The half-bridge configuration is handy when using nonlinear sensors, such as thermistors, since it can partially compensate for the sensor's nonlinearity. However, multiplexing a single resistor to multiple sensors generally requires the use of mechanical relays because the switch resistance will appear in series with the system's sensor.
The circuit shown, which uses solid-state multiplexers, eradicates the effects of multiplexer on-resistance. Multiplexers MPX1 and MPX2 are configured as a double-pole switch. Op-amp U3 buffers the sensor voltage, VT, largely eliminating the effect of the resistance of MPX2. U4 then subtracts VT from the reference voltage, VREF. U1 samples the voltage across the source resistor, RS , while the high dc gain of U2 forces this voltage to be equal to (VREF VT ). The resulting current through the sensor, RT, is exactly the same as in the equivalent circuit and is independent of the resistance of MPX1. The 10k resistors and 100-pF capacitors are included to stabilize the feedback loop.
In order to minimize error, the multiplexer resistance should generally be less than about half the value of RS. There are two limiting factors: the common-mode range of U1 and the output-voltage capability of U2. If the multiplexer resistance is too high compared to RS, the finite common-mode rejection of U1 may degrade the measurement accuracy.
Because a trade-off exists between on-resistance and leakage current, the lowest resistance multiplexer doesn't necessarily provide the smallest error. With the devices and values shown, 16-bit accuracy with less than 15 µs settling time can be achieved. But care must be taken to minimize the stray capacitance appearing across the sensors.
Three of the multiplexer inputs provide a ground reference, a reference resistor measurement, and an open-circuit reference. Measurement accuracy is basically independent of the accuracy and stability of RS, VREF, and the amplifier offset voltages.