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What is the difference between sine wave and non-sine wave ups

Square Wave Output
Inverters are circuits which convert DC into AC.  Inverters are an integral part of UPS (Uninterrupted Power Supplies).  They convert the DC stored in the batteries of the UPS and produce an AC voltage which is provided to connected load in the event of a power failure.  

The AC produced by the inverter is not always a sine wave.  Some inverters produce a square wave.  These inverters are known as square wave inverters.   Square waves can be used where the load on the UPS is going to be mostly resistive loads such as heaters, incandescent lamps, etc.
Modified Sine Wave Output

Another form of inverter output is the modified sine wave or the quasi-sine wave inverter.  These inverter produce a waveform that has an intermediate voltage level which brings it closer to a sine wave.  

Sine Wave
Sine wave inverters produce an actual sine wave. Sine wave inverters are more expensive than the square wave and the modified sine wave inverters.  However, they are ideal as electric devices such as motors, Television sets, chargers are designed to use a natural sine waveform.  Using square wave inverters on these devices can produce harmonic distortion, humming.  This leads to reduced efficiency and loss of power.