Low-frequency drift reduction in the integration of repetitive signals

The integration of very small signals, over periods long compared to the signal duration, causes severe problems owing to drift in amplifiers and integrators. It is particularly desirable to filter out low-frequency drift because of the 1/f characteristic of the integrator. For repetitive signals, it is necessary to maintain the frequency response of the system down to a frequency which is low compared to the repetition frequency, in order to maintain an acceptable phase characteristic. A compromise between the phase characteristic and low-frequency attenuation is necessary using conventional filters. In connection with a hysteresis loop tracer for very small ferrite cores, a method of low-frequency drift attenuation for integrators was developed. It has an advantage over previous methods in that the attenuation applies to low-frequency signal errors, while the bandwidth of the signal to be integrated may be maintained down to any desired frequency, even though it lies in the attenuation band. The method, which is applicable to repetitive signals with zero d.c. component only, integrates samples of the drift at the end of successive cycles of the signal. The sample integral is held constant during the cycle, and is applied to the input in the appropriate sense to correct the drift. It is shown that the attenuation of low-frequency errors is 12 dB per octave, while maintaining the band-width required for the signal. Expressions for the response to an impulse, step function and sinewave are derived.