# Comparator

A comparator is a device that compares two voltages (or currents) and outputs a digital signal indicating which is larger. It has two analog input terminals V+, and V-, and one binary digital output Vo. It is commonly used in devices that measure and digitize analog signals, such as analog-to-digital converters (ADCs).

$$if \ V_+ > V_- \ then \ V_{out} = V_{S+}$$ $$if \ V_- > V_+ \ then \ V_{out} = V_{S-}$$

If the output is digital, then VS+ is H or 1 and VS- is L or 0. It can then be considered to be a one bit analog to digital converter.

A comparator consists of a specialized high-gain differential amplifier. Due to the high gain, Vout is undetermined for the following condition.

$$V_- = V_+$$

A comparator can be implemented using an opamp. The output voltage of the op-amp is given by the equation: $$V_{out} = {A_{OL} \, (V_{\!+} - V_{\!-})}$$ where AOL is the open-loop gain of the amplifier.

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