1. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 42, NO. 3, JUNE 1993 771
A Fully Integrated TemperatureCompensation
Technique for Piezoresistive Pressure Sensors
Muhammad Akbar and Michael A. Shanblatt
Fig. 7. Configuration of the magnetic field measuring system.
D. Magnetic Field Measurement
A Gaussmeter, AID converter, and sweeping mechanism are used
to construct the magnetic field measuring system. Its configuration
is shown in Fig. 7. The Gauss probe is attached to the X-Y plotter
moveable arm where the X-axis velocity is adjustable. When mea-
suring the magnetic flux density distribution in space, the Gauss
probe sweeps horizontally and moves down 0.5 cm in each sweep
measurement step. When measuring the space magnetic flux den-
sity in the axial direction, the X-Y plotter is rotated to have the
Gauss probe sweep vertically. The signal received from the Gauss-
meter is an amplitude modulation signal. Using a low-pass filter
for demodulation, the magnetic flux density is converted into DC
voltage. After a suitable sampling rate is selected, the sampled data
are read into a computer via an A/D converter according to the
sweeping velocity. The results are shown with graphics. The time
constant of the low-pass filter is 0.5 s, and the sweeping velocity
of the X-Y plotter is 2 cm/s.
111. CONCLUSION
The proposed method establishes an exact force model of the
magnetic suspension system by measuring the space magnetic flux
density in the axial direction from an actual system in operation.
The measurement results are substituted into the ideal theoretical
force model and multiplied by a corrective factor. The result is
proved by a mathematical derivation based on the space distribu-
tion of magnetic flux density and the principles of electromagnet-
ics. The corrective factor, which is proportional to the volume cov-
ered by the square of the profile function to the cross section of the
suspended object, is verified. The proposed method for establish-
ing an exact magnetic force model will be suitable for most large-
gap magnetic suspension systems, as the magnetic pole is sym-
metrical. The accuracy of the proposed method is also verified by
using lighter and heavier iron balls as suspended objects. The mag-
netic flux density in the axial direction corresponding to suspension
distance does not vary linearly. With heavier iron balls, the mag-
netic flux density is not proportional to the coil current. The pro-
posed method overcomes all the difficulties of magnetic system
modeling and obtains accurate results for further applications [4].
The proposed method, as well as the measurement process, of-
fers an important step to look into magnetic suspension problems.
It is very useful in experiment system designs.
REFERENCES
[l] D. K. Cheng, Field and Wave Electromagnetics. Reading, MA: Ad-
dison-Wesley, 1989, pp. 289-292.
[2] D. Kahaner, Cleve Moler, and Stephen Nash. Numerical Methods and
Soflware. Englewood Cliffs, NJ: Prentice-Hall, 1989, pp. 372-374.
[3] T. H. Wang, “Design of a magnetic levitation control system-an un-
dergraduate project,” IEEE Trans. on Education, vol. E-29, Nov.
[4] C. E. Lin and Y. R. Sheu, “A real time controlled large-gap magnetic
suspension using one-dimension position measurement,” in IEEE In-
strum. Meas. Technology Conf., New York, May 1992.
1986, pp. 196-200.
Abstract-A fully integratedtemperaturecompensationtechniquefor
piezoresistive pressure sensors is presented. The technique is suitable
for batch fabricated sensors operable over a temperature range of
-4O0C-13O0C and a pressure range of 0-310 kPa. The implementing
hardware for the technique is developed and verified through PSpice
and VHDL simulations. The technique is very effective for pressure
values below 240 kPa and provides reasonable results for higher pres-
sures. The technique is structurally simple and uses standard IC fab-
rication technologies.
I. INTRODUCTION
Ongoing advancements in IC fabrication, micromachining, and
packaging technologies have given rise to the concept of fully in-
tegrated smart sensors in the form of monolithic silicon chips con-
taining both transducers and all required signal-conditioning cir-
cuitry. Interestingly, the performance of the overall device for many
smart sensors is determined more by the interface electronics than
by the transduction element. An important economic implication
for the success of integrated sensors is the use of batch fabrication
techniques to bring down the cost of individual units. But batch
fabrication processes themselves introduce transduction and signal
irregularities which must be considered, further complicating the
issue of full integration. These additional problems are due pri-
marily to component compromises and tolerances.
One such sensor of current interest is the piezoresistive pressure
sensor. Piezoresistors, whose resistivity is dependent on strain, are
placed in a bridge configuration on top of a micromachined dia-
phragm. Stress on the diaphragm causes a current imbalance in the
bridge, which is used to detect pressure changes. A major problem
associated with pressure sensors of this class, however, is their
inherent cross sensitivity to temperature. The influence of temper-
ature on a piezoresistive pressure sensor is exhibited predominantly
by a variation in the output and zero-pressure offset of the sensor.
Moreover, minor processing variations give rise to piezoresistive
tracking errors, which in tum alter the temperature characteristics
for individual sensors.
Temperature compensation techniques have been reported using
laser trimming, extemal resistors, and clever use of material prop-
erties [11-[4]. Generally, these techniques are for limited temper-
ature and pressure ranges and, in many cases, for specific appli-
cations such as biomedical devices. Moreover, these techniques
can involve additional processing steps which often must be per-
formed under sensor operating conditions adding significant time
and cost to the manufacturing process. In some cases, mathemati-
cal compensation has also been employed. But the size and com-
plexity of the interface make it unsuitable for integration with the
sensor [5].
This paper describes a fully integrated temperature compensa-
tion technique especially suited for batch fabrication of piezore-
sistive pressure sensors which, if incorporated with a digital inter-
face, produces a sensor operable from -40-130°C over a pressure
Manuscript received February 14, 1992; revised August 28, 1992.
M. Akbar is with the College of Signals, Rawalpindi46000, Pakistan.
M. A. Shanblatt is with the Departmentof ElectricalEngineering, Mich-
IEEE Log Number 9208058.
igan State University, East Lansing, MI 48824.
0018-9456/93$03.00 01993IEEE

2. I
112
TABLE I
SENSORMODELPARAMETERS
I
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 42, NO. 3, JUNE 1993
Parameter Value
Diaphragmsize 1OOOpm x lOOOpm
Diaphragmthickness 10 pm
Piezoresistor value 2 kn
TCR 1900 ppm/K
Substratedoping 10I6/cm3
Sheet resistance 200 n/square
range of 0-310 kPa. The temperature compensation technique is
presented, and hardware for its implementation is specified. An
analysis of the technique’s effectiveness over the desired pressure
and temperature range is discussed, and the possible use of soft-
ware to implement a part of the technique is outlined.
11. THE SENSORMODEL
A simulation program which requires a low-levelphysical model
is used to generate and evaluate the temperatureand pressure char-
acteristics of the sensor [6]. The parameters of the sensor model
used for evaluating the sensor I/O characteristics as a function of
pressure, temperature, and tracking errors are summarized in Table
I. A value of 2308.29 ppm/K was computed by the simulation
program for the temperature coefficient of piezoresistivity for the
above move1 parameters.
The piezoresistorsare modeled as being diffised in a Wheatstone
bridge configuration on the thin silicon diaphragm. The variations
in piezoresistor values caused by batch fabrication are called track-
ing errors. The piezoresistor values on the same wafer are closer,
but the spread is more for the resistors coming from different wa-
fers. To represent wafer-to-waferprocessing variations, all the pi-
ezoresistors are varied by f 2 0 % from their nominal values. To
add the effect of variations on the same wafer, the f 2 0 % wafer-
to-wafer variation was modulated by a f 2 . 5 % variation [7].Ap-
propriate changes were also made in the sheet resistance and tem-
perature coefficient of resistivity.
111. TEMPERATUREERRORS
The major problem associated with piezoresistive pressure sen-
sors on silicon is their inherent cross sensitivity to temperature.
The sensor output and zero pressure offset are functions of tem-
perature. Moreover, batch fabrication of sensors introduces ran-
dom piezoresistive tracking errors, which in tum change the tem-
perature characteristics for the individual units [8]. The processing
variations cause two types of piezoresistive tracking errors: those
on the same wafer and those which vary from wafer to wafer.
