1. Contents
1 Introduction 2
2 Threshold voltage extraction of a given technology node 2
2.1 Constant-current method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Extrapolation in linear region method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Transconductace extrapolation method in linear region . . . . . . . . . . . . . . . . . . . . . . 2
2.4 Ratio method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Design of differential amplifier of a given specification 4
3.1 Design problem specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Large-signal transconductance characteristics of differential amplifier . . . . . . . . . . . . . . 4
3.3 Voltage transfer characteristics of differential amplifier . . . . . . . . . . . . . . . . . . . . . . 5
3.4 Input common mode range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.5 Slew rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.6 Frequency response of differential amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.7 Problem analysis and Spice code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.8 Magnitude plot and Phase plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4 Electromechanical model of a resonating nano-cantilever-based sensor for high-resolution
and high-sensitivity mass detection 8
4.1 Detection of small changes in mass of the order of attogram . . . . . . . . . . . . . . . . . . 8
4.2 Calculation of snap-in voltage for a given cantilever-driver system . . . . . . . . . . . . . . . . 9
4.3 Calculation of current through cantilever-driver system at resonance frequency . . . . . . . . 9
5 Design of two stage OPAMP 10
5.1 Design problem specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Problem analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.3 Spice code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1

2. DESIGN OF MEMS RESONATOR WITH READOUT
CIRCUITRY
Vishal Pathak
May 17, 2015
1 Introduction
Micro-electromechanical systems (MEMS) have wide application in the development of sensors for the de-
tection of magnitudes in almost any domain. One particular kind of micromechanical device, which is based
on a silicon cantilever, has been recently developed and used as a very sensitive detector of heat, surface
stress or mass or in molecular recognition. In this project, the cantilever will be driven electrostatically to
the resonance by means of a lateral electrode, which is closely placed parallel to the cantilever. A capaci-
tive read-out of the cantilever oscillation will be performed by means of a CMOS circuitry, which has been
designed to be integrated monolithically with the nanocantilever-driver system. A knowledge as precise as
possible of the electrical characteristics of the cantilever-driver system is crucial for a correct design of the
CMOS circuitry.
2 Threshold voltage extraction of a given technology node
2.1 Constant-current method
This methods evaluates the threshold voltage as the value of the gate voltage corresponding to a given
arbitrary constant drain current. Advantages
1. Threshold voltage can be determined quickly with one voltage measurement.
2. Widely used in industry because of its simplicity.
Disadvantages
1. Totally dependent on the arbitrary chosen value of drain current.
2.2 Extrapolation in linear region method
This method consist of finding the gate-voltage axis intercept of the linear extrapolation of the ID − VG at
its maximum first derivative(slope) point (i.e. the maximum transconductance, gm) . The value of threshold
voltage is then calculated by adding VD/2 to the resulting gate-voltage axis intercept. Disadvantages
1. Maximum slope might be uncertain.
2. Mobility degradation effect is not taken into consideration.
2.3 Transconductace extrapolation method in linear region
This method suggests that the threshold voltage corresponds to the gate voltage axis intercept of the linear
extrapolation of the gm − VG characteristics at its maximum first derivative(slope) point.
2

3. 2.4 Ratio method
The ratio of drain current to the square root of the transconductance behaves as a linear function of gate
bias, whose intercept with the gate-voltage axis will equal the threshold voltage.
Advantages
1. Avoid the dependence extracted VT value on mobility degradation and velocity saturation effect.
Considering the dependence of the mobility on the electric field, the new expression of the drain current
is presented in equation
Id =
W
L
Cox
µ0
1 + θ(VG − VT )
VD(VG − VT ) (1)
The transconductance becomes:
gm =
dID
dVG ID=constant
=
W
L
CoxVDµ0
1
[1 + θ(VG − VT )]2
(2)
If the ratio ID/
√
gm is calculated, it results:
ID
√
gm
=
W
L
CoxVDµ0(VG − VT ) (3)
It can be seen from the above equation that the ID/
√
gm ratio is not affected by variations in carrier mobility
due to the transversal electric field. It is obvious that the dependence ID/
√
gm versus VG will be plotted as
a straight line. If the line will be extrapolated at ID = 0 the threshold voltage can be deduced.
Experimental Results
Model Parameter used is .MODEL CMOSN NMOS LEVEL=3 PHI=0.600000 TOX=2.1200E-08 XJ=0.200000U +TPG=1
VTO=0.7860 LD=1.6470E-07 KP=9.6379E-05 +UO=591.7 RSH=8.5450E+01 GAMMA=0.5863 +NSUB=2.7470E+16
NFS=1.98E+12 VMAX=1.7330E+05 +CGDO=4.0241E-10 +CGSO=4.0241E-10 +CGBO=3.6144E-10 CJ=3.8541E-04
MJ=1.1854 CJSW=1.3940E-10 +MJSW=0.125195 PB=0.800000
Figure 1: iD vs VG
Vt0 extracted = 0.78 volts
3

