Gyrator

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The gyrator is an electric circuit which inverts an impedance. In other words, it can make a capacitive circuit behave inductively, a bandpass filter behave like a band-stop filter, and so on. The concept was invented around 1948 by B.D.H. Tellegen of Philips Research Laboratories, Eindhoven ("The gyrator, a new electric network element", Philips Res. Rep. 3 (1948) pgs 81-101). It is primarily used in active filter design.

1 Simulated inductor
2 Operation of the circuit
3 Applications
4 External links

[edit] Simulated inductor

Gyrator simulating Inductance. The two Z_in have the same value

The primary use of a gyrator is to simulate an inductive element in a small electronic circuit or integrated circuit. Before the invention of the transistor, coils of wire with large inductance might be used in electronic filters. A real inductor can be replaced by a much smaller assembly containing a capacitor, operational amplifiers or transistors, and resistors. This is especially useful in integrated circuit technology. Real capacitors are often much closer to "ideal capacitors" than real inductors are to "ideal inductors". Because of this, a synthetic inductor realized with a gyrator and a capacitor may, for certain applications, be closer to an "ideal inductor" than any real inductor can be. Thus, use of capacitors and gyrators may improve the quality of filter networks that would otherwise be built using inductors. Also, the Q factor of a synthesized inductor can be selected with ease.

[edit] Operation of the circuit

The circuit works by inverting the effect of the capacitor. The desired effect is an impedance of the form

$Z = R_\mathrm{L} + j \omega L \,\!$

This is an ideal inductor L with a series resistance R_L. From the diagram, it can be seen that the impedance of the simulated inductor is the desired impedance in parallel with the impedance of C and R.

$Z_\mathrm{in} = \left( R_\mathrm{L} + j \omega R_\mathrm{L} R C \right) \| \left( R + {1 \over {j \omega C}} \right)$

If R is much greater than R_L, this comes close to

$Z_\mathrm{in} = R_\mathrm{L} + j \omega R_\mathrm{L} R C \,\!$

This is the same as a resistance R_L in series with an inductance L = R_LRC. It differs in function from a true inductor due to the parallel RC term, and because R_L is large compared to a real inductor. A real inductor has low internal resistance caused only by the wire it is made of. This limits the Q factor, or accuracy, of filters that can be made with the simulated inductor.

[edit] Applications

The primary application for a gyrator is to reduce the size and cost of a system by removing the need for bulky, heavy and expensive inductors.

Gyrator circuits are extensively used in telephony devices that connect to a POTS system. This has allowed telephones to be much smaller, as the gyrator circuit carries the DC part of the line loop current, allowing the transformer carrying the AC voice signal to be much smaller, due to the massively reduced current. Circuitry in telephone exchanges has also been affected with gyrators being used in line cards.

There are many applications where it is not possible to use a gyrator to replace an inductor: