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# Electronics

## Opamp tutorial

### The noninverting amplifier

In part 2 we made an inverting amplifier. This not always practical, since it requires a negative supply voltage to get a negative output: you can't pull negative voltages out of thin air. Therefore now the noninverting amplifier.

The transfer function of the ideal opamp: $$\bbox[10px,border:2px solid #96BFCB]{ \large{ V_{OUT} = G \cdot (V_+ - V_-) }}$$ $V_+$ is $V_{IN}$, and we can see that $R1$ and $R2$ form a voltage divider which makes $$V_- = \dfrac{R1}{R1 + R2} \cdot V_{OUT}$$ Then $$V_{OUT} = G \cdot \left( V_{IN} - \dfrac{R1}{R1 + R2} V_{OUT} \right)$$ Rearranging gives us $$\left(1 + G \dfrac{R1}{R1 + R2}\right) \cdot V_{OUT} = G \cdot V_{IN}$$ Again we can ignore the term $1$ because $G$ is so much greater, then $$\bbox[10px,border:2px solid #96BFCB]{ \large{ \begin{array} {rcl} V_{OUT} & = & \dfrac{R1 + R2}{R1} \cdot V_{IN} \\ & = & \left(1 + \dfrac{R2}{R1}\right) \cdot V_{IN} \end{array} }}$$

Just like for the inverting amplifier we see that the negative feedback will make both inputs of the opamp equal. But while for the inverting amplifier a gain of less than 1 is possible, for the noninverting amplifier the amplification will always be greater than 1.