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Sensors and Actuators A 118 (2005) 292–297
A magnetic field-induced current-modulating opamp based on CMOS
differential Tesla–Volt multiplier cell for MAGFET 1/f noise reduction
Z.Q. Li, X.W. Sun∗ , S.C. Tan, C.M. Li
School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
Received 20 December 2003; received in revised form 4 August 2004; accepted 23 August 2004
Available online 27 September 2004
Abstract
A magnetic field-induced current-modulating opamp (MCMOP) based on the CMOS differential Tesla–Volt multiplier (TVM) cell for
magnetic field-effect transistor (MAGFET) 1/f noise reduction is reported. It consists of a CMOS differential TVM cell made of a pair of
identical MAGFETs, a fully differential opamp, and a set of chopper-stabilization switches. Due to the modulation effect of the input voltage
on the magnetic field-induced current imbalance, the MCMOP is utilized as a linear magnetic sensor not only to amplify the magnetic signal,
but also to chop and stabilize the signal, so as to suppress the low frequency noise in the MAGFETs themselves. By introducing the MCMOP,
the magnetic noise level of the magneto-opamp (MOP) consisting of the same differential opamp and the same single MAGFET is reduced
from 160 to 25 ␮T/Hz1/2 at 1 Hz. This is a 16 dB improvement of the magnetic resolution.
© 2004 Elsevier B.V. All rights reserved.
Idt: MAGFET; Tesla–Volt multiplier; Magneto-opamp; Magnetic field-induced current modulation; 1/f noise
Keywords: MCMOP; Tesla–Volt multiplier; Chopper-stabilization switches; Noise
1. Introduction
The split-drain magnetic field-effect transistor
(MAGFET) is a kind of MOSFET magnetic field sensors that exploit the Lorentz force of carriers in the inversion
layer operating in the Lorentz current deflection mode. It is
essentially a MOSFET with the drain split into two subregions [1–9]. When a magnetic field is applied perpendicular
to the device surface, the current imbalance will occur
between the split drains. This sensor is of linear magnetic
response, full standard CMOS process compatibility, and
extremely low power consumption. As a MOSFET magnetic
sensor, the split-drain MAGFET itself is also a building
block in the integrated electronic circuits. By developing
the circuit model, its circuit performance, such as output
resistances, capacitances, parasitics, frequency response,
∗
Corresponding author. Tel.: +65 67905369; fax: +65 67933318.
E-mail address: [email protected] (X.W. Sun).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.sna.2004.08.014
and even noise, can be well analyzed and optimized by
taking advantage of the well-established MOSFET SPICE
models for modern CMOS technologies.
Due to the full CMOS process-compatibility and good
linearity, the split-drain MAGFET has been extensively integrated together with post-processing electronic circuits
to form a universal magneto-operational amplifier (MOP)
[10,11], a magnetic field-controlled oscillator [12,13], a
stochastic digital magnetic field detector [14], as well as a
Tesla–Volt multiplier (TVM) [15,16], etc.
In view of the fact, however, that a MAGFET is essentially
a MOSFET with the drain split, large low frequency (1/f)
noise is an intrinsic problem associated with the MAGFET
[17–21] and has not been effectively resolved so far.
The chopper-stabilization technique has long been proved
an effective approach to avoid the low frequency noise and
static offset of an opamp [22]. The CMOS differential TVM
cell presented in [16] can be used to form the chopperstabilized Tesla–Volt multiplying opamp (CSTVMOP), so
Z.Q. Li et al. / Sensors and Actuators A 118 (2005) 292–297
as to suppress the low frequency noise of the Tesla–Volt multiplying circuits.
The chopper-stabilization technique is a demonstrated approach for 1/f noise reduction. Thus, the effective noise reduction in CSTVMOP for the Tesla–Volt multiplication can
be expected. What will be reported here, however, is a novel
application of the CSTVMOP based on the CMOS differential TVM cell as a magnetic field-induced current-modulating
opamp (MCMOP), which is not used as a TVM, but is a linear
magnetic sensor, to reduce the 1/f noise in MAGFET itself.
In the conventional chopper-stabilized opamp and CSTVMOP, the input voltage is chopped at the input stage at a
frequency higher than the corner frequency of the 1/f noise
of the opamp, such that the useful signal is separated from
the 1/f noise before it is amplified. In this case, a small differential input voltage is preferred to avoid its modulation
effect on the noise of the following amplifying stage. For the
proposed MCMOP, however, the current imbalance of the
differential TVM cell, which is a measure of the magnetic
flux density applied perpendicular to the device surface, will
be modulated by the chopped input voltage to a relatively
high frequency, such that the magnetic signal can be separated from the 1/f noise of the MAGFET itself and amplified
by the following opamp, and the overall magnetic resolution
is improved. This 1/f noise reduction is a performance that
is unachievable with a single MAGFET and even with the
conventional MOP. Because the input voltage is now used to
modulate the magnetic signal, a reasonably large amplitude
of the differential input voltage is needed, which is contrary
to the case in the conventional chopper-stabilized opamp.
