Question

QUESTION 3 In the DC-DC buck-boost converter shown in next page assume that all the components are ideal and the converter is operating in continuous conduction mode and is in steady-state (a) Derive the conversion ratio of WI - Draw the circuit diagram when the switch is in on and off states. Use small ripple approximation for your analysis Sketch the current through and the voltage across the inductor when the switch is in on and off states. Include all the relevant X and Y axis details. (8 marks) (b) Find the average output current boundary condition (IoB) (5 marks) Page 3 of 5 End of Semester 2, 2016 ETEN3003 Power Electronics Vo Circuit diagram

Answer 1

Circuit diagram Let D be the duty cycle of switch s rightarrow D = T_on/T [T_on rightarrow on time of switch T rightarrow total time period] so T_on = DT & T_off = T - DT = (1 - D)T a) when the switch is closed D becomes reverse biased. & the circuit becomes Applying KVL in loop (1) v_L = v_s when the switch is on current in inductor rises as shown in waveform Note: for continuous conduction I_min > 0 Because we known that current through inductor i_L = 1/L integral v_L dt or v_L = L di_L/dt so during on time change in current through inductor v_s = L times (Delta i_L)_ON/DT Delta i_ON = I_max = I_min rightarrow (Delta i_L)_ON = v_s DT/L when the switch is opened as the current through inductor forward biases the diode D to allow to cuurent to be flown through the inductor