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Explain state-space average models of basic boost converter?

Mumbai University > Electronics Engineering > Sem7 > Power Electronics 2

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1. Step-up boost converter basics

  • The boost converter circuit has many similarities to the buck converter. However the circuit topology for the boost converter is slightly different. The fundamental circuit for a boost converter or step up converter consists of an inductor, diode, capacitor, switch and error amplifier with switch control circuitry.

  • The circuit for the step-up boost converter operates by varying the amount of time in which inductor receives energy from the source.

  • In the basic block diagram the operation of the boost converter 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 boost converter 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. Boost converter operation

  • When the switch is in the ON position, the inductor output is connected to ground and the voltage Vin is placed across it. The inductor current increases at a rate equal to Vin/L.

  • When the switch is placed in the OFF position, the voltage across the inductor changes and is equal to Vout - Vin. Current that was flowing in the inductor decays at a rate equal to (Vout-Vin)/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 Boost Converter

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$u_1=L\dot{x_1} \ \ \ \ \ \ u_2=C\dot{x_2}+\frac{x_2}{R}$

$ =\begin{bmatrix} \ \dot{x_1}\\ \ \dot{x_2} \\ \end{bmatrix} \begin{bmatrix} \ 0 & -\frac{1}{L} \\ \ \frac{1}C & -\frac{1}{RC} \end{bmatrix} \begin{bmatrix} \ x_1\\ \ x_2 \\ \end{bmatrix} + \begin{bmatrix} \ \frac{1}L & 0 \\ \ 0 & \frac{1}{C} \end{bmatrix} \begin{bmatrix} \ u_1 \\ \ u_2 \\ \end{bmatrix} $

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