Input
output
Non-Inverting Op-Amp Configuration
1.The Input Signal Vin is applied to non-inverting(+) terminal.
2.A voltage divider (formed by R1 and Rf) provides negative feedback to the inverting (–) terminal
Ideal Op-Amp Assumptions
1. No Current Flows into the Input Terminals
$$ I_{+} = I_{-} = 0 $$
2.The Differential Input Voltage is Zero
$$ V_{+} - V_{-} = 0 $$
Since the non-inverting terminal is connected to the input:
$$ V_{+} = V_{in} $$
Therefore,
$$ V_{-} = V_{in} $$
Let i be the current flowing through the resistors
$$ i = \frac{V_{out} - V_{-}}{R_{f}} = \frac{V_{-} - 0}{R_{1}} $$
$$ i = \frac{V_{out} - V_{-}}{R_{f}} = \frac{V_{-}}{R_{1}} $$
For Non Inverting Op-Amp Configuration
$$ V_{+} = V_{-} = V_{in} $$
$$ \frac{V_{out} - V_{in}}{R_{f}} = \frac{V_{in}}{R_{1}} $$
$$ \frac{V_{out}}{R_{f}} = \frac{V_{in}}{R_{1}} + \frac{V_{in}}{R_{f}} $$
$$ \frac{V_{out}}{R_{f}} = V_{in} \left[ \frac{1}{R_{1}} + \frac{1}{R_{f}} \right] $$
$$ \frac{V_{out}}{V_{in}} = R_{f} \left[ \frac{1}{R_{1}} + \frac{1}{R_{f}} \right] $$
$$ \frac{V_{out}}{V_{in}} = \frac{R_{f}}{R_{1}} + 1 $$
$$ A_{v} = \frac{V_{out}}{V_{in}} = 1 + \frac{R_{f}}{R_{1}} $$
where
\[ \boxed { \text{Output Voltage}(V_{out}) = A_{v} . V_{in} } \]
\[ \boxed { \text{Voltage gain}( A_{v}) = 1 + R_{f} \frac{1}{R_{1}} } \]