Vol. 34, No. 11
Journal of Semiconductors
November 2013
A 97 dB dynamic range CSA-based readout circuit with analog temperature
compensation for MEMS capacitive sensors
Yin Tao(尹韬), Zhang Chong(张翀), Wu Huanming(吴焕铭), Wu Qisong(吴其松),
and Yang Haigang(杨海钢)Ž
Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China
Abstract: This paper presents a charge-sensitive-amplifier (CSA) based readout circuit for capacitive microelectro-mechanical-system (MEMS) sensors. A continuous-time (CT) readout structure using the chopper technique is adopted to cancel the low frequency noise and improve the resolution of the readout circuits. An operational trans-conductance amplifier (OTA) structure with an auxiliary common-mode-feedback-OTA is proposed
in the fully differential CSA to suppress the chopper modulation induced disturbance at the OTA input terminal.
An analog temperature compensation method is proposed, which adjusts the chopper signal amplitude with temperature variation to compensate the temperature drift of the CSA readout sensitivity. The chip is designed and
implemented in a 0.35 p
m CMOS process and is 2.1 2.1 mm2 in area. The measurement shows that the readout
circuit achieves 0.9 aF/ Hz capacitive resolution, 97 dB dynamic range in 100 Hz signal bandwidth, and 0.8 mV/fF
sensitivity with a temperature drift of 35 ppm/ıC after optimized compensation.
Key words: capacitive readout circuit; temperature compensation; charge sensitive amplifier (CSA); MEMS sensor
DOI: 10.1088/1674-4926/34/11/115005
EEACC: 1290; 2570D
1. Introduction
Modern micro-machined technologies have shown great
promise in producing low-cost small sensors with high performance and mass production potential. Capacitive MEMS
sensors have shown great advantages of low-power, highsensitivity and relatively simple structureŒ1 . For easy comprehension, capacitive sensors can be considered as a simple plate
capacitor. The measurand gives excitation on the plate area and
the distance between the plates or the permittivity of the insulator between the plates and brings a capacitive change outputŒ2 .
The overall MEMS sensor performance is affected by sensor element design and technology, readout circuit and packaging. A high performance MEMS capacitive sensor cannot
be developed without a good readout circuit design. Due to
the shrinkage of sensor element dimensions, the MEMS sensor output becomes very weak. High performance gyroscopes
and accelerometers need sub-aF (10 18 F) level capacitance
changes to be resolved by readout circuitsŒ3 , which poses a
challenge to low-noise readout circuit design. A majority of
the reported capacitive MEMS sensor readout circuits adopt the
switched-capacitor (SC) topology together with the correlateddouble-sampling (CDS) technique to suppress low-frequency
noise and improve the resolution. The resolution of an SC
charge integration readout circuit is limited by the noise folding
and the high KT /C noiseŒ4 6; 11 . The continuous-time (CT)
sensing topology has superior noise performance compared to
the SC charge integration methodŒ1; 4; 5 .
Temperature drift is another critical issue for high resolution MEMS sensor readout circuit designŒ7 10 . Sensor sta-
bility and behavior in temperature variations is crucial to its
long-term performance. There are two ways to solve the temperature drift problem. One is to control environment temperature to a constant value, which is outside the operation temperature range, with the help of a power resistor or thermoelectric cooler. However, this method will consume a lot of power
and is limited in actual application. The other method is to use
a temperature compensation design for the sensor circuit and
system. In Ref. [8], polynomial fitting is utilized for microgyroscope temperature compensation with the help of an offchip microprocessor. In Ref. [9], a look-up table is stored in the
on-chip EEPROM, containing information relative to the temperature behavior of the sensor. The information is read out
and used in a digital correction algorithm to compensate the
temperature drift of the output.
Yet up till now few published works have implemented
temperature compensation in the analog readout front-end, and
instead used a complex digital logic in the back-end. In Ref. [4],
a temperature-variable gain amplifier with a gain of about 50 at
room temperature is used to compensate the temperature drift.
The compensated gyroscope sensitivity typically varies by 1%.
