DOI 10.5162/IMCS2012/P2.9.6
Analog Wheatstone Bridge−Based Automatic Interface for
Grounded and Floating Wide−Range Resistive Sensors
Andrea De Marcellis, Giuseppe Ferri, Paolo Mantenuto
University of L’Aquila, Department of Electrical and Information Engineering
Via G. Gronchi 18, 67100 L’Aquila, Italy
giuseppe.ferri@univaq.it
Abstract:
An analog interface, based on a modified Wheatstone bridge configuration, for the automatic
estimation of grounded and floating wide-range resistive sensors is here presented. The circuit
maintains the simplicity of the traditional bridge topology but, through a suitable feedback loop,
provides the continuous equilibrium condition employing a Voltage Controlled Resistor (VCR) that
avoids any initial calibration. This feature allows the circuit to operate for a much larger variation of
sensor resistances (with respect to the basic bridge) that can show a variable/unknown baseline,
related to both different physical-chemical parameters and fabrication processes. Preliminary
experimental measurements have shown the system capability to estimate about five decades of both
grounded and floating resistance variations with a more reduced relative error (<2% in the full range,
<0.65% in 1.6 decades) when compared to typical wide-range interfaces performing the Resistanceto-Time (R-T) conversion.
Key words: Analog Circuit, Bridge-Based Circuit, Fully-Analog Interface, Resistive Gas Sensor
Interfaces, Wide-Range Resistive Sensors
Introduction
The state of art on resistive sensor interfaces
shows that there are two main approaches
according to the resistance dependence on
measurand variation: resistance-to-voltage
(R-V) conversion (for low variations) and
resistance-to-time (R-T) conversion (for high
variations) [1]. Wheatstone bridge belongs to
the first class and is typically used only for small
variations of resistive sensors whose base-line
is well known or can be easily evaluated. The
bridge differential output voltage is zero at the
equilibrium condition: this mandatory initial
measurement of the resistance corresponds to
the bridge calibration. Moreover, it shows a low
sensitivity, also proportional to the supply
voltage; in this sense, the use of a differential
voltage amplifier based on Operational
Amplifier (OA) increases the sensitivity but also
the error in the resistance estimation, owing to
its non-ideal parameters (e.g., offset) [1]. In the
literature, there are different solutions
concerning bridge-based interfaces; some of
them consider automatic bridges, but are very
complex since employ digital blocks, analog
switches, MOS transistors etc. [2-5]. Recently,
in [6], the authors have proposed a new fullyanalog auto-nulling bridge-based interface for
wide-range resistive sensor estimation. This
solution has the aim to maintain a simple and
low-cost architecture, capable to estimate any
measurand variation without needing either
sensor
information
about
its
baseline
(uncalibrated solution) or complex techniques,
as scaling factors [7,8].
In this paper, further results (both in DC and in
time-domain) also on a suitable circuit
modification of this bridge, utilizing both
grounded and floating resistive sensors, will be
presented.
When compared with typical wide resistive
range applications (performing an R-T
conversion) [9-11], the proposed circuit
topology shows more reduced relative errors
and measurement times.
The proposed architectures
a)
“Grounded”
sensor
topology
bridge-based
The basic circuit, depicted in Fig. 1, is based on
a classic Wheatstone bridge scheme but
includes a suitable feedback that allows to
avoid any system calibration [6]. Thanks to the
reading of two voltages, it is possible to
estimate continuously the unknown resistance
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DOI 10.5162/IMCS2012/P2.9.6
and its time-variations. Its main novelty relies in
the use of a proper Voltage Controlled Resistor
(VCR), detailed in Fig. 2. At bridge output, an
OA-based
instrumentation
amplifier
is
employed to enhance any bridge unbalancing.
In order to create stability by a negative
feedback, an inverting voltage integrator is
utilized to properly regulate the RVCR value
compensating correctly any bridge unbalancing
through the feedback loop. Because of its input
electrical limits, a voltage divider (RD1 and RD2
in Fig.1 and Fig.3) has been added in the
feedback loop so to limit the control voltage
VCTRL value.
In the classic bridge approach, also referring to
Fig. 1 and Fig. 3, the equilibrium condition is
provided by choosing the resistive components
so that:
RARSENS = RBRVCR ;
(1)
in this case we have:
RSENS =
RB
10R
,
R A (10 − VCTRL )
Referring to Fig. 1, the complete expression for
the estimation of the sensor resistive values
(RSENS), as a function of the other three bridge
resistances (RA, RB and RVCR), the supply
voltage VCC and the bridge differential output
voltage ΔV=VA−VB, is given by the following
equation:
(2)
being
RVCR =
Figure 3. Block scheme of the proposed
uncalibrated Wheatstone bridge “floating" sensor
configuration.
R SENS
R
1 − (VCTRL / 10 )
.
(3)
ΔV R A + RVCR
⎛
⎜ 1 −
R R ⎜ VCC
RVCR
= VCR B ⋅ ⎜
ΔV R A + RVCR
RA
⎜⎜ 1 +
RA
⎝ VCC
⎞
⎟
⎟
⎟.
⎟⎟
⎠
(4)
Because of its electrical limits, RVCR can be
tuned only within about 1.6 decades (settable
changing its internal load R), but, utilizing eq.
