transconductance doubling
It is always interesting when two fairly well-known and certifiably intelligent people disagree on a topic.
It is also instructive to note that when someone makes a fairly unqualified generalization, it is vulnerable to being shot down by one example. In this case, I must agree more with Self and less with Leach.
Marshal has stated pretty much without qualification that gm doubling does not occur. We need only go to an extreme case to see that he is wrong. If we bias an output stage very heavily, we can see this fairly quickly. First, it is sometimes more convenient to think in terms of resistances instead of transconductances, where the "resistance" Re of each output transistor is 1/gm. Now recognize that the Re resistances are in series with the emitter resistors RE on each side. Suppose Re is 0.25 ohm. Suppose that the idle bias is one Ampere. Transconductance will be 40S, making Re a scant 0.025 ohms in the crossover region. We have set up an extreme case where the transconductance of the output transistors is so large that Re is always much, much smaller than RE. In the crossover region, both transistors are on, so the output resistance approaches RE/2. At signal swing extremes, only one transistor is on, so the output resistance approaches RE. Clearly, the relative transconductance of the output stage, as defined by the inverse of the net output impedance, has doubled in the crossover region with respect to its value well outside the XO region.
Indeed Leach hints at this himself on page 3 of his manuscript where he says "The addition of these resistors causes the transconductance to decrease for all values of output current. However, the transconductance decreases less in the crossover region than well away from the crossover region." If you take his subsequent Equations (16) and (19) and plug in Ib to be large into (16), you see immediately the gm doubling.
On page 4 he presents Eq (21) for the optimum value of RE for a Class AB (or optimally-biased B, as Self calls it) amplifier, where RE = Vt/Ib. He then says "Any value of RE greater than the value given by this equation causes the transconductance in the crossover region to exceed the transconductance well away from the crossover region. To calculate a typical value predicted by the equation, let Vt = 25 mV and Ib = 25 mA. We obtain RE = 1 ohm. This is much larger than the value typically used for RE. Thus we could conclude that transconductance doubling cannot be caused by the addition of emitter resistors with values that are typically used in output stages." Huh??
I don't think that conclusion follows. What about the people who don't bias their output stages at a meager 25 mA? Bias the stage at 100 mA and use 0.47 ohm values for RE, and you have entered gm-doubling territory. Bias the stage at 200 mA and use 0.22 ohm ballast resistors and you have entered gm doubling territory.
So I disagree with Leach on this one.
However, in fairness, Self makes a bit much of gm doubling. The effect is there, of course, but IN PRACTICE, compared to other evils, it is not as bad as he would have you believe. Moreover, when a BJT output stage is biased right at the "Class B optimum" it is, in my opinion, overly vulnerable to transient under-bias situations due to thermal mis-tracking. An under-biased Class-B amplifier is just asking for audible crossover distortion. So I would always err on the side of Class AB stages that are biased on the hot side of optimum, as long as I can assure adequate thermal stability.
Cheers,
Bob
It is always interesting when two fairly well-known and certifiably intelligent people disagree on a topic.
It is also instructive to note that when someone makes a fairly unqualified generalization, it is vulnerable to being shot down by one example. In this case, I must agree more with Self and less with Leach.
Marshal has stated pretty much without qualification that gm doubling does not occur. We need only go to an extreme case to see that he is wrong. If we bias an output stage very heavily, we can see this fairly quickly. First, it is sometimes more convenient to think in terms of resistances instead of transconductances, where the "resistance" Re of each output transistor is 1/gm. Now recognize that the Re resistances are in series with the emitter resistors RE on each side. Suppose Re is 0.25 ohm. Suppose that the idle bias is one Ampere. Transconductance will be 40S, making Re a scant 0.025 ohms in the crossover region. We have set up an extreme case where the transconductance of the output transistors is so large that Re is always much, much smaller than RE. In the crossover region, both transistors are on, so the output resistance approaches RE/2. At signal swing extremes, only one transistor is on, so the output resistance approaches RE. Clearly, the relative transconductance of the output stage, as defined by the inverse of the net output impedance, has doubled in the crossover region with respect to its value well outside the XO region.