However the circuit is subject to high non-linearity because of
the open-loop topology of the temperature compensation amplifier. In Ref. [14] a compensated voltage reference is used
to perform precise capacitance to frequency conversion and
get 23 ppm/ıC temperature coefficient. But the circuit shows
high non-linearity and poor readout resolution. In this paper,
we demonstrate an analog temperature compensation method
based on the CSA readout structure with high resolution, good
linearity and low temperature drift.
* Project supported by the National Natural Science Foundation of China (No. 61106025) and the CAS/SAFEA International Partnership
Program for Creative Research Teams.
† Corresponding author. Email: yanghg@mail.ie.ac.cn
Received 2 April 2013, revised manuscript received 20 May 2013
© 2013 Chinese Institute of Electronics
115005-1
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Yin Tao et al.
Fig. 1. Block diagram of the readout circuit.
This paper presents the principle of the CSA-based readout circuits, and the design and implementation of the readout circuits is described in detail. The measurement results and
analysis of the readout circuit are also presented.
2. Theory and analysis
In order to maximize the SNR of the readout circuit, a
continuous time voltage (CTV) sensing scheme based on CSA
is adopted so that the noise performance is not degraded by
the noise folding and switches noise as existing in the switchcapacitor circuits. The proposed readout circuit is consisted of
five parts as shown in Fig. 1, including the compensation voltage generator, the chopper switch, the charge sensing amplifier
(CSA), demodulator and low-pass filter.
To suppress the low frequency 1/f noise and the dc offset, the chopper stabilization technique is used in CSA-based
readout circuits. The chopper technique applies modulation to
transport the input signal to a higher frequency where there is
no flicker noise by switch S1, and then demodulates it back to
the base band after signal processing. The 1/f noise and offset
of the circuit are modulated to high frequency and filtered at the
output by the low-pass filter. In the chopper technique implementation, a compensation voltage generator with the opposite
temperature coefficients against the CSA is designed to compensate the temperature drift of the readout circuit.
Hcsa D
D
Vstep_csa
CsC Cs
Vd AV
Cs C Cf .1 AV /
(1)
Vd
Cf
Vd
;
Cf
1
AV
1
1
Cs
1C
Cf
where Vd is the amplitude of the modulation signal Vmd , i.e. (VH
– VL //2, Cf is the integrate capacitor of CSA, and AV is the amplifier open-loop gain. Apparently, a larger Vd and smaller Cf
lead to a larger sensitivity for the CSA and help to achieve high
resolution. However, Vd amplitude is restricted by the supply
voltage and the minimum Cf value is limited by process. In this
circuit, Vd is designed to be about 0.9 V at room temperature
and Cf to be 1 pF.
The C/V readout sensitivity after demodulation and LPF
is affected by the bandwidth of the CSA. The sensitivity after
demodulation is given by Eq. (2), in which the upper limit of
the modulated CSA output harmonics kcsa is determined by the
CSA bandwidth.
HC=V .t/ D Hcsa
2.1. Transfer function
The CSA is shown in Fig. 1, with a differential capacitive
sensor represented by capacitors CSC and CS connected to
the input terminal. The compensation voltage generator gives
two voltages: VH and VL . With the help of chopper switch S1,
the chopper modulation signal Vmd is generated at the common
node of capacitive sensor CSC and CS . The CSA generates an
amplitude modulated output signal, whose amplitude is Vstep_csa
when there is a capacitance difference (CSC – CS / at the input.
The transfer function of the CSA is
kcsa
X
kD1
kDodd
1
X
mD1
mDodd
4
sin.k 2fchop t /
k
4
sin.m 2fchop t /;
m
(2)
where Hcas is transfer function of the CSA, the last two are
the harmonics of CSA output and that of the demodulation
signal. If the higher frequency harmonics of the modulated
CSA output are filtered due to CSA bandwidth limitation, the
whole C/V readout sensitivity will be reduced accordingly. After the demodulation, only the elements with frequency far below fchop (i.e. n D m) can pass the LPF and form the final output. For example, if the CSA has an ideal low-pass bandwidth
characteristic with cut-off frequency between fchop and 3fchop ,
then the harmonics more than fchop in the modulated signal are
filtered out. The whole C –V sensitivity will be reduced to be
8/ 2 Hcsa (about 81%) as a result. In real implementation,
the choice of the amplifier bandwidth is decided by power consumption limitation and accuracy requirement. The simulation
sensitivity of the proposed circuits is about 0.85 mV/fF.
