Dynamic properties of measuring circuits applied to frequency output transducers

Frequency output measuring transducers transform the measured quantity x into the frequency f or the period T of the output signal. Frequency is usually measured by counting the number of pulses produced by the output voltage during a constant counting time t_c, long enough to minimize a random error. The period is measured by counting the pulses of a reference oscillator in the varying time equal to N periods of the transducer's output signal. Considering the dynamic properties of both measuring chains one may conclude that averaging of the measured occurs, and in order to calculate the dynamic error, an averaging transducer ought to be taken as a reference. The paper indicates that under dynamic conditions the frequency measuring chain may be treated as a really averaging one, the period measuring chain only as an approximately averaging one, and in both cases averaging is not sufficient to eliminate the aliasing error of the sampling procedure. A method for accelerating the measurement and then avoiding the aliasing error is the "one-period method" considered in the paper. The averaging error and delay error of this method are considered in detail, under the assumption that a parameter-controlled oscillator is used as an element of the measuring chain.