Electromagnetic velocity sensing and damping

The simplest transducer both for sensing motions and for exerting forces is an electromagnetic (electrodynamic) device where a coil moves in the field of a permanent magnet, like in a loudspeaker (Fig. 14). The motion induces a voltage in the coil; a current flowing in the coil produces a force. From the conservation of energy it follows that the responsivity of the coil-magnet system as a force transducer, in Newtons per Ampere, and its responsivity as a velocity transducer, in Volts per meter per second, are identical. The units are in fact the same (remember that 1 N m = 1 Joule = 1 V A s). When such a transducer is loaded with a resistor and thus a current is permitted to flow, then according to Lenz's law it generates a force opposing the motion. This effect is used to damp the mechanical free oscillation of passive seismic sensors (geophones and electromagnetic seismometers).

  

Figure 14: Electromagnetic velocity and force transducer

We have so far treated the damping as if it were a viscous effect in the mechanical receiver. Actually, only a small part h_m of the damping is due to mechanical causes. The main contribution (in passive seismometers) normally comes from the electromagnetic transducer which is suitably shunted for this purpose. Its contribution is

$$h_{el}=E^2/2 M \omega_0 R_d$$ (36)

where R_d is the total damping resistance (the sum of the resistances of the coil and of the external shunt). The total damping h_m+h_el is preferably chosen as $1/\sqrt{2}$, a value that defines a second-order Butterworth filter characteristic, and gives a maximally flat response in the passband such as the velocity-response of the electromagnetic seismometer in Fig. 6.