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Explain state-space average models of basic buck converter ?

Mumbai University > Electronics Engineering > Sem7 > Power Electronics 2

Marks: 10M

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1. Basic buck converter or regulator

  • The fundamental circuit for a step down converter or buck converter consists of an inductor, diode, capacitor, switch and error amplifier with switch control circuitry.

  • The circuit for the buck regulator operates by varying the amount of time in which inductor receives energy from the source.

  • In the basic block diagram the operation of the buck converter or buck regulator can be seen that the output voltage appearing across the load is sensed by the sense / error amplifier and an error voltage is generated that controls the switch.

  • Typically the switch is controlled by a pulse width modulator, the switch remaining on of longer as more current is drawn by the load and the voltage tends to drop and often there is a fixed frequency oscillator to drive the switching.

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2. Buck converter operation

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  • When the switch in the buck regulator is on, the voltage that appears across the inductor is Vin - Vout. Using the inductor equations, the c urrent in the inductor will rise at a rate of (Vin-Vout)/L. At this time the diode D is reverse biased and does not conduct.

    • When the switch opens, current must still flow as the inductor works to keep the same current flowing. As a result current still flows through the inductor and into the load. The diode, D then forms the return path with a current Idiode equal to Iout flowing through it.

    • With the switch open, the polarity of the voltage across the inductor has reversed and therefore the current through the inductor decreases with a slope equal to -Vout/L.

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3. Current waveforms at different times during the overall cycle

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  1. State-Space Averaged Model for an Ideal Buck Converter

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u1=L˙x1+x2   x1=C˙x2+x2R

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[ ˙x1 ˙x2]=[ 01L 1C 1RC][ x1 x2][ 1L  0][u1]

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0=L˙x1+x2   x1=C˙x2+x2R

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