### Everything You Wanted to Know about Gyrators but Were Afraid to Ask!

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Summary: Gyrators are real devices, used in IC designs to replace hard to create inductors with capacitors.

Gyrators:

Refer to reference 1. The gyrator is a two port network that is designed to transform a load impedance into an input impedance where the input impedance is proportional to the inverse of the load impedance. The gyrator network can be used to transform a load capacitance into an inductance. This feature is extremely useful in integrated circuit technology where it is difficult to realize physical inductors. The gyrator circuit can be created with just two dependent sources. The model in Figure 1 following displays the schematic of the gyrator macro: Figure 1
Gyrator Schematic

Such a device is present in the B2SPICE version 5 library. Now typically if one wished to model an inductor, one would just imbed an inductor into a circuit rather than using a gyrator and a capacitor. However, in the modeling of an IC it might be convenient, at least at first, to include a gyrator as an ideal device initially, and then after the concept is proven, to add some additional elements to add some non-ideal elements. As will be seen later, one of these is that there will of necessity be some series resistance in the final realization.

Consequently a second iteration of the design might add a series resistance to the gyrated capacitance. Now a realization would generally include operational amplifiers and several other devices, which would bring about several other considerations. Namely, the dynamic range of the opamps as well as their frequency response. Some of those considerations will be considered in the circuits to follow.

Gyrator Realization:

Figure 2 following, from reference 2, shows a gyrator realization: Figure 2
Gyrator realization

Here it can be seen that the input impedance is equal to: Now IF R2 >> R1, Let us model this and see what the results are: Figure 3
GYRATOR test circuit#1

In Figure 1 three diferent realizations are shown. Topmost is a rather idealized op-amp circuit corresponding to that of Figure 2, in a series resonant configuration. Beneath this is an idealized representation of the circuit, and lowest is a gyrator circuit representation.

We know that the circuit representation of the inductor will have a series resistance of about 10 ohms, so we will include that in the models as R6 and R8. It should be noted that, lacking a floating opamp supply, we are limited to inductor realizations where one end is grounded. This means that any filters we might wish to construct are limited to high-pass, band pass and notch type filters without some unusual effort.

The library gyrator produces a value of inductance at the input equal to 'g^2' times the value of capacitance at the output. As this value is equal to R1*R2 in our case, or 107, 'g' becomes its square root.

A graph of this circuit is shown in Figure 4 following: Figure 4
Gyrator circuit response graph

There are three plots in the graph, however the vdb1 and vdb4 traces, the idealized circuit and the gyrator circuit realizations respectively, have identical responses. The blue trace is the idealized opamp realizations. The opamp realization has a finite gain in this case, hence it does not attain the attenuation of the other realizations, and its equivalent inductance is shunted by some other elements.

Conclusions:

It is fairly easy to realize a Gyrator circuit, however, one should take care in modeling it. If one uses an ideal representation or Gyrator device circuit model, one should as a minimum include as a minimum an equivalent series resistance representative of the realization. At some stage one should perform an analysis using an more exact circuit. Several other Gyrator realizations are shown or linked to in the reference documents.

References: