Non clocked (e.g. free running, self oscillating) class d

[analogspiceman]

Let me start this topic with a discussion of two from the many possible modulation schemes for non clocked class d amplifiers. For both schemes the power topology will be assumed to be a standard totem pole switching stage feeding a single output inductor. Linear feedback of current from this output inductor can be used to drive the power stage into oscillations, either by the application of hysteresis, sufficient phase shift, or a combination of the two. Thus, these common types of feedback driven, self oscillating class d amplifiers are really just high power variations of standard phase shift or hysteresis signal oscillators.

Hysteresis control alone suffers a troublesome reduction in oscillation frequency as the amplifier is driven into deep saturation (stopping altogether if the amp is railed). This is not so much a problem for the phase shift technique. Also, with hysteresis control, the period of oscillation varies inversely with rail voltage (since output inductor current slews faster when driven with higher voltage).

These effects can be mitigated by making the hysteresis band a function of rail and output voltages and by filtering the current feedback signal. This latter step not only increases noise immunity when the hysteresis band is squashed at high output levels, but it also introduces phase shift into the negative feedback path. In fact, if the current signal is routed through two or more low pass sections of sufficient size, the mode of oscillation will become phase shift dominated. This happens when the phase shift around the feedback loop reaches 360 degrees at a frequency lower than the natural hysteresis frequency (a phase shift oscillator requires exactly 360 degrees of phase shift around its feedback loop).

Starting around the loop from the high level switched output from the power stage, it is then immediately low pass filtered by the output inductor (yields 90 degrees of phase shift in current). If this were directly fed back to the error amplifier there would only be an additional 180 degrees phase shift (from negative feedback) - not nearly sufficient to cause natural oscillations.

When there is little or no audio modulation, power stage duty cycle remains near 50 percent so that the comparator / modulator provides no phase shift input-to-output and, in a phase shift oscillator, the additional 90 degrees of phase shift required for oscillation by the Nyquist criterion typically comes from two additional high frequency poles in the feedback path (often placed as error amp compensation and as the comparator noise filter). The placement of these high frequency poles controls the frequency shift characteristics of the phase shift type amplifier, with the simplest case being two coincident high frequency poles placed at the intended nominal switching frequency. With this type of oscillator, loop gain, through the mechanism of power stage saturation, is automatically ensured to be exactly unity at the point of 360 degrees phase shift.

When the phase shift class d amplifier is driven to very near saturation (greater than 90 percent duty cycle), the modulation process produces close to 90 degrees of phase shift on its own due to the sawtooth shape of the carrier that appears at the comparator’s input (duty cycle is now a pulse rather than a square wave), so that 360 degrees total phase shift occurs at a 3 to 4 times lower frequency without much contribution from the two additional high frequency poles.

A free running class d amplifier's phase shift oscillator / modulation scheme allows loop gain for audio signals to come within a factor of two or three of the theoretical maximum possible bandwidth of one half the carrier frequency (which varies from the switching frequency at saturation to double the switching frequency at zero output). This is a Good Thing. High inner loop gain cascaded with outer loop gain really drives down unavoidable, open loop deadtime and switch on voltage distortion effects and makes for an inherently very high rejection of power supply noise.

Hopefully this exposition was clear enough to convey my thoughts on how the typical non clocked class d amplifier oscillates and how it leads, not only to a very simple circuit, but a very high performing one as well. In addition to further thoughts on this subject, I am interested in learning about any other variable frequency class d amplifier schemes that are out there.

Thanks for your time and your comments. -- analog(spiceman)

[Jaka Racman]

Hi,

only problem with your modulation scheme is that we need voltage generator to drive loudspeakers, not a current one. You inevitably need outer feedback loop to compensate for varynig loudspeaker impedance and filter capacitor current that becomes significant part of totem pole output current at higher audio frequencies. On the other hand, if one directly integrates totem pole voltage instead of difference between supply voltage and output voltage (as you do with output inductor), then we have all three known self oscillating voltage output topologies:
-hysteretic oscillator
-phase shift oscillator with feedback from rc filtered totem pole output voltage (COM patented by B&O)
-phase shift oscillator with feedback from output LC filter (UcD patented by Philips)

I am sure that someone with better insight will post a better comment.

Best regards,

Jaka Racman

[analogspiceman]

Originally posted by Jaka Racman
Hi, only problem with your modulation scheme is that we need voltage generator to drive loudspeakers, not a current one. You inevitably need outer feedback loop to compensate for varying loudspeaker impedance and filter capacitor current that becomes significant part of totem pole output current at higher audio frequencies.

