Digital calibration methods and apparatus are known having means for removing amplitude errors in transducers, amplifiers, or analog-to-digital converters. FIG. 1A shows a prior art circuit, in which a physical value such as a temperature 10 that is to be measured is converted into an electric signal by a transducer 11. The signal level of the transducer may be increased by an amplifier 12, and unwanted signals and noise may be attenuated by a filter 13. The resulting analog signal is converted to a digital value by an analog-to-digital (A/D) converter 14. The output of the A/D converter 14 is read by a microprocessor system 16.
The microprocessor system 16 contains a stored calibration table 16'. As shown in FIG. 1B the calibration table 16' may be displayed as a graph of uncorrected amplitude readings 18 versus their associated corrected amplitude readings 19. If the transducer 11, amplifier 12, filter 13, and A/D converter 14 have no errors, the calibration graph will be the dashed straight line with unity slope 22. However, offset errors 17, gain errors 21, and non-linearity errors 20 caused by any element in the system are displayed as deviations from the dashed line 22. The microprocessor system 16 examines the uncorrected amplitude reading 15 provided by the A/D converter, then converts it to a corrected amplitude reading 17, typically by interpolation between points on the calibration graph.
It is sometimes the case that the physical value of interest is a waveform which is repetitive with respect to time, such as current waveforms in alternating current (AC) power systems. As with the steady state values described above the waveform can be distorted by the transducer 11, the amplifier 12, the filter 13, and the A/D converter 14.
Both the original waveform of the physical value and the distorted waveform resulting from the conversion process can be decomposed into a Fourier series of pure sine waves, with each sine wave having a unique frequency, amplitude and phase. At any frequency, the transducer, amplifier, filter, or A/D converter can introduce errors in the amplitude, phase shift or both, which can in turn introduce errors in the waveform stored in the microprocessor system.
These types of errors are illustrated in FIGS. 2, 3, 4 and 5. FIG. 2 shows a sample waveform of a physical value with respect to time, consisting of a fundamental frequency, its third harmonic, and its fifth harmonic. FIG. 3 shows the same waveform with the same harmonic amplitude content, but with substantial phase shift errors on the third harmonic and the fifth harmonic. FIG. 4 shows the waveform of FIG. 2 with both harmonic amplitude errors and phase shift errors. FIG. 5 shows the waveform of FIG. 2, with harmonic amplitude errors. It is clear by inspection that the waveforms in FIGS. 2 through 5 are different.
Because these errors to repetitive waveforms are frequency dependent, the prior art method and apparatus for digital calibration are incapable of correcting them. A method and apparatus are needed for calibrating systems which convert physical values having repetitive waveforms to an accurate digital value.