Like its fellow passive electrical components, the resistor and the capacitor, the inductor is not as simple as it seems at first.
I thought it only fitting, since having previously written about capacitors and resistors, to give equal time the third component of the passive triumvirate: inductors, a.k.a. coils.
Put a capacitor and an inductor together in a circuit with a power source, away from the watchful eye of a resistor, and look out. They could wind up in a tug of war together, pitted in an eternal struggle. Both components vie to sap the energy from the other, perhaps successfully for a few fleeting moments, prior to relinquishing it back to the other. Punch, counter punch, and voila, an oscillator.
In principle, an inductor is just a coil of wire. It is usually wrapped around a metal core made of iron or some other ferrite material that acts to increase the inductance.
An inductor stores electrical energy in its electromagnetic fields. Inductor values are expressed in units of Henrys. Most of the typical inductors found on printed circuit boards have small inductance values, expressed in micro-Henrys (μH = 10-6) or milli-Henrys (mH = 10-9).
Like capacitors, inductors serve numerous beneficial purposes, including energy storage, filtering, and yes, even oscillator circuits.
For oscillator applications, a capacitor is paired with an inductor to create a resonant circuit. In a resonant circuit, as mentioned, energy transfers alternately between the voltage in a capacitor and the current in an inductor. The resonant frequency depends on the inductor and capacitor values.
Unlike resistors, which maintain a simple linear relationship between their voltage and current, the inductor maintains a more sophisticated, elitist, differential, relationship. Equation 1 expresses the relationship mathematically.
Equation 1: The differential relationship between inductor voltage and current
The voltage across an inductor is a function of the rate of change in the inductor's current. Based on this relationship, sinusoidal currents produce sinusoidal voltages, exponential currents produce exponential voltages, and linear currents produce fixed voltages. A constant current flowing through an inductor does not produce any voltage, regardless of the constant current's value.
A nifty and sometimes practical application is to apply a square wave voltage across an inductor (left) to create a sawtooth current waveform (right).
In this special case, we can replace the differential expression with Equation 2.
Equation 2: Special case of piecewise linear current
This basic technique is used in some LED drivers to create a constant current source. The resulting LED current is then a triangle wave "ripple" riding on a DC component of current.
The frequency response of an inductor is opposite that of a capacitor. For a DC circuit operating in steady state, the inductor acts as a short circuit. For very high frequencies, the inductor acts as an open circuit. This frequency dependent property makes the inductor useful for filtering applications.
The energy storage capability of a inductor is given by Equation 3.
Equation 3: Energy storage on an inductor
As this expression indicates, the amount of energy an inductor can store is proportional to its inductance and the square of its current, at least in the ideal case.
As with everything in life, there is no perfect inductor. Real inductors have parasitic resistance and parasitic capacitance. Core materials can saturate, effectively reducing the inductance at high currents. These effects limit the current and frequency performance of the inductor.
Just like with the resistor and capacitor, as simple as the inductor appears to be, there are still many important factors to investigate and consider when designing a circuit.
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