April 8, 2008
ECE 315
Prelim # 2 Solution
Spring 2008
This exam is closed book but with 1 page (8.5 by 11 inches) full of notes of your choosing.
Use calculator to get numerical answers. Show all work! Take 90 minutes.
1.
Consider a power n channel MOSFET whose output characteristic in saturation or
active mode is given by:
I
D
=
k
P
2
(
V
GS

V
T
)
2
(1 +
λV
DS
)
.
Now consider that we want to include an internal series resistance in the drain part
of the transistor in the model as shown below in Figure 1.
Figure 1.
The nmos device with
R
ser
added to the model.
a) (10 pts)
Modify the above equation to include the effects of the internal series resistance
R
ser
.
In other words find an equation for
I
R
D
(the drain current with the series
resistance included) which depends on
V
GS
,
V
DS
and
R
ser
.
•
First we need to express
V
DS
as a function of
I
D
so that ohm
’
s law can be used
to add to the series resistance drop to the drain source voltage. Re arranging the
equation above, we can write:
V
DS
=
1
λ
2
I
D
k
P
(
V
GS

V
T
)
2

1
.
•
Now we add the ohmic drop on
R
ser
and replace
I
D
with
I
R
D
:
V
DS
=
1
λ
2
I
R
D
k
P
(
V
GS

V
T
)
2

1
+
I
R
D
R
ser
.
•
Solving this equation for
I
R
D
yields the answer as:
I
R
D
=
1 +
λV
DS
2
k
P
(
V
GS

V
T
)
2
+
λR
ser
.
The output characteristics for the model excluding the internal series resistance
is plotted below in Figure 2 for a value of
V
GS
= 2
volts.
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ECE315
April 8, 2008
Page 2
Figure 2.
Power nmos output curves with
V
GS
= 2
volts.
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 Spring '07
 SPENCER
 Microelectronics, Transistor, Vin, series resistance, internal series resistance

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