Hawksford wrong on amp topology for current driving loudspeakers? - diyAudio
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Old 6th November 2003, 02:00 PM   #1
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Default Hawksford wrong on amp topology for current driving loudspeakers?

I am referring to Mills/Hawksford in JAES, Vol. 39, no. 3 and 10 of 1989. In these articles, the authors show that current drive helps to reduce compression and Le variation distortion, at the same time pushing the response drop out to higher frequencies. The reduction in distortion was significant at 100 Hz and impressive at 3 kHz. The price was the loss of damping around resonance, which resulted in a response peak. While mechanical damping or a Linkwitz pole shifter would work, they preferred a feedback system with a second coil on the former, because it is more independent of production variation of the driver resonance parameters.

The part that I want to question is the design of the transconductance amplifier, i.e. the controlled current source. The standard approach is to use a standard non-inverting voltage feedback amplifier, connecting the loudspeaker Z_L between output and inverting input, and then connecting a resistor R_f between noninverting input and ground. The voltage gain is essentially 1+Z_L/R_f.

The current gain gm = I_out/V_in is what we are interested in in a current drive application. Assuming the output impedance of the amp to be zero, gm = A / (Z_L + R_f*(1+A)).

The authors say that the amplifier open loop gain A is freqency dependent, and that Z_L is both frequency dependent and nonlinear. Both effects lead to a modulation of system transconductance and hence interface distortions.

They define a gain error function, and assuming an allowable gain error of 0.1%, R_f = 0.5 Ohms and Z_L (max) = 20 Ohms, they require A>92 dB which is evidently not realistic of the audio frequency band. This led them to design open-loop common-base cascode output stages. Their designs have up to 68 dB distortion, so they are trading driver distortion for semiconductor distortion.

I think that their criterion is mistaken. We are not at all interested in absolute gain. Asking for a gain error of +/- 0.5 dB over frequency is probably more than sufficient. Lastly, at a given frequency, distortion due to impedance variation of the driver should be attenuated by at least 10 dB.

Ok, lets look at an example. I will simplify by ignoring phase (because I dont have complex impedance for the driver) and A droop with load. This will introduce a small error, but will certainly not change the order of magnitude.

I chose the Excel W22EX001. Minimum impedance is 6 Ohms at 200 Hz. Maximum is 20 Ohms at 30 Hz (fs). At 5 kHz, way beyond the sensible operating range of the driver, impedance is 13 Ohms due to Le. I then chose the rather humble LM3886. It has a gain of 100000 (100dB) at 30 Hz, 31500 at 200 Hz and 1400 at 5 kHz.

So lets look at gain over frequency: at 200 Hz, gain is 31500/(6+0.5*(31501))= 1.9991749 A/V. At 30 Hz, gain is 100000/(30+0.5*100001)=1.99878 A/V, down 0.0017 dB from 200 Hz, i.e. clearly way better than any Q compensation circuit. At 5 kHz, gain is 1400/(13+0.5*1401)=1.962, i.e. 0.16 dB down from 200 Hz. Here, the effect of the loss of open loop gain is evident, but the result is still perfectly acceptable.

Then for surpression of nonlinear effects. At 200 Hz, the impedance of 6 Ohms is almost purely real. The authors maintain than the VC temperature can go to 200C, which would result in a roughly 80% increase impedance. Lets throw in an additional increase in inductance over displacement (I realize the time scales are different!) and say impedance doubles to 12 Ohms (which is more than generous, given that the Z due to impedance is close to zero at 200 Hz). In a voltage driven case, output would halve, ie. be down 6 dB. With our humble amp, gain would be down 0.038%, i.e. 0.0033 dB!!
At 5 kHz, there is less available gain. At the same time, inductance is responsible for roughly half the impedance. A 180C temperature increase and 10% inductance increase could together cause the impedance to go from 13 to 18.5 Ohms. In voltage drive, the signal would drop 42% or 3.1 dB. With current drive, wed see 1.9% or 0.16 dB drop. Assuming the nonlinearities result directly in harmonic distortion (which they dont because temperature effects are too slow), distortions would still be 27 dB higher than for voltage drive.

So this seems to prove that a standard amplifier topology with overall voltage feedback can be successfully used for current driving amps. If a discrete amp with higher bandwidth was used, I am sure total distortion due to driver and amplifier nonlinearities will be lower than for the Hawksford open loop buffer designs.

One issues remains, though. The inductance of the loudspeaker causes the closed loop voltage gain to grow at 20 dB/oct beyond a few kHz. At the point where the closed and open loop curves meet, the rate of intercept will be 40 dB/oct which guarantees oscillation. The remedy is to shunt the driver with a series combination of a resistor and a capacitor. This network should begin to shunt the driver above 20 kHz and stabilize loop gain before the intercept point.

Thoughts? Comments? Flames?


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Old 6th November 2003, 08:35 PM   #2
PRR is offline PRR  United States
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I'm going to need a whole pot of coffee before I understand all that.

