nfb
Well, I need some time to look at all that involved algebra, but the points mentioned I can agree to:
- there is an element of infinity: in fact, the summer block with the pos feedback, open loop, has infinite gain. That is why the A-thd becomes zero: you divide it by infinity.
- indeed it breaks down with higher frequencies, as do all amps, feedback or not (unless you make the pos feedback track the poles&zeros of the G-block..?)..
Jan Didden
Well, I need some time to look at all that involved algebra, but the points mentioned I can agree to:
- there is an element of infinity: in fact, the summer block with the pos feedback, open loop, has infinite gain. That is why the A-thd becomes zero: you divide it by infinity.
- indeed it breaks down with higher frequencies, as do all amps, feedback or not (unless you make the pos feedback track the poles&zeros of the G-block..?)..
Jan Didden
Hm, let's see now. You can't go from fig. 1 to fig. 2 except in
theory, with a perfect amplifier, since you assume that you
can generate a perfect inverse to the transfer function of
the amplifier, ie. 1/(A*Va+f(Va)).
Fig. 3 is a slightly different variant, where A is cancelled and
indeed serves no purpose at all. The overall amplification is
set by G and beta, so all useful amplification is done in the
amplifying summation block and the whole problem is moved
there. You require an amplifier with a gain G s.t. G*beta is
the closed-loop amplification. That is, you must use an amplifier
in the summation block. This amplifier will also have distorsion,
noise etc. so the problem has just moved.
theory, with a perfect amplifier, since you assume that you
can generate a perfect inverse to the transfer function of
the amplifier, ie. 1/(A*Va+f(Va)).
Fig. 3 is a slightly different variant, where A is cancelled and
indeed serves no purpose at all. The overall amplification is
set by G and beta, so all useful amplification is done in the
amplifying summation block and the whole problem is moved
there. You require an amplifier with a gain G s.t. G*beta is
the closed-loop amplification. That is, you must use an amplifier
in the summation block. This amplifier will also have distorsion,
noise etc. so the problem has just moved.
Christer said:
Christer, I can go from fig1 to fig2 exactly: one thing is sure: Va=Vo/A always, every freq, with or without clipping. In fact, it is DEFINED that way. That's about the only thing that is ideal here!
In fig3, A is cancelled as far as its properties is concerned, but it is required to generate Vo so that the nfb loop can be closed. If you let A do the bulk of the work (the output stage), you can put in any crummy output stage and still have a great amp. You are right that the problem is moved to the summer block, but it is a quite different problem now: just a small signal amp block to be powerfull enough to drive the output stage. No need to tweak the gain very high to get low distortion, no problem with the stability problems that normally plague very high gain amps.
Jan Didden
Re: Can't quite cut it with the Big Boys, but anyway...
Well, the infinite gain is there when the pos fb factor equals the forward gain G. Less pos feedback means less than infinite gain. More pos feedback means that the output switches phase. But of course you can't run an infinite gain stage by itself, it needs a neg feedback loop to be usefull, and that is seen in fig 3.
So what we need is an amp block with a precise defined gain. You can use a neg fb amp as the gain block, for which the gain can be precisely set, and then wrap the defined pos fb around it. Works like a charm.
Jan Didden
Circlotron said:
Well, the infinite gain is there when the pos fb factor equals the forward gain G. Less pos feedback means less than infinite gain. More pos feedback means that the output switches phase. But of course you can't run an infinite gain stage by itself, it needs a neg feedback loop to be usefull, and that is seen in fig 3.
So what we need is an amp block with a precise defined gain. You can use a neg fb amp as the gain block, for which the gain can be precisely set, and then wrap the defined pos fb around it. Works like a charm.
Jan Didden
Reply to John Cox:
I can't for some reason quote your equation, but starting from the very first, which I agree to. I can't make the jump to your result. But remember that we must set betaP to 1/G, then we get:
Vin*G*A + Vo - Vi*A - betaO*Vo*G*A=Vo
which reduces to Vo(1-1+betaO*G*A)=Vi(GA-A)=Vi*A(G-1)
This then goes to Vo/Vi=A(G-1)/betaO*G*A and then we see that A drops out to give what I showed in my earlier post that now Vo/Vi=[(G-1)/G]*1/betaO.
Agreed?
