EE 603      Final Exam        Date 12-13-01    Time 1:00 – 3:00 PM

 

Put only one problem on a piece of paper, it may continue onto other sheets. Write on only one side of a piece of paper. Put your name on each page you hand in. Show your work for partial credit.

 

Problem 1                 35 points

 

a)       Draw the general collector characteristic curves of a MOSFET rated at 600V, for positive ID and positive VDS. The threshold voltage of the MOSFET is 5V and the transconductance parameter Kp = 4 A / V2. Include curves for VGS = 4V, VGS = 10V, and VGS = 15V. Numerically label your axis. Draw and label the circuit symbol for the MOSFET indicating the positive polarity of drain current, drain to source voltage, gate to source voltage, and the gate current. Label the gate drain and source.                                                                                                                                               5 points

b)       Draw and label the circuit symbol for the IGBT indicating the positive polarity of the collector current, collector to emitter voltage, gate to emitter voltage, and the gate current. Label the gate, collector, and emitter                                                                                                              5 points

c)       The MOSFET in part a) is used in a dc/dc step up converter like the one in Fig. 1 with a 20A inductor current, Vin =100V and Vout = 200V. What is the current in the MOSFET when the gate voltage is 15V and when the gate voltage is 1V?                                                                 5 points

 

Fig. 1

 

d)       Assuming the inductor ripple current and the output ripple voltage can be ignored (continuous conduction mode with L large) draw the turn on and turn off MOSFET switching transient waveforms when the gate voltage goes from zero to 15V. Include VGG, VGS, VDS, ID, Idf, Vdf. Be sure to show the relative timing between the waveforms and the diode reverse recovery transient. Numerical values for the diode reverse recovery transient are not required.                                             5 points

e)       Indicate the turn on and turn of delay times on your waveforms in part d). No numerical values of time are required but the numerical value of the gate voltage at the end of the delay time is required.                                                                                                                                     5 points

f)         Indicate the Miller time at both turn on and turn off. What is VGS during the Miller time?                                                                                                                                            5 points

g)       Indicate the current rise and fall times on your waveforms in part d). No numerical values of time are required but a numerical value of the gate voltage at the beginning and end of the rise and fall times is required.                                                                                                         5 points

 

 

Problem 2                 30 points

 

Fig. 2

 

The design requirements for the continuous conduction mode step up converter in Fig. 2 are

 

Input voltage

160V

Output voltage

250V

Switching frequency

100kHz

Rated (maximum) output power

500W

Peak-to-peak output ripple voltage

< 5% of Vout

Peak-to-peak input ripple current

<5% of Iin

Heatsink surface temperature

85C

 

a)       What is the steady state value of the duty cycle?                                                       5 points

b)       Draw the open loop average model for a constant duty cycle.                                       5 points

c)       What are the average input current and the average output current?                              5 points

d)       What is the minimum value of L?                                                                               5 points

e)       What is the minimum value of C?                                                                              5 points

f)         Draw the linearized average model and specify the numerical values of all of the circuit parameters.                                                                                                                                      5 points

 

 

Problem 3     35 points

 

Fig. 3

 

Assume the duty cycle of Q1 and Q4 are equal and equal to D. Further assume Q2 and Q3 are on whenever Q1 and Q2 are off so this circuit is guaranteed to always be in the continuous conduction mode. Let the switching frequency Fsw = 100kHz and Vin = 200V.

 

a)       What are the maximum and minimum values of Vo?                                                   5 points

b)       What is the filter break frequency (Fb) compared to the switching frequency (Fsw)?       5 points

c)       Draw the circuit schematic of the average model for computing the output voltage.         3 points

d)       Draw the low frequency (F < Fb steady state) schematic of the average model. 2 points

 

Assume the duty cycle D varies as  where Fac = 8.333kHz.

 

e)       What is the average VL, VR, as a function of duty cycle and the output voltage as a function of time (an equation) assuming Fac < Fb?                                                                           5 points

f)         How many switching cycles are there per ac cycle?                                                    5 points

g)       Plot the average VL as a function of time for one cycle.                                               5 points

h)       Plot the instantaneous duty cycle and the instantaneous VL as a function of time for one cycle.                                                                                                                               5 points

 

 

For the fun of it (no credit) if you have time, plot the instantaneous Vo as a function of time for one cycle.