Editing Gyrator (section)

==== Operation ====

In the circuit shown, one port of the gyrator is between the input terminal and ground, while the other port is terminated with the capacitor. The circuit works by inverting and multiplying the effect of the capacitor in an [[RC circuit#Differentiator|RC differentiating circuit]], where the voltage across the resistor ''R'' behaves through time in the same manner as the voltage across an inductor. The op-amp follower buffers this voltage and applies it back to the input through the resistor ''R<sub>L</sub>''. The desired effect is an impedance of the form of an ideal inductor ''L'' with a series resistance ''R<sub>L</sub>'':
<math display="block">Z = R_L + j \omega L.</math>

From the diagram, the input impedance of the op-amp circuit is
<math display="block">Z_\text{in} = (R_\text{L} + j \omega R_L R C) \parallel \left(R + \frac{1}{j \omega C}\right).</math>

With ''R<sub>L</sub>RC'' = ''L'', it can be seen that the impedance of the simulated inductor is the desired impedance in parallel with the impedance of the RC circuit.  In typical designs, ''R'' is chosen to be sufficiently large such that the first term dominates; thus, the RC circuit's effect on input impedance is negligible:

<math display="block">Z_\text{in} \approx R_L + j \omega R_L R C.</math>

This is the same as a resistance ''R<sub>L</sub>'' in series with an inductance ''L'' = ''R<sub>L</sub>RC''. There is a practical limit on the minimum value that ''R<sub>L</sub>'' can take, determined by the current output capability of the op-amp.

The impedance cannot increase indefinitely with frequency, and eventually the second term limits the impedance to the value of ''R''.