chap02

# chap02 - 2 Principles of Steady-State Converter Analysis...

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2 Principles of Steady-State Converter Analysis 2.1 INTRODUCTION In the previous chapter, the buck converter was introduced as a means of reducing the dc voltage, using only nondissipative switches, inductors, and capacitors. The switch produces a rectangular waveform as illustrated in Fig. 2.1. The voltage is equal to the dc input voltage when the switch is in position 1, and is equal to zero when the switch is in position 2. In practice, the switch is realized using

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14 Principles of Steady-S ta te Converter Analysis power semiconductor devices, such as transistors and diodes, which are controlled to turn on and off as required to perform the function of the ideal switch. The switching frequency equal to the inverse of the switching period generally lies in the range of 1 kHz to 1 MHz, depending on the switching speed of the semiconductor devices. The duty ratio D is the fraction of time that the switch spends in position 1, and is a number between zero and one. The complement of the duty ratio, is defined as (1 – D ). The switch reduces the dc component of the voltage: the switch output voltage has a dc component that is less than the converter dc input voltage From Fourier analysis, we know that the dc component of is given by its average value or As illustrated in Fig. 2.2, the integral is given by the area under the curve, or The average value is therefore So the average value, or dc component, of is equal to the duty cycle times the dc input voltage The switch reduces the dc voltage by a factor of D. What remains is to insert a low-pass filter as shown in Fig. 2.3. The filter is designed to pass the dc component of but to reject the components of at the switching frequency and its harmonics. The output voltage v ( t ) is then essentially equal to the dc component of The converter of Fig. 2.3 has been realized using lossless elements. To the extent that they are ideal, the inductor, capacitor, and switch do not dissipate power. For example, when the switch is closed, its volt- age drop is zero, and the current is zero when the switch is open. In either case, the power dissipated by the switch is zero. Hence, efficiencies approaching 100% can be obtained. So to the extent that the com- ponents are ideal, we can realize our objective of changing dc voltage levels using a lossless network.
2.2 Inductor Volt-Second Balance, Capacitor Charge Balance, and the Small-Ripple Approximation 15 The network of Fig. 2.3 also allows control of the output. Figure 2.4 is the control characteristic of the converter. The output voltage, given by Eq. (2.3), is plotted vs. duty cycle. The buck converter has a linear control characteristic. Also, the output voltage is less than or equal to the input voltage, since Feedback systems are often constructed that adjust the duty cycle D to regulate the converter output voltage. Inverters or power amplifiers can also be built, in which the duty cycle varies slowly with time and the output voltage follows.

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## This note was uploaded on 01/17/2010 for the course EL 5673 taught by Professor Dariuszczarkowski during the Spring '09 term at NYU Poly.

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chap02 - 2 Principles of Steady-State Converter Analysis...

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