Indeed Leach hints at this himself on page 3 of his manuscript where he says "The addition of these resistors causes the transconductance to decrease for all values of output current. However, the transconductance decreases less in the crossover region than well away from the crossover region." If you take his subsequent Equations (16) and (19) and plug in Ib to be large into (16), you see immediately the gm doubling.
On page 4 he presents Eq (21) for the optimum value of RE for a Class AB (or optimally-biased B, as Self calls it) amplifier, where RE = Vt/Ib. He then says "Any value of RE greater than the value given by this equation causes the transconductance in the crossover region to exceed the transconductance well away from the crossover region. To calculate a typical value predicted by the equation, let Vt = 25 mV and Ib = 25 mA. We obtain RE = 1 ohm. This is much larger than the value typically used for RE. Thus we could conclude that transconductance doubling cannot be caused by the addition of emitter resistors with values that are typically used in output stages." Huh??
I don't think that conclusion follows. What about the people who don't bias their output stages at a meager 25 mA? Bias the stage at 100 mA and use 0.47 ohm values for RE, and you have entered gm-doubling territory. Bias the stage at 200 mA and use 0.22 ohm ballast resistors and you have entered gm doubling territory.
So I disagree with Leach on this one.
However, in fairness, Self makes a bit much of gm doubling. The effect is there, of course, but IN PRACTICE, compared to other evils, it is not as bad as he would have you believe. Moreover, when a BJT output stage is biased right at the "Class B optimum" it is, in my opinion, overly vulnerable to transient under-bias situations due to thermal mis-tracking. An under-biased Class-B amplifier is just asking for audible crossover distortion. So I would always err on the side of Class AB stages that are biased on the hot side of optimum, as long as I can assure adequate thermal stability.
Cheers,
Bob
Re: Re: I repeat my Request
So how many MOSFET pairs do you need to parallel up to compete, in terms of linearlity, with a BJT class A stage?
I don't see the MOSFET gm disadvantage to be "largely irrelevent" here.
Cheers,
Glen
Bob Cordell said:
So how many MOSFET pairs do you need to parallel up to compete, in terms of linearlity, with a BJT class A stage?
I don't see the MOSFET gm disadvantage to be "largely irrelevent" here.
Cheers,
Glen
Re: Re: Re: I repeat my Request
Hi Glen,
I think the short answer is you need however many MOSFET pairs as you do for a BJT Class A amplifier. The main point being that when the MOSFETs are biased for Class A they have quite a bit of gm in the first place, and secondly the complementary characteristics of the positive and negative side gm fluctuations tend to cancel.
In the earlier example I cited, there were five MOSFET pairs for a 100-watt Class-A amplifier. The number of pairs needed to operate class A is assumed to be about the same for MOSFET or BJT. As I indicated, and as Nelson confirmed, the distortion of a MOSFET output stage in Class A should be very low. Also, I believe in that example I estimated the net output impedance of the output stage, before feedback, to be only about 0.05 ohms.
Given these conditions, why do you not see the gm disadvantage as largely irrelevant?
Cheers,
Bob
G.Kleinschmidt said:
Hi Glen,
I think the short answer is you need however many MOSFET pairs as you do for a BJT Class A amplifier. The main point being that when the MOSFETs are biased for Class A they have quite a bit of gm in the first place, and secondly the complementary characteristics of the positive and negative side gm fluctuations tend to cancel.
In the earlier example I cited, there were five MOSFET pairs for a 100-watt Class-A amplifier. The number of pairs needed to operate class A is assumed to be about the same for MOSFET or BJT. As I indicated, and as Nelson confirmed, the distortion of a MOSFET output stage in Class A should be very low. Also, I believe in that example I estimated the net output impedance of the output stage, before feedback, to be only about 0.05 ohms.
Given these conditions, why do you not see the gm disadvantage as largely irrelevant?
Cheers,
Bob
Re: transconductance doubling
It is even more interesting when a third steps in and tries to mediate the dispute. However, you pointed to a meager 25mA of bias current. But Ib is BASE current, not collector current. Does this modify your point of view?
Bob Cordell said:
It is even more interesting when a third steps in and tries to mediate the dispute. However, you pointed to a meager 25mA of bias current. But Ib is BASE current, not collector current. Does this modify your point of view?
Hi,
in the discussion above Ib = output stage bias current, sometimes referred to as Iq (quiescent current).
Some may argue that Iq also includes the voltage amp stage quiescent current demand. If that were so then even Iq is ambiguous.
in the discussion above Ib = output stage bias current, sometimes referred to as Iq (quiescent current).
Some may argue that Iq also includes the voltage amp stage quiescent current demand. If that were so then even Iq is ambiguous.
Re: Re: Re: Re: I repeat my Request
I disagree. In my opinion, when going the class A route, output device linearity is of great importance. There is no point in dissipating all that power if you're not going to aim for the best linearity. Source followers are not as linear as emitter followers and BJT’s benefit from being paralleled up just as MOSFETs do. Take a look at the Vgs Vs Id curves of the IRFP240 for drain currents in the range of a few amperes – eeuk!
From my experience in building/prototyping the various blocks of my rail-tracking 500W class A with 60MHz/35MHz Sanken BJT’s, the output impedance and distortion figures quoted by both you and Nelson look lame, and that is before I apply EC.
I have, finally, finalised the schematic for my bridged 500W amp and am proceeding to draw up the final schematics and layout the final board designs. I’ll be posting lots more about it in the future.
Here is a quick peek-a-boo of about 2/10 of the final circuit, which I’m currently drawing up (EC is as in Figure 4 of the Hawksford paper):
EDIT:
Before some clown cries "that can't work", the common mode output voltage is controlled by steering the LTP tail current's.
Bob Cordell said:
I disagree. In my opinion, when going the class A route, output device linearity is of great importance. There is no point in dissipating all that power if you're not going to aim for the best linearity. Source followers are not as linear as emitter followers and BJT’s benefit from being paralleled up just as MOSFETs do. Take a look at the Vgs Vs Id curves of the IRFP240 for drain currents in the range of a few amperes – eeuk!
From my experience in building/prototyping the various blocks of my rail-tracking 500W class A with 60MHz/35MHz Sanken BJT’s, the output impedance and distortion figures quoted by both you and Nelson look lame, and that is before I apply EC.
I have, finally, finalised the schematic for my bridged 500W amp and am proceeding to draw up the final schematics and layout the final board designs. I’ll be posting lots more about it in the future.
Here is a quick peek-a-boo of about 2/10 of the final circuit, which I’m currently drawing up (EC is as in Figure 4 of the Hawksford paper):
An externally hosted image should be here but it was not working when we last tested it.
EDIT:
Before some clown cries "that can't work", the common mode output voltage is controlled by steering the LTP tail current's.
Re: Re: Re: Re: Re: I repeat my Request
Hi Glen,
I did not say that output stage nonlinearity in a Class A amplifier was not important. It is obviously very important.
What I said was that a MOSFET output stage biased into Class A will have very, very good linearity. Although a BJT output stage may ultimately achieve a slightly lower output impedance, it has other issues to contend with, such as beta droop and ft droop, and the larger currents needed to drive it when the output current rate of change is large. However, those Sanken devices are nice parts and so these may not be very serious problems in the case you describe.
The output stage distortions Nelson and I were talking about were WITHOUT NFB and without EC.
In the hypothetical 100W Class A MOSFET amplifier I described, the output operating current range of each MOSFET was in the range of 0 to 1.0 ampere.
"source followers are not as linear as emitter followers". There you go again with an overly-broad generalization. It may often be true, but it is not always true.
Keep us posted on the actual measurements of your amplifier, it looks like an interesting design.
Cheers,
Bob
G.Kleinschmidt said:
Hi Glen,
I did not say that output stage nonlinearity in a Class A amplifier was not important. It is obviously very important.
What I said was that a MOSFET output stage biased into Class A will have very, very good linearity. Although a BJT output stage may ultimately achieve a slightly lower output impedance, it has other issues to contend with, such as beta droop and ft droop, and the larger currents needed to drive it when the output current rate of change is large. However, those Sanken devices are nice parts and so these may not be very serious problems in the case you describe.
The output stage distortions Nelson and I were talking about were WITHOUT NFB and without EC.
In the hypothetical 100W Class A MOSFET amplifier I described, the output operating current range of each MOSFET was in the range of 0 to 1.0 ampere.
"source followers are not as linear as emitter followers". There you go again with an overly-broad generalization. It may often be true, but it is not always true.
Keep us posted on the actual measurements of your amplifier, it looks like an interesting design.
Cheers,
Bob
Re: transconductance doubling
Bob,
I don't think Leach's statement should be considered as unqualified, even though it might appear to be at first blush.
To be more specific, Leach's qualification comes in the Eq (21) you mentioned on page 4, where RE = Vt/Ib, qualified with "Any value of RE greater than the value given by this equation causes the transconductance in the crossover region to exceed the transconductance well away from the crossover region." Using an Re defined by this equation, raising Ib further increases transconductance in the crossover region because the previously set selected Re now exceeds the limit.
Thus, if Ib is set, at say, 113ma, Leach's equation specifies an Re no larger than .22 ohms, which is pretty much in line with Self's optimum class B bias of 107ma. Other combinations of Re and Ib also fall in line with Self's optimum class B bias.
Using this example, if Ib is raised for the same Re of .22, Leach says that this Re value is thus greater than that which causes the transconductance in the crossover region to exceed the transconductance well away from the crossover region, therefore stating that transconductance rises at higher biases above Self's optimum class B.
This supports my previous statement of dissimilar definitions of classes. It appears that Self's optimum class B bias is the upper limit of Leach's qualification of Eq (21). Viewed another way, anything up to Self's optimum class B appears to meet Leach's view of class AB.
Using your example value of 100ma, Leach's qualification states that for any value of Re greater than .25 (your .47 example), transconductance in the crossover region will exceed that well away from the region.
For 200ma, an Re of .125ohm (your .22 example) is the upper limit.
Thus, your Re examples exceed Leach's upper limit before transconductance rise.
Therefore, there appears to be consistancy with Leach and Self in that for a given Re, raising Ib above Self's optimum class B bias current causes a rise in transconductance in the crossover region. The inconsistancy appears to be in the definition of operating classes.
Self also notes that if operated in class AB (i.e., above optimum bias), a lower value of Re gives lower distortion (primarily due to gain lowering into 4 ohms with higher Re vs 8 ohms). Thus, if you bias higher than Self's optimum, as you advocate to keep out of thermal underbiasing, it would appear that reducing Re would be in order both from Leach's Eq(21) and Self's observation of distortion at higher Re.
Bob Cordell said:
Bob,
I don't think Leach's statement should be considered as unqualified, even though it might appear to be at first blush.
To be more specific, Leach's qualification comes in the Eq (21) you mentioned on page 4, where RE = Vt/Ib, qualified with "Any value of RE greater than the value given by this equation causes the transconductance in the crossover region to exceed the transconductance well away from the crossover region." Using an Re defined by this equation, raising Ib further increases transconductance in the crossover region because the previously set selected Re now exceeds the limit.
Thus, if Ib is set, at say, 113ma, Leach's equation specifies an Re no larger than .22 ohms, which is pretty much in line with Self's optimum class B bias of 107ma. Other combinations of Re and Ib also fall in line with Self's optimum class B bias.
Using this example, if Ib is raised for the same Re of .22, Leach says that this Re value is thus greater than that which causes the transconductance in the crossover region to exceed the transconductance well away from the crossover region, therefore stating that transconductance rises at higher biases above Self's optimum class B.
