Calculate RMS
Not all forces and sources of power are in steady states. Many sources of power vary by their nature. This variation, when expressed in simple mathematics, often results in descriptions of the source that vary into both positive and negative numbers. A good example of the variation between positive and negative numbers exhibited by power sources is house current. As house current is generated by rotating magnetic processes, the voltage provided at the house outlets is sinusoidal. This sinusoidal power causes positive currents to flow into the house when the sinusoid is in a positive part of the waveform, and draws current back out of the house when the sinusoid is in a negative part of the waveform. This alternating current, commonly called AC, can make it seem at first glance that the total power to the house is zero. However, power has no sign. Both positive and negative waveforms deliver power to the house, differing in electrical angular phase, but not in power. To express the delivery of power to the house, simple signed algebra is inadequate. The waveform must be treated as if it is always positive. Compensation also must be made for the variation in the waveform magnitude. A sinusoidal waveform varies between peak and zero constantly, and delivers different amounts of power depending on the electrical angle of the waveform. The concept of Root Mean Square (RMS) takes both the sign reversal and magnitude variation of the drive waveform into account. Although RMS calculations can be useful in some other areas, RMS calculations were originally defined to accurately express the electrical power being supplied by an AC waveform. RMS values are a statistical representation of power delivered by a varying power source. Use these tips to learn how to calculate RMS.
Steps
- Understand how units are expressed electrically.
- The voltage supplying power to a load (V) creates a current in the load (I) related to the resistance of the load (R).
- The relationship between these units is V = I x R. Power (P) is (square of I) x R. As I = V divided by R, power can also be expressed as (square of I divided by R) times R, or (square of V) divided by R.
- Identify what RMS is. RMS is defined as the square root of the average of the squares of the peaks of the waveforms that make up the power source.
- For example, if the incoming power source were characterized as 4 waveforms added together with waveform peaks of A1, A2, A3 and A4, the RMS would be the square root of ((the sum of the 4 A values squared (divided by 4)).
- Note that RMS calculations are independent of frequency. A waveform that is oscillating faster than another spends less time at the peak value, but also spends less time in the lower power areas of the electrical phase of the driving waveform. The variation between peak power and minimal power of the higher frequency waveform is sharper and faster than that of the lower frequency waveform, but the faster repetition of those values exactly cancels out the variation. 2 identically shaped waveforms of different frequencies deliver the same power.
- Find the relationship between the peak value and the RMS value of a sine wave. The sine wave is expressed as an amplitude A times the sine of (2 pi times frequency times time). Only the amplitude A matters. A sinusoidal waveform that peaks at A has an RMS value of A divided by the square root of 2. For example, a measurement of the 120 volt RMS power delivered to the house would show that the incoming sine wave peaks at 120 times the square root of 2, or 170 volts.
- Derive the RMS power of a square wave. As a square wave alternates between positive and negative values of the stated peak with no electrical phase loss, the RMS calculation need only turn all negative values into positive values. This results in A being the same for both peak and RMS of a square wave.
- Calculate the RMS power of a sawtooth wave. A sawtooth wave is less efficient than a sine wave in delivering power. The relationship between peak and RMS of a sawtooth is that RMS equals A divided by the square root of 3.
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