An experimental 4-th order linear audio power amplifier

[GK]

Hello all,

Here are some details of an experimental audio amplifier design I have come up with that I hope will set a precedent for low distortion.

It is essentially a conventional audio power amplifier wrapped up into a conditionally stable 4-th order feedback loop to maximise feedback in the audio frequency spectrum.

A detection circuit that automatically senses whenever the amplifier enters a non-linear region of operation (such as during power up / down or when approaching/entering clipping/saturation) electronically and seamlessly switches the feedback loop into an unconditionally stable, 1st order system for the duration that the amplifier remains in a non-linear region of operation. This maintains stability under all operating conditions (well, that is the plan anyway  )

I actually derived this idea from the Hypex patent by Class-D amplifier designer Bruno Putzeys for a 5-th order self oscillating class D amplifier. See here:
http://www.google.com/patents/US20110068864

However Class D doesn’t excite me much and I’d like to have a go at applying the principle to a linear amplifier. Here is a simplified/preliminary schematic:




The majority of the loop gain throughout the audio frequency spectrum and three of the poles of the 4-th order system are provided by the three series-connected integrator stages U2 through U4. There are also three zeros which cause the open loop response to revert to a single pole roll-off as the loop gain goes through 0dB, thus making the system conditionally stable. Here is the fourth-order loop gain and phase response:



Now, the capacitor of each integrator is connected in parallel with an analogue switch. When these three analogue switches are activated, the integrators are turned from integrators into basic inverting stages. When this happens the feedback loop transforms into a 1st order system. Here is the open loop gain and phase response with the switches activated:



The trick to the whole concept of course, is the detection circuit that activates the analogue switches, switching the control loop into a 1st order system whenever the amplifier begins to enter saturation. This is achieved by a window comparator based on IC’s U6 and U7 that effectively monitors the “error voltage” at the virtual earth of the feedback resistor network. Any major +/- voltage deviation here indicates that the amplifier is coming “out of regulation” and this is when the detection circuit activates to switch to a 1st order response. So then, does it work? Well, here is the amplifier clipping at 20 kHz with almost 6dB of overdrive: (EDIT - the schematic has since been modified - see reply#8).



The green trace the amplifiers voltage output, the purple trace is the detector output and the red trace is an amplified version of the virtual earth signal. As can be seen, there isn’t a hint of global loop oscillation as the system automatically reverts from a conditionally stable 4-th order one to an unconditionally stable 1-st order one during the saturation/clipping interval.
   
And finally, here is the (unsaturated, 4-th order-operating) square wave response at 20 kHz:



Note that the overshoot of the conditionally stable 4th order loop is successfully suppressed by the signal input filter (R18, C7) which implements a pole slightly below the frequency at which the three integrators are zeroed out. 

I hope to get a real life experimental prototype built up an operational in the week or so.
 

[GK]

Hmpff. I guess Nth-order control loop theory and design is a boring topic then. 

Unless I’m a dunderhead and missing something in a serious way I think the concept is sound, but success in real life I think will be dependant on the “saturation” detector being made sufficiently sensitive. A more refined circuit than what I posted above may be required. My current plan is to capacitively couple (to eliminate DC offsets) the buffered virtual ground (summing junction) signal to a moderate-gain limiting amplifier prior to the window comparator. This way the circuit could be configured to easily trigger on mV's of “error” signal. A better window comparator design having hysteresis to eliminate oscillation will also be implemented in the initial prototype.

Any ideas? Sounds good? If the Hypex “N-core” amplifier modules were not so expensive I would have bought one already to reverse engineer it, with particular interest in the saturation detection circuitry.

Also, can anyone suggest a good performing analogue switch that operates on +/-15V supply rails and has lower parasitic capacitances than the DG4XX series? To simplify board layout my preference right now is for “single” devices.
 

[robrenz]

Not boring, just way beyond me being able to make any valuable input 

[c4757p]

Hmpff. I guess Nth-order control loop theory and design is a boring topic then. 

Not at all! Damn, I missed this post yesterday. And...

Not boring, just way beyond me being able to make any valuable input 

But I can still salivate, can't I?

[GK]

LOL. Well, we will just have to wait until the first soldered prototype materialises before drooling too much  . However hoping that the concept works as seamlessly in real life as it does in SPICE I am quite excited already about the potential. An amplfier with a distortion residual at any power level and any audio frequency indistingushable from the <-120dB THD+N residual floor of my THD analyser ( http://www.users.on.net/~glenk/thd/thd.htm ) is a very real possibility.
There is also potential scope for increasing the order beyond the 4th just by adding additional integrator stages.

