gyrator question (how does these two circuits be equal)

[liletian]

Hi Guys
In wikipedia gyrator, they use a amplifer to replace the gyrator. They claimed the attached circuit are equivilent.
First, I can not equal these two circuits.
Second, even they can equal, how does it relative to the gyrator idea? In other words, how can a op-am function as a gyrator? Normaly you use two for OTA with a capacitor to get inductance. I do not understand here how one op-am can replace four OTA.
Thanks a lot

 

[LvW]

As I have often discovered: Don't blindly trust Wikipedia!
Both circuits don`t have the same input impedance.
For ideal opamp the input impedance is Z=(RL+sL)/(1+RL*sC).
An active realization of a grounded (ideal and lossfree) inductance uses two opamps or two OTA's.

 

[albbg]

In general, the input impedance of the two circuits is not the same. However under some hypothesis they can be very similar, so you can use the op-amp circuit to simulate an inductor in a limited frequency range. Please refer to https://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-20.pdf