Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics.

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kind of a long answer

Posted by tomservo (M) on August 17, 2006 at 11:02:34

In Reply to: What happens to back EMF with a feedback amplifier? posted by morricab on August 17, 2006 at 05:01:34:

Hi

Back EMF is a voltage generated by a electrodynamic motor that is in motion.
A loudspeaker Voice coil and magnet are a DC motor, driven by an AC signal.
The BL product is the the length of wire time the field (in Tesla) or, because of the dimensions, is also the number of Newtons of force per amp the motor will produce.
The Back EMF is exactly linked to the BL product as the motor’s ability to be a generator is proportional to its force per Amp rating.
Fwiw, over all motor strength has to include the resistance so a good equalizer is to use BL / sqr root of Rdc, force per Watt figure of merit.

A reactive load is one which is not resistive, that is the current phase is not at zero degrees as it is with a pure resistance.
The current phase can either lead or lag the Voltage drive signal depending if the reactance is capacitive or inductive.
Most real loads are a combination of reactance and resistance.
A pure reactance has a current phase shifted 90 degrees one way or the other, real loads have less phase shift.
A phase shift of 90 degrees has profound impact on the output stage of an amplifier, it requires the stage to deliver full rated current at the point the output voltage is zero (not max as in a resistive load) so heating is dramatically greater.
So much greater that most Safe operating area protections schemes do not allow this.

A sealed box woofer:
The speaker motor produces X force per Amp AND its back EMF exactly reflects the motor’s Velocity.
For an acoustically small point source, one finds the acoustic radiation resistance for a small source is sloped, a constant radiator velocity would cause a rising response here.
To make "flat" response in this case, the radiator Velocity must be rolled off at -6 dB per octave. This slope of the radiation resistance is also "different" than slopes caused by reactance, there is no normal attendant phase shift with the radiation resistance slope, mostly just a frequency dependent resistance.
One needs a first order slope to make flat response, this is accomplished by an R/C filter.
The "filter" is the Rdc of the driver with the moving mass of the driver which is reflected through the motor as a capacitance.
If you model a sealed box and then increase the motor strength, you see immediately that there is less bass response as you raise effectively raise the RC corner frequency compared to Fb.
In the mid band, the RC filter makes the woofer an acceleration based response system, what one finds when you measure actual acoustic phase is that the radiated sound lags the input Voltage by about -90 degrees, a result of the RC filter’s phase which was not canceled out by the radiation resistance.
The woofer is in a box too, this box is a spring force, in parallel with the driver suspensions spring force, both in parallel with the moving mass.
At some low frequency, the magnitude of these forces are equal but opposite and you have box resonance (Fb). Here, there is no reactance and both the electrical and acoustic phase is at about zero degrees. Below resonance, a woofer’s phase tends towards +90 degrees as the spring force (looks like an inductor) dominates.
Above mid band, the series L reactance (which could be ignored down low) becomes equal but opposite to the mass / capacitance and the Rmin impedance point is reached.
Here too the electrical and acoustic phase has risen to about zero degrees.
Bottom line, there are only two points in the frequency response where a sealed box woofer "looks like" a resistor, most of the time is reactive / resistive.
This same phase shift is why a direct radiator like a woofer can’t preserve a complex input waveshape, that can only happen when the acoustic phase is near zero or -180 over a significant bandwidth.

TIM distortion that John mentioned is an effect cause by insufficient open loop bandwidth and large -fb. It looks like this, picture an amplifier that had old slow output transistors int he output stage. Having just come from the alter of negative feedback, you decide to implement a huge amount of gain in the preceding stages so that you can use the feedback to bump your response out to 30KHz.
The output stage can only swing from one voltage to another at a certain speed, if you put in a square drive voltage, the output is limited to some "slew rate" from Voltage A to Voltage B.
Now, you make a test signal that has a high frequency sine wave superimposed on a square wave and drive the amplifier.

Now, the ouput stage can’t go from A to B instantly, during the time it is "trying" to get there, all of the negative feedback signal is applied to help "correct" the lagging output.
All that can can easily saturate a preceding stage too and one saturated, transistors take a lot longer to recover as they take time to "unstick" (pump out the base current).
So, during the entire time, between the end of the last plateau to where the amp settles at the new voltage and "unsticks", ALL of the higher frequency signal has been lost.
In the 70’s M. Otalla recognized this issue and coined the term "Transient Intermodulation Distortion" TIM. I had a pair of HK amps "back then" that were made under his criteria and except for running hot, were nice amps.

Personally, I think there are rules and then there are rules.
For example Nyquist criteria says that a sample rate must be 2 or more times the sampled signal, yet, in the real world, one finds that is no where near enough as it can report the same signal as zero to full level depending on the phase.

If how things were done resulted in the simple resistive Voltage source an amplifier is thought to be, there is no way one could make an amplifier ring driving a capacitance with a square wave.
One could compare the amplifier input to the output while driving a complex load (loudspeaker) with music to "see" what the deviation looks / sounds like, but I don’t know if they do that.
I better stop rambling.

Tom

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