Design Ideas: March 1, 1996

Testing electromechanical transducers can be as simple as measuring a dc voltage. The circuit in Figure 1 and an accompanying test method enable you to measure the damping coefficient ([beta]) of speakers, microphones, seismic geophones, and other transducers that exploit electromagnetic phenomena. You can also tailor this method for testing electrostatic devices, such as capacitive micromachined sensors. In general, you can measure the damping in any second-order system or signal, which conforms to the following basic equation for the free transient process:

where u(t) is the voltage, U_o is the amplitude, b is the damping in the physical system or exponential decay in signals, and f_o is the natural resonant frequency.

The measurement method requires that you first stimulate the transducer with a step function during a certain period of time. Then, you remove the stimulus and integrate the positive and negative half waves of the transducer's signal in its free transient-response mode. Integral transforms have excellent noise immunity to both electrical noise and mechanical vibration. Moreover, the overall accuracy is totally independent of the step function's amplitude. It is also somewhat independent of the absolute accuracy of the components and dc measurements; they only must be ratiometric.

The circuit in Figure 1 specifically tests a seismic geophone whose natural frequency is within 4 and 14 Hz and whose damping coefficient is 0.6. You can also customize the circuit for any other type of transducer. The circuit consists of the transducer under test, which the circuit depicts as an equivalent series connection of L_COIL and R_COIL, a reference voltage V_REF with current-limiting resistor R_REF, switches S1 to S3 (which may be of any type), an IC_1A-based precision rectifier, and a couple of analog integrators based on IC_1B and IC_1C. The supply voltage is ±5V, and V_REF equals 2.5V.

To run the test, apply the step current to the transducer by turning all switches on. The duration of this stimulus must be long enough for all transients to settle. After this time, open all switches synchronously, and the circuit will start processing the free transient voltage u(t). Once this process is complete (it typically takes 5 to 10 periods of natural frequency f_o), you can calculate [Beta] using V₁ and V₂. Assuming for simplicity that the time constants of both integrators are equal, that is R₄C₁=R₅C₂=[tau], the calculation for damping is

Provided that R₂=R₃ and R₄C₁=R₅C₂, the tolerance of these components and that of V_REF won't affect the circuit's overall accuracy. Also, the absolute value of V₁ and V₂ is not important; the equation for [beta] only uses their ratio. This feature makes it possible to use any analog or digital ratiometer instead of a DMM.

R₁ can have a effect on [beta]; R₁ must be large to avoid significant errors. Alternatively, you can add a simple high-impedance voltage follower before the rectifier stage using the last available op amp of the TLC2274 quad package. The TLC2274 op amp works well for this circuit because of its rail-to-rail operation, low supply voltage, extremely low input current, and high input impedance. Other general-purpose op amps are also applicable. (DI #1836)