4. Figure 2: gm
Figure 3: iD/
√
gm vs VG
3 Design of differential amplifier of a given specification
3.1 Design problem specification
3.2 Large-signal transconductance characteristics of differential amplifier
Defining Equations:
vID = vGS1 − vGS2 =
2iD1
β
−
2iD2
β
(4)
ISS = iD1 + iD2 (5)
Solutions:
iD1 =
ISS
2
+
ISS
2
(
βv2
ID
ISS
−
β2v4
ID
4I2
SS
) (6)
iD2 =
ISS
2
−
ISS
2
(
βv2
ID
ISS
−
β2v4
ID
4I2
SS
) (7)
These relationships are useful for vID < 2 ISS/β.
Differentiating iD1(or iD2) with respect to vID and setting vID = 0 gives transcondutance of differential
4

5. Figure 4: Problem specification
amplifier
gm =
diD1
dvID vID=0
=
βISS
4
=
K1 ISSW1
4L1
(8)
Figure 5: Transconductor characteristics of differential amplifier
3.3 Voltage transfer characteristics of differential amplifier
Voltage transfer characteristics of current mirror load circuit. The differential-in, differential-out transcon-
ductance is twice gm and can be written as
gmd =
diout
dvID (vID=0)
=
K1 ISSW1
L1
(9)
3.4 Input common mode range
Another important characteristics of a differential amplifier is input common mode range,ICMR. ICMR is
found by setting vID to zero and vary vIC until one of the transistor in the differential amplifier is no longer
5

6. Figure 6: Voltage transfer characteristics
saturated.
Highest Common Mode Voltage
vIC(max) = VT N1 + VDD − VSG3 (10)
Lowest Common Mode Voltage
vIC(min) = VSS + VDS5(sat) + VGS2 (11)
3.5 Slew rate
The slew-rate performance of the differential amplifier depends on the value of ISS and the capacitance from
the output node to ac ground. Slew rate is defined as the maximum output voltage rate, either positive or
negative. Since the slew rate in the differential amplifier is determined by the amount of current that can
be sourced or sunk into the output capacitor, the slew rate of differential amplifier is given by
SlewRate =
ISS
C
(12)
where C is the total capacitance connected to the output node.
3.6 Frequency response of differential amplifier
3.7 Problem analysis and Spice code
Procedure
1. Pick ISS to satisfy the slew rate knowing CL and the power dissipation.
2. Check to see if Rout still specify the frequency response, if not change ISS or modify circuit.
3. Design W3/L3(W4/L4) to satisfy the upper ICMR.
4. Design W1/L1(W2/L2) to satisfy gain.
5. Design W5/L5(W6/L6) to satisfy lower ICMR.
Analysis
1. To meet the slew rate, ISS >= 60µA. For maximum power dissipation, ISS <= 151.15µA
2. f−3db of 100kHz implies that Rout <= 530kΩ . Therefore Rout = 2
(λN +λP )ISS
<= 530kΩ . Choose
ISS = 105.575uA .
6

7. Figure 7: Frequency Response
Figure 8: Design methodology
3. Vin(max) = VDD − VSG3 + VT N1
2.55 = 3.3 − VSG3 + 0.57
VSG3 = 1.32 = 2ID(sat.)
kp
W3
L3
− 0.60
W3
L3
= W4
L4 = 9.257 = 10(approx.)
4. Gain = 100 = gm1Rout = gm1
gds2+gds4
= 9.33 W1
L1
W1
L1
= W2
L2
= 114.87 = 120(approx.)
5. Vin(min) = VSS + VDS5(sat.) + VGS1
1.15 = 0 + 2ID1
kn
W1
L1
+ 0.57
VDS5(sat.) = 0.514
W5
L5
= 3.787 = 4(approx.)
Spice Code
*differential amplifier
.include "D:p35p35_cmos_models_tt.inc"
7

8. Vdd 4 0 3.3
mp 2 2 4 4 pmos w=10u l=1u
mp2 3 2 4 4 pmos w=10u l=1u
mn 2 a 1 0 nmos w=120u l=1u
mn1 3 b 1 0 nmos w=120u l=1u
mn2 1 5 0 0 nmos w=4u l=1u
mn3 5 5 0 0 nmos w=4u l=1u
Is 4 5 dc 105.575u
Cl 3 0 3p
*input
vd1 a 7 ac 50mv
vd2 7 b ac 50mv
vcm 7 0 dc 1.55v
*analysis
.ac dec 10 10 10mega
.plot ac v(3)
.end
3.8 Magnitude plot and Phase plot
Figure 9: Magnitude plot
4 Electromechanical model of a resonating nano-cantilever-based
sensor for high-resolution and high-sensitivity mass detection
4.1 Detection of small changes in mass of the order of attogram
Assume the mass we want to measure is added to the cantilever.
δm = 26k
1
(fres − δf)2
−
1
(fres)2
(13)
8

