What are gyrators and negative impedance converters, and how are they used?

A gyrator converts capacitance to inductance (and vice versa) through impedance inversion: Zin = k^2/Zload. Using op-amps and resistors, large inductance values impossible with physical inductors can be synthesized for low-frequency filters. Negative impedance converters (NIC) create negative resistance for oscillators, active filters, and canceling losses. NICs require careful stability analysis as they can cause unintended oscillation. Both are essential for active filter and oscillator design.