Analyze and design a boost converter - analytically

Question

Analyze and design a boost converter and its controller given the following specifications:

An input voltage of 20V < V_in < 30V and an output of V_out = 50V over a load range of 10W < P_out < 100W. Switching frequency is f_sw = 250kHz.

Hardware Design

1) Design the inductor (L) and capacitor (C). The current ripple Δi_L should be below 5% of the average inductor current IL at the maximum load under any V_in. The steady state ripple ΔV_out is below 2% of the steady-state value of the output voltage. For the designed L, find the value of I_out,crit at the boundary of DCM and CCM. Plot I_out,crit vs. V_in.

2) For designed L, suppose there are four cores available listed below, select the core size to use the space maximum, design the inductor's number of turns N and the wire (use American wire gauge table) size.

Steady-state Analysis

3) Analytically determine and draw the expected current and voltage waveforms for each component in your circuit at both light and heavy load.

4) Using PSpice/Matlab software, simulate the circuit under the heavy and light load conditions (provide schematic of the whole system). Plot the voltage and current of each component within 3 to 5 switching periods in the steady-state. Validate that the output of your simulation matches your analytical calculations in (2).

Modeling and Controller Design

5) Based on your designed circuit, considering the parasite resistance of the inductor r is 0.2Ω, using the average state-space method and small-signal technique to the transfer function v^~o(s)/d^~(s). Draw the open-loop bode plot of the frequency response (with matlab/pspice, not hand drawing).

6) Design a proportional-integral (PI) controller (recommend to use matlab siso toolbox) so that phase margin of the loop transfer function should be over 35^o, and the crossover frequency is no larger than 10kHz. Provide the close loop bode plot (with matlab/pspice).

System Simulation

7) Using PSpice/Matlab software, simulate the designed circuit with controller, 1) V_in = 25 + 5*sin(2Π*60*t), simulate output voltage vo which should be a constant value, plot both V_in and v_o in a same figure with time range more than 16.7ms; 2) measure the dynamic of the output voltage together with the disturbance of input or load through designing disturbances in load and input voltage. a) input voltage disturbances: V_in step change from 20V to 30 V; 2) load change from 10W to 100W. [Plot the disturbance, i.e., V_in, Load, and the output voltage of the converter in a same figure]

Write a report that documents that describes your results and observations from parts (1)-(7). Make sure all plots are well labeled and that explanations contain solid analytical foundations.

Make sure the figures are organized, neat and easy to be read and they are drawn by the software not by hand. Do NOT plot one graph per page.