Pulse Width Modulated DC-DC Converters
For the first time in power electronics, this comprehensive treatment of switch-mode DC/DC converter designs addresses many analytical closed form equations such as duty cycle prediction, output regulation, output ripple, control loop-gain, and steady sta
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Capacitor, Inductor, and Transformer
1.1 Introduction
From the viewpoint of power handling capability, electronic circuits can roughly be placed into two groups: signal processing circuits and power processing circuits. In general, the power level processed by the signal processing circuits ranges from a fraction of 1 milliwatt to several milliwatts. In contrast, the power processing circuits treat power flow exceeding several watts. Besides being distinguishable in power level, the two groups also differ in their current handling capability. Whereas signal processing circuits treat currents of no more than several milliamperes, the current level managed by power processing circuits ranges from a few amperes to hundreds of amperes. Owing to the higher current levels in power processing circuits and the fact that high current capacity is directly translated to the requirement of larger wire size and components, the physical size of the power processors tends to be large. As a result, power processing assemblies are often very bulky, difficult to manufacture, and costly in price. Therefore, to save manufacturing cost and to minimize equipment volume, it is essential to thoroughly understand the two passive elements, capacitors and inductors, which play major roles in power electronics, but also take up the most space. With the above understanding, this chapter reviews the terminal electrical properties of both devices. First, the definition of capacitance is examined along with the interaction of electric variables pertaining to a capacitor. Then the equivalent circuit of a capacitor is examined. The magnetic device is also visited by emphasizing the dynamic property of magnetic cores and the interlinking nature of magnetic parameters.
3 K. C. Wu, Pulse Width Modulated DC/DC Converters © Springer Science+Business Media Dordrecht 1997
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Chapter 1 - Capacitor, Inductor, and Transformer
1.2 Capacitance and Capacitor Traditionally, capacitance is given as the ratio between the stored charge, Q, and the sustained voltage, V. Therefore, in the most simple form
C=
fi(t) . dt Q =v(t) V
where C, Q, and V have the units of Farad, Coulomb, and Volt, respectively. However, being presented as the ratio of two time-varying quantities, the capacitance seems to be a variable. This of course cannot be further from the truth. Rather, the conventional physical equation defining the capacitance of a pair of dielectrically isolated plates tends to lend more weight behind the origin of capacitance, namely
A C=e·d
where d is the plate separation, A the plate surface area, and e the dielectric constant. This equation, in addition to freeing the definition of electrical terminal variables (voltage and current), neatly consolidates the geometrical and the material aspects of a real device. Moreover, it implies a constant and a somewhat controllable device value, which depends solely on the device geometry and the material constant. With the capacitance being established as a constant, the electric charge associated with a capacito
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