115005-2
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Yin Tao et al.
Fig. 2. Equivalent circuit of the CSA for noise analysis.
Fig. 3. Thermal noise contributions from the OTA to the CSA with
different x D Cin /CT .
2.2. Temperature compensation
Equation (1) shows that CSA sensitivity is proportional to
the modulation signal amplitude (Vd /. So an analog temperature compensation can be realized by designing Vd (T ) with a
proper temperature characteristic. Considering that the transfer
function of CSA Hcsa (T ) has a 1st-order temperature coefficient (TC) ˛1 when Vd is constant (i.e. Vd D Vd0 / and can be
given by Eq. (3),
Hcsa .T /jVd D Vd0 D Hcsa; 0 Œ1 C ˛1 .T
T0 /;
(3)
where T is chip temperature, T0 is initial room temperature,
and Hcsa; 0 is CSA sensitivity at T0 with Vd D Vd0 .
By making Vd (T ) with 1st-order temperature coefficient
˛2 , the compensated transfer function of the CSA is shown in
Eq. (4). When ˛2 D ˛1 , the 1st-order temperature drift of
the CSA output can be diminished and the CSA sensitivity is
compensated.
Hcsa; comp .T / D
D
Hcsa .T /
Vd .T /
Vd0
Hcsa; 0 Œ1 C ˛1 .T
Vd0
T0 /
fVd0 Œ1 C ˛2 .T
T0 /g
Hcsa; 0 Œ1 C .˛1 C ˛2 /.T
the noise of the chopper driving signal and the input referred
equivalent noise of the OTA respectively.
Because of the fully differential structure of the CSA, the
noise contribution of the chopper driving signal (vN n; md / is proportional to the input capacitance C , which can be regarded
as the mismatch of the differential structure. And the noise PSD
at the output of the CSA is given by
2
vn;
o
f
D
2
vn;
amp
f
CT
Cf
2
C
2
vn;
md
f
Cin
Cf
2
:
(5)
From Eqs. (5) and (1), the equivalent input capacitance
noise of the CSA is thus derived as
v
s
u
2
2
u v2
vn;
C 2
Cs2
t n; amp CT
md
D
C
=Hcsa
f
f
Cf
f
Cf
v
u
2
2
vn;
1u
t vn; amp
md
.CT /2 C
.C /2 ;
D
Vd
f
f
(6)
where CT is the total capacitance at the amplifier input.
T0 /:
(4)
In the similar way, if there is a temperature drift in the
micro-sensor sensitivity, whose temperature coefficient is ˛3 ,
1st-order temperature compensation on the whole system can
be accomplished by using a Vd (T ) with temperature coefficient
˛2 D .˛1 C ˛3 /.
2.3. Noise analysis
Since chopper stabilization is employed, the flicker noise
can be effectively cancelled as long as that the 1/f noise corner
frequency is lower than half of the chopper frequencyŒ11 . Thus
the thermal noise is the main noise source to be considered. An
equivalent circuit of the CSA is shown in Fig. 2, in which Cp
represents the sum of interconnect/ bonding parasitic capacitances and the input capacitance of the input transistors in the
amplifier. The two voltage sources vN n; md and vN n; amp represent
CT D Cs C Cp C Cf :
(7)
Figure 3 gives the contributions of the OTA and the chopper driving signal to the whole CSA noise predicted from
Eq. (6) as functions of x D Cin /CT . As the curves illustrate,
the noise due to the OTA is far larger than that from chopper
driving signal, when x is small (i.e. Cin is far smaller than Cs
and CT /, which is the normal condition for linearity consideration when the readout circuit is used to interface the MEMS
capacitive sensors. This result helps to lessen the low-noise requirement of the chopper driving signal generator design. From
Eq. (6), in order to improve the accuracy of the capacitance
measurement, the following approaches should be made: (1)
minimize the noise of the OTA, (2) maximize the amplitude of
the chopper driving signal Vd , and (3) try to reduce the parasitic
capacitance of the bonding wire by single-chip integration, for
example.
