Gyrator

The gyrator or positive impedance inverter 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. It is primarily used in active filter design and miniaturization.

Simulated inductor

An example of a gyrator simulating inductance, with an approximate equivalent circuit below. The two Z_in have similar values in typical applications.

A gyrator is a four terminal or a two port device, 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. 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.

Additionally, 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.

Since gyrators use active components, they only function as a gyrator within the power supply range of the active element. Hence gyrators are usually not very useful for situations requiring simulation of the 'flyback' property of inductors, where a large voltage spike is caused when current is interrupted.

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 R_L:

From the diagram, the input impedance of the op-amp circuit is:

With R_LRC = 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:

This is the same as a resistance R_L in series with an inductance L = R_LRC.

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.

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. For example, RLC bandpass filter characteristics can be realized with capacitors, resistors and operational amplifiers without using inductors. Thus graphic equalizers can be achieved with capacitors, resistors and operational amplifiers without using inductors because of the invention of the gyrator.

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 elimination of DC current through it. Circuitry in telephone exchanges has also been affected with gyrators being used in line cards. Gyrators are also widely used in hi-fi for graphic equalizers, parametric equalizers, discrete bandstop and bandpass filters such as rumble filters), and FM pilot tone filters.

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

• High voltage systems utilizing flyback (beyond working voltage of transistors/amplifiers)
• RF systems (RF inductors are usually small anyhow)
• Power conversion, where a coil is used as energy storage.

See also

• Negative impedance converter (which can be used to implement a negative inductor with a capacitor)

References

External links

• Good description of this form of the simulated inductor — Elliot Sound Products
• Another description, with the same circuit
• LC filter design using equal value R gyrator, an alternative design
• An alternative circuit
• Webarchive backup: Another alternative circuit
• Discussion of the gyrator in general and a macro for Micro-Cap V
• Java simulation of this circuit
• Single transistor gyrator for telephony applications
• SPICE Analysis of gyrator for telephony applications