EE 603 Power Electronics

Homework # 3 Due February 1, 2006

In Mohn/Underland/Robbins browse chapters 1 and 2. Read chapter 7.

Problem 1

The above a DC/DC converter is used to produce the 3V required by a microprocessor from standard 5V logic power. The diode used in the circuit is a Schottky diode with a 0.5V forward drop. The MOSFET’s on resistance with a 15V gate to source voltage is 0.045W. You may assume the capacitor and inductor are loss-less. The load is 20W with an output voltage of 3V.

a) Assuming the inductor current is never zero, plot Vs(t) over two cycles accounting for the diode and MOSFET voltage drops. Be sure to label your axis.

b) What is the average value and the rms value of Vs(t)?

c) What must the duty cycle of the MOSFET be?

d) What is the dc component of the current in the inductor at the conditions specified above?

e) Derive a simple relationship for the peak-to-peak ripple current in the inductor in terms of the duty cycle assuming the output voltage is constant and use this expression to determine L so that the peak to peak ripple current at the worst case duty cycle is 10% of the dc current. What is the peak-to-peak ripple current at the duty cycle in c).

f) Compute the approximate rms and peak-to-peak value of the first harmonic of the ripple part of Vs(t).

g) Estimate C so that the rms value of the output ripple voltage is less than 1% of 3V. What is the peak-to-peak output ripple voltage?

h) Compute and plot the magnitude of the output voltage transfer function of the filter from Fmin = 1000Hz to Fmax = 10MHz. Using MATHCAD of MATLAB to simplify your work.

i) What is the highest frequency that can pass unattenuated through your filter design?

j) Use the first harmonic of Vs(t) and the output voltage transfer function to compute the peak-to-peak output ripple voltage for a duty cycle of 0.5.

k) Use the first harmonic of Vs(t) and the current transfer function to compute the peak-to-peak ripple current in L for a duty cycle of 0.5.

Problem 2

A basic chopper circuit has an input voltage equal to 160V, an output voltage equal to 70V, a 100W resistive load, and operates at 100 kHz. Let L = 2.8mH, and C equal 0.1026mF. Using MATHCAD of MATLAB or any program of your choosing do the following

a) Analytically compute the Fourier coefficients for the Fourier series of Vs(t).

b) Using your analytical Fourier series for Vs(t), plot Vs(t) using the first 20 harmonics (o to 19) and the first two harmonics (0 to 1) for the conditions above. Plot the voltage every 0.1ms.

c) Compute the Fourier series for the inductor current. Plot the inductor current using the first 20 harmonics and the first two harmonics for the conditions above.

d) Compute the Fourier series for the output voltage. Plot the output voltage using the first 20 harmonics and the first two harmonics for the conditions above.