Zero pressure offset and the sensor output are functions of the
tracking errors as well as the temperature. Thus the accumulated
error can be subdivided into three parts as
~ T O ~ I= %(set + %e + etemp.
eoffse,is the zero pressure offset voltage. It is caused primarily by
the same wafer tracking errors, which cause an imbalance in the
piezoresistive bridge. The offset error is also a functionof temper-
ature. q eis the error caused by wafer-to-wafer and same wafer
tracking errors. These errors are manifested as a shift in the sensor
response curve in proportion to their magnitude.
etempare the errors which are present even in a sensor with per-
fectly matched piezoresistors. These errors are introduced by the
temperature sensitivity of the piezoresistive coefficients [9]. More-
over, the wafer-to-wafertracking errors also vary the values of the
piezoresistive coefficients. The magnitude of this error voltage in-
creases linearly (to a first-order approximation) on either side of
the reference temperature over the stated temperature range.
The sensor response as a function of temperature, for a sensor
with matched piezoresistors, has a negative slope for all pressure
values. Moreover, the error magnitude increases with the applied
pressure [7].To compensate for this error, a diffused resistor, which
has a positive temperature coefficient of resistivity, can be used to
derive a temperature signal of the corresponding magnitude. But
this signal can not be used directly for all pressure values because
the signal magnitude is not a function of the applied pressure. To
overcome this difficulty, the temperature signal has to be scaled to
take care of various pressure ranges. The scaled temperature signal
then may be added to the pressure output. The temperature signal
is positive or negative depending on the pattem of tracking errors.
IV. THETEMPERATURECOMPENSATIONTECHNIQUE
The zero pressure offset and the errors caused by the same wafer
processing variations can effectively be handled by the double-
bridge temperature compensation technique [101. It makes use of
two bridges: a piezoresistive bridge fabricated on the thin dia-
phragm and an identical compensation bridge located on the bulk
part of the sensor chip. The output of the first bridge is a function
of pressure, temperature, and processing variations, whereas the
compensation bridge response is dependent on temperature and
processing variations only. The difference of the two bridge out-
puts removes the zero pressure offset and the variations caused by
the same wafer tracking errors.
The output of the double-bridge technique compensates suffi-
ciently for same wafer variations, but the sensor response still
shows a temperature dependency caused by the temperature sen-
sitivity of the piezoresistive coefficients. Remaining errors in the
output are removed by a new temperature compensationtechnique
which makes use of a temperature half-bridge. The results of the
double-bridge compensation technique and the temperature half-
bridge output are processed digitially to produce the final temper-
ature-compensated output. A block diagram of the compensation
circuit is shown in Fig. 1.
The temperature half-bridge is located on the bulk part of the
chip, and its response is dependent on temperaturealone. A circuit
to implement the compensation technique is shown in Fig. 2. The
temperature half-bridge is driven by a constant current source. A
single resistor R2 is sufficient to obtain the temperature signal, but
RI has been added to offer a higher load resistance to the current
source. Any value may be chosen for RI to suit the design of the
current source since it does not have any effect on the operation of
the temperature compensation technique. A value of 2 kQ, identical
to the other bridge resistors, is suggestedfor simplicity. The shape,
size, and value of R2 are identical to the parallel resistors on the
piezoresistive bridge. This is to ensure the same wafer-to-wafer
tracking errors for R2 and the piezoresistors.
The current source provides a constant current of 1.25 mA. This
value has been chosen as the center of the tracking errors and the
temperature range. The output for the compensation resistor with
no tracking error at the room temperature for this current is 2.5 V.
The current value is used to set a reference for the design with
respect to the sensor structure and the temperature range. Varia-
tions of the reference temperature do not alter the effectiveness of
the technique. With another reference, the sensor response will still
be insensitive to temperature, but a corresponding shift will result
in the compensated output.
The voltage across R2 is subtracted from a 2.5 V reference to
obtain the temperature signal. The polarity of the resulting tem-
perature signal is determined by the values of the tracking errors

3. I
I
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 42, NO. 3, JUNE 1993 773
Fig. 1. Block diagram of the temperaturecompensation technique.
- - -
Fig. 2. Half-bridgetemperaturecompensation technique.
