## Objective

Find all voltages (and currents) in an electronic circuit that contains operational amplifiers.

## Procedure

Verify that the following conditions are met:

• Negative feedback circuit

• Ideal operational amplifier

Add the following “rules” to Node Voltage Analysis:

• Write a KCL equation at both input nodes (V+, V-) of the opamp (except if the voltage is known, e.g. set by a source)

• Do not write an equation for the output node of the opamp (Vout).

• Add V+ = V- to the equations to solve the circuit.

## Example: Differencing Amplifier

Let’s use NVA to determine Vout as a function of Vin+ and Vin- (ignore the part number, the circuit works with any opamp). Write KCL equations for nodes Vin+ and Vin- (steps 5 to 7 have been combined for brefity). No equations are needed for Vout (NVA opamp analysis rule) or the inputs Vin+ and Vin-.

\begin{align} \frac{V^- - V_{in-}}{R_1} + \frac{V^- - V_{out}}{R_2} &= 0 \\[3mm] \frac{V^+ - V_{in+}}{R_1} + \frac{V^+}{R_2} &=0 \\[3mm] V^{+} &= V^{-} \end{align}

Solve the equations to get

$V_{out} = \left(V_{in+} - V_{in-} \right) \frac{R_2}{R_1}$

The circuit amplifies the difference of the input voltage, a very useful function for example with bridge circuits.

Reference: Schaum’s Outline of Electric Circuits, Seventh Edition, Section 5.4.