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In Reply to: Re: I fixed a bias problem in my Mosfet follower (experiment #1 continued) posted by mfc on June 30, 2003 at 20:02:34:
"How lightly loaded are the output stage CFs in a Solid State
amplifier with respect to this discussion?
Since CFs are used as output stages, and speakers are the load,
how well behaved can this arrangement be?"
Ever hear about the "Super Linear Cathode Follower" that Allen Wright uses? I don't know if he invented it or he just coined the name, but it's pretty neat.First, much nonlinearity in cathode followers occurs because the plate current changes with changing Vg (and Vk). To combat that, a constant current source is used as the load for maximum cathode resistance. Second, since Vpk is also moving, there is distortion with Vg and Vk moving. To combat that, you add a "cascoded" stage from the Vk output and run another cathode follower back up to the plate voltage. In this arrangement as Vk moves, Vp moves with it as it follows Vk dynamically (with a level shift of course). Then you have a situation where Vpk and Ip are both constant with varying Vg and Vk. This forces Vgk to be constant. In other words, the original cathode follower never moves from its central bias point on any parameter with the signal, to a first order approximation!
The SLCF sounds very transparent so long as the load is not difficult and doesn't upset the constant currents and voltages around the cathode follower. The more you load it down, the less constant these operating points can be, same as before. I have heard an amp where it had a CF modified to be a SLCF and the difference was very nice.
It is also interesting to note that a FET and a pentode do not change behavior much with changing Vpk or Vds when operating in the constant current region (saturation region). So it does not need the plate voltage to be held constant with respect to its cathode like a triode (or BJT). What I am suggesting is that good power MOSFETs have that one advantage over BJTs, and pentodes over triodes. Maybe MOSFETs are better than BJTs as followers despite the fact that there is a tighter voltage control of Vbe over a Vgs for this one reason.
I seem to recall a schematic where someone used BJT followers on the output of an amp and used a cascoded BJT to hold Vce constant for increased linearity.
Follow Ups:
"In other words, the original cathode follower never moves from its central bias point on any parameter with the signal, to a first order approximation!"Kurt, if I read you right, then I would venture that J.R. MacDonald figured this out sometime in the early 1950's (Rev Sci Inst 25:2) although he was really just trying to reduce the input C to vanishing levels in order to take Hall effect measurements. MacDonald's topology shows a CC-loaded CF with a cascode on the plate.
Thorsten Loesch shows a very simple and elegant version of this circuit using a FET CCS:
http://www.fortunecity.com/rivendell/xentar/1179/theory/vasfda/vasfda.html
In 1960 Phillip Read published "Ultralinear Cathode Followers" (Rev Sci Inst 31:9). Read states that, by his method, "the harmonic distortion may be made arbitrarily small." Read's circuit uses a modified White follower.
Thanks for the references, Scott. It seems someone has already done it, but someone else later will often reuse or reinvent the idea and call it by another name. You are like a walking encyclopedia for tube audio.
Hi Kurt,> Then you have a situation where Vpk and Ip are both constant with
> varying Vg and Vk. This forces Vgk to be constant. In other words,
> the original cathode follower never moves from its central bias
> point on any parameter with the signal, to a first order
> approximation!I'm thinking in terms of transfer curves and feedback these days.
Just a mode to be in and kind of interesting for now. What I've
seen in doing some hi-res simulations is that signal swing relative
to a transfer curve is very important in determining the linearity
of the stage (neglecting feedback for the moment). This seems to
be because transfer curves are linear in their middle part, and
non-linear at their extremes.What you are talking about above in terms of transfer curves and
feedback is that the operating point can be very well confined so
that a signal won't cause much movement up and down the transfer
curve. Ideally, it would stay at a single point! This should make
for a very linear stage I would bet (without trying it). I might
have to try investigating the SLCF.What my previous message was saying and the very interesting thing
that clicked with me is to think about a CF in terms of feedback...
Picture a simple CF. It has an unbypassed cathode resistor...
this causes feedback to occur. To get as near to feedback=0 as you
can get with a CF, replace the cathode resistor with a current
source. In this case there still is a feedback mechanism. It is the
load. In fact, the load is now *the primary* feedback mechanism.
