April 24, 1997

Mixed-signal algorithm tests transducers

Alex Belousov, Rego Park, NY

A simple test procedure (Reference 1) allows you to measure damping coefficient beta in electromechanical transducers, such as speakers, microphones, and seismic geophones. The method is based on stimulating the transducer with a dc step current, I_S, and then separately integrating the positive and negative half-waves of the transducer's terminal voltage, V(t), after removing the step current. The integrals of the positive and negative waveforms contain all the necessary information to calculate beta. Integral transforms provide excellent immunity to both electrical noise and mechanical vibrations. The method given here provides a relatively simple and practical implementation of the measurement technique.

Figure 1 shows an equivalent circuit of the transducer in the broken-line box. beta and the natural resonant frequency, f₀, are functions of the electromechanical equivalents L_EM, C_EM, and R_EM. The simplified equation for V(t) is

A problem arises from the fact that the coil inductance L_COIL (given in the transducer spec or measured with an LRC bridge), also stores energy during the stimulus. This energy discharges at the beginning of the integration cycle, causing a sharp voltage spike that also undergoes integration. This integrated spike introduces a consistent error in the measurement. The error voltage at the integrator's output is uppercase deltaE=L_COIL·I_S/lowercase tau, where lowercase tau=R₄C₁ is the time constant of the analog integrator. You can eliminate this methodical error (typically, 0.5 to 2%) by using a mixed-signal-processing (MSP) approach. The principle of the MSP approach follows.

Initially, the switch-control lines of the µC all turn on, thus causing the stimulus current to flow through the transducer and at the same time discharging (zeroing) the integrating capacitors, C₁ and C₂. Switches S₁ to S₃ can be either electromechanical or solid-state units. The duration of the stimulus must be long enough to allow the transients to settle (typically, five to 10 periods of f₀). The ADC10734 measures the voltage drop, V_S, in the sense resistor, R_S; you can thus calculate the stimulus current: I_S=V_S/R_S. You can program the ADC10734 via its serial interface to measure the true differential signal between CH0 and CH1. (Send control sequence MA0 to MA4 to Pin DI, as shown in Table 1.) Reference 2 gives more details on programming the ADC10734.

After the control sequence, all switches open synchronously and the circuit starts processing the free-transient voltage, V(t). Upon completion of the processing (after five to 10 periods of f₀), voltages V₁ and V₂ stabilize, as shown in Figure 2. The first stage, IC_1A, is a simple precision rectifier whose outputs drive the inverting integrators, IC_1B and IC_1C. The unity-gain inverter using IC_1B keeps both dc outputs positive, a necessary condition for the ADC10734 to operate properly (using channels CH2 and CH3). Assuming for simplicity's sake that lowercase tau=R₄C₁=R₅C₂, the formula for calculating the damping coefficient is

Thanks to its low power consumption, the circuit is well-suited for portable, battery-powered operation. Input resistor R₁ should have a large value to minimize its influence on damping. The quad op amp, LMC6484, allows you to use values as high as 1 Megohms for R₁ through R₅. Other suitable op-amp choices include the LMC6084 (precision), the LMC6064 (precision and micropower), the LMC6574 (micropower and 2.7V supply), and the LMC6584 (low power and 1.8V supply). You could simplify the analog portion of the circuit by eliminating the inverting stage, IC_1D. To do that, substitute an ADC10834 for the ADC10734. The ADC10834 is basically the same ADC (10 bits plus sign, serial-I/O interface, multiplexer with S/H, and reference), but the ADC10834 has the additional ability to measure negative voltages because it uses dual power supplies.

The ADC10834 consumes 59 mW compared with the single-supply ADC10734's 37 mW. The control sequence in Table 1 is the same for both ADCs. For higher precision, you could upgrade the circuit to use the ADC12034 (12 bits plus sign), which also features a serial interface and low power consumption. You can implement this method with any type of popular 8/16-bit mC, including (but not limited to) the 8051, 6805, PIC16/17, or COP families. (DI #2025)

References

1. Belousov, Alex, "Simple procedure tests transducer," EDN, March 1, 1996, pg 144.

2. Data Acquisition Handbook, National Semiconductor, 1995, pg 2 to 342.

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