Learn the math behind AC to DC power conversion and how to power DC devices from an AC source.
Converting AC to DC
Physically converting alternating current (AC) power to direct current (DC) power involves several steps and a device called a rectifier. Fortunately, working out the mathematical conversion is quite simple.
In general, we express DC voltage as AC RMS voltage. RMS stands for root mean square and refers to the square root of the average (arithmetic mean) of the squares of all values in the set. In the case of typical sinusoidal AC waveforms, the RMS over all time is equal to the RMS of one period of the wave. This is possible since we presume the wave to be identical each period.
RMS for a standard AC waveform is equal to the peak voltage divided by the square root of two, as shown in this RMS to DC formula:
RMS Equation for AC to DC Conversion:
If we know the peak voltage of an AC, we can quickly figure out the necessary DC voltage. Divide the peak voltage by the square root of two to obtain the RMS voltage, which is equivalent to the required DC voltage. It is important to note that this determines the theoretical DC voltage equivalent based on the peak AC voltage, not the exact DC voltage that will result from any real-life conversion. Unfortunately, only hypothetical conversions maintain 100 percent efficiency.
Putting Theory into Practice
We can use the RMS equation above to determine and allow the conversion of AC to power DC devices. As a theoretical example, an incandescent light bulb will grow equally brightly on 141V AC (peak voltage) and 100V DC, since we express the RMS of 141V peak as:
This equation also allows us to work backward from the device, knowing its DC power requirement, to calculate the necessary input AC. With this information, we can convert the AC supply from the power grid to the appropriate voltage to power the device. Remember, of course, that in a real-life application, you’ll need to account for losses due to inefficiency in the conversion. This equation can provide a good starting point for practical applications.
Converting AC to DC voltage is quite simple mathematically and provides a basis for understanding the necessary conversions to successfully power DC devices from a standard AC supply from the power distribution grid.
