This study finds the optimum coil resistance, rc.opt, which maximizes the signal-to-noise ratio (SNR) of an electromagnetic (EM) seismometer and amplifier combination. The optimum coil resistance is shown to be the product of a seismometer factor (SF) times the noise resistance, Rn, of the amplifier. The seismometer factors range from 1.13 to 3.66 for the nine EM seismometers considered. The minimum noise figure solution, in which the amplifier noise resistance is set equal to the coil resistance, is shown to correspond to the special case in which there is no damping resistor present. It is also shown that the optimum form for the noise resistance is a constant independent of frequency and that this feature can be approximated with FET-like components such as the MAT-02. Examples of using rc.opt are given using both the 5500-ohm and the 500-ohm 1-Hz L4-C seismometers paired with the OP-27 and LT1028 operational amplifiers, respectively. It is pointed out that, although the resulting amplitude signal-to-noise ratios (ASNRs) are approximately equal, it is best to choose the seismometer-amplifier pair having the larger generator constant because it results in a larger signal. Furthermore, if the coil resistance is not the optimum value, the resulting decrease in the ASNR is less if the coil resistance is chosen greater than the optimum rather than less.
The deleterious effects of mismatching seismometer and amplifier are shown by comparing ASNRs for the GS-13 seismometer paired with three different amplifiers. The degradation in ASNR is found to be as large as a factor of 3. It is pointed out that mismatching would not be done purposely but can inadvertently occur when connecting an EM seismometer to a seismic recorder whose input noise resistance properties are unknown, as in generally the case. It is recommended that manufacturers of seismic recorders obtain the necessary input noise data from the component manufacturers and supply the input noise resistance to users.
Finally, the three commonly used single-ended preamplifier circuits used for EM seismometers are compared in terms of their resulting ASNRs. The same seismometer and amplifier are used in all three circuits. For the GS-13/MAT-02 pair, the noninverting, parallel damping resistor circuit resulted in an ASNR that was 3.8 times larger than that for the inverting, parallel damping resistor circuit, and 3 times larger than that for the inverting, series damping resistor circuit.