9. Figure 10: Phase plot
Assume no changes in elastic constant.
4.2 Calculation of snap-in voltage for a given cantilever-driver system
Snap-in voltage is maximum voltage that can be applied if the applied voltage exceeds that value, the
cantilever will colapse into the driver and will remain in that position irreversibly. The snap-in voltage
correspond to the first unstable deflection of the total potential energy and can be calculated by finding a
minimum of the first derivative of the total potential energy.
xsi = 0.44s (14)
Vsi = 0.22
E w3s3
l4
(15)
4.3 Calculation of current through cantilever-driver system at resonance fre-
quency
The static capacitance of the cantilever-driver system, C0, increases when a dc voltage is applied. The new
capacitance Cp is
Cp = C0(1 + κ(Vdc))(F) (16)
C0 =
lt
s
(17)
where κ is electromechanical coupling parameter calculated by κ = 2k
lt
s3 Vdc
2
The model also describes the current component induced by the dc voltage applied to the vibrating
cantilever by a series RSLSCS branch in parallel to Cp :
CS = 1.798κC0 (18)
LS =
1
2πCSfres
(19)
RS =
1
Q
LS
CS
(20)
The total current that flows between the driver and the cantilever is finally determined by firstly calculating
the impedance of RSLSCS||Cp and then computing the current induced through this impedance when Vacopt
is applied.
9

10. Figure 11: Small signal electromechanical model of oscillating cantilever-driver system.
5 Design of two stage OPAMP
Figure 12: Two stage OPAMP
5.1 Design problem specifications
1. VDD = 2.5V and VSS=−2.5
2. Av > 5000V/V
3. Gain bandwidth product,GB = 5MHz
4. −1V < ICMR < 2V
5. Slew Rate,SR > 10V/µs
6. CL = 10pF
7. Power Dissipation,PDiss. <= 2mW
10

11. 8. Phase margin,PM=60◦
5.2 Problem analysis
Design procedure
1. Choose the smallest device length that will keep the channel modulation parameter constant and give
a good matching for current mirror.
2. From the desired phase margin, choose the minimum value for Cc that is, for a 60◦
phase margin choose
Cc < 0.22CL (21)
This assumes z >= 10GB.
3. Determine the minimum value for the ”tail current”’ from
Ibias = SR.Cc (22)
4. Design for S3 from the maximum input voltage specification.
S3 =
Ibias
kp[VDD − Vin(max) + Vtn + Vtp]2
>= 1 (23)
5. Design for S1(S2) to achieve the desired GB.
gm1 = GB.Cc (24)
S1 =
g2
m1
knIbias
(25)
6. Design for S5 from the minimum input voltage. First calculate VDS5(sat) then find S5.
VDS5 = Vin(min) − VSS −
I5
β1
− Vtn >= 100mV (26)
S5 =
Ibias
kn[VDS5(sat.)]2
(27)
7. Find the S6 and I6 by letting the second pole(p2) be equal to 2.2 times GB.
gm6 = 10gm1 (28)
S6 = S4
gm6
gm4
(29)
I6 =
g2
m6
2kpS6
(30)
8. Design S7 to achieve the desired current ratio Ibias and I6.
S7 =
I6
IIbias
S5 (31)
9. Check power dissipation and gain.
PDiss. = (Ibias + I6)(VDD + |VSS|) (32)
Av =
2gm2gm6
Ibias(λ2 + λ3)(λ6 + λ7)
(33)
10. If the gain is not met, the current Ibias can be decreased.
11

12. 5.3 Spice code
* Two stage OPAMP
.option limpts= 1000
vin+ 1 0 dc 0 ac 1.0
vdd 4 0 dc 2.5
vss 0 5 dc 2.5
vin- 2 0 dc 0
CL 3 0 10p
xopamp1 1 2 3 4 5 OPAMP
.subckt OPAMP 1 2 6 8 9
.model NMOS NMOS VTO = 0.7 KP = 110U GAMMA = 0.4 LAMBDA = 0.04 PHI = 0.7
.model PMOS PMOS VTO = -0.7 KP = 50U GAMMA = 0.57 LAMBDA = 0.05 PHI = 0.8
mp1 4 4 8 8 pmos w=15u l=1u
mp2 5 4 8 8 pmos w=15u l=1u
mn1 4 2 3 3 nmos w=3u l=1u
mn2 5 1 3 3 nmos w=3u l=1u
mn3 3 7 9 9 nmos w=4.5u l=1u
mn4 7 7 9 9 nmos w=4.5u l=1u
mp3 6 5 8 8 pmos w=94u l=1u
mn5 6 7 9 9 nmos w=14u l=1u
cc 5 6 3p
Ibias 8 7 30u
.ends
.op
.TF v(3) vin+
.ac dec 10 1 10meg
.print ac vdb(3) vp(3) v(3)
.end
5.4 Results
Figure 13: Frequency response
12

13. Figure 14: Magnitude plot
Figure 15: Phase plot
13