START
U1
Digitize the
pressureand
temperaturesignal
1
Yes
‘I
Shift by 1
I I I
outputs
(+)
Fig. 3. Flow chart for the half-bridge temperature compensation tech-
nique.
F r o “ From ADC
Pressureregister Temperatureregister
. 1 . 1 . . .
plop9
4.1 . 1 . 1 . . .P2 Pi Sign T9
4.1
T2 T1
P10‘0’ P9 ‘0’ P8 f8 P2 f2 P1 ‘1
sign
s11 s10 52 s1
Fig. 4. Hardware for the half-bridge temperature.compensation technique.
and the operating temperature range. Depending on the pattem of
the tracking errors, the polarity temperature signal may remain the
same over the entire temperature range, or it may change polarity
at some predetermined temperature value. The temperature signal
is amplified, digitized, and stored in a register. The response of the
double-bridge compensation circuit is simultaneously available in
a second register. The temperature bridge output is scaled down
for various ranges of applied pressure and added to the compen-
sation bridge output. The temperature signal may be positive or
negative. A flow chart of the compensation algorithm is shown in
Fig. 3.
V. THEHALF-BRIDGECOMPENSATIONHARDWARE
A suitable half-bridge circuit block diagram for the temperature
compensation technique is shown in Fig. 4. The circuit has been
verified using very high speed integrated circuit (VHSIC) hardware
description language (VHDL). The analog outputs of the double-
bridge compensation and the temperature half-bridge are simulta-
neously digitized by two analog-to-digital converters (ADC’s) and
stored in two 10-bit registers. The function of the circuit is to shift
the output of the temperature half-bridge by 1,2, or 3 and then add
it to the pressure output derived from the difference of the com-
pensation and the piezoresistive bridges. The pressure output is
always positive, whereas the temperature output may either be pos-
itive or negative. Moreover, the magnitude of the temperature out-
put is smaller than half the pressure output, and thus it can fit in a
9-bit register.
The digital output from the two ADC’s is available in the pres-
sure and temperature registers. The temperature output is divided
by two simply by ignoring the LSB and hardwiring the remaining
8 bits to the shifting circuit. The shifting of the temperature register
contents is implemented by an array of 8, 2-3 multiplexers. Zeros
are hardwired to M7 and M8, to pad the high order bits of the
temperature signal for 2- and 3-bit shifts. The control inputs (num-
ber of shifts), co and c,, to the multiplexers are determined by the
three higher order bits of the pressure output. A simplification of
the Boolean function yields coand cIasploandpIop9,respectively.
The sign bit of the temperature bridge output is obtained from the
dual-slope ADC and stored in the MSB of the temperature register.
The shifted temperature output and the pressure output are added
by a 10-bit controlled adder circuit to produce a temperature-com-

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114
3
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 42, NO. 3, JUNE 1993
.................................................................................
175kPa
I I I I
-
1.75
1.5
1.25
1
0.75
output
Voltage
(v)
Compensated ............
Uncompensated
-
.............................................
I I I I
-40 0 40 80 120
Temperature("C)
Fig. 5 . The compensated sensor response as a function of the temperature.
pensated output for the sensor. Zeros are hardwired in the t9 and
tlo bit positions of the adder to make the temperature signal a 10-
bit number. 1's complement or 2's complement implementations
may be used for the controlled adder circuit as hardware and the
time delay requirements for the two approaches are similar. In both
cases the sign bit and an array of XOR gates are used to obtain the
controlled complementation of the shifted temperature output. For
the 2's complement approach the sign bit is also used as the carry
input to the adder.
VI. RESULTS
Three sensor structures with 0%, +20%, and -20% tracking
errors were investigated. A large number of simulations were run
to obtain sensor performance data for the desired pressure and tem-
perature range. The compensated and the uncompensated responses
as functions of temperature for the sensor with no tracking errors
are shown in Fig. 5.
