Back EMF (Henry Pasternack)
Back-EMF
Date: Tue, 20 Jul 1999 11:50:49 -0400
Subject: Back EMF.
Hi, Ken. I have to disagree with your conclusions regarding speaker behavior. DC voice coil resistance is in series with the amplifier output terminals and is on the order of 5.5 Ohms for a typical 8 Ohm woofer — much higher than the output impedance of most reasonable amplifiers. Therefore, there’s no special significance to having zero output impedance. It matters not that the voice coil resistance is in the speaker. It might just as well be an external resistor with a superconducting voice coil, and the effect would be the same.
For a given drive voltage, cone motion is of constant angular velocity, not amplitude. This means the excursion goes down as a function of frequency throughout the driver midband because the motion is mass-controlled. At the positive and negative peaks of excursion, the cone stops moving and the back EMF is zero. At this point, the acceleration is determined solely by the applied voltage, the flux in the gap, the number of turns of the voice coil, and the moving mass of the driver. Knowing the frequency, the magnitude of the excursion, and the peak acceleration, we also know how fast the driver will be moving at the zero crossing. At this point, the back EMF cancels the applied voltage and the net acceleration is zero. Were this not so, the extra “shove” due to uncanceled drive would add energy to the cone, causing it to speed up and move farther over successive passes and eventually come to equilibrium. The number of cycles it takes for the driver to reach steady state is a function of the frequency and the system Q. Even with zero amplifier output impedance, the motion of the cone is not in any sense of the word “controlled” by the amplifier because of voice coil resistance. If the coil and amplifier had zero resistance, the driver Q would be zero, the low-frequency cutoff would be at infinite frequency, and the bandwidth would be zero. The audiophile ideal of “infinite damping” is actually a completely undesirable condition.
This is actually a very counter-intuitive subject. Most of the postings I have seen in this thread that claim to have it right are marred by serious misconceptions.
-Henry
