Understanding Energy Storage Elements[Inductors, Capacitors]

How do the Inductors & Capacitors Store the energy?
                        Inductors and Capacitors are the fundamental energy storage elements. These are the essential basic components to build any power electronics circuit. Understanding the nature of these passive components is the first step to learn about the Switching Power Supplies. In this post, also it is explained that how these elements play a vital role in SMPS circuit.

Inductance is the name given to the property of a circuit whereby there is an e.m.f. induced into the circuit by the change of flux linkages produced by a current change.

When the e.m.f. is induced in the same circuit as that in which the current is changing, the property is called self-inductance(L) . When the e.m.f. is induced in a circuit by a change of flux due to current changing in an adjacent circuit, the property is called mutual inductance(M) . The unit of inductance is the henry(H) .
A circuit has an inductance of one henry when an e.m.f. of one volt is induced in it by a current changing at the rate of one ampere per second.

Inductors store the electrical energy in the form of electro magnetic field.  An Inductor has an inductance of one henry if a change of current of one ampere/second produces one volt across the inductor.

V = L di/dt 
where V = voltage across Inductor in Volts
L = Inductance in henry
i   = Current through the inductor in Ampere

From the above equation we can conclude the following points:

  • The current through an inductor cannot change instantaneously.
  • The voltage across the inductor changes instantaneously from positive to negative when we switch from storing energy in the inductor to removing energy from the inductor. ( ie, The di/dt is changing from positive to negative)
  • The converse of the equation is
    I = 1/L∫Vdt + Iinitial
    It is used to find the inductor current when we know the voltage across the inductor. 

A capacitor is an electrical device that is used to store electrical energy. Next to the resistor, the capacitor is the most commonly encountered component in electrical circuits. For example, capacitors are used to smooth rectified AC outputs, they are used in telecommunication equipment—such as radio receivers—for tuning to the required frequency, they are used in time delay circuits, in electrical filters, in oscillator circuits, and in magnetic resonance imaging (MRI) in medical body scanners, to name but a few practical applications.

Capacitors store electrical energy in the form of electro static field. The following equation gives the definition of a Capacitor. 

Q = CV
                    where Q = Charge
                                  C = Capacitance in Farad
                                  V = Voltage across Capacitor in volts
ie, A Capacitor is one farad if storing one coulomb of charge creates one volt.

The charge is nothing but integral of current.
q = ∫i    , i = dq/dt

The following equations describe a capacitor in terms of voltage and current.
V = 1/C ∫i dt + Vinitial

I = Cdv/dt
                        The current waveform of the filter capacitor of a switching power supply is typically a sawtooth waveform. The change in voltage in the output waveform is called as ripple voltage.

The goal of the capacitor is to limit this ripple voltage. We can control the ripple voltage by controlling two variables. ie, by increasing the capacitance (C) or by decreasing dt. One of the major advantage of the Switching Power Supplies is that we can make dt very small by increasing the switching frequency. It allows the value of C also be very small.

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