Gyrator circuits simulate the function of an inductor. A typical inductor has an inductance of millihenries, and inductors with large inductances are not feasible for real application. Inductors are basically just wire wrapped into loops. The inductance value is given by the number of loops, times the flux emanating from the inductor, divided by the current passing through. Given this relation, it's not hard to see why large inductor values are hard to produce. A typical gyrator circuit can easily function as an inductor with an inductance of one henry or more.

Standard gyrator circuits are composed of some kind of transistors or operational amplifiers, along with resistors and capacitors. No matter how they are composed, their function is the same. More complex gyrator circuits can produce abnormally high inductance values, but simple ones are relatively easy to design and produce.

Of course, a gyrator does not have all of the properties a proper inductor coil would have. The important thing about gyrators is the fact that their impedance is the same as an inductor's. The impedance for an inductor is equal to LS. L is the inductance. S is equal to omega, the frequency, times j, the square root of negative one. j is used instead of i in electrical engineering because i is used to represent current. The overall impedance relation of a gyrator circuit is equal to some function of the resistances and capacitances present inside, times S. This is important, because other basic elements have quite different relations. If an (xS) relation is necessary in a circuit, and x must be large, gyrators are the way to go.

Since capacitors and resistors are so much cheaper to use than inductors, circuit designers try not to use inductors whenever possible. The impedance relation for a resistor is just its resistance, R, while the impedance relation for a capacitor is 1/(SC), where C is the capacitance. So inductors become necessary when impedance must increase with frequency. Shrewd use of capacitors, resistors, and other elements to make gyrators allow for high inductances and easier circuit design.

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