact DC level can't be set, but you can design so it stays near a median value.
Note that you could do something like that with cascoded triodes without buffering, and get pentode-ish gain.
> Some ACCURATE mathematicians out there?
I'm no math-head, but I don't see that simplifications like gain/feedback tell you how it will "sound". Even if the simple equation says some term cancels, in real life it won't. And I think 30+ years of "point-oh-oh-oh THD" have shown that canceling some terms (the easy ones) does not always sound better.
> active loads ...with a current source in the tail
When I need precision, or easy calculation, yes transistors are a darn-sight easier to get what I want to get, at the gross level of bias and gain.
Have you worked with a boot-strapped amplifier? Yes it is a wacky idea, but it can work astonishingly well. There are things a bootstrap can't fix (BJT AB crossover distortion) but many things bootstrap very well, with features that are non-obvious until you slam it on the 'scope. And as for DIY: nice thing about bootstraps is that they usually work and are hard to kill.
Wollcott's cross-coupled positive feedback is, however, past my skill-set. That type of thinking went out of fashion when BJTs made "too much" gain. I know I've seen an explanation of how much PFB you can run, and ISTR that inside a NFB loop it can be enormous. One limit is device nonlinearity, but the cross-coupled PFB seems to give first-order cancellation of that.
Without the gain-boosting PFB, but with the bootstrapping: note that if you can stand a fairly low input impedance (~1K), the Wollcott can give high gain and enormous drive in just two bottles. His products run banks of output tubes: the cathode-follower can pump all those grids with relative ease. The boostrapping is unconditionally stable. The triode-pentode tube can be a low-price TV tube.
??? The grid-cathode port IS a diode.
Oh, you mean a sand-diode? Extra part with nonlinear capacitance? Sure! Only: why? In my rough-analysis, G-K conduction in the vacuum drops CF gain to half which drops volt-amp gain to 1/10th or so. We don't want gain to vanish, just not go crazy. Instead of adding a 30-ohm diode to the 1,000-ohm diode, pad-out the cathode follower output with a few K. Such a resistor is shown, though no value given. This too exposes the nonlinear capacitance of the G-K diode, but a vacuum diode's capacitance is much less non-linear than a silicon on the edge of conduction.
> Just use a set of high value resistors from the plates to control the voltage reference level for the common referenced active loads.
I don't have M-J fig 2.49 handy, but if I picture this: you could wind up with one tube saturated and the other cut-off. i.e.: the correct total current but no control of current-split. This gets worse as gain increases.
A way to get high AC gain and DC level is to feed each pentode's screen from its plate, via an R-C decoupling network. This leads to a low value of R, so put in a buffer. A simple emitter-follower will work. The exact DC level can't be set, but you can design so it stays near a median value.
Note that you could do something like that with cascoded triodes without buffering, and get pentode-ish gain.
> Some ACCURATE mathematicians out there?
I'm no math-head, but I don't see that simplifications like gain/feedback tell you how it will "sound". Even if the simple equation says some term cancels, in real life it won't. And I think 30+ years of "point-oh-oh-oh THD" have shown that canceling some terms (the easy ones) does not always sound better.
> active loads ...with a current source in the tail
When I need precision, or easy calculation, yes transistors are a darn-sight easier to get what I want to get, at the gross level of bias and gain.
Have you worked with a boot-strapped amplifier? Yes it is a wacky idea, but it can work astonishingly well. There are things a bootstrap can't fix (BJT AB crossover distortion) but many things bootstrap very well, with features that are non-obvious until you slam it on the 'scope. And as for DIY: nice thing about bootstraps is that they usually work and are hard to kill.
Wollcott's cross-coupled positive feedback is, however, past my skill-set. That type of thinking went out of fashion when BJTs made "too much" gain. I know I've seen an explanation of how much PFB you can run, and ISTR that inside a NFB loop it can be enormous. One limit is device nonlinearity, but the cross-coupled PFB seems to give first-order cancellation of that.
Without the gain-boosting PFB, but with the bootstrapping: note that if you can stand a fairly low input impedance (~1K), the Wollcott can give high gain and enormous drive in just two bottles. His products run banks of output tubes: the cathode-follower can pump all those grids with relative ease. The boostrapping is unconditionally stable. The triode-pentode tube can be a low-price TV tube.
Hi PRR,
"Oh, you mean a sand-diode?"
