This document discusses inductors, including how their inductance is determined by construction parameters like number of turns and core material. It describes how inductors are constructed by winding wire into coils and how the inductance increases with more turns. The limitations of inductors for integrated circuit design are discussed. Finally, it provides examples of calculating inductor voltage from current and energy stored in an inductor from power delivered.

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Session 16C: Focus
 Inductors
◦ L in terms of Construction parameters
◦ Windings
◦ Limitations of Inductor
◦ Energy Stored in an Inductor
 Problems

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Construction of Inductors

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Construction of an Inductor
 Physical inductor is constructed by winding a length
of wire into a coil.
 This serves effectively to increase the current that is
causing the magnetic field
◦ And also to increase the “number” of neighbouring
circuits into which Faraday’s voltage may be induced
 The result of this twofold effect is that the
inductance of a coil is approximately proportional
to the square of the number (N2 term) of complete
turns made by the conductor out of which it is
formed

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L in terms of Construction Parameters
What is the direction of flux here?
 L is in henries
 μ = μο μr is the effective permeability of the core
 μr is the relative permeability of the core
 μο is the Permeability of Free Space (4.π.10-7)
 N is the Number of turns
 A is the Inner Core Area (π.r2) in m2
 l is the length of the Coil in metres

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Windings
 The wire or conductor which constitutes the coil is
called the winding.[
 Windings in which the turns touch, the wire must be
insulated with a coating of enamel (thin layer of
coating, which is an insulator) to prevent the current
from passing between the wire turns

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Inductance of an Inductor
Factors affecting Inductance:
a) The number of turns of wire in the inductor.
b) The material of the core.
c) The shape and size of the core.
d) The shape, size and arrangement of the wire making up the
coils.
 Because inductance depends on so many variable quantities
◦ It is quite difficult to calculate it accurately
 External effects caused by other components can also affect
its value of inductance once it is assembled in a circuit

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Limitations of Inductors
 Practical inductors typically range from a few micro-
henrys to tens of henrys.
 From a circuit design standpoint it is important to note
that inductors cannot be easily fabricated on an
Integrated Circuit (IC) chip
 And therefore chip designs typically employ only the
following elements that can be easily fabricated in
microcircuit form
◦ Electronic devices (Diodes, transistors)
◦ Resistors, and
◦ Capacitors
◦ Though, at times, rarely inductors are made inside ICs

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Problem 1
 Given the waveform of the current in a 3 H inductor, determine the
inductor voltage and sketch it.

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Problem 2
 The current in a 10-mH inductor has the waveform shown below,
determine the voltage waveform.

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Energy Stored in L
Power delivered to the inductor can be used
to find the energy stored in it:
Energy stored in the magnetic field is:
Assuming the
Initial current
stored in L to be zero,
similar to capacitor:

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Problem 3
 Find the total energy stored in the circuit:
This circuit has only DC sources. Based on our earlier discussions about
capacitors and inductors and constant sources, we can replace
the capacitors with open circuits and the inductors with short circuits

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Problem 3 … contd.
Apply KCL at node A:
Apply KVL outside loop:
Total Energy stored:

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Session 16C: Summary
 Inductors
◦ L in terms of Construction parameters
◦ Windings
◦ Limitations of Inductor
◦ Energy Stored in an Inductor
 Problems

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References
Ref 1 Ref 2