A precise measuring system based on the least squares method is developed for audio frequency voltage. The system consists of an analog-to-digital converter and a personal computer. An unkown voltage applied to the system is converted into discrete data with the usual sampling method or the frequency compressed sampling method, and precisely expressed as a polar vector by means of the least squares method. Some basic properties of the system, such as accidental errors of parameters estimated by the least squares method, effect of asynchronous sampling and frequency characteristics are studied. Thus, it is estimated that the unknown voltage of about 5 Vms is measured with standard doviation of 5×10^-5 in magnitude and 5×10^-5 rad. in phase angle in frequency range of 10 Hz‾100kHz.
This voltage measuring system is applied to compose a voltage ratio measuring system for ratio measurement of two voltages of a frequency. The system consists of a pair of the voltage measuring systems. The specific errors, namely systematic errors of the system are easily eliminated from each measured values by self-calibration. It is estimated that uncertainties of measured values are 5×10^-5 in magnitude and 5×10^-5 rad. in phase difference in frequency range of 10Hz‾100kHz, when two voltages of 5Vms are compared by this system.