The uncompensated output shows a large sensitivity to the tem-
perature variations. This is caused by the temperature dependence
of the piezoresistive coefficients. The compensated output for lower
pressure values is slightly overcompensated. The uncompensated
output for 205 kPa shows a temperature coefficient of -2.44
mV/K. The temperature coefficient of the compensated output for
the same applied pressure is reduced to a modest value of 74.9
pV/K or roughly more than an order of magnitude. The compen-
sated response as a function of pressure for the same sensor struc-
ture is shown in Fig. 6.
The plots provide the worst case error band for the extreme tem-
perature values of -40°C and 130°Cover the entirepressure range.
The solid curve in the middle shows the response at room temper-
ature. The sensor response at the intermediate temperature values
lies inside the error band. The compensation becomes less effective
for the pressure values higher than 240 kPa. It is noted that the
reduction in the effectiveness is more pronounced for the extreme
temperature values. For the temperature range of O"C-8O0C, the
worst case error band is reduced to less than half the value shown
in the figure. The maximum error voltages observed for -40°C
and 130°C are less than one-tenth of a volt with the full-scale out-
put of 1.69 V.
The compensated response of the sensor with 20% tracking er-
rors is shown in Fig. 7. The response is similar to that of the sensor
structure with no tracking errors. The maximum output in this case
is 2.0 V. The error voltage for the pressure values below 240 kPa
output
Voltage
(VI
35 100 165 230 295
Pressure (kPa)
Fig. 6. The compensated output for the sensor with no tracking errors.
output
Voltage
(VI
-400~_ _ _ _ _
130°C............
2
30°C
.5 -
1-
0.5 -
0 I I I I
35 100 165 230 295
Pressure (Ha)
Fig. 7. The compensated output for the sensor with +20% tracking errors.
6 -I Compensated ............
Uncompensated
5
Pressure
5 -
Pressure
Sensitivity
(mVWa)
4-
is less than 0.025 V. The error band expands above this pressure
to a maximum value of 0.1 V for 310 kPa at 130°C.
The pressure sensitivity for the compensated and the uncompen-
sated sensor with -20% tracking errors is shown in Fig. 8. Again,
the effectiveness of the technique is reduced for pressures above

5. I
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 42, NO. 3, JUNE 1993
240 kPa. The pressure sensitivity for the uncompensated sensor is
11.27 pV/kPa-K. It improves to 5.13 yV/kPa-K at 310 kPa and
becomes almost independent of the temperature at a pressure of 175
kPa with an insignificant value of 0.15 pV/kPa-K.
VII. DISCUSSION
The temperature compensation technique presented will effec-
tively eliminate large tracking errors of f20%. The technique also
covers a wide temperature and pressure range. The balancing of
these three parameters to minimize the compensation errors is a
very complicated task. If the required pressure. or temperature range
is lower, or the magnitude of the tracking errors is less, the error
band for the technique will be smaller, and its performance will be
better. The half-bridge technique provides very accurate results for
pressure values below 240 kPa over the entire temperature range.
The temperature outputs are fixed for a particular tracking error
pattern. The temperature output is divided by powers of 2 to obtain
corrections for various pressure ranges. The division by 2 (shift
right) is conveniently handled by the digital circuit. The response
for the lower pressure values is effectively trimmed by scaling the
temperature by factors of 4 and 8, but for higher pressure values
the divide-by-2 correction step provides a rather coarse trimming.
This expands the error band for the pressure values above 240 kPa.
The output for the higher pressure values can be refined and errors
reduced by using a scale factor between 0.5 and 1 (nonintegral
powers of 2). This will require a larger amount of compensation
and control circuitry and may defeat the advantageous structural
simplicity of this design.
The temperature bridge output and the partially compensated
pressure outputs may also be processed using software. In this case,
the function of the hardware shown in Fig. 4 is performed by the
software. This approach assumes the availability of an embedded
or an external processor. The register contents for the pressure and
the temperature are read and manipulated by the processor. The
temperature bridge response in this case may be scaled down to
any desired value and then addedkubtracted to the pressure output.
This approach produces precise compensation results, but it re-
quires a processor and its associated overhead to replace the simple
hardware of Fig. 4. Moreover, the software processing will be con-
siderably slower than the direct hardware implementation.
