Editing Operational amplifier (section)

==== Non-inverting amplifier ====
[[Image:Op-Amp Non-Inverting Amplifier.svg|frame|An op amp connected in the non-inverting amplifier configuration]]
In a non-inverting amplifier, the output voltage changes in the same direction as the input voltage.

The gain equation for the op amp is
:<math>V_\text{out} = A_\text{OL} (V_+ - V_-).</math>

However, in this circuit ''V''<sub>−</sub> is a function of ''V''<sub>out</sub> because of the negative feedback through the ''R''<sub>1</sub> ''R''<sub>2</sub> network. ''R''<sub>1</sub> and ''R''<sub>2</sub> form a [[voltage divider]], and as ''V''<sub>−</sub> is a high-impedance input, it does not load it appreciably. Consequently
:<math>V_- = \beta V_\text{out},</math>

where
:<math>\beta = \frac{R_1}{R_1 + R_2}.</math>

Substituting this into the gain equation, we obtain
:<math>V_\text{out} = A_\text{OL} (V_\text{in} - \beta V_\text{out}).</math>

Solving for <math>V_\text{out}</math>:
:<math>V_\text{out} = V_\text{in} \left( \frac{1}{\beta + \frac{1}{A_\text{OL}}} \right).</math>

If <math>A_\text{OL}</math> is very large, this simplifies to
:<math>
  V_\text{out} \approx \frac{V_\text{in}}{\beta}
                     = \frac{V_\text{in}}{\frac{R_1}{R_1 + R_2}}
                     = V_\text{in} \left(1 + \frac{R_2}{R_1}\right).
</math>

The non-inverting input of the operational amplifier needs a path for DC to ground; if the signal source does not supply a DC path, or if that source requires a given load impedance, then the circuit will require another resistor from the non-inverting input to ground. When the operational amplifier's input bias currents are significant, then the DC source resistances driving the inputs should be balanced.<ref>An input bias current of 1&nbsp;μA through a DC source resistance of 10&nbsp;kΩ produces a 10&nbsp;mV offset voltage. If the other input bias current is the same and sees the same source resistance, then the two input offset voltages will cancel out. Balancing the DC source resistances may not be necessary if the input bias current and source resistance product is small.</ref> The ideal value for the feedback resistors (to give minimal offset voltage) will be such that the two resistances in parallel roughly equal the resistance to ground at the non-inverting input pin. That ideal value assumes the bias currents are well matched, which may not be true for all op amps.<ref>{{cite web |author=Analog Devices |title=Op Amp Input Bias Current |date=2009 |id=Tutorial MT-038 |publisher=Analog Devices |url=http://www.analog.com/static/imported-files/tutorials/MT-038.pdf |access-date=2014-05-15 |archive-date=2015-02-13 |archive-url=https://web.archive.org/web/20150213055046/http://www.analog.com/static/imported-files/tutorials/MT-038.pdf |url-status=dead }}</ref>