Amplified Speakers

Unified Amplifier/Speaker Design

With a component system, the amplifier is designed to provide a flat response over the entire audio range (which is relatively easy) and the speakers are designed to do the same (which is relatively impossible).

A much better approach (albeit more expensive) is to drive each speaker independently. One can then use active crossover filters to provide a truly flat response.

Consider the following circuit, where G1, G2 & G3 represent cross-over filters and M1, M2 & M3 are gain functions for analog models of the tranfer functions (including diaphram velocity to far field sound) for the three speakers. (See speaker models.)

          +--- R ------ M1 ---+
          |                   |
          |        +--- G1 ---*--- V1
          |        |
          *--- R ------ M2 ---+
          |        |          |
          |  |\    |          |
V0 -- R --*--| >---*--- G2 ---*--- V2
          |  |/    |
          |        |
          *--- Z --*--- G3 ---*--- V3
          |                   |
          +--- R ------ M3 ---+

  V1 = -G1 V0 / (G1 M1 + G2 M2 + G3 M3 + R/Z)
  V2 = -G2 V0 / (G1 M1 + G2 M2 + G3 M3 + R/Z)
  V3 = -G3 V0 / (G1 M1 + G2 M2 + G3 M3 + R/Z)

and the total sound response is given by

  V1 M1 + V2 M2 + V3 M3 -> -V0  as  Z -> infinity.

Since (G1 M1 + G2 M2 + G3 M3) -> 0 as f->0, a finite impedance Z is needed to stabilize the op-amp. In fact, one can design Z so as to band-limit the output.

Since this filter provides a flat response for ANY G1, G2 and G3, the only function they serve is to distribute power between the speakers. The minimum power solution occurs when G1 = M1 Z1, G2 = M2 Z2, and G3 = M3 Z3 where Z1, Z2 and Z3 are the input impedances of the three speakers.

Similarly, one need not worry about acoustic damping or standing wave resonances. If they are correctly modeled, the filter will compensate appropriately. The only design criteria for the speakers and their enclosures is being able to produce sufficient sound volume over the desired frequency range and to distribute their impedance ranges so as to minimize total power consumption.

The actual implementation could be achieved using a DSP instead of op-amps. The resulting circuit would be less expensive, the models more accurate, and one could include features like automatically reducing the volume so as not to damage the speakers (instead of using fuses).

High Power D/A Converter

Instead of using a low power D/A converter and an class A amplifier, one could drive the speakers directly from the power supply using step-down choppers and a timer delay.

The following shows a "class A" chopper circuit. V1 and V2 are outputs of the DSP/timer (on/off) and Vout is fed back to an A/D converter (and the DSP). V1 and V2 are used (respectively) to produces positive and negative output voltages, and are never both on at the same time.

                       +---*-- V+
                       |   |
                   Q2|/E   |
          Q1|/C------|     D2
 V1 -- R1 --|        |\C   |
            |\E        |   |
              |        |   |
          G --*        *---*-- L1 --*------*-- Vout
              |        |   |        |      |
          Q3|/E        |   |        C1  Speaker
 V2 -- R2 --|      Q4|/C   |        |      |
            |\C------|     D1       +------*-- G
                     |\E   |
                       |   |
                       +---*-- V-

Q2 and Q4 are power transistors which drive the speaker. Q1 and Q3 simply interface between the low voltage V1 and V2 and the power transistors.

When V1 is positive (on) then Q1 and Q2 turn on and current flows from V+ through inductor L1 to charge C1 and drive the speaker. When V1 shuts off, current continues to flow through L1 from V- through diode D1. Since Vout can take on negative values, D1 has to be connected to something even more negative.

Similarly, when V2 is negative (on) then Q3 and Q4 turn on, driving Vout negative. When V2 shuts off, current continues to flow through L1 from V+ through diode D2. L1, C1 and the speaker form a 20 KHz low pass (reconstruction) filter.

One can achieve the desired voltage by using timers clocked much faster than the sampling frequency to adjust the start/stop times. To minimize wasted power, V1/V2 should be turned on/off only once per sampling interval. However, to achieve, say, 12 bits of accuracy with this approach one would need to clock the timers at least 2^12 times the sampling frequency. Alternatively one could use multiple choppers with different inductances connected to C1, or allow multiple chops per sampling interval.

Vout is used to drive a Kalman filter to estimate the state of the reconstruction filter, which in turn is used to compute control signals V1 & V2.

By adjusting both the start and stop times, one has two degrees of freedom per sampling interval. This means that one can derive a control law to do more than just achieve the next desired Vout, such as also minimizing the error on the following Vout. This would help prevent overcompensation (instability), since there is a significant delay between when V1/V2 turns off and when Vout hits its peak value.