Yes, of course the amp's final output characteristic should be a low impedance voltage source, but it is best to start locally with a controlled current source to linearize the inductor, then leapfrog one's way to the desired voltage source output characteristic.

On the other hand, if one directly integrates totem pole voltage instead of difference between supply voltage and output voltage (as you do with output inductor), then we have all three known self oscillating voltage output topologies:
-hysteretic oscillator
-phase shift oscillator with feedback from rc filtered totem pole output voltage (COM patented by B&O)
-phase shift oscillator with feedback from output LC filter (UcD patented by Philips)

IMO maximum potential fidelity is best reached by feeding back the state variables from the actual plant (the output recovery filter) rather than an approximation of them (such as derived from an RC network). That way there can be no troublesome build up of difficult-to-clear errors signals on the compensation components when they keep blindly integrating past the point when the output filter components have saturated or railed.

I also think that patent issues may be circumvented by using a hysteresis scheme with "heavy filtering" such that the result really becomes a hysteresis / phase shift combo modulator. The bulk of audio class d patents drive me crazy because most of their ideas are borrowed from or at least follow after well documented techniques from the switched mode power supply and motor control fields. Oh well, call it an audio circuit and suddenly you are a genius.

[Bruno Putzeys]

Originally posted by analogspiceman

Also, with hysteresis control, the period of oscillation varies inversely with rail voltage (since output inductor current slews faster when driven with higher voltage).

Hysteresis feedback is therefore taken from the output stage itself, not from a fixed-voltage internal node.

[Bruno Putzeys]

Originally posted by analogspiceman

Yes, of course the amp's final output characteristic should be a low impedance voltage source, but it is best to start locally with a controlled current source to linearize the inductor, then leapfrog one's way to the desired voltage source output characteristic.

As pointed out earlier, the thought process used to obtain a given feedback function is a separate issue from the actual realisation. Direct attack by mathematics produces the same outcome. While in its basic state the "leap frog" method implies the use of current feedback, it can be readily transformed into a circuit employing only voltage feedback and having exactly the same loop characteristics.

Originally posted by analogspiceman

IMO maximum potential fidelity is best reached by feeding back the state variables from the actual plant (the output recovery filter) rather than an approximation of them (such as derived from an RC network). That way there can be no troublesome build up of difficult-to-clear errors signals on the compensation components when they keep blindly integrating past the point when the output filter components have saturated or railed.

You are correct to point out this is an opinion.
There is no practical reason why a class D amplifier should be equipped with an output filter of order exceeding 2. To use only the output filter to hold the state variables limits the available loop order to 2. Higher orders of integration would by necessity require a higher order output filter. If anything, small-signal integrators are cheaper than power inductors.
Furthermore, the use of linear integrators (as opposed to saturatable ones like coils) will help reduce distortion from the coils whereas the coils themselves, used as integrators, will be ineffective at cancelling their own distortion!

Originally posted by analogspiceman

I also think that patent issues may be circumvented by using a hysteresis scheme with "heavy filtering" such that the result really becomes a hysteresis / phase shift combo modulator.

I know for certain that the UcD patent states the use of a comparator "substantially free from hysteresis", which means that applying hysteresis and modifying the feedback circuit in order to nullify the negative effects of this would not suffice to get from under the cover of the patent.

Originally posted by analogspiceman
Oh well, call it an audio circuit and suddenly you are a genius.

This is symptomatic of audio in general. Your clear expose on a useful method of constructing a control loop is likely to buy you instant guru status. Try and convince me you wouldn't enjoy that

Cheers,

Bruno

[Jaka Racman]

Hi Bruno,

I do not know how familiar are you with currernt mode control which has been workhorse of SMPS industry for the last 20years. In comparison with SG3524 modulator it provided two advantages: reduction of one pole in transfer function and free pulse by pulse current limiting. Phase shift modulation would stand no chance there because nobody would buy power supply with 400mV ripple at the output. So I understand Analogspiceman's motives when he proposed his scheme. His original proposal would certainly not fall under UcD patent. If any, then original Bose patent for current mode control would be in place, but I think it has already expired. Also I think that "substantially free of hysteresis" is there because of certain T... patent .

Analogspiceman, I agree with you that current mode control is the best way to deal with multipole output filters. But Bruno had already explained why more than second order is not necessary, and you can always use multiphase ripple cancelation technique with second order filter. The only advantage of current mode control in class D amplifier I see is inherent current limit protection.

Best regards,

Jaka Racman

[Bruno Putzeys]

Originally posted by Jaka Racman
I do not know how familiar are you with currernt mode control which has been workhorse of SMPS industry for the last 20years.

