Switch Mode Power Supply (SMPS) Topologies (Part II) - Microchip

AN1207BUCK CONVERTERThe Buck Converter converts a high input voltage intoa lower output voltage. It is preferred over linearregulators for its higher efficiency.Topology EquationsFigure 1 shows the basic topology of a Buck Converter.The Q1 switch is operated with a fixed frequency andvariable duty cycle signal.FIGURE 2:VDCQ1BUCK CONVERTERTOPOLOGY: TON PERIODD1LOVLCOVOUTFIGURE 1:VDCQ1BUCK CONVERTERTOPOLOGYAccordingly, voltage VI is a square-wave s(t). TheFourier series of such a signal is shown in Equation 1.EQUATION 1:This means that the square-wave can be representedas a sum of a DC value and a number of sine waves atdifferent, increasing (multiple) frequencies. If this signalis processed through a low-pass filter (Equation 2), theresulting output (DC value only) is received.EQUATION 2:VID1A LoCo low-pass filter extracts from the square-waveits DC value and attenuates the fundamental andharmonics to a desired level.Q1 CLOSED (TON PERIOD)In this configuration, the circuit is redrawn as shown inFigure 2. The diode is reverse-biased so that itbecomes an open circuit.LOVLst () = A-- τ + ΣsinTCOVOUTwaves_with_frequency_multiple_of_the_square_wave_frequencywhere:τ = the duty cycleT = the periodA = the square-wave amplitudes f() t = A-- τ = constTBased on Figure 2, the voltage on the inductor is asshown in Equation 3.EQUATION 3:V L= V DC– V Qon ,– V OUTThe inductor current (having a constant time derivativevalue) is a ramp:( V DC– V Q, on– V OUT)i L() t = i L( 0)+ -------------------------------------------------------tL OAt time TON, equals:( V DC– V Qon ,– V OUT)i L( T ON) = i L( 0)+ -------------------------------------------------------T ONWhere T ON is the duration of the time interval when theswitch Q1 is closed.Q1 OPEN (TOFF PERIOD)As shown in Figure 3, when the switch Q1 opens, theinductor will try to keep the current flowing as before.FIGURE 3:VDCQ1BUCK CONVERTERTOPOLOGY: TOFF PERIODD1As a result, the voltage at the D1, LO, Q1 intersectionwill abruptly try to become very negative to support thecontinuous flow of current in the same direction (seeFigure 4).LOVLL OCOVOUTDS01207B-page 2© 2009 Microchip Technology Inc.