Yes, their non-linear capacitance is really only a problem near zero volts across the diode, by which time one is in clipping anyway. Putting in a sand diode is a good idea just for protection of tubes at warmup or from overdrive. The grid resistor should work well though for clipping and is simpler.
"the correct total current but no control of current-split. This gets worse as gain increases."
Ahh, yes, I was thinking of a SS amplifier with DC coupling where the global NFB would take care of this. With coupling caps in the lineup, one does need a DC servo on the screens (or G1s) as you suggested. Using a little AC neg. feedback too, like in the Johnson patent mentioned in another thread recently, would also help linearize the gain too. Pentodes and cascodes having 3/2 power law responses without any feedback.
"30+ years of "point-oh-oh-oh THD" have shown that canceling some terms (the easy ones) does not always sound better."
I agree fully. The P-P or cross-coupled architecture will also leave just odd harmonics. The concern about the distortion formula above is that it does not agree with the one given in the patent and would leave one vulnerable to significant odd order distortion from the high gain stage tube (D1).
I would much prefer something like an error correction output stage or active ultralinear over the positive feedback design, particularly for a class AB output (but these are tricky to implement in class AB). For P-P designs, I think one should get the higher odd harmonics reduced below audibility since the even harmonics that might hide them are largely gone. Clipping and power supply interactions are other areas one needs to get right.
"Have you worked with a boot-strapped amplifier?"
I haven't actually used bootstrapping before, but I have read some critiques of the technique. The main one being that since it is a form of positive feedback, any distortion in the output stage gets fed back to the driver. If the amplifier's output stage is a clean design then it should be OK. (ie, class A) Putting a SS current source in series with the bootstrap feedback would be a nice way to block distortion feedback, but would complicate the design and chew up a little driver B+ headroom.
Don
"Oh, you mean a sand-diode?"
Yes, their non-linear capacitance is really only a problem near zero volts across the diode, by which time one is in clipping anyway. Putting in a sand diode is a good idea just for protection of tubes at warmup or from overdrive. The grid resistor should work well though for clipping and is simpler.
"the correct total current but no control of current-split. This gets worse as gain increases."
Ahh, yes, I was thinking of a SS amplifier with DC coupling where the global NFB would take care of this. With coupling caps in the lineup, one does need a DC servo on the screens (or G1s) as you suggested. Using a little AC neg. feedback too, like in the Johnson patent mentioned in another thread recently, would also help linearize the gain too. Pentodes and cascodes having 3/2 power law responses without any feedback.
"30+ years of "point-oh-oh-oh THD" have shown that canceling some terms (the easy ones) does not always sound better."
I agree fully. The P-P or cross-coupled architecture will also leave just odd harmonics. The concern about the distortion formula above is that it does not agree with the one given in the patent and would leave one vulnerable to significant odd order distortion from the high gain stage tube (D1).
I would much prefer something like an error correction output stage or active ultralinear over the positive feedback design, particularly for a class AB output (but these are tricky to implement in class AB). For P-P designs, I think one should get the higher odd harmonics reduced below audibility since the even harmonics that might hide them are largely gone. Clipping and power supply interactions are other areas one needs to get right.
"Have you worked with a boot-strapped amplifier?"
I haven't actually used bootstrapping before, but I have read some critiques of the technique. The main one being that since it is a form of positive feedback, any distortion in the output stage gets fed back to the driver. If the amplifier's output stage is a clean design then it should be OK. (ie, class A) Putting a SS current source in series with the bootstrap feedback would be a nice way to block distortion feedback, but would complicate the design and chew up a little driver B+ headroom.
Don
Can you provide a reference? The only thing I found is Cherry, E.M., "A power amplifier improver", JAES 29, pp 140-147, Mar 1981.smoking-amp said:
This is not correct; it does not require unity gain. See section 3 in
Hawksford, M.O.J., "Towards a Generalisation of Error Correction Amplifiers", Proc. Institute of Acoustics, vol. 13, pt 7, pp 167-190, Nov 1991.
[Edit:] WTF is wrong with the forum software? It's not handling the first link right. Moderator, please fix the link, I can't get it to work no matter what I do.
Hi Nixie,
What I meant by unity gain was that the correction only need be sized to correct the error, rather than the umteen zillion times greater gain needed for conventional NFB. As the generalized paper explains, the feedback correction amplitude does need some equivalent attenuation if the stage being corrected has gain.