In this paper, we shall firstly introduce the CMOS differential TVM cell functioning as a linear magnetic sensor, and
then present the MCMOP for 1/f noise reduction. The improved magnetic resolution of MAGFET using the magnetic
signal-modulating technique will be demonstrated.
2. Principle
2.1. Magnetic sensitivity of the differential TVM cell as
a linear magnetic sensor
293
Fig. 1. Circuit schematic diagram of the differential TVM cell made of
two identical n-channel MAGFETs. B is the magnetic flux density applied
perpendicular to the device surface.
where µn is the carrier mobility, Cox is the gate capacitance,
W/L is the aspect ratio of the individual MAGFET, Vth is the
threshold voltage of the MAGFET, Sr is the relative sensitivity
of the single MAGFET, and B is the magnetic flux density
applied perpendicular to the MAGFET surface.
When vin in Eq. (1) is fixed at a constant, the differential
TVM cell functions like a linear magnetic sensor. Its equivalent relative magnetic sensitivity, Sr eq , can be derived as
Sr
eq
=
I
2x
Sr
=
(I1 + I2 )B
1 + x2
(2)
where x = (vin /2)/(VGS − Vth ). It is clear that Sr eq ≤ Sr ,
and Sr eq reaches its maximum, Sr , when x = 1. This is quite
reasonable, because only one MAGFET of the differential
TVM cell is working when x = 1, while the other is cut-off.
2.2. Definition of magnetic resolution
The resolution of a magnetic sensor is a measure of the
magnetic sensing capability of the device. It embodies the
minimum magnetic flux density detectable by the sensor, and
is characterized by the magnetic noise floor of the sensor.
Unlike the sensitivity, which can be boosted by the postamplifying circuitry, the resolution cannot.
The magnetic noise of a magnetic sensor is measured by
its power spectral density (PSD)
SB (f ) =
S(f )
Sa2
(3)
The CMOS differential TVM cell proposed in [16] is redrawn in Fig. 1, where a pair of identical MAGFET devices,
MM1 and MM2 are in parallel with each other working in
the active region, and their drains are cross-connected. In the
figure, VGS and vin are the common- and differential-mode
voltages between the two gates of the MM1 and MM2, respectively, I is the current flowing through a MAGFET, ␦I
is the magnetic field-induced current imbalance between the
two drains of a MAGFET, and the subscripts 1 and 2 identify
the two MAGFETs. The difference of the output current of
the TVM cell has been expressed in [16] as
where S(f) denotes the electric (current or voltage) noise PSD
of the sensor, Sa is its absolute (current or voltage) magnetic
sensitivity, and f is the frequency. Over a given frequency
band [f1 , f2 ], the minimum detectable magnetic flux density
is the flux density value when the signal-to-noise ratio is equal
to 1, which is given by
f2
f2
f1 S(f ) df
Bmin =
SB (f ) df =
(4)
Sa
f1
µn Cox W
I = Sr
(VGS − Vth )vin B
L
The magnetic resolution is then defined as the minimum detectable magnetic flux density at certain frequency in a frequency bandwidth of 1 Hz.
(1)
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Z.Q. Li et al. / Sensors and Actuators A 118 (2005) 292–297
Fig. 2. Circuit schematic diagram of the MCMOP. Φ is the clock.
2.3. The MCMOP and MOP
Fig. 3. Circuit schematic diagram of the MOP.
The functioning of Eq. (1) is two-fold: first, the configuration shown in Fig. 1 is a Tesla–Volt multiplier; second,
a dc signal of B can be indirectly modulated by vin without cutting off the MAGFET devices, which means that the
chopper technique can then be imported to indirectly modulate B to a higher frequency and separate B from the 1/f
noise in the MAGFETs themselves. In this arrangement, the
differential TVM cell acts as a linear magnetic sensor with
virtual B-modulating capability. Thus, by incorporating this
differential TVM cell into a chopper-stabilized opamp, not
only the CSTVMOP becomes true, but the MCMOP is also
available to reduce the 1/f noise in MAGFET.
