EE 603 Power Electronics

Homework # 4 Due February 13, 2006

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

Problem 1

In the last homework you designed the DC/DC converter above. It produces the 3V required for a microprocessor from the standard 5V logic power. The diode 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. The computed value of the capacitor was 6.3mF and the computed value of the inductor was 9.5mH. The circuit operates at 200kHz.

a) Using the Spice default value of kp and L = 1mm, what must the MOSFET’s W be in order to achieve a KP of 2.67A/V²?

b) What is the MOSFET channel’s on resistance with a gate voltage of 15V and a threshold voltage equal to 2.5V?

c) What must Rd be in the MOSFET model?

d) Recall that the exponential diode model is

What must Is be for v_f = 0.5V at a current i_f = 6.667A with n = 1? Recall KT/q = 25mV.

e) What is the period and pulse width for the pulse when the required duty cycle is 0.673?

f) What is the maximum value of t_ceiling that you can use for a Spice simulation of the above circuit?

g) Build a Spice model of the circuit above setting the circuit and device parameter values equal to the ones computed above. For the diode, one parameter value (Is) must be set. For all of the others use the Spice default values. Note this means there will be an x next to the parameter rather than a value. In particular the default Cj = 0 and the default TT = 0. For the MOSFET four parameter values (Vt, Rd, L, W) must be set. Use the level 1 MOSFET model with all of the others MOSFET parameters set to the Spice default values. Simulate your circuit. For your input pulse waveform gate to source, set the pulse period and pulse width equal to the values from part e) and make the pulse rise and fall times equal to 50ns. Estimate the t_ceiling with the added information of the input rise and fall times. Also estimate how long the circuit will take to reach steady state.

h) Run the simulation until the circuit reaches steady state. If your simulation does not converge you can make t_ceiling smaller and/or go to the convergence options sub-menu in the simulation menu and increase the absolute error tolerance to 1mA or 1mA. You can also set the number of Gmin steps to 500. How long does it take for the circuit to reach steady state?

i) Plot the drain current and diode current on one plot. Plot the inductor current and Vs(t) on another plot. Finally plot Vs(t) and the output voltage on another plot. Observe the inductor voltage and the capacitor current, you do not have to hand the inductor voltage and the capacitor current waveforms in.

j) What is the forward drop across the on MOSFET when it is on? What is the forward voltage drop across the diode? What is the peak-to-peak inductor ripple current? What is the peak-to-peak output ripple voltage?

k) Make the load resistor 5 times bigger and simulate your circuit again. Plot the output voltage and inductor current on the same plot.

Problem 2

In the circuit above Vin = 160V, R = 49 W, C=.1 uF, and L = 2.8 mH. At t = 0 the duty cycle takes a step change in value from 0.2 to 0.8.

a) What are the initial (D=0.2) and final values (D=0.8) of the average inductor current? Is this circuit operating in the continuous conduction mode for both loads? Equivalently is the average inductor current greater than the peak-to-peak ripple current for both loads? Assume switching frequencies of 100 kHz and 5 kHz and that the output ripple voltage may be neglected.

b) What are the initial and final values of the output voltage?

c) Estimate the settling time of the circuit to this step change. Is the switch period short compared to this time for a switching frequency of 100 kHz and 5 kHz?

d) Plot the output ripple voltage as a function of time in steady state with D = 0.8 with a switching frequency of 100 kHz and 5k Hz (use MATHCAD, MATLAB, or your computer language of choice).

e) Use the nonlinear discrete time model of this circuit to simulate the circuit with a switching frequency of 100 kHz and 5k Hz (use MATHCAD, MATLAB, or your computer language of choice). Is this model valid? What must you check?

f) Repeat e) with the average model.