DC to DC Conversion: Boost Converter Design Bryan R. Reemmer Team 5 March 30, 2007 Executive Summary This application note will outline how to implement a boost, or step-up, converter. It will explain the electro-mechanical workings of the circuit, as well as common sources for error. As there are many chips available to perform this type of DC-DC conversion, a specific example of a chip-based solution is provided. Keywords: Boost converter, step-up converter, DC-DC converter, MAX5026
Table of Contents Introduction 3 Objective 3 Design 3 Analysis. 4 IC Implementation... 5 Results 5 Conclusions 6 References.. 7 2
Introduction DC to DC converters are extremely important in battery-powered electronic devices, such as MP3 players and laptop computers. Those electronic devices often contain several subcircuits, each requiring a voltage level different than that supplied by the battery. Even worse, the voltage of a battery declines as its stored power is drained, so it does not output a constant voltage level. DC to DC converters offer a method of generating multiple controlled voltages from a single battery voltage, thereby saving space instead of using multiple batteries to supply different parts of the device. A boost converter is simply is a particular type of power converter with an output DC voltage greater than the input DC voltage. This type of circuit is used to step-up a source voltage to a higher, regulated voltage, allowing one power supply to provide different driving voltages. Objective The purpose of this document is for the reader to become familiar with the function and implementation of a boost converter. A basic design will be discussed along with a specific application of an integrated circuit (IC) solution. Design A boost converter is part of a subset of DC-DC converters called switch-mode converters. The circuits belonging to this class, including buck, flyback, buck-boost, and push-pull converters are very similar. They generally perform the conversion by applying a DC voltage across an inductor or transformer for a period of time (usually in the 100 khz to 5 MHz range) which causes current to flow through it and store energy magnetically, then switching this voltage off and causing the stored energy to be transferred to the voltage output in a controlled manner. The output voltage is regulated by adjusting the ratio of on/off time. As this subset does not use resistive components to dissipate extra power, the efficiencies are seen in the 80-95% range. This is clearly desirable, as it increases the running time of battery-operated devices. The basic boost converter circuit consists of only a switch (typically a transistor), a diode, an inductor, and a capacitor. The specific connections are shown in Figure 1. Figure 1: Standard layout of a Boost Converter. 3
Analysis Examining the circuit for two cases (switch open and switch closed) is fairly straightforward, assuming ideal components, and provided that there is constant current flow through the inductor. This case is referred to as continuous mode operation. Figure 2: Current flow through the converter, depending on the state of the switch Applying Kirchhoff s rules around the loops and rearranging terms yields an intuitive result: V V O IN 1 = 1! D That is to say, the gain from the boost converter is directly proportional to the duty cycle (D), or the time the switch is on each cycle. Figure 3 graphically demonstrates this. Figure 3: Inductor current and duty cycle vs. time In some cases, the amount of energy required by the load is small enough to be transferred in a time smaller than the cycle length. In this case, the current through the inductor falls to zero during part of the period. This is called discontinuous operation. 4
The only difference, then, is that the inductor is completely discharged at the end of the cycle. Although slight, the difference has a strong effect on the output voltage equation. Compared to the expression of the output voltage for the continuous mode, this expression is much more complicated. Furthermore, in discontinuous operation, the output voltage not only depends on the duty cycle, but also on the inductor value, the input voltage, and the output current. IC Implementation In order to implement the switching necessary for the converter to work, it is desirable to find an IC solution. The 5026 chip, from MAXIM, is one such solution. The typical circuit from the MAX5026 data sheet is shown in Figure 4. In this circuit, the output voltage, VOUT, is determined by the ratio of fixed resistors R1 and R2. These two resistors form a voltage divider that feeds a fraction of the output voltage back to the feedback (FB) pin, creating a closed-loop system. The system is at equilibrium when VOUT is generating the desired output voltage and the R1 and R2 voltage divider feeds back 1.25V to the FB pin. When VOUT is lower than the desired output voltage (the voltage fed back to FB is below 1.25V), the DC-DC converter IC attempts to deliver additional power until FB reaches 1.25V. & VOUT # R 1 = R2 $ ' 1! Equation 1 % VREF " & R1 # VOUT = VREF $ + 1! Equation 2 % R2 " Equation 1 is directly from the MAX5026 data sheet. Solving Equation 1 for VOUT yields Equation 2 where VREF, the FB Set Point, is 1.25V for the MAX5026. Figure 4: MAX5026 implementation of a boost converter. Results The output voltage obtained during this study was not a full 30V. The actual output was approximately 28V. The discrepancy is most likely due to losses in the board, as well as to non-ideal devices (most notably the inductor). 5
In the analysis above, all components were assumed ideal. It was assumed that the power is transmitted without losses from the input voltage source to the load. However, parasitic resistances exist in all circuits, due to the resistivity of the materials they are made from. Therefore, a fraction of the power managed by the converter is dissipated by these parasitic resistances. This is why the efficiencies are not at a perfect 100%. For the sake of simplicity, the inductor is assumed the only non-ideal component, and that it is equivalent to an inductor and a resistor in series. This is reasonable because an inductor is made of one long wound piece of wire, so it is likely to exhibit a non-negligible parasitic resistance. Furthermore, current flows through the inductor both in the on and the off states, so any non-ideal effects will be more pronounced. Reworking the earlier equations with the added inductor resistance (R L ) changes the gain equation to the following: V V O IN = R R L 1 ( 1! D) + 1! D Even without the full derivation, the equation makes intuitive sense. If the inductor resistance is zero (an ideal inductor), the equation above becomes equal to the ideal case; however, as R L increases, the voltage gain of the converter decreases compared to the ideal case. Also, the effect of R L increases with the duty cycle, D. Figure 5 displays these effects graphically. As the inductor becomes less ideal, the possible gain drops off sharply from the theoretical value, especially as the duty cycle grows above 50%. Figure 5: Non-ideal inductors can rapidly degrade boost converter performance. Conclusions 6
DC-DC converters are an excellent way to get the most use out of a single power supply. Though the total power must remain constant, one can efficiently trade off between current strength and voltage levels to power a variety of sub-circuits without costly extra batteries. 7
References MAX5026 Datasheet: <http://www.ortodoxism.ro/datasheets/maxim/max5025-max5028.pdf> DC-DC Converter Basics: <http://www.powerdesigners.com/infoweb/design_center/articles/dc- DC/converter.shtm> Simple Converter: <http://www.elexp.com/t_dc-dc.htm> +30V DC-DC Converter: <http://www.interq.or.jp/japan/se-inoue/e_ckt28.htm> DC-DC Converters: A Primer: <http://www.jaycar.com.au/images_uploaded/dcdcconv.pdf> Breakthrough efficiency levels: <http://www.futurlec.com/news/national/dc_converter.shtml> 8