This supports my previous statement of dissimilar definitions of classes. It appears that Self's optimum class B bias is the upper limit of Leach's qualification of Eq (21). Viewed another way, anything up to Self's optimum class B appears to meet Leach's view of class AB.
Using your example value of 100ma, Leach's qualification states that for any value of Re greater than .25 (your .47 example), transconductance in the crossover region will exceed that well away from the region.
For 200ma, an Re of .125ohm (your .22 example) is the upper limit.
Thus, your Re examples exceed Leach's upper limit before transconductance rise.
Therefore, there appears to be consistancy with Leach and Self in that for a given Re, raising Ib above Self's optimum class B bias current causes a rise in transconductance in the crossover region. The inconsistancy appears to be in the definition of operating classes.
Self also notes that if operated in class AB (i.e., above optimum bias), a lower value of Re gives lower distortion (primarily due to gain lowering into 4 ohms with higher Re vs 8 ohms). Thus, if you bias higher than Self's optimum, as you advocate to keep out of thermal underbiasing, it would appear that reducing Re would be in order both from Leach's Eq(21) and Self's observation of distortion at higher Re.
Re: Re: transconductance doubling
Some parts of Leach's paper here just seem to be inexplicable.
I see what you are saying, but if Leach is merely arguing that transconductance doubling doesn't happen if you follow Self's guideline, then why did Leach bother to write the paper?
Look on page 7 of his paper, where he begins a paragraph "To see how the falacy of "transconductance doubling" has arisen, consider ... Figure 8." It sure looks to me like he is disagreeing with Self on this, and I don't think it can be explained by a difference in semantics between optimally biased Class B and Class AB.
His speculation on how the thing got started is also not an argument I've ever seen.
I just don't know. I can't explain his manuscript. I also can't believe that a reviewer would have let a manuscript with such ambiguity get by.
Cheers,
Bob
pooge said:
Some parts of Leach's paper here just seem to be inexplicable.
I see what you are saying, but if Leach is merely arguing that transconductance doubling doesn't happen if you follow Self's guideline, then why did Leach bother to write the paper?
Look on page 7 of his paper, where he begins a paragraph "To see how the falacy of "transconductance doubling" has arisen, consider ... Figure 8." It sure looks to me like he is disagreeing with Self on this, and I don't think it can be explained by a difference in semantics between optimally biased Class B and Class AB.
His speculation on how the thing got started is also not an argument I've ever seen.
I just don't know. I can't explain his manuscript. I also can't believe that a reviewer would have let a manuscript with such ambiguity get by.
Cheers,
Bob
Re: Re: Re: transconductance doubling
Not trying to defend the paper so much as to figure out the conflict myself. I think what Leach is arguing is that it doesn't happen in AB amplifiers (see his title). So I think the conflict comes about in the definition of AB.
This is not a case of semantics. It is a case of the difference in simulation between figures 8 and figure 10. His argument is that the manner of simulating the situation as in figure 10 is incorrect, leading to the plots in figure 9, and leading to the conclusion that gm doubling occurs.
Nor I. But I never heard of "optimum class B" instead of class AB before Self seemed to have coined the phrase.
This is not a reviewed paper. It is a response that Leach wrote when he himself reviewed a paper submitted about gm doubling. Leach's paper is a result of his review and analysis of the submitted paper, which didn't get published. Perhaps the submitted paper can be found in AES preprints some where.
Bob Cordell said:
Not trying to defend the paper so much as to figure out the conflict myself. I think what Leach is arguing is that it doesn't happen in AB amplifiers (see his title). So I think the conflict comes about in the definition of AB.
Bob Cordell said:
This is not a case of semantics. It is a case of the difference in simulation between figures 8 and figure 10. His argument is that the manner of simulating the situation as in figure 10 is incorrect, leading to the plots in figure 9, and leading to the conclusion that gm doubling occurs.
Bob Cordell said:
Nor I. But I never heard of "optimum class B" instead of class AB before Self seemed to have coined the phrase.
