Massachusetts Institute of Technology
Department of Electrical Engineering
6.012 Electronic Devices and Circuits
Spring 1998
April 28, 1998 - Design Problem 2
Due May 8, 1998
1. Circuit
The design problem involves designing a common source amplifier, as
shown in Figure 1. The amplifier is a common source amplifier (M1) with a
current source supply (M2). This amplifier is driven by another amplifier,
on the same chip, whose Thevenin equivalent is modeled by vIN and RS,
where vIN = 1.5 V DC + vin and RS = 1 kΩ. The voltage source VOS models the
offset voltage of this amplifier, which drives a capacitive load of 1pF.
This amplifier must meet very strict gain, bandwidth and output swing
requirements while occupying a minimum amount of area on the chip. The
degrees of freedom that you have are the dimensions of M1 and M2 (W and
L for each transistor), and VB (the bias voltage of the gate M2).
3V
VB
R S = 1 kΩ
v IN
VOS
~
±
M2
v OUT
M1
CL = 1 pF
Figure 1: Circuit for Design Problem 2
2 Design Objectives
Here are your goals:
1. The voltage gain A V ≥ 50. To calculate the voltage gain, use the small
signal models for M1 and M2 biased in saturation.
2. The bandwidth of the circuit, f3dB, must be greater than 5 MHz. For a
voltage gain of 50, this means that you need to have a gain greater than
0.707*50 = 35 at 5 Mhz. This is shown asymptotically below.
v
A V = out
v in
≥ 50
log f
f 3dB
(≥ 5 MHz)
3. The output should be able to swing from 1 V to 2 V.
v
OUT
2V
output swing = 1 V
1V
time
4. The total area of the circuit should be minimized. Only M1 and M2
should be considered in the area calculation and each transistor’s area
should be computed as follows.
6 µm
L
6 µm
W
The total area of the above transistor is W*(12 µm + L).
3. Analysis
Voltage Gain
The voltage gain of a common source amplifier with a current source
supply is:
A v = g m (ro roc )
Bandwidth
Open circuit time constants is a method for determining the frequency
response of an amplifier. Assuming that we have a transfer function with
no zeros (or if the zero frequencies are large compared to the lowest pole) we
can write the transfer function in the following form:
v out
A v0
A v0
,
=
⇒
n
v in
1 + b1 jω + ... + bn jω
(1 + jωτ1 )...(1 + jωτ n )
where A v0 is the gain at DC. If we assume that the amplifier’s frequency
response is dominated by one pole, then for frequencies close to the lowest
pole, we can approximate the transfer function as:
v out
A v0
A v0
≅
⇒
v in
1 + b1 jω
1 + jωτ 1
The value of b1 can be computed by summing the product of each
capacitance and the Thevenin resistance seen by that capacitance when all
other capacitances are set to zero (open circuited) and the sources are shut
off. These RC products are called open-circuit time constants.
For example, in the following simple circuit:
R1 C1
vin
~
R2
C2
the open circuit time constants for C1 and C2 respectively are
τ C 1 o = C 1 (R 1 + R 2 )
τ C 2 o = C2 R 2
and the bandwidth is determined by
1
1
1
1
.
f 3dB ≅
=
=
=
N
2πb1
2π[C1 (R 1 + R 2 ) + C2R 2 ]
2 π τ C 1o + τ C 2 o
2π ∑ τ C io
(
)
i=1
Using this method allows one to see which capacitance and/or open circuit
resistance is dominating the frequency response which is extremely helpful
to circuit designers. For a full discussion on open circuit time constants
read Section 10.4.4 (pp. 646 - 651) of the textbook.
Output Swing
The output swing of the amplifier is determined by HSPICE as the range of
output voltage for which the gain is greater than or equal to 50. In this
design, you will need to perform a dc sweep using VOS by adding a line
similar to the following to your HSPICE file:
.dc vos -50e-3 50e-3 .1e-3
This will create a .sw0 file that is viewable in HSPLOT and will look like:
VOUT
slope ≥ 50
VOUT,MAX
VOUT,MIN
VOS,MIN VOS,MAX
VOS
The output swing is simply V OUT,MAX - V OUT,MIN . The offset voltage that will
give this output swing is the middle of the high gain region or
VOS,MAX + VOS,MIN
VOS,opt =
. For hand calculations, the output swing is the
2
range of output voltage for which the NMOS and the PMOS are in their
saturation (linear) region of operation.