115005-3
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Fig. 4. (a) Block diagram of the charge sensing amplifier. (b) Schematic of the OTA in the CSA.
3. Design and implementation
3.1. Charge sensitive amplifier
The block diagram and schematic of the charge sensing
amplifier is shown in Fig. 4. The OTA in the CSA is composed of two partsŒ12 : the differential mode OTA (DMO) and
the common mode OTA (CMO). The DMO serves as the C –V
converter with integration capacitor Cf . It consists of a amplify
stage and an output common mode feedback (OCMFB) cell.
For noise consideration, a telescope structure is employed and
the size of the input transistors is properly enlarged. A chopper
frequency of 1 MHz at Vmd is chosen which is above twice of
the OTA 1/f noise corner frequency. The DMO exhibits a high
GBW of 230 MHz and 64 dB open-loop gain, which promises
a highly accurate and good linearity C –V conversion.
Notice that the impedance of the input terminals of the
DMO is very high. Their potentials will be unpredictable and
vulnerable to interference without proper dc biasing. In this
work these nodes are reset to Vicm by ˚1 switch periodically.
Such a bias scheme provides a low-impedance dc path with
small parasitic capacitance and minimum noise injected by the
biasing circuit. The time interval between the reset phase needs
to be small enough to ensure that the high impedance node voltage is not evidently affected by charge injection or current leakage. The resetting clock (˚1 / frequency in the proposed circuits
is the 1/16 of the chopper frequency.
To suppress the disturbance introduced by the strong chopper carrier, a CMO is adopted as shown in Fig. 4. The CMO is
configured in negative feedback topology to stabilize the common mode voltage of the CSA input terminal. The common
mode potential at the CSA input is stabilized as in Eq. (7). The
CMO needs adequate bandwidth and gain to guarantee an effective virtual short between the DMO input and Vicm , and Ccf
is set as large as 20 pF to minimize the disturbance of the chopper signal. In order to enhance the driving capability, a source
follower output stage is added to the CMO, of which the GBW
exceeds 50 MHz with 20 pF feedback capacitance Ccf .
Vic; CMO D Vd
Cs
Cs
Vd
: (8)
Cs C Ccf .1 C Av; CMO /
Ccf Av; CMO
Figure 5 validates the effectiveness of the common mode
Fig. 5. Simulation results of the input and output common mode potentials of the CSA.
potential stabilization. When a Vd with 1 MHz frequency and
0.9 V amplitude is applied, the proposed CMO circuits successfully suppress the disturbance of the input common mode
potential for the DMO below 400 V and the output common
mode potential below 8 V, which has little influence on CSA
readout circuits.
3.2. Compensation voltage generator
Figure 6 shows the schematic of the compensation voltage
generator, whose structure is normally used as a low-voltage
bandgap voltage source. In this paper, it is used to generate
chopper voltages Vd D (VH – VL //2 with a proper temperature
coefficient for the chopper modulation signal. Q1, Q2, R1 , R2
and M9, M10 compose the core of the current sourceŒ15 , whose
output current is transformed to VH and VL with the help of load
resistor R3 and R4 . M1–M8 is an OTA used to keep the voltage at nodes A and B equal. The chopper modulation voltage
amplitude Vd , which is half of the voltage between VH and VL ,
and is its temperature coefficient are given in Eqs. (9) and (10).
115005-4
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Yin Tao et al.
Fig. 6. Schematic of the compensation voltage generator.
Vd D
VH
VL
2
1
@Vd
D
@T
2
1
D
2
VT ln n
VBE2
C
R1
R2
ln n kB
1 @VBE2
C
R1 q
R2 @T
R3 ;
R3 ;
(9)
(10)
where kB is Boltzmann’s constant. The terms in Eq. (10) are
positive and negative temperature dependent, respectively. By
carefully tuning R2 , a desired voltage with negative or positive temperature coefficient can be derived. In order to trim the
output temperature coefficient, the value of resistor R2 in the
circuit is designed to be controlled by 5-bit control code (C).
