Resistance bridge for low-resistance sensor

Question

I have a fuel tank sensor that reports the remaining fuel with a resistance between 10 ohms (empty) and 180 ohms (full). I want to read this value using the Analog In of an Arduino (or ADS1115, not a big difference). The voltage range of the digital input is 0-5V. The obvious solution I came up with is the following:

^{simulate this circuit – Schematic created using CircuitLab}

Now this has two big problems: First, the measured range is only between 5V/190 * 180 = 4.7V and 5V/20 * 10 = 2.5V, which uses less than half of the resolution of the ADC. And second, when the tank is empty, the resistance chain has only 20 ohms, resulting in a 250mA leak current. If my math isn't completely rusted, using a larger value for R1 solves problem two, but worsens problem 1.

How do I read the value of the sensor, so that the range of the analog in has the best possible resolution, and avoid heating everything up?

Notes:

• It appears that the sensor must measure to ground, so one end must be at GND. If helpful, this could eventually be relieved.
• I do have a bunch of resistors, capacitors and even transistors available if that helps. I do not have any op-amps (and getting one would be difficult at this time).

Answer 1

Typically for this sort of thing you might want to pick a resistor value somewhere near the middle of the range, perhaps 100 ohms. That will limit the current to about 45mA and the dissipation in the 100 ohm resistor to about 200mW.

That will give you an ADC input from 9.1% of range to 64% or about 55% of the full scale range,which is probably more than good enough even with the on-chip Arduino ADC let alone the TI 16-bit outboard ADC, considering the crude nature of such sensors, with a 180 ohm resistor. The crudeness is masked by slow indicator response on the dashboard and a lack of fine divisions on the meter scale. Using a resistor near mid-range will also make the nonlinearity as a function of resistance less pronounced (the nonlinearity as a function of fuel tank contents may be another matter- depending as it does on the mechanical construction and shape of the fuel tank).

If you are insistent on using more ADC range you can buffer, filter and offset/add gain with an op-amp but I doubt it has much merit.

However there is an unstated issue here- unless there is a separate wire back from the sensor for ground (requiring a more complex differential measurement), the ground potential may vary significantly from ground at your circuit due to various return currents such as tail lights, rear wiper motor, turn signals etc. passing through the chassis. This is perhaps not so serious with crude measurements on a 12V circuit but at 5V is worse and it gets worse again for reduced sensor current.

Presumably you're rather more interested in the reading as the sensor resistance approaches 10\$\Omega\$, which is where the effect will be more significant.

Answer 2

Consider feeding the meter with a constant current source. This will give you a linear voltage relationship with the pot angle (but remember that the tank cross-section may not be uniform so this has to be taken into account).

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. A constant current source consisting of Q1, Q2, R1 and R2. (The meters are only to display the simulation results.)

How it works:

• R1 biases Q1 on and current starts to flow through R2, Q1 and R3 (the level sensor).
• When the voltage across R2 reaches about 700 mV Q2 starts to turn on and steals the bias from Q1. This prevents it turning on any further and so limits the current to 0.7/R2.

The simulation shows that with R2 = 47 Ω you'll get about 15 mA through the sender across the full range and that you'll get > 2.5 V for the ADC. You can play with the simulator above to vary R2 but give yourself some safety margin for reliable operation.

Answer 3

I do have a bunch of resistors, capacitors and even transistors available if that helps. I do not have any op-amps [...]

Your wish is my command :)

Not the swiftest op-amp in the world, and not particularly exciting, but does the job. Breadboarded, seems to work. The discrete implementation could benefit from either higher supply voltage or a cascode on Q3, Q7, Q8 to boost the DC gain. Input current is a couple or dozen nA. V2 is a LED + a top-side 100uA current source. Current consumption on the breadboard is below 4mA even when hot.

The sensor is driven with 1mA. Voltage gain is 18x, and internal compensation seems unnecessary at this gain. Output range is about 0.3V to 4.2V.

I didn't check anything else - that will depend somewhat on layout, transistor choices, etc. Generally, any jellybean transistors will work, but there's a benefit to higher gain and lower gain spread. Since there are many operating currents, for super precise DC operation it's necessary to match at least some transistors at their operating current. Q20/Q23 are at a slight disadvantage since their current depends on the beta of Q21/Q22 - matching them pairwise would be beneficial for offset voltage tempco. The cascode current source is not particularly match-sensitive by design. The cascode pair Q31 and Q32 would benefit from matching. The output stage is LM358 flipped upside down.

^{simulate this circuit – Schematic created using CircuitLab}