VIII. CONCLUSION
A new temperature compensation technique for piezoresistive
pressure sensors has been presented. The technique presented has
very convincing advantages. The compensation circuitry is struc-
turally simple and suitable for batch fabrication. It is implement-
able using common IC fabrication technologies. The technique does
not require post-manufacturing compensation of individual units
under sensor operating conditions, and no external components are
required. This is contrasted to current techniques reported in the
literature which require costly and time-consuming adjustment,
most often by laser trimming, of resistors in each individual unit.
Finally, the technique reported here is suitable for a very wide tem-
perature range, is very effective for pressure values below 240 kPa
and provides reasonable results for higher pressures. These fea-
tures make this technique very attractive for the mass production
of low-cost piezoresistive pressure sensors.
115
ACKNOWLEDGMENT
The authors sincerely thank Professor Kendall D. Wise of the
University of Michigan for providing the SENSIM simulation pro-
gram which was essential to this work.
REFERENCES
[l] G. Kowalski, “Miniature pressure sensors and their temperature
compensation,” Sensors and Actuators, vol. 11, no. 4, pp. 367-76,
May-June 1987.
[2] P. Kopsytynski and E. Obermeier, “An interchangeable silicon pres-
sure sensor with on-chip compensation circuitry,” Sensors & Acrua-
tors, vol. 18, no. 3-4, pp. 239-45, 1989.
[3] J. Bryzek, R. Mayer, and P. Barth, “New generation of disposable
blood pressure sensors with digital on-chip laser trimming,” in IEEE
Solid State Sensor and Actuator Workshop, Hilton Head Island, SC,
June 1988,pp. 121-122.
[4] T. Ishihara, K. Suzuki, and M. Hirata, “CMOS integrated silicon
pressure sensor,” in Proc. IEEE Custom Integrated Circuits Conf.,
May 1986,pp. 34-37.
[5] C. Gross and T. Worst, “Intelligent interface for electronic pressure
sensors,” in WESCON/87 Conf.Record, San Francisco, CA, Nov.
[6] K. Lee and K. D. Wise, “SENSIM: A simulation program for solid-
state pressure sensors,” IEEE Trans. Electron Devices, vol. ED-29,
pp. 34-41, Jan. 1982.
[7] M. Akbar and M. A. Shanblatt, “Piezoresistive pressure sensor
modelsfor temperaturecompensation,” in Proc. 2Ist Pittsburgh Conf.
on Modeling and Simulation, Pittsburgh, PA, May 1990, pp. 1721-
1726.
[SI M. Akbar, “Interface circuit for piezoresistive pressure sensors,”
Ph.D dissertation, Michigan State University, Dec. 1991.
[9] 0.N. Tufte and E. L. Steltzer, “Piezoresistive properties of Silicon
diffusedlayers,” J. Applied Phys., vol. 34, no. 2, pp. 313-18, Feb.
1963.
[lo] M. Akbar and M. A. Shanblatt, “Temperature compensation of pie-
zoresistive pressure sensors,” Sensors and Actuators, vol. 33, no. 3,
1987, pp. 1-6.
pp. 155-162, 1992.
A New Method for Low-Capacitance Probing
Alfonso Carlosena, Rafael Cabeza, and Luis Serrano
Abstract-In this paper a method is suggested to cancel theinput ca-
pacitance of instruments and probes used in measurements. This is
proposed as an alternative to conventional attenuating passive and ac-
tive probes. The idea is demonstrated with a practical device that is
able to nullify the parasitic capacitance to less than 2 pF without in-
troducing signal attenuation.
I. INTRODUCTION
It is well known that one of the main sources of error when deal-
ing with measurements using either scopes or network analyzers is
that of the limited frequency response of probes. The reactive na-
ture of the probe impedance together with the input impedance of
the instrument severely degrades the fidelity of the signal to be
Manuscript received May 20, 1992; revised October 27, 1992.
The authors are with the Dept. Automhtica, Electr6nica e Ingineria de
Sistemas, UniversidadPliblicade Navarra, Campusde Arrosadia, E-31006
Pamplona, Navarra, Spain. L. Serrano’s work was supported by the GOV-
ernment of Navarra under Grant Number OF 36011990.
IEEE Log Number 9207672.
0018-9456/93$03.00 01993IEEE