Rather well

Current mode control of class D output filters has also been described by Karsten Nielsen but he stopped at 2nd order, probably because that was where the output filter stopped.

For a class D amp, it's much more efficient to perform current mode control on the output cap instead of the coil. Controlling cap current has all the advantages of controlling coil current except that the loop does not heed or control actual output current (thus maintaining a low output impedance inherently).
Because of that, controlling capacitor current will result in vastly lower output impedance than can ever be achieved through traditional inductor current mode control.
The reasoning extends to higher order filters. At each tap in the filter, you attach a PD (R + C parallel) control takeoff which are summed to form the control signal. Presto: same loop gain around the switching power stage, lower output impedance.

Yes, I am saying this is a better method than leapfrog.

[analogspiceman]

Originally posted by analogspiceman
Also, with hysteresis control, the period of oscillation varies inversely with rail voltage (since output inductor current slews faster when driven with higher voltage).

Originally posted by Bruno Putzeys
Hysteresis feedback is therefore taken from the output stage itself, not from a fixed-voltage internal node.

Yes, and as I noted, "These effects can be mitigated by making the hysteresis band a function of rail and output voltages", but a further practicality is worth noting as well. Since the output voltage switches with some small delay with respect to the comparator input to which hysteresis is being applied, in order to avoid possible chattering at the comparator's output, supplement the delayed feedback with a nominally equal amount of capacitively coupled hysteresis taken locally, directly from the comparator's output. Its time constant should be set to maintain a constant amount of total hysteresis before, during and after the transition over to the hysteresis from the main output.

This tip brought to you by the school of hard knocks. -- analog(spiceman)

[Bruno Putzeys]

Originally posted by analogspiceman


Yes, and as I noted, "These effects can be mitigated by making the hysteresis band a function of rail and output voltages", but a further practicality is worth noting as well. Since the output voltage switches with some small delay with respect to the comparator input to which hysteresis is being applied, in order to avoid possible chattering at the comparator's output, supplement the delayed feedback with a nominally equal amount of capacitively coupled hysteresis taken locally, directly from the comparator's output. Its time constant should be set to maintain a constant amount of total hysteresis before, during and after the transition over to the hysteresis from the main output.

Never had this problem. I'm afraid the quality of my board layouts is getting in the way of me getting hard knock education

[analogspiceman]

Originally posted by Jaka Racman
[...] So I understand Analogspiceman's motives when he proposed his scheme. His original proposal would certainly not fall under UcD patent. If any, then original Bose patent for current mode control would be in place, but I think it has already expired. Also I think that "substantially free of hysteresis" is there because of certain T... patent .

[RANT] Coming, as I do, from the SMPS side of things, the audio patent examiners never cease to amaze me with the extremely low opinion of what they hold as obvious to one skilled in the art of audio engineering. A few people believe in toob amps direct coupled to 4 ohm loads or buy into speaker cables made from oxygen free virgin copper conductors big enough to weld with and they seem to think we are all idiots.

I know audio is just waking up to an alarm that went off more than twenty years ago for power supplies and dc motor control. There, techniques such as current mode control, self oscillation, phase staggered paralleled output stages, linear-switcher combos are old hat. Don't the patent guys pay attention to related fields? Or is their attention more relating to supplementing their patent pay? [/RANT]

For these reasons, several years ago I decided to put leapfrog and whatever else I've come up with into the public domain via the internet in forums such as this one and various engineering newgroups.

Originally posted by Jaka Racman
Analogspiceman, I agree with you that current mode control is the best way to deal with multipole output filters. But Bruno had already explained why more than second order is not necessary, and you can always use multiphase ripple cancellation technique with second order filter.

Although many, perhaps most, applications are tolerant enough of output ripple to allow the use of just one L/C filter section, when bandwidth and EMI suppression must both be maximized, it is probably unwise not to consider multiple section and a high order feedback scheme. In such cases, how could the efficacy of the same amount of L and C spread out over two sections not provide more effective filtering?

Originally posted by Jaka Racman
The only advantage of current mode control in class D amplifier I see is inherent current limit protection.

Although certainly not necessary in all cases, many designs may be required to operate continuously into a short circuit or may need to have a well controlled time (and/or temperature) dependent current limit in order to get the maximum possible power from a given set of output devices with limited heatsinking. Also, just as with parallel operated or multiphase power supplies, current mode control ensures automatic current sharing without further circuitry when multiple output stages are tied together. This can be a big problem when voltage mode controlled stages are tied together.

Regards -- analog(spiceman)