Sensors such as strain gages, RTDs (resistance temperature detectors), and thermistors produce a resistance that’s proportional to force or temperature. If you measure a sensor’s resistance, you can calculate the physical parameter. Circuits such as resistance bridges can help you measure the unknown resistance.
Figure 1 shows a typical bridge circuit where R_{T }is the unknown resistance. By substituting a programmable amplifier for R_{EQ}, you can balance the bridge. Resistance R_{EQ} can force V_{BRIDGE} to 0 V, from which you can calculate R_{T} and convert its value to units of force or temperature.
Figure 1.  By measuring V_{BRIDGE} and adjusting R_{EQ}, you can balance a bridge circuit and calculate R_{T}. 
The circuit in Figure 2a is a programmable amplifier whose output voltage is proportional to the digital input code of the DAC (digitaltoanalog converter). The DAC and amplifier A1 form a programmable inverting amplifier. The circuit actually functions as a divider because its gain, or transfer function, is less than 1. The difference between voltages V_{IN} and V_{OUT} forces a current through resistor R. You can use that value to calculate R_{EQ} in the bridge circuit. Figure 2b shows the equivalent circuit for the programmable amplifier.
Figure 2.  a) Programming the DAC’s output voltage changes R_{EQ}, which can balance a bridge circuit. b) Equivalent circuit. 
Using a microcontroller or a PC, you can adjust R_{EQ} by programming the DAC’s output voltage and then measuring the voltage across the bridge and adjusting R_{EQ} until the bridge comes into balance. Because A1 is an inverting amplifier, the circuit’s gain is
where the D terms represent the values of the DAC’s bits. If you use a 12bit DAC, then N = 12.
To calculate R_{EQ}, you need to know the current in the circuit. If you assume that buffer amplifier A2 has infinite input impedance and zero bias current, then you can calculate I_{IN}, which is
and
To test this circuit, simply connect a variable DC voltage source to V_{IN} and measure the effective resistance with an ohmmeter. Table 1 shows the expected and actual resistance and the calculated error for the circuit with a 12bit DAC.
Table 1.  Output resistance vs. input code (R = 10 k, N = 12)  

Figure 3 contains the schematic of a circuit that uses a comparator across the bridge. You can connect the comparator’s digital output to a microcontroller or PC that then can adjust the DAC’s output voltage. You can calculate R_{EQ} and then calculate R_{T}, from which you can calculate strain or temperature based in the resistance curve of your sensor.
Figure 3.  This schematic of a circuit uses a comparator across the bridge. 
Using the circuit in Figure 1, you can generate digitally controlled resistor values with just one precision component, resistor R. If you need to increase the gain of the circuit, you can replace voltagefollower A2 with a noninverting amplifier configuration.