It seems that the nested feedback loop idea as proposed by Cherry in JAES has not been received well by amplifier designers due to practical difficulties. I believe the main substance there was to provide additional loop gain at the higher frequencies, then a controlled rapid gain dropoff before stability problems ensued.
A better nested loop example would be the J - loop idea: patent # 6201442 by James and Hildebrandt 2001. Also used in a commercial amplifier in Australia earlier I heard.
By figure 2.4, I assume you mean from the "generalization" paper.
For a P-P amplifier, I would envision an added diffl. stage that would compare attenuated output signals on the xfmr primary with the output tubes grid drive signals using resistor summing nodes at the diffl amp grids. An error correction (further attenuated down by diffl. cathode degen. or split resistor driver plate loads to compensate for diffl. amp stage gain) would be fed back (from the diffl. plates) into the plate circuits of the previous driver tubes so as to produce the grid drive signal corrections. These would tend to look like partial bootstrapping for the driver plate loads.
As pointed out in the article, some feedforward is helpful so that the error correction loop does not have to operate on the edge of instability. (some feedforward allows the feedback correction to be reduced below the unity error correction level, eliminating the unity gain around the correction loop) So I would also include some coupling of the diffl. ampl plates to the output tube screen grids as a feedforward active ultralinear path.
With typical high gain in the output tubes (conventional grounded cathode outputs) , the feedback attenuations become very critical since a small gain shift of the output tubes could push the loop into instability. This, I think, being the usual motivation for applying error correction only to low gain (and hence usually fairly stable gain) output stages. For the tube case, I would address this issue by using a partial CFB xfmr configuration, and taking the output signal samples from the output tube cathodes.
I have just completed collecting the requisite CFB xfmrs and associated supplies to try this out. So it is on the agenda. However, due to my recent move and thereby some lack of equipment, it is proceeding slowly. (Also due to too many other equally interesting projects running in parallel: true complementary P-P SET emulation, inverse triode feedback, 4 phase switchmode ferrite OT, and an extreme bandwidth long E-I common mode coupled xfmr. .... I need a staff to carry out the revolution!)
Don
What I meant by unity gain was that the correction only need be sized to correct the error, rather than the umteen zillion times greater gain needed for conventional NFB. As the generalized paper explains, the feedback correction amplitude does need some equivalent attenuation if the stage being corrected has gain.
It seems that the nested feedback loop idea as proposed by Cherry in JAES has not been received well by amplifier designers due to practical difficulties. I believe the main substance there was to provide additional loop gain at the higher frequencies, then a controlled rapid gain dropoff before stability problems ensued.
A better nested loop example would be the J - loop idea: patent # 6201442 by James and Hildebrandt 2001. Also used in a commercial amplifier in Australia earlier I heard.
By figure 2.4, I assume you mean from the "generalization" paper.
For a P-P amplifier, I would envision an added diffl. stage that would compare attenuated output signals on the xfmr primary with the output tubes grid drive signals using resistor summing nodes at the diffl amp grids. An error correction (further attenuated down by diffl. cathode degen. or split resistor driver plate loads to compensate for diffl. amp stage gain) would be fed back (from the diffl. plates) into the plate circuits of the previous driver tubes so as to produce the grid drive signal corrections. These would tend to look like partial bootstrapping for the driver plate loads.
As pointed out in the article, some feedforward is helpful so that the error correction loop does not have to operate on the edge of instability. (some feedforward allows the feedback correction to be reduced below the unity error correction level, eliminating the unity gain around the correction loop) So I would also include some coupling of the diffl. ampl plates to the output tube screen grids as a feedforward active ultralinear path.
With typical high gain in the output tubes (conventional grounded cathode outputs) , the feedback attenuations become very critical since a small gain shift of the output tubes could push the loop into instability. This, I think, being the usual motivation for applying error correction only to low gain (and hence usually fairly stable gain) output stages. For the tube case, I would address this issue by using a partial CFB xfmr configuration, and taking the output signal samples from the output tube cathodes.
I have just completed collecting the requisite CFB xfmrs and associated supplies to try this out. So it is on the agenda. However, due to my recent move and thereby some lack of equipment, it is proceeding slowly. (Also due to too many other equally interesting projects running in parallel: true complementary P-P SET emulation, inverse triode feedback, 4 phase switchmode ferrite OT, and an extreme bandwidth long E-I common mode coupled xfmr. .... I need a staff to carry out the revolution!)
Don
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