1. Homework #1 due in class Friday, September 5, 2014
Solve any five of the listed problems.
1. A switching power converter is designed to have efficiency of 95% at an output of 200 W.
The efficiency increases linearly, to 96% at 300 W, and decreases linearly to 94% at 100 W.
The rated minimum output is 40 W. The converter components will be damaged if the total
power lost exceeds 12 W. What upper limit on output power should be given for this converter?
2. The converter of problem #1 is built, and turns out to be slightly less efficient than expected,
with 94.5% at 200 W, 95.5% at 300 W, and so on in a linear manner. The total power loss must
be less than 12 W. What upper limit on output power should be given?
3. In the polarity reversing circuit of Example 1.6.1, energy balance is used to find the output
based on switch operation half of each period. What will the output be if the left switch is on
75% of T and the right is on the remaining 25% of T?
4. The customers in a city use electricity at an average rate of 10 GW. Of this amount, about
30% is used for fluorescent lighting. The electricity average price is $0.10 per kilowatt-hour of
energy. A new type of power converter supports 40% energy use reduction for this type of
lighting. If every customer installed it, how much money would be saved per year?
5. The circuit in Example 1.6.6 is to be evaluated more generally. The switch turns on whenever
the ac voltage is greater than Vpeak/k where k is an adjustable parameter. The switch turns off
one-half cycle later. What is the average output voltage as a function of k?
6. An electric motor drives a load that averages 50 HP of mechanical power. The average motor
efficiency is 87%. The cost of the motor was $500. Take the cost of electricity to be $0.10 per
kWh. The system was designed to operate for 20 years.
a) What is the energy cost over the 20 year operating life?
b) An inverter with a cost of $2000 is available that will optimize motor operation and support an
overall average efficiency of 90%. What is the energy cost over 20 years?
7. List at least five products you own (or that are in a home you rent) that require electrical
energy conversion.
8. An inverter delivers a square wave output at 50 Hz with a peak value of 400 V. What is the
RMS voltage?
