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Reprinted from the Proceedings of the Measurement Science Conference Symposium and Workshop, January 1992
A Wheatstone Bridge for the Computer Age
Les Huntley
Metrology Manager
John Fluke Mfg. Co., Inc.
Everett, Washington 98206
ABSTRACT
Guildline's 9975 Current Comparator Resistance Bridge [3, 4] provides excellent accuracy for values smaller than 10
kilohm, but is a manual instrument which requires a skilled operator. (Another system for making automated
measurements of resistance in this range is presented at this conference [5].) Furthermore, while it excels in the
measurement of low-valued resistors, its performance degrades rapidly at values above about 100 kilohm. Instruments for
measuring high valued resistors automatically and with the desired accuracy were not available at the time this effort was
undertaken. This paper describes a modification of the familiar Wheatstone bridge circuit which has the desired qualities.
INTRODUCTION
Application of Process Metrology [1, 2] to the calibration control of the 5700A Multifunction Calibrator forced Fluke's
Standards Laboratory to find means for rapidly and automatically verifying all ranges, levels and functions of the
instrument. Since the calibrator contains internal resistance standards ranging in value from 1 ohm to 100 Megohm, and
the internal metrology of the 5700A makes it possible to measure these resistors with very good accuracy, it was essential
that the Standards Laboratory find means for making these same measurements with even greater accuracy.
The Wheatstone Bridge, the venerable workhorse of the resistance measuring laboratory, has seemed to be a candidate for
inevitable replacement by modern, computer controlled measuring systems. A recent revision of the traditional circuit, in
which two of the resistors are replaced by precision direct voltage calibrators, admirably adapts the Wheatstone bridge to
the computer age. Addition of a bus-controlled switch for connecting standards and unknowns makes this a completely
automated resistance measuring system, and provides means for comparing 4-terminal resistors. This paper describes the
implementation in the Fluke Primary Standards Laboratory and presents results for measurement of resistors in the range
100 ohms to 290 Megohms.
THEORY
The Wheatstone bridge circuit (Figure 1) has been widely used for many purposes. Its equations are simple:
il = V/ (R1 + R2)
i2 = V/ (R3 + Rx)
At null,
iIR2 = i2Rx
from which, substituting the currents,
Rx/R2 = R3/Rl
In a common configuration, R2 is an adjustable resistor which is adjusted to produce a null reading at the detector. Often
R1 and/or R3 can also be adjusted to vary the bridge ratio, R3/Rl, and thus the range of resistance which can be measured
with a given resistance range at R2.
While this arrangement is well suited and much used for manual measurements of two-terminal resistors, it requires
considerable modification (into a Kelvin bridge, for example) to be made compatible with four-terminal resistors. Equally
serious in the present application is the fact that computer switchable, infinitely (or nearly so) adjustable resistance
standards are not available. And, because of the inherent instability of resistors, if they were available, they would require
frequent, highly accurate calibrations to maintain their accuracy.
In the process of looking at other nulling circuits, notably the twin-tee and transformer ratio arm bridges, it was realized
that the Wheatstone circuit could operate very nicely with two resistors replaced by voltage sources. The basic idea is
presented in Figure 2. At detector null, the equations are:
i = (V1 + V2) /(R1 + R2)
V1 = iRl = (V1 + V2) R1/ (R1 + R2)
V2 = iR2 = (V1 + V2) R2/ (R1 + R2)
from which is obtained
Vl/V2 = R1/R2
If one (or both) voltage source is sufficiently adjustable, the null condition can be obtained with arbitrary R1 and R2. If it
(or they) and the detector are computer controllable, the nulling process can be automated. If means can be found for
automatically inserting standard and test resistors into the circuit for measurement, the whole measurement process can be
completely automated.
A measurement is accomplished by connecting the standard as R1 then adjusting V1 for a null on the detector. This
provides the first equation:
V1/V2 = RS/R2 [1]
The test resistor is then substituted for the standard and V 1 adjusted to restore null,
V1'/V2 = RX/R2 [2]
Dividing [2] by [1]
V1'/V1 = RX/RS
and the value of the test resistor is obtained as a ratio of voltages times the value of the standard resistor. If V1 is provided
by a highly linear variable voltage source, such as a modern calibrator utilizing a pulse-width-modulated DAC, the
accuracy can be quite acceptably high.
Figure 3 shows that leakages to ground cannot affect the measurements. Resistance from the source end of R1 to ground
shunts the source and has no effect other than increasing the current drawn from the source. Resistance from the detector
end of R1 to ground shunts the detector, and may decrease sensitivity but cannot affect the null condition. From the
symmetry of the circuit, it is apparent that the same conditions apply to R2.
It should be kept in mind that this circuit provides a three- terminal measurement of resistance whether or not it is in fact a
two-terminal or four-terminal device. This fact has implications for the measurement of high valued resistors for use in a
two-terminal configuration.
As drawn, the circuits apply only to two-terminal resistors. Figure 4 shows the modifications needed to accommodate
those with four-terminals. Also shown is the method for dealing with changes in connection resistance when resistors are
substituted into the measuring circuit. The connection between the two resistors is made between the "current" or "source"
terminals, and the voltage sources sense externally through leads attached to appropriate terminals on the resistors.
When the test resistor is substituted for the standard, there will be some change in connection resistance, as well as a
change in the resistance between the "source" and "sense" terminals of the resistors. This small change in resistance can
cause errors in measurement of resistors smaller than 10 to 100 kilohm, depending upon the accuracy desired and the
magnitude of resistance change. These changes can be compensated for by making two null measurements for each
resistor, one with the detector connected to point "a" and the other to point "b".
With the detector connected to point a,
Va/V2 = RS/ (R2+ Ra) [3]
where Ra is all the resistance between the sense-source connection points on the two resistors. With the detector connected
to point b,
Va'/V2 = (RS + Ra)/R2 [4]
Dividing equation [4] by [3],
Va'/Va = [(RS + Ra) /R2 ] [ (R2 + Ra) /RS ]
which can be reduced to
(Va'/Va