Bob Cordell said:
This is not a reviewed paper. It is a response that Leach wrote when he himself reviewed a paper submitted about gm doubling. Leach's paper is a result of his review and analysis of the submitted paper, which didn't get published. Perhaps the submitted paper can be found in AES preprints some where.
Re: Re: Re: Re: Re: Re: I repeat my Request
Beta droop can be avoided in high power output stages with several parallel connected pairs and it can also be combated, to a large degree with an adequate driver stage.
I agree that a MOSFET class A output stage can have very good linearity, but I think a BJT's can do better.
Yes, I know that. My BJT stage does significantly better BEFORE I apply EC and global NFB.
I think that it is generally true.
I'm working on it (along with about 500 other projects 😉 )
Cheers,
Glen
Bob Cordell said:
Beta droop can be avoided in high power output stages with several parallel connected pairs and it can also be combated, to a large degree with an adequate driver stage.
I agree that a MOSFET class A output stage can have very good linearity, but I think a BJT's can do better.
Yes, I know that. My BJT stage does significantly better BEFORE I apply EC and global NFB.
I think that it is generally true.
I'm working on it (along with about 500 other projects 😉 )
Cheers,
Glen
Re: Re: transconductance doubling
I think Bob is right on this one. An RE calculation using Ib is meaningless unless the beta is known. An Ic value of 25mA would typically give RE=1 ohm. I think it was just a mis-print on Leach's behalf.
Tony
pooge said:
I think Bob is right on this one. An RE calculation using Ib is meaningless unless the beta is known. An Ic value of 25mA would typically give RE=1 ohm. I think it was just a mis-print on Leach's behalf.
Tony
BJT vs. MOSFET
I have a modest proposal that might help resolve the ambiguity surrounding the discussion around BJT vs. MOSFET. The approach is conceptually simple: agree upon a figure of merit and a method for measuring that figure of merit.
For starters, one might consider examination of the output stage in isolation, driven by an ideal source into an ideal load. Rail voltages and idle current could be fixed. It might be possible to examine distortion products and at least determine if such factors as gm doubling, Ft, etc are as critical as some say they are. While examining an output stage in isolation is certainly an artificial situation, it might help us to understand what factors are at work and to quantize those factors.
In an earlier thread I simulated (I know that is a dirty word for some, but I don't have a complete audio lab) output stages for three types of devices: BJT, lateral MOSFET, and vertical MOSFET. Interestingly, the distortion products for the three were not that different, being in the range of -60 to -65 dB. I wonder if there is really that much difference in performance between device types for well designed output stages.
Does anyone else have measured or simulated comparisons for different types of output devices?
I have a modest proposal that might help resolve the ambiguity surrounding the discussion around BJT vs. MOSFET. The approach is conceptually simple: agree upon a figure of merit and a method for measuring that figure of merit.
For starters, one might consider examination of the output stage in isolation, driven by an ideal source into an ideal load. Rail voltages and idle current could be fixed. It might be possible to examine distortion products and at least determine if such factors as gm doubling, Ft, etc are as critical as some say they are. While examining an output stage in isolation is certainly an artificial situation, it might help us to understand what factors are at work and to quantize those factors.
In an earlier thread I simulated (I know that is a dirty word for some, but I don't have a complete audio lab) output stages for three types of devices: BJT, lateral MOSFET, and vertical MOSFET. Interestingly, the distortion products for the three were not that different, being in the range of -60 to -65 dB. I wonder if there is really that much difference in performance between device types for well designed output stages.
Does anyone else have measured or simulated comparisons for different types of output devices?
Re: BJT vs. MOSFET
John Linsley Hood did it. See: "Expert Witness", EW+WW, August 1995, pp. 684-685.
And the winners are.....(drum roll please).....MOSFETs. 😀
Cheers, Edmond.
PS: Please don't ask me for a copy, as I don't have a scanner.
analog_guy said:
John Linsley Hood did it. See: "Expert Witness", EW+WW, August 1995, pp. 684-685.And the winners are.....(drum roll please).....MOSFETs. 😀
Cheers, Edmond.
PS: Please don't ask me for a copy, as I don't have a scanner.