Non-inverting amplifier

A non-inverting amplifier uses an operational amplifier to produce an output voltage with the same polarity as its input voltage. The input voltage $$V_{\mathrm{in}}$$ is applied to the non-inverting input, marked $$+$$.

A feedback resistor $$R_{\mathrm{f}}$$ connects the output to the inverting input, marked $$-$$. A second resistor $$R_l$$ connects the inverting input to ground. These resistors form a voltage divider that feeds part of the output voltage back to the inverting input.

The feedback is negative: if the output rises, the voltage fed back to the inverting input rises, opposing the change. In normal operation, the ideal amplifier adjusts its output until the voltages at its two inputs are equal. The inverting input is therefore at $$V_{\mathrm{in}}$$.

Non-inverting amplifier gain

For an ideal operational amplifier, no current enters the inverting input. The voltage divider therefore sets the voltage at that input to $$V_{\mathrm{out}}R_l/(R_{\mathrm{f}}+R_l)$$. Equating this to $$V_{\mathrm{in}}$$ and rearranging gives the closed-loop voltage gain:

The two resistances set the gain. For positive resistor values, the gain is positive and greater than one, so the output is not inverted relative to the input. The equation applies while the amplifier can produce the required output voltage within its supply limits.