Quick comments:

> The inductance of the loudspeaker causes the closed loop voltage gain to grow at 20 dB/oct

You mean "per decade", not per octave. Or maybe you meant 6dB/oct. No matter.

> The authors maintain than the VC temperature can go to 200C, which would result in a roughly 80% increase impedance.

Yes, it can, thanks to the miracle of modern epoxy.

But should it? Does it?

If the amp is clipping, or the cone is slapping, there is no point in talking about clever ways to reduce speaker distortion.

The peak/average ratio for speech/music, averaged over the several second thermal time constant of a voice coil, is in excess of 10dB. If the coil over-heats (melts -or- compresses) at 20 watts, then we need way more than 200 watts of amplifier. If the cone is working down to its bass power limit, it slaps before it overheats.

Find out for yourself if thermal compression is an issue. Put a double-pole switch on the speaker, so you can instantly switch the speaker from amplifier to ohm-meter. Lock the meter on the 19.9Ω range so you get a reading without waiting for auto-range. Measure the speaker's cold resitance. Play the speaker loud for several minutes. Switch to ohm-meter, get a reading much-much quicker than 10 seconds (a typical time constant for voice coil thermal mass). To be exhaustive, play loud for several hours to warm-up the magnet (the voice coil's main heatsink, with a time constant of several minutes) and check again.

I suspect (but have not experimented) that if you are not clipping or slapping, your voice coil resistance won't rise more than 10%.

Of course if it does rise as much as 50%, thermal compression is only a small part of the problem. Efficiency is half, effective damping (not damping factor) is half, response plots go whacky. This can't easily be compensated outside the speaker. If the coil is so hot its resistance rises, it is a "different" speaker than the one you bought. We are resourceful gentlemen and women; Why abuse a driver that much?

In large-room high-level work, sometimes we do run into thermal compression. But this is a very different world than hi-fi.

Anyway: do speakers distort? Aside from long-excursion non-linearity, I say they don't harmonic distort enough to care about. The 2nd and 3rd harmonics may be high numbers but are lower than the ear's distortion. The 4th and 5th are much less, and the 8th and 9th tend to be below noise limit.

Speakers do make Doppler IM distortion. LOTS of IM distortion. In many 2-way systems this is by far the largest distortion in the whole system, and limits "clean" output. OTOH, for many young people who grew up on over-excursion boom boxes, they don't think a system is loud until they wind it up to high IM. I note a fairly consistent 5%-10% Doppler IM level when I walk around the dance studios here, no matter what kind of system is playing. Even "good hi-fi" systems often exceed 1% at "reasonable" levels. Why worry about fractional-percent harmonic nonlinearity when we are knee-deep in IM byproducts?
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Old 6th November 2003, 09:34 PM   #3
dimitri is offline dimitri  United States
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Default Why worry about fractional-percent harmonic nonlinearity please stop it

There are three main contributions to loudspeaker non-linearities.

Firstly, non-linearities can be found in the motor & motor magnet system caused by variations in the bx l products with cone displacement, a change in the voice coil inductance and induced emf with the cone excursion, and heating effects.

Secondly, there are mechanical non-linearities due to suspension stiffness of the loudspeaker spider and outer rim, mechanical clipping, compression, & hysteresis effect of the voice coil, the cone material and design of the closed-box system.

The third factor which contributes to its non-linearities are the Doppler distortion effect. The Doppler effect causes mainly phase modulation because the time delay varies with the changed distance between moving diaphragm and fixed listening point.

Some (like Moir) believe modulation distortion is more objectionable, than harmonic. Other have disagreed. However, the least possible distortion, no matter what the origin, is a primary design goal.

For additional info please visit www.klippel.de
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Old 7th November 2003, 07:07 AM   #4
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First of all, the first Hawksford paper on current drive is well worth reading. In fact, while he keeps emphasizing the compensation of the compression effect, the harmonic distortion reduction is probably more important and impressive.

It should not be forgotten that harmonic distortion is caused by motor and suspension nonlinearities. The other, and probably more harmful manisfestation of these nonlinearities is IMD. And I am pretty sure that this kind of IMD sounds nastier than Doppler IMD, which is essentially a linear mixing process. By the way, both kinds can be countered by using larger drivers, at the cost of polar response.

I do agree with PRR that VC heating is most probably insignificant in cone drivers (both due to its small magnitude and long time constant), but what about tweeters, especially ribbon drivers which have a very low thermal mass?

But back to the main topic, I did not want to discuss the merits of current drive (which are clear to me), but the question whether 0.1% absolute current gain accuracy is really needed, which did drive Mills and Hawksford down the road of open-loop current gain stages.
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Old 7th November 2003, 01:58 PM   #5
dimitri is offline dimitri  United States
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the 0.1% absolute current gain accuracy is not really needed, what is really needed is high and linear output impedance and linear transfer function

I do agree with PRR that VC heating is most probably insignificant in cone drivers

why not open the magazine/web site/etc? why use imagination, which can failed
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Old 7th November 2003, 02:43 PM   #6
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Interesting! But what kind of power do people use at home? I'd say 1 W of average power is pretty devastating....
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