The figure illustrates a dc-excited Anderson-loop circuit that includes (1) thermocouples for measuring the temperature of the strain gauge and (2) a signal-conditioning circuit that separates the temperature and strain-gauge signals in the sense that one output voltage is proportional to the change in the strain-gauge resistance and another voltage is proportional to the thermoelectric voltage indicative of the temperature of the strain gauge.

The concept of the Anderson loop was discussed previously in three articles in *NASA Tech Briefs*; namely, "Constant-Current Loops for Resistance-Change Measurements" (ARC-11988), which appears elsewhere in this issue; "The Anderson Current Loop" (DRC-00001), Vol. 18, No. 12, (December 1994), page 30; and "Patent Statement on the Anderson Current Loop" (ARC-13376), Vol. 20, No. 11 (November 1996), p. 12a. To recapitulate: In the basic Anderson current loop, voltage drops in lead wires are excluded from measurement by use of the well-known Kelvin technique, in which a known current is supplied via two lead wires to a resistance to be determined, the voltage across this resistance is coupled to a high-input-resistance voltmeter via two other lead wires, and the voltage drops in these voltage-measurement lead wires can be neglected because they carry negligible current by virtue of the high input resistance of the voltmeter.

Here, a known constant current *I* is supplied to a strain gauge of resistance* R* + *ΔR*, (where *R* is an initial value and *ΔR *is a change caused by the combined effects of strain and temperature). The strain-gauge resistance is connected in series with two thermocouple wires of resistance *R*_{w1} and *R*_{w2}, respectively. These wires are both made of the same one of two thermocouple alloys and are of the same length, so that *R*_{w1} = *R*_{w2}. Two other wires (*R*_{w3 }and *R*_{w4}) made of the other thermocouple alloy, are connected to the terminals for measuring the voltage drop in the strain-gauge resistance. A reference resistor (*R*_{ref} = *R*) at a reference or ambient temperature is also connected in series with the strain-gauge resistance.

The thermoelectric voltage of thermocouple (*R*_{w1}, *R*_{w3}) is given by

*v*_{TC1} = *v*_{11} - *v*_{12};

the thermoelectric voltage of thermocouple (*R*_{w2}, *R*_{w4}) is given by

*v*_{TC2} = *v*_{21} - *v*_{22}.

The thermoelectric-output-voltage level of each thermocouple represents the temperature of its connection to the strain gauge.

Straightforward algebraic manipulation of the equations that relate the terminal voltages *v*_{1} through *v*_{4} with the voltage drops in the various resistances and with the thermoelectric voltages yields the following equations for the desired output voltages:

*v*_{TC} = (*v*_{1} - *v*_{3})/2

and

*I**ΔR*= (*v*_{2} - *v*_{4}).

As indicated in the figure, the terminal voltages *v*_{1} through *v*_{4} are coupled to Anderson subtractors comprised of buffered differential level shifting amplifiers wired to implement these equations. The subtractor outputs are then the out put thermoelectric voltage *v*_{TC }and resistance-change voltage *I**ΔR*.

*This work was done by Karl F. Anderson of Analytical Services and Materials for *Dryden Flight Research Center. *DRC-96-10*