Gyrator circuits

Hi guys, this is a circuit called gyrator or positive impedance inverter.
Its a well known fact that inductors can't be used in integrated circuits due to their large size and limited range of production( typically from micro Henry to tens of Henry only.)

So, We use someting called a gyrator, which inverts the effect of a capacitance to make it act like an inductance.Since capacitors and resistors can be fabricated over a wide range and accuracy, we get inductors of our choice by altering the resistances and capacitance.
Operation of the circuit
The circuit works by inverting the effect of the capacitor. The desired effect is an impedance of the form of an ideal inductor L with a series resistance RL:
Z=Rl+j.w.L
From the diagram, the input impedance of the op-amp circuit is:
Z(in)=(Rl+j.w.Rl.R.C)||(R + (1/j.w.C))
With RLRC = L, it can be seen that the impedance of the simulated inductor is the desired impedance in parallel with the impedance of C and R. In typical designs, R is chosen to be adequately large that the dominant term is:
Z(in)=Rl+j.w.Rl.R.C
This is the same as a resistance RL in series with an inductance L = RLRC.
In typical applications, both the inductance and the resistance of the gyrator is much greater than that of a real inductor. Gyrators can be used to create inductors from the microhenry range up to the megahenry range. Real inductors are typically limited to tens of henries. Real inductors have parasitic series resistances from hundreds of microhms through the low kilohm range. The parasitic resistance of a gyrator depends on the topology, but with the topology shown, series resistances will typically range from tens of ohms through hundreds of kilohms. Q of an LC filter can be either lower or higher than that of a real LC filter – for the same frequency, the inductance is much higher, the capacitance much lower, but the resistance also higher. Gyrators will typically have higher accuracy than real inductors, due to the lower cost of precision capacitors than inductors.