(4), it is possible to extend the estimation on
RSENS range up to about five decades.
b) “Floating” sensor bridge-based topology
In this section a suitable modification of the
previous topology is proposed. This idea comes
from the fact that some resistive sensors cannot
be used as grounded elements. As depicted in
Fig. 3, the sensor has been placed in the upper
part of a bridge branch; the equilibrium
condition is provided now by:
Figure 1. Block scheme of the proposed
uncalibrated Wheatstone bridge “grounded" sensor
configuration.
RARB = RSENSRVCR
from which, considering eq. (3), we can write:
RSENS =
Figure
2: Scheme of the proposed VCR.
(5)
R A RB ⎛ VCTRL ⎞
⎜1 −
⎟.
R ⎝
10 ⎠
(6)
Comparing eq. (6) with eq. (2), it is evident that,
concerning the control voltage VCTRL, with
respect to the previous configuration, the
opposite trend is performed. The complete
expression for the estimation of the sensor
resistive values, as a function of the other three
bridge resistances, the supply voltage and the
bridge differential output voltage is given now
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DOI 10.5162/IMCS2012/P2.9.6
by the following eq.(7). The range estimation on
RSENS is extended to about five decades.
RSENS
ΔV R A + RVCR
⎛
⎜ 1 +
VCC
RA
R R
= A B ⋅ ⎜⎜
ΔV R A + RVCR
RVCR
⎜⎜ 1 −
RVCR
⎝ VCC
⎞
⎟
⎟.
⎟
⎟⎟
⎠
(7)
Experimental results
In order to develop a simple and efficient lowcost interface for wide-range resistive sensors,
the following devices (supplied at ±15V) have
been chosen: the analog four quadrant
multiplier AD633 as a VCR, the low input noise
OA LF411 for the inverting voltage integrator
and the differential instrumentation amplifier
INA121
at
bridge
output.
Preliminary
experimental measurements conducted on a
PCB, with high accuracy sample resistances,
have confirmed that the VCR is able to work for
about 1.6 decades as expected and its
operative range can be set by tuning its internal
load. Experimental results on VCR have shown
that the nearest to the electrical limit VCTRL is,
the less accurate the estimation value
becomes; for this reason, in the bridge, we
have calculated the VCR value by using the
voltage divider technique thanks to the voltage
VA reading, as follows:
RVCR = R A
VA
.
VCC − VA
a)
“Grounded”
topology
Figure 4. Differential output ΔV and voltage control
signal VCTRL as function of resistance variations
(“grounded” sensor configuration).
Figure 5. Experimental percentage relative error vs.
sample resistance (“grounded” sensor configuration).
(8)
sensor
bridge-based
Experimental results, obtained through high
accuracy sample resistors, are here reported. In
Fig.4 ΔV and VCTRL voltages, for resistive range
100Ω÷10MΩ, are shown. In order to minimize
the estimation error, we have utilized the
RA=3.3kΩ,
following
values:
VCC=10V,
RB=33kΩ, R=1kΩ, RINT=470kΩ, CINT=3.3nF,
RD1=10kΩ, RD2=20kΩ. In the auto-tuning range,
that is about (5.6÷170)kΩ, the control voltage
VCTRL assumes those values which force the
bridge differential output ΔV to be null. Out of
this range, VCTRL reaches the saturation level,
the VCR provides its minimum/maximum value
and is not possible to dynamically follow any
sensor anymore. This implies that until the
circuit is working in the automatic range, eq. (2)
can be utilized but, to have better estimation
results, is preferable to use always eq.s (4) and
(8). Theoretical expectations have been
confirmed, as shown in Fig.5 where the
percentage relative error estimation is reported.
The error is confined within (-0.8÷2)% for five
decades variations; in the automatic range, it is
within 0.2%.
Figure 6. Differential output ΔV and voltage control
signal VCTRL as function of resistance variations
(“floating” sensor configuration)
Figure 7. Experimental percentage relative error vs.
sample resistance (“floating” sensor configuration).
b) “Floating” sensor bridge-based topology
Maintaining
the
same
setting
values,
measurement tests have been made also on
the floating configuration. Experimental results
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DOI 10.5162/IMCS2012/P2.9.6
with high accurate sample resistors are shown
in Fig.6; as expected, in its automatic range,
(6.2÷194)kΩ, the interface is able to
compensate any sensor variation by applying
those VCTRL values which force the bridge
differential output ΔV to be null. Until the
interface is working within the automatic range,
the resistive sensor estimation is possible by
applying eq. (6). However, in order to have
better estimation results, eq. (7) has been used.
Fig.7 shows the percentage relative error trend,
which is confined within (-2÷0.5)% on five
resistive decades, while, inside the automatic
tuning range, it is lower than 0.2%.
Time variations experimental results
Further tests have been conducted on the
fabricated PCB where an equivalent sensor
behavior has been emulated by dynamically
switching high accurate resistances. Fig.8 and
Fig.9 show the control voltage VCTRL and the
bridge differential output ΔV trends, in
“grounded” and “floating” sensor configurations,
respectively (within the automatic operating
range). As expected, meanwhile the bridge
differential output voltage is forced to be null by
the suitable value of VCTRL, this last assumes
totally different values, according to theoretical
expectations. The calculated percentage
relative error is low and is in a good agreement
with the error profiles shown in Fig.5 and Fig.7.
Conclusions
In this paper, the classic Wheatstone bridge
configuration has been modified to be
employed for wide variations and unknown
sensor resistance measurements. Experimental
results have shown an accurate estimation (in
terms of low percentage error) of the unknown
resistive sensor, up to five decade variations.
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Figure 8. VCTRL and ΔV time response for sample
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Figure 9. VCTRL and ΔV time response for sample
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