A Negative Impedance Converter (NIC) is an op-amp circuit that makes a passive component look like its negative-valued cousin. Connect a 10 kΩ resistor to a NIC and the input port behaves like −10 kΩ. Push current in, voltage rises instead of dropping. This sounds like cheating physics — it isn't. The op-amp is sourcing energy from its supply rails to invert the V/I relationship at the port.

The classic topology (current-inverting NIC, or INIC):

• Op-amp with input signal driving the non-inverting (+) input
• Two equal resistors R1 = R2 forming positive feedback from output to (+) input
• The impedance Z you want to invert connects from the inverting (−) input to ground
• Negative feedback path: output back to (−) input through Z

Because the op-amp forces V− = V+ = Vin, the voltage across Z equals Vin, so the current through Z is Vin/Z. But that current is supplied by the op-amp output, not by the input source. The input port instead sees current flowing out of it (because R1=R2 forces a mirrored current from the input node), giving Zin = −Z.

Key formula: With matched feedback resistors, Zin = −(R1/R2)·Z. Set R1 = R2 = 10 kΩ and Z = 4.7 kΩ resistor → input impedance is −4.7 kΩ.

Real-world application: tone-control cancellation in a guitar pickup loading circuit. A magnetic pickup has its own coil inductance and the cable capacitance forms a resonant low-pass that dulls high frequencies. By placing a NIC-generated negative capacitance (−50 pF to −200 pF) in parallel with the cable, you cancel the cable's parasitic C and restore treble response. Commercial "buffer" pedals from EHX and Lehle use this trick. Hi-fi MM phono preamps use the same technique to cancel cartridge loading.

Other uses:

• Boosting Q in passive filters: a negative resistor cancels coil losses, sharpening LC resonance
• Oscillator startup: negative resistance overcomes tank losses (essentially how every LC oscillator works internally)
• Loudspeaker damping: negative output impedance from the amplifier cancels voice-coil resistance, tightening bass

Stability warning: NICs are inherently borderline unstable. Connect a negative resistor across a real positive resistor of equal magnitude and you have an oscillator (or a latch-up). Always ensure the net resistance at every node remains positive at DC, and verify with a Nyquist plot if the loop matters. A common failure mode: the NIC works on the bench but latches to a supply rail when the source impedance drops unexpectedly.

Rule of thumb: keep |−Z| larger than the smallest positive impedance it will ever see in parallel. Violate that and your "tone restorer" becomes a 2 MHz oscillator.