Jan Didden
I can't for some reason quote your equation, but starting from the very first, which I agree to. I can't make the jump to your result. But remember that we must set betaP to 1/G, then we get:
Vin*G*A + Vo - Vi*A - betaO*Vo*G*A=Vo
which reduces to Vo(1-1+betaO*G*A)=Vi(GA-A)=Vi*A(G-1)
This then goes to Vo/Vi=A(G-1)/betaO*G*A and then we see that A drops out to give what I showed in my earlier post that now Vo/Vi=[(G-1)/G]*1/betaO.
Agreed?
Jan Didden
Jan
If you follow and verify my initial circuit equation then I am confident of the resulting transfer function as I cheat and use the Maple symbolics subset in MathCad (not endorsing MathCad or Maple vs any other symbolic package, it’s just the only one I’ve tried – and errors do still creep in as I find hand massaging the machine result is necessary for human readability and then I back substitute for machine verification)
My point in keeping the positive feedback separate (as Beta_p) is that it aids understanding the limitations of the real circuit where tolerances and passive network limits will prevent Beta_p from equaling 1/G: then you can ask “what if Beta_p equals 1/G to 0.1% up to 100 KHz” and then decide that 1/(1000A) can be approximated as zero and gain the insight that the positive feedback around G has added a large gain inside your feedback loop in series with A and by how much the gain could be limited by the G amplifier (and Beta_p) feedback resistor tolerances
My equation reduces to yours when Beta_p is replaced with 1/G and A does indeed drop out – it just doesn’t satisfy my curiosity about what happens in a real circuit
I do want to thank you for posting an interesting circuit and I would like to see the 1953 patent you feel anticipates it
If you follow and verify my initial circuit equation then I am confident of the resulting transfer function as I cheat and use the Maple symbolics subset in MathCad (not endorsing MathCad or Maple vs any other symbolic package, it’s just the only one I’ve tried – and errors do still creep in as I find hand massaging the machine result is necessary for human readability and then I back substitute for machine verification)
My point in keeping the positive feedback separate (as Beta_p) is that it aids understanding the limitations of the real circuit where tolerances and passive network limits will prevent Beta_p from equaling 1/G: then you can ask “what if Beta_p equals 1/G to 0.1% up to 100 KHz” and then decide that 1/(1000A) can be approximated as zero and gain the insight that the positive feedback around G has added a large gain inside your feedback loop in series with A and by how much the gain could be limited by the G amplifier (and Beta_p) feedback resistor tolerances
My equation reduces to yours when Beta_p is replaced with 1/G and A does indeed drop out – it just doesn’t satisfy my curiosity about what happens in a real circuit
I do want to thank you for posting an interesting circuit and I would like to see the 1953 patent you feel anticipates it
OK then, if we try to set the gain of the opamp at -1 by means of 2 equal value resistors, the gain will not be exactly -1 unless the open loop gain of the opamp is infinite. So the "precisely defines gain" falls slightly on the low side. Same error effect for positive feedback I expect. So if we haven't got the gain set exactly as we want is that going to do any great harm?janneman said:
new wheels within wheels
Well, we now get to the details of the implementation, which is OK with me.
What happens when G is less then calculated, the pos fb is slightly too large, right? That means the cancellation is not perfect. I did some experiments to make the pos fb adjustable, and adjust it to get min THD. There is a clear null when the ratios are just right.
On the other hand, if you have a modern opamp and you wire it up for say a gain of 1 or 2, what is the deviation from that due to non-infinite opamp open loop gain? Just a couple of ppm's probably?
We shouldn't think that this topology in practise gives zero THD; nothing on the great earth of us ever will. My goal was to get a very high open loop gain to make the nfb very effective, without the problems of instability and/or complex amplifier stages to reach stable, high open loop gain.
My initial experiment had as summing block a unity-gain current conveyer (current-in to current-out). Because I knew the current gain to be (close to) one, loading the output by a known resistor I got a precisely defined voltage gain. Then I wrapped the pos fb around that. Unfortunately, that particular IC is no longer commercially available.
Jan Didden
Well, we now get to the details of the implementation, which is OK with me.
What happens when G is less then calculated, the pos fb is slightly too large, right? That means the cancellation is not perfect. I did some experiments to make the pos fb adjustable, and adjust it to get min THD. There is a clear null when the ratios are just right.
On the other hand, if you have a modern opamp and you wire it up for say a gain of 1 or 2, what is the deviation from that due to non-infinite opamp open loop gain? Just a couple of ppm's probably?
We shouldn't think that this topology in practise gives zero THD; nothing on the great earth of us ever will. My goal was to get a very high open loop gain to make the nfb very effective, without the problems of instability and/or complex amplifier stages to reach stable, high open loop gain.
