Измерение переменного тока: методы и точность определения среднеквадратичного значения.

For the measurement of an alternating current the signal is often converted into a direct current of equivalent value, the root mean square (RMS). Simple instrumentation and signal converters carry out this conversion by filtering the signal into an average rectified value and applying a correction factor. The value of the correction factor applied is only correct if the input signal is sinusoidal. True RMS provides a more correct value that is proportional to the square root of the average of the square of the curve, and not to the average of the absolute value. For any given waveform, the ratio of these two averages is constant and, as most measurements are made on what are (nominally) sine waves, the correction factor assumes this waveform; but any distortion or offsets will lead to errors. To achieve this, a true RMS converter requires a more complex circuit.

If a waveform has been digitized, the correct RMS value may be calculated directly. Most digital and PC based oscilloscopes include a function to give the RMS value of a waveform. The precision and the bandwidth of the conversion is entirely dependent on the analog to digital conversion. In most cases, true RMS measurements are made on repetitive waveforms, and under such conditions digital oscilloscopes (and a few sophisticated sampling multimeters) are able to achieve very high bandwidths as they sample at much higher sampling frequency than the signal frequency to obtain a stroboscopic effect.

The RMS value of an alternating current is also known as its heating value, as it is a voltage which is equivalent to the direct current value that would be required to get the same heating effect. For example, if 120 V AC RMS is applied to a resistive heating element it would heat up by exactly the same amount as if 120 V DC were applied. This principle was exploited in early thermal converters. The AC signal would be applied to a small heating element that was matched with a thermistor, which could be used in a DC measuring circuit. The technique is not very precise but it will measure any waveform at any frequency (except for extremely low frequencies, where the thermistor's thermal capacitance is too small so that its temperature is fluctuating too much). A big drawback is that it is low impedance: that is, the power used to heat the thermistor comes from the circuit being measured. If the circuit being measured can support the heating current, then it is possible to make a post measurement calculation to correct the effect, as the impedance of the heating element is known. If the signal is small then a pre amplifier is necessary, and the measuring capabilities of the instrument will be limited by this pre amplifier. In radio frequency (RF) work, the low impedance is not necessarily a drawback since 50 ohm driving and terminating impedances are widely used. Thermal converters have become rare, but are still used by radio hams and hobbyists, who may remove the thermal element of an old unreliable instrument and incorporate it into a modern design of their own construction. Additionally, at very high frequencies (microwave), RF power meters still use thermal techniques to convert the RF energy to a voltage. Thermal based power meters are the norm for millimeter wave (MMW) RF work.