EE4902 C2009
HW Set 2
Due in class Friday January 30.
To make life easier on the grader:
•
Be sure your NAME and ECE MAILBOX NUMBER are prominently displayed on the
upper right of what you hand in.
•
When appropriate, indicate answers with a box or underline
•
Work as neatly as possible
You may assume T = 300K unless otherwise indicated.
1)
[Resistor design]
It is required to make an opamp circuit with voltage gain = 2 using the noninverting
circuit shown below. This problem concerns design of the resistor used for R
1
and R
2
.
a)
You are considering making the resistor out of one of the following layers:
•
Bottom metal layer (M1)
•
Polysilicon (POLY)
•
Pchannel drain diffusion (P+)
•
Nwell (N_W).
How many squares are required in each case for a 10k
Ω
resistor? Use the process
parameters handed out in class; also available at
http://ece.wpi.edu/~mcneill/handouts/16umParameters.pdf
Ignore the effects of contact resistance.
b)
What length L is required if a width of W = 2.4μm is used?
c)
Compare the total area required for both resistors in each of the different layer options.
d)
Find the parasitic capacitance from the resistor material to substrate in each case.
e)
Given your results from (c) and (d), which layer is the best choice for a 10k
Ω
resistor
in IC design, and why?
R
2
10k
!
R
1
10k
!
V
in
V
out
+

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2)
[Capacitor design; matching]
To avoid the DC power dissipation associated with resistors, most analog IC designs
use capacitive voltage dividers in the opamp feedback. An example is the gainof2
circuit shown below:
a)
Show that the gain of the circuit is
v
OUT
v
IN
=
1
+
C
1
C
2
b)
You are considering whether to make the capacitor plates from polypoly2 (POLY
POLY2) or metal1metal2 (M1M2). From the 1.6μm process parameters, what is the
available capacitance per unit area in F/μm
2
for each option? Estimate the area in μm
2
required for a value of 1pF for each option. Which choice is better, and why?
c)
You wisely decide that each capacitor is to be made from polypoly2. For simplicity,
the plates of the capacitor will be square (W=L) as shown. Determine the dimension
required to realize the 1pF value indicated.
d)
Now suppose that each dimension of each capacitor is subject to independent random
variation of ±0.1μm. For example, a W of 10μm could be anywhere from 10.1μm to
9.9μm. For the opamp circuit, what are the maximum and minimum possible gains
for the "worst case" combinations of W
1
, L
1
, W
2
, L
2
?
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 Spring '01
 MCNEILL
 Integrated Circuit, MOSFET operating region, Ron b

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