If it wasn't for the precedent established by the 5th-order "N-core" amplifiers by Hypex I don't think this is a concept that I would have ever considered workable or worth experimenting with.

 

[digsys]

Hmpff. I guess Nth-order control loop theory and design is a boring topic then.   

More that many people have no idea what it means :-)  Way over my head. I did dabble with valve amps and early silicon
types in my younger years. In a "specialist" case like this, I'd bump the thread occasionally for the next few days. I know
there are several audio-freaks that habit here, you just need to ferret them out !

Also, can anyone suggest a good performing analogue switch that operates on +/-15V supply rails and has lower parasitic capacitances than the DG4XX series? To simplify board layout my preference right now is for “single” devices. 

I used to remember using a TI one ages ago, when I did mixing desks. I'd have to see if I can find the old drawings.
On another note, can you repair Valve amps :-) ?

[GK]

I think I am going to end up selecting a DG4XX series after all. The "off" in/out capacitance of 8pF for the devices I am looking at really are small enough and the parts are readily available in easily soldered SOIC. There are some other nicer parts available but teenie little 8-pin SOT-23's kind a suck for a home brew PCB.
I've repaired a few valve amps that I have owned myself, but never anyone elses 

[GK]

Unless I’m a dunderhead and missing something in a serious way I think the concept is sound, but success in real life I think will be dependant on the “saturation” detector being made sufficiently sensitive. A more refined circuit than what I posted above may be required. My current plan is to capacitively couple (to eliminate DC offsets) the buffered virtual ground (summing junction) signal to a moderate-gain limiting amplifier prior to the window comparator. This way the circuit could be configured to easily trigger on mV's of “error” signal. A better window comparator design having hysteresis to eliminate oscillation will also be implemented in the initial prototype.

OK, I've done a fair bit more experimentation now and I appear to be getting this "saturation" detection under control. It turns out that a significantly more complex overall detection system is going to be required for the best overall control of the clipping event. Just detecting the "error voltage" at the virtual earth appears to be adequate for the taming of stability, but not for the cleanest possible recovery from clipping, particularly at low frequencies and at only very slight/minimal onset amplitude clipping/saturation.

The amplitude of the "error" signal is proportional to frequency, due to the decreasing open loop gain as frequency increases. This means that the threshold of detection has to be set high enough to accommodate the amplitude of the error signal at the highest audio frequencies under normal operating conditions. For example, if the amplifier has a loop gain of 54dB (500 Av) at 20kHz, and the output of the amplifier clips against the rails at +/-30V, then the amplitude of the error signal will be 30V/500 = 60mV peak at 20kHz, at the onset of clipping. For a reasonable margin of safety the detection threshold could therefore be set to, say +/- 100mV.

This makes the detection system rather sensitive and effective to a clipping event at 20kHz (as demonstrated in my simulation as shown in my opening post), but a great deal less so at 20Hz. This is because the loop gain is a great deal higher at 20Hz than it is at 20kHz (especially in an n-th order system) and the amplitude of the error signal is so low that it essentially lives down in the noise. At 20Hz, an error signal amplitude as large as +/-100mV represents a significant aberration in the output signal, and the clipping recovery performance is nowhere near as good as it is at 20kHz. In fact my sims show significant (ugly) output voltage waveform distortion both entering and leaving clipping to a degree that I do not consider acceptable. 

One cure would be to deliberately kill the open loop gain such that the open loop bandwidth is equal to 20kHz. This would make the the loop gain throughout the audio frequency spectrum essentially constant. This means that the amplitude of the error signal from 20Hz to 20kHz would also be essentially constant, and the threshold of detection constantly optimal throughout the audio band. However this would mean limiting the loop gain at all frequencies to only that which can be safely applied for stability reasons and adequate phase margin at 20kHz; which is essentially hobbling the amplifier and NOT making full use of negative feedback.

Fortunately, however there is a better cure. I am currently working on a complementary detector which senses a clipping event by monitoring and triggering on the slightest conduction of the anti-saturation clamp transistors applied to the stage that those who are familiar with basic amplifier topologies will recognize as the "VAS" in my simplified simulation schematic.

I say "complementary" as this detector will not make the one monitoring the virtual earth error signal obsolete. Their digital outputs will be ORed together to the analogue switch control line. The "error" signal still needs to be monitored to cater for "saturation" events that are not related to clipping, such as when the power output stage protection circuitry limits the load current due to a short or excessively low impedance load being connected to the speaker terminals.

