# Negative resistance circuit

The circuit is inputted with a 200Hz sine wave and the amplitude is varied. I believe the circuit is operating with negative feedback. But also the 8.2K resistor is then switched to an 18K resistor in which it is then operating in positive feedback. Struggling to understand the negative resistance aspect. Can anyone help me understand what is happening in this circuit?

Negative resistance happens when the circuit sources current. This doesn't happen with passive devices like resistors or capacitors. Amplifiers can sink and source current, in this circuit the amplifier will source current as the current through R1 increases. If the circuit is solved it will look like a resistor with negative resistance.

R = -I/V

This is how the opamp behaves.

The circuit is equivalent to: simulate this circuit – Schematic created using CircuitLab

To understand why consider pins 2 & 3 of the Op-amp. Because we have negative feedback these must be at the same potential. For this to be the case the output (pin 6) must be twice that of pin 3. The current in R2 is same as it would be if the bottom of R2 were connected to 0V but in the opposite direction: flowing upwards instead of downwards. It therefore looks like a resistor with a negative value.

Circuits like this are sometimes called Negative Impedance converters (NIC).

First off, I think it's referred to as "negative resistance" because the input current has the opposite polarity of the input voltage. As you raise the input voltage, the input current comes out of the input instead of flowing in as it would under a normal resistive load.

As to why the feedback goes from negative to positive: You actually have both negative and positive feedback paths in your design. Your negative feedback gain is 0.5. With an 8.2K input resistor--less than the 12K feedback--your positive feedback gain is under 0.5, and the negative dominates. With an 18K input resistor, your positive feedback gain is over 0.5, and the positive feedback dominates.