And the value of R2 can be expressed in Eq. (11), in which
R2; 0 is the normal value of R2 , RTRIM is the unit resistor value
for trimming, and Cn is the n-th bit of the control signal which
is 0 or 1.
R2 D R2;0 C
5
X
nD1
Cn 2 n
1
RTRIM :
Fig. 7. Simulation results of (a) Vd amplitude and CSA sensitivity versus temperature (normalized to the value at 27 ıC) and (b) readout
circuit optimized sensitivity temperature drift.
(11)
The temperature compensation simulation results of the
whole readout circuit are shown in Fig. 7. With a constant chopper modulation signal, the CSA exhibits a negative temperature dependent sensitivity. Therefore, a positive dependent Vd
is needed for compensation. By carefully tuning the compensation voltage generator, an overall readout sensitivity with temperature drift of only 30 ppm/ıC can be obtained, as is shown
in Fig. 7(b).
3.3. Demodulator and low-pass filter
The demodulator in this paper is implemented with two
pairs of switches with a dummy structureŒ12 . And a 4th-order
passive RC LPF is used to filter out the modulated 1/f noise.
Between the demodulator and LPF, a pair of switches is added
to stop the invalid signal transferring when the reset switch in
the CSA is closed (i.e. at ˚1 phase) and avoid an undesirable
spike voltage at the output.
4. Measurements
The readout circuit is designed and implemented in a
standard 0.35 m 2-poly/4-metal CMOS process by Global
Foundries. The chip measures 2.1 2.1 mm2 and operates with
a single 5 V supply. Figure 8 is the micrograph photo of the
Fig. 8. Micrograph of the implemented readout circuit.
readout chip with the sub-blocks marked. A temperature sensor
is integrated on chip to provide chip temperature information.
The performance of the capacitive readout circuit was verified with two programmable on-chip capacitor arrays connected to the chip input. Figure 9 gives the circuit transient response to a stepwise capacitive input signal with 2 kHz step frequency generated by on-chip capacitor arrays. Figure 10 gives
the measurement response of the readout circuit to the input
capacitance, while fixing one of the input capacitor array and
varying the other in 100 fF steps. The C –V sensitivity of the
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Fig. 9. Transient response to stepwise capacitive input.
Fig. 11. The normalized sensitivity amplitude–frequency characteristic of the readout circuit.
Fig. 10. Circuit output versus input differential capacitance.
readout circuit is about 0.8 mV/fF, which is slightly smaller
than the simulation result of 0.85 mV/fF due to the fact that the
parasitic capacitance at the CSA input terminal degrades the
bandwidth of the CSA and reduces the C –V sensitivity. The
linear input capacitance range of the readout circuit is about
˙700 fF with non-linearity of 0.3%. The linear input/output
range is mainly limited by the nested-cascode structure of the
charge sensitive amplifier. The bandwidth of the readout circuit is tested and shown in Fig. 11. The –3 dB bandwidth of the
readout circuit is larger than 23 kHz, which makes the circuit
also suitable for MEMS sensors with high resonant frequency.
The readout sensitivities with different temperature compensation control code C are tested and shown in Fig. 12. By
carefully tuning the compensation voltage generator, a proper
dependent Vd is derived. The temperature drift of the readout
sensitivity can be reduced to only 0.0035 mV/fF. In this condition, the temperature coefficient is about 35 ppm/ıC, which
is reduced by 15 times compared to the uncompensated TC of
550 ppm/ıC. At the same time, after compensation the TC of
the output offset is about 38 ppm/ıC with constant 400 fF capacitive input. The test results agree with the simulation results
and prove the validity of the temperature compensation method
in this paper.
Figure 13 shows the measured
p output noise of the readout
circuit, which is about 715 nV/ Hz at 2.5 kHz, corresponding
p
to an input equivalent capacitive noise of 0.9 aF/ Hz. When
the circuit is used to readout a capacitive input with 100 Hz sig-
Fig. 12. Measured readout circuit sensitivity versus temperature.
Fig. 13. Measured output noise PSD with/without temperature compensation.
nal bandwidth, it can detect a minimum capacitance of 9 aF. So
the dynamic range of the readout circuit is larger than 97 dB.