Now if the load isn't well behaved (reactive), then feedback won't
occur at the 180 degrees like it is supposed to and won't be well
behaved either. This would cause problems.Other types of stages (like a common cathode, or transformer) have
their feedback determining component more isolated from the load.This leads me to wonder about Solid state output stages that use
followers in the power output stage connected to a load (speaker)
that isn't well behaved at all. If the load is now the primary
feedback determining part of the circuit, and a load isn't well
behaved, then this would lead to problems, unless the supporting
circuitry can hold the devices so that they don't swing much over
their transfer curves.
And if "the supporting circuitry can hold the devices so that they don't swing much over their transfer curves" then we eliminate nonlinearity so we can now add feedback without causing multiplication (ideally).
Hi Scott,I wish their was a better term for multiplication. It makes it
seem like these terms (harmonics) weren't present in the first
place. It looks like they are always present, they are just
buried way down and possibly under the noise floor.
I see from a previous message...http://www.audioasylum.com/forums/prophead/messages/4028.html
...that you realized this too. Non-linearities just cause these
terms to increase in amplitude.Back to this other train of thought I'm currently riding...
and not being that familiar with solid state output stages...isn't
an emitter follower a common power amplification stage? Does the
argument about the load being the primary feedback determining
component in an emitter follower set off alarm bells with you?Mike
"I wish their was a better term for multiplication."The right word I think is *intermodulation*. "Multiplication" is used to highlight the fact that higher harmonics are increased in certain topologies (by a sort of "IM shaping" process).
"...isn't an emitter follower a common power amplification stage?"
The most common, I would say.
"Does the argument about the load being the primary feedback determining component in an emitter follower set off alarm bells with you?"
It does, and this is something that Nelson Pass begins to address in his Mar 1978 Audio article, "Cascode Amp Design". His Fig. 3 shows an amplifier operating near the center of the transfer curve (mapped onto the actual collector characteristics in this case). His Fig. 7a shows an emitter-follower with CCS. His Fig. 7b shows the same circuit with a cascode (which being a SS version of the Loesch CCCF I cited earlier). Pass's Fig. 8b shows the spectrum for the CCS circuit. It shows strong harmonics. His Fig. 8c shows the spectrum for the cascode-CCS circuit. It shows virtually no harmonics.
His Fig. 5 shows the region of cascode operation, which maintains Vce constant. This corresponds to horizontal characteristics.
Unfortunately Pass doesn't show distortion when the cascoded emitter-follower is loaded by a loudspeaker. He does imply there will be moderate distortion if the amp is not operated in pure class A.
Actually the emitter follower is one of the best output stages possible, for several reasons: First, it has a very low intrinsic output impedance. Second, it can be very linear on an absolute basis, because the dynamic change in voltage across the Vbe junction will be a small fraction of the total voltage across the load. Three, an emitter follower will 'bootstrap' most of its non-linear input capacitance or Cbe to reduce the effective capacitance to a much lower value. Four, an emitter follower is very wide bandwidth. Five, the pentode like characteristics of a bipolar transistor buffer the output stage from power supply variations. etc. This also goes for FET's, in general.
However, this is under ideal conditions. To make this possible, you must bias the transistor so that it can operate at or near its best operating point, and you must drive the transistor with a low impedance source, or else you will get distortion from non-linear beta and varying input impedance of the output stage with load impedance changing. Many designs make serious errors in not driving the transistor follower with a low enough impedance.
Hello,> First, it has a very low intrinsic output impedance.
Yes, relative to an 8 ohm speaker load, an emitter follower
built with some beefy transistors could make 8 ohms seem like
a light load. That means it doesn't have to "put out" all that
much. Seeing that light loading causes harmonics to go way down
in an emitter follower, I can see that this would give an emitter
follower a chance to perform well.What bugs me though is this inherent problem that the load is
part of the feedback loop. I'm kind of wondering into uncharted
territory when I start thinking about frequencies where feedback
isn't exactly 180 degrees and the effect this has. Any thoughts
or references along these lines would be welcome. One general
question is: What effect does feedback have when it isn't
exactly 180 degrees?Mike
> What effect does feedback have when it isn't
exactly 180 degrees? <If it's 360 degrees it becomes an oscillator. If it's not exactly 180 degrees as most feedback loops get into near the point where the gain gets to one, the difference from 180 degrees is called the phase margin and this results in various amounts of overshoot on a transient response. So any deviation from 180 degrees of feedback is subject to some miscues in transient performance.
With respect to how much steady state distortion reduction you get, I believe you can take the real part as the sole contributor. The amount of imaginary part will have no help nor hindrance in that regard I believe because it does not oppose the signal nor increase the signal - it is "orthogonal" to the signal, which is therefore neutral in steady state conditions. I'm not reading any technical manual, I am just thinking out loud here. Scott will probably give us the exact answer to that if he is so inclined to do so.
