EE 603 Power Electronics
Homework # 1
Due January 18, 2006
In Mohn/Underland/Robbins browse chapters 1 and 2. Read in chapter 2 sections 2.2,
2.4, 2.6, and 2.8. Start reading chapter 7.
Problem 1
+

R1
Vin
+

V
f
i
f
Vout
+

Vin is a sinewave with a pea
k value Vp
a)
Sketch V
f
, Vout, and i
f
for one complete cycle of Vin. Label your sketches showing
the time relationship between the various waveforms.
b)
Compute the average and rms values of Vin, i
f
and Vout.
c)
Sketch the power in the resistor.
d)
What is the averag
e power in the resistor?
Problem 2
+

R1
Vin
Vout
+

Vin is a sinewave with a peak value Vp
a)
Sketch Vout for one complete cycle of Vin.
b)
Compute the average and rms values of Vout.
c)
Sketch the power in the resistor.
d)
What is the average power in
the resistor?
Problem 3
+

R1
Vin
i
Vout
+

R2
a)
What is Vout in terms of Vin, R1 and R2?
b)
Assume R1 << R2. Expand your answer from part a) in a Taylor series about the
point R1 = 0
stopping at the R1
3
term.
c)
What is the approximate value of Vout if R1 = 0
?
d)
Using your approximate Vout from part c), what is the current equal to?
e)
Now that you have an approximate value of the current, you can obtain a more
accurate estimate of Vout. Us
ing your current from part d), what is the voltage
across R1 (no longer assume it is zero) and what is a better estimate of Vout?
f)
Using your better estimate of Vout from part e), what is a better estimate of the
current?
g)
Using your better estimate of the c
urrent from part f), what is a better estimate of the
voltage across R1 and thus R2?
h)
Repeat the process in f) and g) getting better and better estimates of Vout. Do this
until you get an R3 term. At this point compare your estimate of Vout using the
iterat
ive method outlined in c) through g) to the Taylor series result. Comment.
Problem 4
The family of characteristic curves for a particular MOSFET is shown below. The drain
current in amps is plotted versus the drain to source voltage in volts for gate vol
tages
going from zero volts to 7V in one volt steps. The MOSFET is used in the circuit also
shown below. The input voltage is 5V. You may detach the MOSFET’s characteristic
curves and hand them in with your solution.
2.5
20k
Vin
V
CC
=
20V
a)
Label the
triode region and the saturated region on the plot. Indicate the boundary
between the triode region and the saturated region.
b)
Estimate the MOSFET’s threshold voltage. Note that there are two ways to make
this estimate.
c)
Estimate the value of Kp for the MOSF
ET. Be sure to give Kp’s units.
d)
For the above circuit, plot the circuit’s load line (solve the problem graphically) on the
MOSFET’s characteristic curves. Numerically label the x and y axis intercepts and
the slope of the line.
e)
For the circuit above, what
is V
DS
and I
D
when the input voltage Vin is equal to 5V?
Indicate the circuit’s operating point on your plot. You can obtain V
DS
and I
D
from
your graph or analytically. Graphical accuracy is adequate.
f)
When Vin is changed to 7V, what is the value of V
DS
and
I
D
? Indicate the circuit’s
new operating point on your plot. You can obtain V
DS
and I
D
from your graph.
Graphical accuracy is adequate.
g)
When Vin is changed to 1V what is V
DS
and I
D
? When Vin is changed to 15V what is
V
DS
and I
D
?
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
I
D
Vds

V
A
V
GS
= 7V
V
GS
= 6V
V
GS
= 5V
V
GS
= 4V
V
GS
= 3V
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