Back EMF - some considerations

[Jorge]

There is a lot of arguments going on at the forum re the influence of back EMF.
Just to give some perspective to beginners, here is a simulation, using as a load a real speaker model (also posted in the forum):

U1 is a high gain voltage stage (gain = 10K, BW = 30MHz) like the input section of an amp, U2 is an unity voltage/high current gain stage, like a triple EF output.
Zo is the open loop output impedance of U2.

The components to the right of Zo model the speaker, to which a 10V peak (possibly a very high value) back EMF is apllied at 110 Hz, where the speaker is reactive.

First, the circuit, with U2 input connected to ground - this is a no feedback situation.

[Jorge]

Now, the voltage at the right side of Zo - the amp's output.

Thre is about 500mV peak showing that without feedback the damping factor is of 16 at 8 ohms.

[Jorge]

Now, let's close the NFB loop, connecting the + input of U2 to the output of U1.

The voltage at the right side of Zo is some 500uV peak, showing that damping has increased about 1000 times.

The question then is; how was this achieved, which are the effects on sound quality?

[Jorge]

Here we have the voltage ar the output of U2 - 500 mV, the same value there was at the amp's output before feedback!

Just ot make it clearer, it's shown also the EMF voltage in red just to make it clear that U2's voltage is almost 180 deg out of phase with the EMF one.

As a conclusion, no additional stress was placed in the amp (in both cases the amp's output was 500 mV) due to feedback.

[jcx]

to my ears continually referring to “back emf” in describing loudspeaker/amplifier interaction is extremely dissonant, like using “scattering coefficient” for resistance or “recombination rate” for transistor current gain – it is a physically correct, useful concept at a detailed level in the modeling hierarchy but using it where the higher level model works is a kind of intellectual “thought impediment” akin to stuttering in speech – it derails more discussions of dynamic loudspeaker behavior than it informs

the useful electrical terminal model of a dynamic loudspeaker is that of a complex impedance composed of the voice coil electrical parameters coupled to a electro-mechanical transformer that converts the force and velocity at the voice coil to electrical terminal I and V – the mechanical mass, spring constant and damping of the cone/suspension/box look like additional C, L, and R at the dynamic driver’s electrical terminals

the linear model of the loudspeaker load as a complex impedance network gives pretty useful estimates of I, V and phase with whatever signal you care to convolve with it

dynamic loudspeaker drivers are noticeably nonlinear, particularly at low frequencies, these nonlinearities can be accommodated in the electrical terminal model of the driver, see:

http://www.klippel.de/background/introduction.asp

you can find hard numerical data in Klippel’s work that permits putting strong limits on how much loudspeaker nonliearities can influence dynamic driver electrical terminal behavior

as ingrast has pointed out laundry lists of possible physical effects are not useful to the engineer until you can put numbers on them to rank their relative influence, Klippel’s models let you bound the possible effects of driver nonlineariy

one physical effect that can readily be dismissed by consideration of the numbers is “microphone” effect:

dynamic loudspeakers are “bi-directional” transducers so that the law of reciprocity applies; a loudspeaker is as efficient in converting incident sound pressure on its cone to electrical terminal I,V as it is in converting the electrical input to sound – since direct radiator dynamic drivers struggle to reach even 1% efficiency any “round trip” electrical – sound – electrical effects are < 0.01% of the power into the speaker’s electrical terminals, since we are dealing with driver resonace peaks, voice coil heating dRseries and crossover impedance dips of > +100%/-50% the microphone behavior of the loudspeaker is merely a curiosity

[Jorge]

I tried to make an expalanation that non-engineers, but with general knowledge of electronics could understand.

The 'Back EMF' name was focused in that audience.

[jcx]

not blaming you Jorge, Graham’s recent writing has stuck us with the term for now, I am surprised John Curl hasn't been by to claim priority over Graham with his "Interface Intermodulation Distortion" from the '70s

Of course Bode formalized sensitivity analysis of linear feedback networks in his book in 1945 which allows calculating the effect of feedback on the output impedance of an amplifier

In “modern” (maturing in the 60s) control theory you will see "disturbance" input blocks that model noise, distortion or "exogenous"(external) inputs to the control system, the output disturbance sensitivity/rejection with respect to a disturbance signal source connected to the output is a 1st order design goal in control theory however much Graham’s writing makes it seem a new subject

Reducing nonlinear effects is the first, and major motivating advantage claimed for the invention of negative feedback in Black's patent - the objection that linear theory doesn’t apply because we're interested in nonlinear effects is naive; from the outset of negative feedback engineers have been exploring theoretical extensions such as "local linearization" and the small gain theorem to explain and expand on the distortion reducing effect of negative feedback observed in real world circuits

Cherry specifically addressed the "interface intermodulation distortion" issue in audio power amplifiers in the 80's in several JAES articles

To have to deal with Graham"s imprecise, even misleading “discussion” in the face of such a rich background of engineering history is frustrating, maybe you can lead some current diyers confused by Graham’s writings into the beginnings of this well understood subject (by "engineers" in the large, if not enough audio designers)

[Jorge]

I feel the biggest problem to real audio advancement is that 'miths' are treated as 'truth', in a religious way.

I have no dubt that a given amp driven by a given source and driving a given set of speakers may sound better to someone's ears.

Then this system becomes the rule by which all others shall be judged, as an absolute reference.

One should be humble enought to recognise that such a reference doesn't exists, even live music is not a reference - one likes simphonic orchestra, other likes hard rock...

And it's interesting that this thread has been read over 150 times and no other posts besides ours...

[janneman]

Originally posted by Jorge
Here we have the voltage ar the output of U2 - 500 mV, the same value there was at the amp's output before feedback!

Just ot make it clearer, it's shown also the EMF voltage in red just to make it clear that U2's voltage is almost 180 deg out of phase with the EMF one.

As a conclusion, no additional stress was placed in the amp (in both cases the amp's output was 500 mV) due to feedback.

Jorge,

May I be # 151...

So far, no surprises. The damping with fb increased 1000 times because you have 60dB of feedback. The input at U2 is still 500mV (actually a little less, about 0.1% less, that's where the remaining 500uV come from), but in opposite phase because it has to cancel the impressed voltage. Agreed so far?

Jan Didden

[janneman]

Jorge,

Maybe we should try to get a bit closer to real life. What about rolling off the gain of the input amp with a simple RC at the output, say starting at 1kHz, to emulate a real amp? See if there appears an 'internal overdrive' as some will claim? Then do the same with a 10kHz signal impressed?

Jan Didden