In many cases it is very difficult to obtain the right indictor. The series resistance needs to be very low, the Q needs to be very high or just the value needs of the inductor needs to be so large that it is impossible to use a conventional coil. In all these case a gyrator might be handy.
Very simply said: a gyrator is a circuit that acts like an inductor.
Of course there are also many limitations to a gyrator, since it is an active circuit you need a power supply, in same cases even a symmetrical power supply. The current through the inductor is limited to the what the active devices transistors and/or opamps can handle. When the current through the coil is abruptly changed the self-induction of teh coil might normally create large induction voltages that might hundreds of volts. With a gyrator this is always limited to the voltage supply of the circuit. Also the frequency in the application of the gyrator is often limited to the transistion frequency Ft of the active devices. And finally, almost all gyrator circuits require that on end of the virtual-coil is connected to ground.
But if all of these limitations are kept in mind it can still be a very versatile circuit. The applications are numerous, 50 Hz noise killer, in a receiver to kill that birdie, or that make a tuned circuit to filter out that single CW signal. In a harmonic distortion meter, etc.
The circuit here below is not original but I was just curious to understand how it worked. So on a Saturday morning I sat together with pencil and paper and started dissection the circuit. Below are the results.