The circuit setup for the MCMOP is drawn in Fig. 2, which
is in the same form as a CSTVMOP. It is different from the
CSTVMOP in that the differential mode input voltage, vin , is
now set to a constant to indirectly modulate the magnetic flux
density, B. Assuming the dc gain of the differential opamp is
K and the gain at chopping frequency is KC , we have
µn Cox W
(VGS − Vth )vin B
L
where Eq. (1) has been imported. The absolute magnetic sensitivity of the MCMOP can then be written as
vo = KC · I · R = KC RSr
Sa
MCMOP
=
µn Cox W
vo
= KC RSr
(VGS − Vth )vin
B
L
(5)
When only one MAGFET of the differential TVM cell is
turned on, the other is cut-off, and no chopper is applied, the
MCMOP shown in Fig. 2 degrades to a conventional MOP.
Its circuit schematic diagram is shown in Fig. 3. Its absolute
magnetic sensitivity can be written as
Sa
MOP
= KRSr I1 = KRSr
µn Cox W
(VGS − Vth )2
2L
netic noise PSDs of the MCMOP and MOP can be achieved
and compared.
3. Results and discussions
The differential TVM cell as shown in Fig. 1 has been
fabricated in a standard 0.6 ␮m CMOS process. The aspect
ratio of each MAGFET was set to W/L = 60 ␮m/100 ␮m. The
relative magnetic sensitivity of a single MAGFET, Sr , was
measured to be 2.7%/T.
In Figs. 2 and 3, the fully differential opamp is made of
AMP01 and OP37 [23] with gain of 1000, the switches used
are ADG201A and ADG202A, the resistance of R is 4.7 k
for easy biasing, and VGS is always set to 3 V. Since the gain
stage is formed by AMP01, which is an instrumentation amplifier with very low noise level, this circuit is suitable to
examine the noise performance of the differential TVM cell
and the MAGFETs.
3.1. Sensitivities of the MCMOP and MOP
The magnetic sensitivities of the MCMOP and MOP were
measured to be Sa MCMOP = 9.82vin (V/T) with vin in Volt
and Sa MOP = 14.2 V/T, respectively. They will be used to
characterize the magnetic noise PSDs of the MCMOP and
MOP. It is clear that the absolute sensitivity of the MCMOP
is scaled by vin .
3.2. 1/f noise measurement and comparison
(6)
where VGS is the voltage drop between the gate and source of
the working MAGFET, and I1 is the current flowing through
the MAGFET.
By characterizing the voltage noise PSDs at the output
nodes of the MCMOP and MOP and manipulating them according to Eq. (3), where the absolute magnetic sensitivities
have been given in Eqs. (5) and (6), respectively, the mag-
The Stanford Research Systems Model SR770 FFT Network Analyzer was used for the 1/f noise measurement.
The corner frequency of the 1/f noise of the MAGFET
exceeds 100 kHz, which is a frequency unreachable for
the AMP01 and SF770. When gain is set to 1000, the
−3 dB cut-off frequency of the AMP01 is 26 kHz. Thus,
the chopping frequency in the experiments was set to
20 kHz.
Z.Q. Li et al. / Sensors and Actuators A 118 (2005) 292–297
For viewing the noise in the frequency range from 1 Hz
to 1 kHz, all the noise spectra shown in the following figures
are merged from two spectra that were measured within two
different frequency spans. This is the reason of the sudden
change of the fluctuation range of the noise spectra near the
frequency of 100 Hz.
In order to study the indirect B-modulating functionality of
the differential input voltage of the differential TVM cell, the
magnetic flux density-equivalent noise spectra for the MOP
and the MCMOP were tested. Since the absolute magnetic
sensitivity of the MCMOP is strongly affected by vin as shown
in Eq. (5), the spectra for the MCMOP have been obtained
for various vin values. The results are shown in Fig. 4(a),
where the square line is for the MOP, and the others are for
the MCMOP under different vin values. Here the rms value
is adopted for the noise spectra.
It can be seen that the magnetic noise density increases
when vin decreases. This is due to the heavy scaling of the
magnetic sensitivity of the MCMOP by vin . Although a small
vin has a weak disturbance on the noise, it also has a weak
295
Fig. 5. Comparison of voltage noise spectra between TVMOP and opamp.
modulating effect on magnetic current. Thus, in the MCMOP,
a large vin (higher than 0.5 V) is preferred for achieving a
reduced magnetic noise level. When vin = 1 V, the magnetic
resolution at 1 Hz is improved from 160 ␮T/Hz1/2 of the MOP
to 25 ␮T/Hz1/2 of the MCMOP.