My revised detection scheme appears to be working rather well in the simulator and I will post updated "preliminary" results after another evening of experimentation and circuit revision / concept evolution.







   
 

   
 

[GK]

OK, a bit earlier than expected. I just posted the revised schematic and edit the opening post to show it. The schematic now incorporates the clipping detector comparators as mentioned, having their outputs ORed with the error signal detection comparators. The circuit is still rather primitive and none of the comparators have any hysteresis, so there is a little comparator oscillation on state changes to very low dv/dt signals, but besides that the clipping performance at all frequencies is now almost perfect. He it is at 1kHz. Again the "saturation" comparator output / analogue switch control line (red trace) is plotted along with the amplifiers voltage output, demonstrating how the loop response reverts to 1st order during the clipping interval.






 

[ftransform]

If you tell me what the hell this thing is useful for I will etch a board and make it myself.
It sounds pretty awesome, I know a little bit about dbs, degrees, poles and zeros, but 

A sonic welder? A boom box? Is this kind of circuit useful for driving some kind of transducer? I feel like doing anything mechanical with what you are building is totally over kill.

[DrGeoff]

Missed this thread, interesting.
Have used MAX333's before (Off C = 5pF, +-15V rails), although not in this application.
Is your detector going to detect the clipping event or will it detect the onset of clipping, allowing a margin to react before the clipping event?
Or rather than a clipping detector, a distortion detector, comparint the input and output signals (with scaling) to sense the onset of clipping or non-linearities in output?

[GK]

If you tell me what the hell this thing is useful for I will etch a board and make it myself.
It sounds pretty awesome, I know a little bit about dbs, degrees, poles and zeros, but 

A sonic welder? A boom box? Is this kind of circuit useful for driving some kind of transducer?

Just a speaker for playing tunes  . The aim is to get the distortion extremely low, simply as an exercise in design. Mind you a typical forum audiophile would fall over himself to pompously inform you with petty glee just how horrible such a contraption would supposedly sound due to the use of all that evil negative feedback and "blind faith" in measurement, so depending on who you listen to driving a speaker with it may or may not be a good thing.

I am currently laying out a PCB for the first real life prototype to test the feasibility of the concept. If it actually works out, I will design a complete, functional and practical amplifier module along the lines described, with full details including PCB Gerber files to be published on my website like my other projects and projects pending.

     

[GK]

Is your detector going to detect the clipping event or will it detect the onset of clipping, allowing a margin to react before the clipping event?
Or rather than a clipping detector, a distortion detector, comparint the input and output signals (with scaling) to sense the onset of clipping or non-linearities in output?

The clipping detector shown works by detecting current conducted by the VAS anti-saturation clamp, so clipping has to begin for the comparator to react. However, as far as my simulations go this seems to be adequate. I'll know for sure though after conducting some thorough testing on the up-coming prototype. I have also considered a "preemptive" rail-tracking comparator that triggers on voltage thresholds just below the actual threshold of clipping. That's currently my plan B.
Your suggestion of a distortion detector may also be a feasible solution, but I'm thinking rather as a more sensitive detector of saturation not related to clipping (instead of the current scheme of simply triggering on excessive amplitude of the virtual earth "error" signal). Pretty much any good idea or detection concept in on the cards at this early stage of the experimental design 
 

[GK]

Not boring, just way beyond me being able to make any valuable input 

Hey, just on a previously discussed topic, that may be of interest, one of the ~30 ancient texts on analog computing that I have tracked down from secondhand booksellers over the net has a really cool chapter on mechanical computing elements. See the attached pics for a taster 

The book is Analog Methods, second edition, Karplus & Soroka.
 

[robrenz]

Just like the electronic versions those things would work great if you could turn off friction and gravity and have infinitely rigid material that had no mass. Plus machine the curves with no error, but that should be easier on material with no mass

[GK]

You know back in the day the inaccuracies of these kind of computing machines wasn’t that much of a limiting factor in a lot of circumstances, as the variables for the problems they were used to solve were often representative of physical phenomenon which could not be measured or ascertained by indirect methods with a great deal of precision in the first place.

[SeanB]

Mechanical ones were used for decades as autopilots, the Dakota used one that ran on engine vacuum to power it, and it was reasonably reliable, enough so that you could let go of the controls and have "Charlie" fly the plane for hours. Add a bit of electrical parts and you got the later autopilots that could go cross continent with minimal error.