The output noise of the circuit without temperature compensation is also given in Fig. 13, in which condition the chopper signal Vmd is generated by off-chip low-noise arbitrary generator
AFG3252. Although the proposed temperature compensation
method brings some increase in the output noise of the readout circuit, it helps to improve the temperature stability of the
115005-6
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Table 1. Summary of the readout circuits’ specifications and comparison with previous work.
Parameter
Ref. [13]
Ref. [14]
Ref. [16]$
Ref. [18]
Sensitivity
0.19
kHz/fF
2.236
mV/fF
—
0.926 mV/fF
p
Noise floor (aF/ Hz)
—
7.1
4.3
—
Minimum detection (aF)
5 106
71
40
11–60
capacitance
(100 Hz BW)
(87 Hz BW)
Input capacitance range (pF)
5–31000
˙0:2
˙4
—
Dynamic range (dB)
71
69
100
94
Non-linearity (%)
>1
—
0.01
0.21
–3 dB bandwidth (Hz)
—
—
87 (max.)
—
Chopper frequency (kHz)
—
40
—
1000
TC of sensitivity/output off- 23 / —
300 /—
26 / —
— / 43
set (ppm/ıC)
(0–70 ıC)
( 40 to 125 ıC)
( 40 to 125 ıC)
Process
0.35 m CMOS
0.32 m BCD
—
0.5 m CMOS
Operation current (mA)
0.149
0.035
0.7
1.5
Supply voltage (V)
3.3
3.3
2.7–5.25
5
This work
0.8 mV/fF
0.9
9
(100 Hz BW)
˙0:7
97
0.3
> 2300
1000
35 / 38
( 40 to 85 ıC)
0.35 m CMOS
2.5
5
Capacitance to frequency; $ Capacitance-to-digital
Fig. 15. Output noise of the micro-gyroscope with the proposed readout circuit.
per technique in the CSA. The resolution
p of the gyroscope can
thus be calculated to be about 0.01 ı /s/ Hz, which proves the
low-noise characteristic of the readout circuit. The measured
performance of the readout circuits are summarized and compared with previous work as shown in Table 1.
Fig. 14. Scale factor and residual error of the micro-gyroscope with
the proposed readout circuit.
5. Conclusions
circuit and sensor system.
To prove the validity of the proposed readout circuit, it is
used to interface a bulk micromachined capacitive-sensing gyroscopeŒ17 . The measured scale factor is about 13 mV/ı /s with
a maximum nonlinearity of 0.65‰over the range of ˙200 ı /s
DC rotation, as shown in Fig. 14. The result shows a very good
linearity of the readout circuit under small capacitance input.
The inset in Fig. 14 gives the microgyroscope response to the
step input rotations from ˙0.1 ı /s to ˙0.5 ı /s. The response
clearly shows that the gyroscope can resolve input rotation as
ı
small as 0.1p
/s. Figure 15 shows the typical output noise floor
of 123 V/ Hz around 1 Hz. The noise is almost flat in the
low-frequency range from 0.1 to 50 Hz, as shown in Fig. 11,
which verifies the 1/f noise suppression of the proposed chop-
A CSA-based readout circuit for MEMS capacitive sensors that simultaneously achieves low-temperature dependence
and a low noise floor has been designed in this paper. The
proposed readout scheme combines a continuous time readout
topology and the chopper technique to reduce the output noise.
In addition, an analog temperature compensation method for
readout sensitivity has been well validated. The readout circuit
achieves a sensitivity of 0.8 mV/fF with temperature dependence as low as 35 ppm/ıC, and 97 dB dynamic range
with
p
an input referred capacitive noise floor of 0.9 aF/ Hz. The
circuit can be used in the capacitive signal readout of high precision MEMS sensors such as gyroscopes and accelerometers.
The chip is used to interface an MEMS gyroscope sensor and
the measurement results prove the validity and performance of
the readout circuit.
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Acknowledgment
The authors wish to thank Professor Jiao Jiwei at the
Shanghai Institute of Microsystem and Information Technology, CAS, for the gyroscope sensor elements and test support.
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