Electronic Devices and Circuit - Inductors, Study notes of Analysis and Design of Digital Integrated Circuits

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 We have examined the resistor

and the capacitor in detail.

 In this chapter we shall consider

a third element, the inductor,

which has a number of response

characteristics similar in many

respects to those of the

capacitor.

 (^) The induced voltage is depends upon:

◦ Number of flux lines cut per unit of time ◦ Speed of the conductor ◦ Strength of magnetic field  (^) The greater the number of flux lines cut per

unit time (by increasing the speed with which the conductor passes through the field), or the stronger the magnetic field strength (for the same traversing speed), the greater will be the induced voltage across the conductor.

 (^) If the conductor is held fixed and the

magnetic field is moving so that its flux lines cut the conductor, the same effect will be produced.  (^) If a coil of N turns is placed in the region of

a changing flux, a voltage will be induced across the coil as determined by Faraday’s law:

 The ability of a coil to oppose any change

in current is a measure of the self-

inductance L of the coil. Inductance is

measured in henries (H).

 Inductors are coils of various dimensions

designed to introduce specified amounts

of inductance into a circuit.

 The inductance of a coil varies directly

with the magnetic properties of the coil.

 Where N represents the number of turns;

  is the permeability of the core;

 A is the area of the core in square meters;

 and l is the mean length of the core in

meters;

where Lo is the inductance of the coil with an

air core.

Substituting = r  0 into previous Eq. yields

 (^) Inductors are not ideal as Capacitors.

They are always associated with

◦A resistance equal to the resistance of

the turns.

◦a stray capacitance due to the

capacitance between the turns of the

coil.

 (^) For the inductor, however, R (^) l must often be

included in the analysis.  (^) The level of R (^) l can extend from a few ohms

to a few hundred ohms.

 (^) Induced voltage can also represented like

this

 (^) If the current through the coil fails to

change at a particular instant, the induced voltage across the coil will be zero.  (^) For dc applications, after the transient effect

has passed, di/dt =0, and the induced voltage is

 (^) At the instant the switch is closed, the inductance of the coil will prevent an instantaneous change in current through the coil.  (^) The potential drop across the coil, vL, will

equal the impressed voltage E as determined by Kirchhoff’s voltage law since vR=iR=(0)R=0V.  (^) The current iL will then build up from zero,

establishing a voltage drop across the resistor and a corresponding drop in vL.

 (^) The current will continue to increase until

the voltage across the inductor drops to zero volts and the full voltage appears across the resistor.  (^) Initially, the current i (^) L increases quite

rapidly, followed by a continually decreasing rate until it reaches its maximum value of E/R.