Draw the Equivalent Circuits for Periods DT, and D'Ts - Engineering Assignment Help

Assignment Task :

Consider the DC-DC Converter shown above. MOSFET Qi conducts during D and blocks during D'. Diode D1 conducts during D' and blocks during D.

Answer the following questions. 
a) Draw the equivalent circuits for periods DT, and D'Ts.

b) Assuming ideal and lossless components, solve for the voltage transfer function, (V/V,), for CCM operation and assuming small ripple. This expression must be written in terms of the duty cycle (D and/or D').

c) Derive ripple expressions for all passive components. All expressions must be written in terms of either V1, V, D, D', T„ f,, and the passive components (L, R, C). Note that a given expression does not contain all these variables, but it may not be written in terms of variables not listed in the previous sentence. f, is the switching frequency, which is 1/T5.

d) For an input voltage V, = 12 VDC, an output voltage V = 28 VDC, a nominal output current of 2 Amps, and 1% ripple for every passive component, choose the quiescent duty cycle, D, and the required inductor and capacitor values.

e) Qi has on-resistance R,, = 0.01 S2 and Cd, = 100 pF. D1 has forward voltage V5 = 0.6 V, junction capacitance C, = 50 pF, reverse recovery charge Qr = 100 nC, and reverse recovery time tr = 100 ns. Assuming the inclusion of these loss sources do not significantly perturb the previous lossless, CCM, small ripple equations (i.e. those equations, voltages, and currents are still valid), write an equation for total power dissipation of the converter when the output current is 2 Amps.

f) What is the maximum switching frequency to achieve efficiency of 85% when the output current is 2 Amps? How many Watts are dissipated at this switching frequency when the load current is 2 Amps? You must show your work / equations used to find the answer.

g) For this application, the output current fluctuates depending on the state of the electrical system it powers. Derive an expression for the critical load resistance, Rc,t, that defines the CCM/DCM boundary. What is the value of Rcrit? 

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