4. Device Models
NMOS
µCox
VT
Cox
Cov
Cjo
Cjsw
W min
Lmin
Ldiff
λ
µA
V2
50
0.5 V
2
fF
µm 2
0.5
0.1
fF
µm
fF
µm 2
0.5 µfFm
6 µm
1.5 µm
6 µm
0.067
L min
L
PMOS
µA
25 V 2
-0.5 V
2
fF
µm 2
0.5
0.3
fF
µm
fF
µm 2
0.35 µfFm
6 µm
1.5 µm
6 µm
0.067
L min
L
The HSPICE MOSFET models you should use are given below. Make sure
you are using the correct models. The minimum dimensions are listed in
the table above. Also keep in mind that λ is a function of length.
n-MOSFET
.MODEL N1 NMOS LEVEL=1 VTO=0.5 TOX=1.72E-8
+LAMBDA=0.067 KP=50e-6 CJ=1E-4 CJSW=5E-10 PB=0.95
p-MOSFET
.MODEL P1 PMOS LEVEL=1 VTO=-0.5 TOX=1.72E-8
+LAMBDA=0.067 KP=25e-6 CJ=3E-4 CJSW=3.5E-10 PB=0.9
5 HSPICE Analysis
Operating Point Analysis
To ensure that the output voltage is in the middle of the high gain region,
tell SPICE to perform a dc sweep of the offset voltage:
.dc vos -50e-3 50e-3 .1e-3
Then tell SPICE to find the exact value of the offset voltage that biases the
output where you want it using the .measure command:
.measure dc voffset find v(1) when v(4)=VOUT,OPT
where VOUT,OPT is the optimal output voltage that you determine from hand
calculations, v(4) is the output voltage and v(1) is the value of vos. Set vos
equal to the voffset that SPICE computes and re-run your simulation to
verify the bias. To verify that your circuit is properly biased, add the
following line to your SPICE input file:
.op
This tells SPICE to compute all bias voltages and currents in your circuit.
AC Analysis
To verify the small signal performance of your circuit, an ac analysis is
necessary.
.ac dec 10 1 100e6
The above line enables SPICE to measure quantities such as small signal
gain and bandwidth. To perform an AC analysis in SPICE, there must be
an AC source in your circuit similar to:
vin 2 3 -5 ac 1
This declares vin as a mixed signal voltage source with a DC value of -5 V
and an AC value of 1. When SPICE performs an AC analysis, it uses the
small signal models, that is why an AC amplitude of 1 V will work.
To measure the gain of the circuit, make use of the .measure command:
.measure ac vmax max v(4)
This causes SPICE to compute the maximum AC voltage of node 4 over the
range of frequencies specified in the .ac statement, where vmax is the
product of the small signal voltage gain and the AC input voltage
amplitude. If an AC amplitude of 1 is chosen, then vmax will correspond to
the maximum small signal voltage gain.
To measure the bandwidth of your circuit include the following in your
SPICE file:
.measure ac f3db when v(4) = 'vmax*0.707' fall=1
This makes use of the vmax that was previously measured and that the
definition of bandwidth is where the gain of the circuit falls to 12 of its
nominal value.
6 Report
We ask that you write up a report detailing your design efforts. Since we are
allowing considerable latitude in the design, it is imperative that we be able
to understand what you have done, so be clear and concise. If we do not
understand it, we will not be able to assign a good grade. The following
must be in the report:
1. The first page will summarize your hand calculated and SPICE
simulated results for each of the specifications. Use the final page of
this handout for that purpose.
2. Next should be an explanation of the approach you took to arrive at
the design. In other words, tell us what you did to set the gain, output
resistance, and how you tried to minimize the area. Explain your
reasons for these choices. Also discuss your frequency response
curve and explain why you got what you did. Show your open circuit
time constants to back up your explanation.
3. The next two or three pages should show summaries of your hand
calculations. In this section, you should have the values you designed
for W and L for each transistor. In addition, show hand calculations
for the gain, bandwidth and voltage swing specifications that we have
asked you to meet.
4. Include the HSPICE input file(s) you used to verify your final design.
Again, please place these file(s) in a publicly readable directory in
your account so that we may copy them and run our own simulation.
Write your username and the directory and filename in the space on
the summary page.
5. Include HSPICE output, including operating point and voltage gain
calculation. Also include plots of the frequency response and the dc
sweep of the input to your circuit.
6.012 Design Problem 2 - Summary of results
Due: May 8, 1998
Name:_____________________________
HSPICE
input
Collaborator’s
username:___________
filename(s):__________________________________
name:______________________________________
Design Parameter
voltage gain, AV
output swing
input offset voltage
PMOS bias voltage, VB
Specification
≥ 50
≥ 1 Vpp
-----------------------------
Calculated
Transistor Parameter
width, W
length, L
Area
NMOS (M1)
PMOS (M2)
Simulated
------------
TOTAL
-------------------------------