My initial experiment had as summing block a unity-gain current conveyer (current-in to current-out). Because I knew the current gain to be (close to) one, loading the output by a known resistor I got a precisely defined voltage gain. Then I wrapped the pos fb around that. Unfortunately, that particular IC is no longer commercially available.
Jan Didden
Folks,
Somewhat off track, but yesterday I took my picnic hamper and motored across to Circlotron. Melbourne is a huge city of 2500 square kilometres; I'm in a NW suburb, and he is in a far East suburb some 30 miles away.
Knowing our mutual friend is something of a nascent genius I wanted to hear his latest SE inductor loaded amp. I took along my own CCS loaded, SE hybrid amp as a reference, called the Glass Harmony. It uses a 6SL7 front end and a SS SE output stage to produce 28W of audio from a 150W dissipation. I brought along a couple of high quality D'Appolito speakers with the new X25G Vifa ring tweeter for auditioning purposes. Both our amps are hulking beasts, though Graham's is double the efficiency of mine. He uses a combination of IC buffer and SE mosfet voltage amplification for his front end.
The Circlotron amp is bloody good sonically. I was bowled away by how close it was to the GH! They sound very similar, although the SS front end is not as rich and warm as the 6SL7. There is no shortage of strong, deep bass on Graham's amp, and I can report that the inductive loading works extremely well. His choke is around 400mH, passes 3.5A and drops about 320mV. It's quite a large piece of kit, very heavy, and very cleverly made and implemented.
Graham is also a world class expert on power supply technology and has been extensively involved with ignition systems for drag car racing and power supply design. His workshop was a veritable Aladdin's cave of interesting parts and projects; it was wonderful to study such fascinating projects in another mans' shed! A number of private companies have recognized his special abilities and commissioned him to develop circuits.
His study resembles a programmers cave in a small software company; there are no less than five PCs there, all using weird and unconventional configurations for different purposes. His two sons appear to be highly computer literate as well.
We enjoyed a pleasant few hours discussing electronics. Here is a humble, intensely courteous man with a towering ability at technology - there is nothing he can't do. A quick perusal of his incredible contribution to this forum shows that his is a rare intellect. The company that employs him is lucky indeed!
I hope Graham and I keep in touch, and would like to express my public appreciation of a rare and shining talent, and a gratitude that he is willing to share it with all of us right on this forum.
Thank you, Graham!
Hugh
Somewhat off track, but yesterday I took my picnic hamper and motored across to Circlotron. Melbourne is a huge city of 2500 square kilometres; I'm in a NW suburb, and he is in a far East suburb some 30 miles away.
Knowing our mutual friend is something of a nascent genius I wanted to hear his latest SE inductor loaded amp. I took along my own CCS loaded, SE hybrid amp as a reference, called the Glass Harmony. It uses a 6SL7 front end and a SS SE output stage to produce 28W of audio from a 150W dissipation. I brought along a couple of high quality D'Appolito speakers with the new X25G Vifa ring tweeter for auditioning purposes. Both our amps are hulking beasts, though Graham's is double the efficiency of mine. He uses a combination of IC buffer and SE mosfet voltage amplification for his front end.
The Circlotron amp is bloody good sonically. I was bowled away by how close it was to the GH! They sound very similar, although the SS front end is not as rich and warm as the 6SL7. There is no shortage of strong, deep bass on Graham's amp, and I can report that the inductive loading works extremely well. His choke is around 400mH, passes 3.5A and drops about 320mV. It's quite a large piece of kit, very heavy, and very cleverly made and implemented.
Graham is also a world class expert on power supply technology and has been extensively involved with ignition systems for drag car racing and power supply design. His workshop was a veritable Aladdin's cave of interesting parts and projects; it was wonderful to study such fascinating projects in another mans' shed! A number of private companies have recognized his special abilities and commissioned him to develop circuits.
His study resembles a programmers cave in a small software company; there are no less than five PCs there, all using weird and unconventional configurations for different purposes. His two sons appear to be highly computer literate as well.
We enjoyed a pleasant few hours discussing electronics. Here is a humble, intensely courteous man with a towering ability at technology - there is nothing he can't do. A quick perusal of his incredible contribution to this forum shows that his is a rare intellect. The company that employs him is lucky indeed!
I hope Graham and I keep in touch, and would like to express my public appreciation of a rare and shining talent, and a gratitude that he is willing to share it with all of us right on this forum.
Thank you, Graham!
Hugh
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