A current-programmed boost converter is employed in a low-harmonic rectifier system, in which the input voltage is a rectified sinusoid: vg(t) = VM| sin(?t)|. The dc output voltage is v(t) = V VM. The capacitance C is large, such that the output voltage contains negligible ac variations. It is desired to control the converter such that the input current ig(t) is proportional to vg(t) : ig(t) = vg(t)/Re, where Re is a constant, called the emulated resistance. The averaged boost converter model of Fig. 18.9a suggests that this can be accomplished by simply letting ic(t) be proportional

A current-programmed boost converter is employed in a low-harmonic rectifier system, in which the input voltage is a rectified sinusoid: vg(t) = VM| sin(?t)|. The dc output voltage is v(t) = V VM. The capacitance C is large, such that the output voltage contains negligible ac variations. It is desired to control the converter such that the input current ig(t) is proportional to vg(t) : ig(t) = vg(t)/Re, where Re is a constant, called the emulated resistance. The averaged boost converter model of Fig. 18.9a suggests that this can be accomplished by simply letting ic(t) be proportional to vg(t), according to ic(t) = vg(t)/Re. You may make the simplifying assumption that the converter always operates in the continuous conduction mode. (a) Solve the model of Fig. 18.9a, subject to the assumptions listed above, to determine the power _p(t)_Ts . Find the average value of _p(t)_Ts , averaged over one cycle of the ac input vg(t). (b) An artificial ramp is necessary to stabilize the current-programmed controller at some operating points. What is the minimum value of ma that ensures stability at all operating points along the input rectified sinusoid? Express your result as a function of V and L. Show your work. (c) The artificial ramp and inductor current ripple cause the average input current to differ from ic(t). Derive an algebraic expression for _ig(t)_Ts , as a function of ic(t) and other quantities such as ma, vg(t), V, L, and Ts. For this part, you may assume that the inductor dynamics are negligible. Show your work. (d) Substitute vg(t) = VM| sin(?t)| and ic(t) = vg(t)/Re, into your result of part (c), to determine an expression for ig(t). How does ig(t) differ from a rectified sinusoid?

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