# Is it possible to make a non-inverting amplifier with positive feedback?

The 'classic' non-inverting amplifier configuration uses negative feedback. What happens when the + and - terminals are switched? Based on my pencil-and-paper analysis and a Circuitlab simulation, it seems that the result is the same. Is this correct? Can we make a non-inverting amplifier with positive feedback?

Derivation for the positive feedback non-inverting amplifier: I assume that input impedance is infinite, output impedance is zero, and the output voltage is given by

$$V_{out} = A(V^{+} - V^{-})$$

Now using the voltage divider equation,

$$V^{+} = V_{out} \frac{R_b}{R_a+R_b}$$

and for the negative terminal, we have

$$V^{-} = V_{in}$$

Substituting into the equation for the output voltage,

$$V_{out} = A(V^{+} - V^{-}) = AV_{out} \frac{R_b}{R_a + R_b} - AV_{in}$$

$$V_{out}(1 - A \frac{R_b}{R_a + R_b}) = -AV_{in}$$

$$V_{out} = \frac{-AV_{in}}{1 - A \frac{R_b}{R_a + R_b}}$$

If the input frequency is relatively low, and both resistors are of a similar order of magnitude, then

$$A \frac{R_b}{R_a + R_b} >> 1$$

$$V_{out} \approx \frac{-AV_{in}}{ - A \frac{R_b}{R_a + R_b}} = V_{in} \frac{Ra + R_b}{R_b}$$

Which is the formula commonly given for the output of the classic non-inverting amplifier. So is there any difference between these two circuits? If so, where does my analysis fail? What is a more accurate way of analyzing the positive feedback circuit presented below?

EDIT: As suggested by Jasen, the positive feedback circuit I posted is a Schmitt Trigger. The Wikipedia article on Schmitt Triggers explains it fairly well. It turns out that they key to analyzing it is to solve for the voltages at the input terminals and then treat the Op-Amp as a comparator. That is, find equations for V+ and V-, and then ask the question "When does V+ > V- hold?"

• You need to take into account the dynamics of the op-amp in order to do a stability analysis. See this pdf for an example – helloworld922 Nov 8 '15 at 6:04
• $V_+$ is equal to $V_-$ when there is a lot of gain in the op-amp and when there is negative feedback through passive components. the output continually adjusts itself to whatever value it needs to be for the voltage difference across $V_+$ and $V_-$ to be virtually zero. – robert bristow-johnson Nov 8 '15 at 6:39