Ideally, the 1/f noise spectra of the MCMOP should be flattened. The residual non-zero slope is caused by the modulation effect of vin on the low frequency noise of the MAGFETs.
The direct magnetic noise reduction of the MCMOP from
MOP is shown in Fig. 4(b). A negative value in dB means a
decreased magnetic noise density by using the MCMOP, and
vice versa. The magnetic resolution improvement at 1 Hz for
vin = 1 V is 16 dB.
3.3. Evaluation of suppression of 1/f noise in MAGFETs
When no chopper-stabilization is applied, the MCMOP
shown in Fig. 2 is actually a Tesla–Volt multiplying opamp
(TVMOP). When the TVM cell in Fig. 2 was replaced by
a pair of 47 k resistors and no chopper-stabilization was
applied, the voltage noise at the opamp output node was
also measured and compared with the original TVMOP noise
spectrum as shown in Fig. 5. The noise in the new circuitry
can be deemed generated from the opamp. It is clear that
the opamp voltage noise density for the resistor-only circuits
at 1 Hz is only around 6% of that of the TVMOP. Even if
this 6% noise component were fully removed in the chopperstabilization case, its contribution to the overall noise reduction would only be 0.016 dB, which can be ignored. Thus,
the noise reduction in MCMOP comes mainly from the suppression of the noise in the two MAGFETs of the TVM cell.
4. Conclusion
Fig. 4. Magnetic noise comparison between the MOP and MCMOP. (a)
Magnetic noise spectra of the MOP and MCMOP under different modulating
voltage. (b) Magnetic noise reduction of the MCMOP from MOP.
A differential Tesla–Volt multiplying cell has been
designed, fabricated and incorporated with the chopperstabilization technique to form a MCMOP. By modulating the
magnetic field-induced current, so as to indirectly modulate
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Z.Q. Li et al. / Sensors and Actuators A 118 (2005) 292–297
the magnetic flux density in the MCMOP, the low frequency
noise in the MAGFET itself has been suppressed, such that
the magnetic resolution of the MAGFET has been improved.
Acknowledgements
The authors are grateful to Dr. Zhaofeng Zhang and Dr.
Zhiheng Chen for stimulating discussions on MOSFET and
opamp noise issues.
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Biographies
Zhiqing Li obtained the B.Eng. and M.Eng. degrees in solid-state devices and electronic materials from University of Electronic Science and
Technology of China, Chengdu, China, in 1985
and 1988, respectively. After receiving the M.Eng.
degree, he joined Shantou Ocean Enterprises
(Group) Company, Shantou, China, as an Engineer. Since October 1995, he has been appointed
Director of Magnetic Tape Factory, Shantou Sun
Magnetic Recording Materials Co., Ltd, Shantou,
China, to be in charge of general management of
the factory. He is currently working towards the PhD degree in electrical
and electronic engineering at Nanyang Technological University, Singapore. His research interests are in integrated magnetic sensors and analog
IC design.
X.W. Sun was born in Beijing, China. From 1986
to 1994, he studied at Tianjin University, China,
where he received his B.Eng., M.Eng. and PhD
degrees all in photonics. From 1994 to 1998, he
studied at the Hong Kong University of Science
and Technology where he received his second
PhD degree in electrical and electronic engineering. He has been with the Division of Microelectronics in the School of Electrical and Electronic
Engineering of Nanyang Technological University
as an Assistant Professor since 1998. His research
interests focus on nanotechnology, optoelectronic thin films and devices,
magnetic latch, and display technologies. Dr. Sun is a member of IEEE
and Society for Information Display (SID). He is the founding Chair of
SID Singapore and Malaysia Chapter.
Soo Chiang Tan obtained the B.Eng. and M.Eng.
degrees in electric and electronic engineering
from Nanyang Technological University, Singapore, in 2000 and 2003, respectively. After receiving the M.Eng. degree, he joined Nanyang Technological University as an Research Associate.
His research interests are in Liquid-Crystal-onSilicon and OLED-on-Silicon microdisplays and
IC design.
Z.Q. Li et al. / Sensors and Actuators A 118 (2005) 292–297
C.M. Li received his PhD in 1986 from Wuhan
University, PRC. After two year postdoctoral
experience in UIUC, USA, he has worked in Motorola with positions of Distinguished Member
of Technical Staff and Science Advisory Board
Associate. Currently, he is an Associate Professor
in Nanyang Technological University, Singapore.
297
His major interest covers chemical/biological sensors, bioMEMS and
biochips, molecular electronics, energy storage systems and nanoscience.
He was awarded as Motorola Master Innovator and Motorola Distinguished Innovator. He has 54 published papers and 33 issued US patents.