[GK]

Coincidentally, this morning I picked up my second Korn & Korn book; Electronic Analog Computers, second edition, 1956, from the post depot. Just had a chance now to put my feet up and have a flick through. It contains a whole section on the simulation of airplane flight and auto pilot systems. How cool is that?!



 

[toli]

Hello GK,

First I must admit I didn't read all of the posts in the thread, just the first few so what I'm asking might have been discussed already.

The idea is very interesting indeed, and I must say I really like it. I see you took into account the inductance of the load with the zobel network, however, did you also check the response caused by the clipping detectors under different conditions/frequencies? While I didn't think about it too much so I might be completely wrong, I'd assume the way it enters/recovers from clipping can have a very large effect on the stability of this feedback loop.
In a way, to me, it seems similar to some of the current limiting circuits in regulators (as both of them change the operation of the feedback loop during operation), making the current limiting too fast can result in stability issues under certain load conditions. I know you did a simulation and posted the results in the first post, however I think different load conditions and frequencies should be tested to be certain there isn't an issue.

Again I might be completely wrong, and in that case you can just ignore it

[lewis]

Is the goal of the design to produce an amplifier with the lowest THD possible? If so, you might want to look into Hawksford Error Correction. Bob Cordell has some great material in this regard, and Dougls Self offers some excellent insights for reducing the THD of LIN-topology amplifiers, some of which I'll mention below.

My experience with buggering about with the feedback network of a high-gain amplifier is that 'you're in a world of shit', especially when you connect the amp to a reactive load and feed it a music signal, but my knowledge of control theory here is very limited. The key is when you test the amp under real world conditions, ensure you test the amp under real world conditions! A simulated reactive load gives a good indication of stability without damaging voice coils. http://www.aikenamps.com/spkrload.html

The output stage looks pretty darn good, emitter degeneration on the differential pair loaded with a degenerated current mirror is a very good idea, as is the overcurrent protected and buffered VAS (although there's no conventional output current protection so it may not be needed). The miller compensation is slightly unusual, at first sight the 470R looks too high and/or shouldn't be needed, but if it works what the hell. You might want to consider 2-pole miller compensation, it increases open loop gain in the audio bandwidth giving you more feedback, but my knowledge is limited here.

Replacing the series diodes in the current sources with a green LED tracks the Vbe thermal drift a bit better; a 2-transistor current source improves accuracy and stability. Biasing the current source with two series resistors with a heavy capacitor down to the negative rail at the midpoint improves PSRR. Decoupling the differential pair with a simple RC or a capacitor multiplier on each rail improves PSRR dramatically. A cascode on the diff-pair has a similar effect. You may also need a few uH series output inductor (8-10 turns of thick wire around a pencil works well) with a 1-10R resistor in parallel with it before the output zobel but after the feedback take-off point to improve stability on transients. All these little techniques can reduce the distortion of the amplifier before feedback is applied resulting in substantial gains in performance when the loop is closed.

But definitely look into Hawksford.

[GK]

OK; the goal at the moment is to develop an verify the feasibility of the "Nth-order" control scheme. The design shown is only a basic/simplified one knocked up in the simulator for the purpose of evaluating the feasibility and operation of this high-order feedback and stability control scheme; the actual discrete power amplifier part isn't at all intended to be an advanced, an ultra low distortion, or even a complete design in its own right. I am currently working on the PCB for a 5th-order implementation of the scheme detailed (four op-amp integrators rather than three) based on a small, 8W/8R discrete op-amp design. At this stage there is no point in prototyping anything more elaborate to proof or otherwise the concept.

To be honest I'm not particular enamored with Hawksfords "error-correction" scheme. It's just another method of applying an increased amount of negative feedback around the power output stage which can be done just as effectively by other means without the need for a critical distortion "null" adjustment. 

The 470 ohm resistor in series with the Miller compensation capacitor introduces a small amount of phase lead to improve the phase margin at the unity loop gain frequency. 2-pole compensation applied here would not be entirely compatible with the overall concept as implemented - which as shown thus far is in fact a 4-pole system.
 

[GK]

Hello GK,

First I must admit I didn't read all of the posts in the thread, just the first few so what I'm asking might have been discussed already.