I think the real part can show a negative feedback or a positive feedback. If for example the feedback is less than +/-90 degrees it can be considered positive feedback (negative resistance in the feedback loop) and if it is more than +/-90 degrees then it is negative feedback (positive resistance). Even with positive feedback it might not oscillate. For oscillation to occur the real feedback times the loop gain must be greater than or equal to one. Again, I don't think the imaginary part plays much of a role in the steady state.
Hi Kurt,I guess I should clarify. I wasn't referring to Nyquist or
Bode diagrams or any of the basics. I was more thinking about
phase modulation of the signal, when the feedback deviates
just slightly from perfect.Mike
When the phase modulates, IMD occurs. The spectrum of phase IMD contains the same frequency components as amplitude IMD, but their phases differ by pi/2. AIMD is usually associated with signal-induced gain variations (e.g., transistor beta nonlinearity); PIMD is usually associated with signal-induced variations in shunt C (e.g., Cc-b). If you want to crunch the numbers see Cherry, "Amplitude and Phase of Intermodulation Distortion," JAES, May 1983.For an interesting discussion of cathode followers vs anode followers driving capacitive loads at high f's, see Keen, "Anode-Follower Derivatives," Wireless Eng, Jan 1953. Hint: one does better on negative cycles, the other on positive cycles.
For cathode followers driving C with large signals see Cocking, "Cathode-Follower Dangers," Wireless World, Mar 1946.
Hi Scott,> The spectrum of phase IMD contains the same frequency components as
> amplitude IMD, but their phases differ by pi/2.Ahh, very interesting. Would the amplitude of PIMD depend on the
amount of phase deviation from 180?PIMD seems like a real interesting challenge to look at. I think
I'll try a few things and then report back. It would certainly be
worth reading those articles, thanks for providing the references.
Exactly along the lines of what I was hoping for. Do you get these
real old articles online, or thru a library?
Thanks,Mike
"Would the amplitude of PIMD depend on the amount of phase deviation from 180?"Mike, the amplitude of PIMD depends on the sensitivity of the amplifier to fractional changes in gain-BW product brought on by signal-induced capacitive variations in devices such as BJT's. You can see how this sort of thing relates to complex frequency and group delay. Think of it as signal-induced *changes* in group delay.
PIMD is seen most commonly in poorly-executed feedback amplifiers but can occur elsewhere. Wide open-loop BW amplifiers with high feedback factors reduce PIMD right along with all the other IMD's (excepting TIMD which has to be dealt with at the feedback summing junction). This is another argument for reducing driver impedance, as jc suggested earlier for another purpose.
"Do you get these real old articles online, or thru a library?"
I get 'em the old-fashioned way, by standing for hours over a hot mimeo-, er, photostat machine at the periodicals archive. A comparatively small number of vintage articles have appeared online. I had to go to the Imperial College basement archive (next to the Science Museum in Kensington) to get some of these British articles of c. 1920. Found some more at the Royal Society, and a few more at the London Patent Office. Mostly I get 'em closer to home: e.g., from SCU, SJSU, Stanford, and UCB.
Hi,> Think of it as signal-induced *changes* in group delay.
OK, I get the picture now. Thanks
It seems like there is a lot of rediscovering of old ideas that
have been forgotten. I guess you can just ignore them altogether and
mix things up and see what happens. I think it is fun to be able to
do both.
"It seems like there is a lot of rediscovering of old ideas that
have been forgotten."Yeh, but it's a helluva lot easier to rediscover an old idea than to discover it in the first place. The thing is, old ideas are "in the air". Even if the full-blooded idea no longer circulates, parts of it still exist to tickle the fancy and spark the "new" discovery.
What bothers me is people who don't look very hard for their precedents.
> I was more thinking about phase modulation of the signal, when the feedback deviates just slightly from perfect. <But I think it's the same situation. Phase modulation is a transient property, and goes away in the steady state condition. The phases will be altered by step conditions and ring and settle back to no phase modulation. Phase modulation is also a noise induced property, but that's another story, as noise introduces unsettled conditions constantly.
Well, Pass makes no secret that class A operation rules, and that means high idle currents, not just in the output stage but in the driver stage. Not the kind of thing we're likely to see in an op-amp anytime soon.It's interesting that Pass has given up trying to force the operating point in favor of simpler designs.
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