EE 603 Power Electronics

Homework # 7 Due March 22, 2006 (hand in March 24, 2006)

Read the 555 timer chip specification at www.engr.uky.edu/~radun.

Problem 1

A schematic of the basic step down converter is shown in Fig. 1.

Fig. 1 Basic step down converter.

Vin is 35V and the desired Vout is 24V. The load is 3A. The MOSFET switching frequency is 25kHz.

a) What is the required duty cycle and what is the value of the load resistance?

b) Choose L so that the peak-to-peak ripple current in the inductor is 10% of the load current. Use the worst case D for your calculation. What is the peak-to-peak ripple current at the duty cycle in part b)?

c) Using your worst case estimated ripple current in L, and modeling the L as a current source, compute C so its worst case peak to peak ripple voltage is 1% of its DC value.

d) Ideally, will the capacitor ripple voltage change as the load changes?

e) Draw the complete average model of the circuit labeling all quantities.

f) Let where Do is the duty cycle you calculated in part a). What is the approximate maximum frequency (F_sys) of the duty cycle?

g) Make a Spice model of your average model. Compute the start up transient when the circuit starts from a zero inductor current and a zero output voltage for the constant duty cycle in part b). Plot the average input current and the average output voltage for this transient. Give your t_stop and your t_ceiling.

h) Starting your circuit from the steady steady state of part g), use your average Spice model to plot the average input current and the average output voltage for the duty cycle in f) and for a frequency of 1kHz. Give your t_stop and your t_ceiling.

i) Sketch the actual input current and the average input current for two switching cycles.

Problem 2

a) For the load current in problem 1, what is the minimum MOSFET Kp that you can use in a Spice simulation of the circuit in Fig. 1 in problem 1? Estimate a reasonable MOSFET Kp to use in a Spice simulation.

b) What would a reasonable MOSFET on resistance be for the circuit and conditions in problem 1?

Fig. 2 Basic step down converter.

Vin is 35V and the desired Vout is 24V. The load is 3A. The MOSFET switching frequency is 25kHz. The L is 2mH, the C is 20mF, the MOSFET’s Kp is 1 A/V², the MOSFET’s threshold voltage is 2V, and the MOSFET’s on resistance is 0.15W. All other MOSFET and diode parameters are their default values. Use the MAX944CSD comparator from the B2 Spice categories/comparator menu for your comparator.

c) What is the value of the MOSFET’s drain resistance (the source resistance is zero) for the MOSFET in Fig. 2.

d) Make an average Spice model like the one in problem 1 and compute the step response of the circuit for the inductor current and capacitor voltage starting from zero with the required constant duty cycle. Plot the output voltage for this transient. Give your t_stop and your t_ceiling.

e) Make a detailed Spice model including the MOSFET, diode, comparator, etc and compute the step response of the circuit for the inductor current and capacitor voltage starting from zero with the required constant duty. Plot the output voltage for this transient. Give your t_stop and your t_ceiling.

Problem 3

A data sheet for the 555 timer integrated circuit is on the web. Use the data sheet to answer the following questions. Assume the circuit is operating from 15V_DC. That is, the ground lead is at 0V and the V_CC pin is at 15V_DC.

a) Will the circuit operate from two 1.5V batteries in series instead of the 15V?

b) A 466mA-hour 15V_DC battery is used to power the 555. Neglect external circuitry and estimate how long the battery will typically last (what is the battery's life?). Estimate the worst case battery life.

c) Estimate the smallest value a resistor connected from the output pin to ground can have?

d) Does the circuit reset on a high or a low reset voltage?

e) What do think happens if the reset pin is left open?

f) Will Q₁₄ (the discharge transistor) turn on when the output is high or low?