Precision measurement of wide-band signals

Abstract

Modern precision instruments measuring root-mean-square (rms) values of periodic wide-band signals characteristically have high measurement accuracy at audio frequencies and relatively low accuracy at high frequencies. This is due largely to specific features of their design [1]. Most precision instruments measure currents and voltages indirectly, by computing with the aid of multiplying and dividing devices. These devices have an intrinsic error component proportional to the squared input signal frequency [1]. Accordingly, they error increases rapidly with frequency.Here we propose a method of accurate measurement of voltage, and effective, reactive, and total power based on the measurement of these variables with the aid of a coarse wide-band converter and automatic calibration of this converter after each measurement against a reference narrow-band converter. The calibration signal is the measured signal whose highfrequency portion of the spectrum has been suppressed by a filter. The error of the wide-band converter found in the test is automatically considered when the results of measurements are processed. The measurement procedure is composed of two cycles.In the first cycle the switch S is in position 1 and the measured signal U x, bypassing the low-pass filter LPF, is applied to the input of a wide-band converter C w. The output code of the latter N 1 is stored in the computer PC (Fig. 1). In the second cycle switch is set to position 2 and the measured signal is applied simultaneously to C w and to a precision narrow-band converter C O that converts the rms voltage into a code. The output codes N 3 and N 2 of the narrow-band and wide-band converters also are stored in the PC.The desired value of the measured signal is calculated either from U x = NINz/(cN3) (multiplicative correction) or U x = c-l [Nl - (N 3 -N2)] (additive correction), where c is a constant defined in the calibration of the entire measuring instrument. The sequence of cycles is arbitrary.The filter parameters are chosen to suppress all signal frequencies above the upper operating frequency range of the converter C 0.Let us find the U x measurement error using the multiplicative correction method. The output code of the precision converter C O is given by N 2 = cU0(l + 80), where U 0 is the filter output voltage, and 8 o is the relative error c,e the precision converter. The convener C O output voltage and, correspondingly, the error 80 do not change during measurement. Because of this, there is no reason to consider separately the multiplicative and additive components of the converter error. The code N 3 is given by N 3 = c[Uo(1 + 8 t) + AU], where 81 and AU are respectively the relative multiplicative and absolute additive errors of the wide-band converter. The code N I = c[Ux(1 + 81 + AS) + AUxF(J) + AU], where A8 is the increment of the multiplicative error 81 due to the nonlinearity of the wide-band converter response caused by the change of its input voltage from U 0 to U x without considering the frequency error, A8 depends on th...