Several variants of half division two-dimensional method are proposed, which is the basis of a fundamentally new approach for constructing measuring instruments for sinusoidal or periodic electrical quantities. These measuring instruments are used in the diagnosis of electric power facilities. The most general variant, called midpoint method, is considered. The proposed midpoint method allows you to measure much smaller than using widespread methods, alternating currents or voltages, especially when changing the amplitude of the measured signal in very wide ranges, by 1–2 orders of magnitude. It is shown that using the midpoint method it is possible to suppress sinusoidal or periodic interference in the measuring path, in particular, to measure small alternating current when sinusoidal or periodic interference is 1–2 orders of magnitude higher than the useful signal. Based on the results of comparative tests, it was found that the current measuring device implementing the midpoint method is an order of magnitude more sensitive than the currently used high-precision measuring instruments.