The idea is very interesting indeed, and I must say I really like it. I see you took into account the inductance of the load with the zobel network, however, did you also check the response caused by the clipping detectors under different conditions/frequencies? While I didn't think about it too much so I might be completely wrong, I'd assume the way it enters/recovers from clipping can have a very large effect on the stability of this feedback loop.
In a way, to me, it seems similar to some of the current limiting circuits in regulators (as both of them change the operation of the feedback loop during operation), making the current limiting too fast can result in stability issues under certain load conditions. I know you did a simulation and posted the results in the first post, however I think different load conditions and frequencies should be tested to be certain there isn't an issue.

Again I might be completely wrong, and in that case you can just ignore it

Yes, you are quite right about the clipping. In a "conditionally stable" feedback system like this clipping is one of those scenarios which can result in the amplifier breaking into uncontrollable and unquenchable global loop oscillation. However this is something I hope to have overcome with my detection scheme which automatically switches the feedback order to a safe 1st order system whenever an unsafe state of operation is encountered. My text books tell me that so long as the amplifier is operating in a linear region, the total phase shift can go well through 360 degrees, but so long as the open loop gain reverts back to a 6dB per octave (single pole) slope before crossing through unity gain, the system as a whole will be "conditionally stable".
 
 

[TheRevva]

Just like the electronic versions those things would work great if you could turn off friction and gravity and have infinitely rigid material that had no mass. Plus machine the curves with no error, but that should be easier on material with no mass

So you're saying that if we switch the source material from unobtainium to nonexistium, we'll be sweet?
Some of the best aspects of this nonexistium include:
1: The pirce per kG is ideal!
2: Travel at the speed of light (c) finally becomes easy
The downside is that I haven't found a supplier that stocks the nonexistium.  All my normal suppliers suggest the unobtainium as a 'possible replacement' (probably because they achieve a better sales margin?)

I'll keep searching and let y'all know.

[GK]

Hello all.

Attached is a picture of my initial prototype amplifier built just to test the concept. It is in fact a fifth-order ("5-pole") implementation of the scheme (having four op-amp-based integrator stages) based around a low-power discrete power amplifier that clips at 15W into a 4 ohm load.

At the moment the circuit board shown contains all of the circuitry bar the detection/comparator circuitry required to automatically switch the control loop between a 1st order system and a 5th order system. My initial concern was just to verify that a 5th order control loop could really work. To be honest in theory I pretty much new that it would work, but I just had to actually build a real life prototype and see it work with my own eyes. The way the shown prototype works in its current state of construction is that I can manually switch it between a 1st order system and a 5th order system by asserting the logic control line for the analog switches which short the capacitors of the four series-connected integrator stages.

I can happily report that, so long as the amplifier is operated within its linear region of operation (ie not driven into clipping), it is 100% stable in the 5th order mode of operation with any signal stimulus I have (exhaustively) tested it with. The prototype implementation has a relatively conservative unity loop gain "crossover" frequency of 650kHz and slightly over 60dB of global loop feedback at 20kHz. The prototype has a modified gain distribution amongst the integrator stages for better noise performance. I have achieved an input-referred noise equivalent to an input resistance of 4k. As far as I have been able to measure distortion thus far, in the 5th-order mode there doesn't seem to be any discernible distortion products breaking through the noise floor at any operating frequency.

At the moment, if the amplifier is driven into clipping in the 5th order mode, it predictably breaks out into (non-destructive) global loop oscillation, and remains in an oscillatory state until I manually switch it into 1st order mode, as I have not fully yet implemented the error-sensing control circuity to do the switching automatically before global loop oscillations even have the chance to begin.

However, from my very positive (and somewhat exhaustive) experimental results thus far I am left with little doubt that the basic scheme is sound. Over the next several nights I will complete a prototype implementation of the control circuitry and report perhaps next weekend with some oscilloscope trace photos or videos to demonstrate the stability of the completed system if anyone is interested.

From this point forward though I am not willing to reveal any actual circuit details or expound upon topological modifications I have made to the basic scheme outlined in my opening post. There are also issues concerning the control circuitry that deal with stability during power up and power down which I have not elaborated on, but are necessary for a functioning and practical real-world implementation.

The reason for this "secrecy" is because I have since potentially made a deal with an audio electronics magazine to have an advanced design for a high power, ultra-low distortion amplifier module, based on my high-order control loop scheme roughly outlined in this thread, published; pending on the success of my initial prototype as shown here.

However, having already started a thread on the experiment, I figured I could at least update it with a report on its success or otherwise without a conflict of interest if anyone is interested.

[digsys]

I wish you good luck with your publishing possibility. Even though I haven't done much on audio / amplifier design for many years,
(except some valve stuff), I certainly follow your R+D progress. You have at least ONE listener :-)