# Circuit design for high resistance sensor measurement

#### sagi4422

Joined Aug 29, 2009
34
Hi All,

I am a newbie in the field of electronics but have enthusiasm to learn and build.

I have a project I am involve in which needs from us to build a high-resistance sensor measurement system.

The sensor, because of the in-stability of fabrication, can have a baseline resistance between 10MOhm to 70MOhm.

The quest here is to measure the above resistance values and even expend it to 1MOhm to 70MOhm with at least 5% of accuracy

The sensor frequency is very slow, <40Hz and it is operated on a battery of ~3/5V.

My request is to build a circuit that will measure the sensor's resistance and will have a range of measurement as described above.

I did some research in the Analog search engine and I didn't find the specific terms I am looking for but this is what I came so far:

Building a wheatstone bridge with 3 legs with 100MOhm. The 4th leg is the sensor. This gives me an output voltage range of 0.3V to 1.6V (if powered by 3.3V). Both output leads goes to a differential in-Amp with high input impedance (20G). Vout due to its low current, goes to a unity-gain op-amp and than to an 12BIT ADC.

I was wondering whether I am in the right direction.

Any feedback is welcomed.

Sagi

#### #12

Joined Nov 30, 2010
18,210
Here is an idea: Apply 3.3 volts to the sensor. The current will be from 47.143 nanoamps to 3300 nanoamps. Deliver that current to the input of an inverting amplifier with a feedback resistor which scales the output voltage to a range that is convenient.

The output voltage will be logically backwards, but you asked about the first stage.

#### Alec_t

Joined Sep 17, 2013
11,739
Last edited:
• DickCappels

#### sagi4422

Joined Aug 29, 2009
34
I cannot apply more than 5V without destroying its capabilities

#### Alec_t

Joined Sep 17, 2013
11,739

#### sagi4422

Joined Aug 29, 2009
34
Why is it better to measure the oscillation ?

#### #12

Joined Nov 30, 2010
18,210
Why is it better to measure the oscillation ?
Nobody said which is better for your purposes. That is for you to judge. We are just offering different methods, and we two probably won't be the last to try.

#### sagi4422

Joined Aug 29, 2009
34
Thanks.
I have to say I am not familiar with Oscillation measurement so I prefer to stick with Voltage/Current measurement.

Thanks,
Sagi

#### MikeML

Joined Oct 2, 2009
5,444
What do you have available in the way of measurement tools?

DMM?
Oscilloscope?
Frequency Counter?
Arduino?

• GopherT

#### crutschow

Joined Mar 14, 2008
25,651
Another option:
Use a 16-bit converter instead of a 12-bit.
Add a high resistance (perhaps about 50MΩ) in series with the sensor and apply power to the resistor from the A/D reference voltage.
That way any power supply voltage variation will have no effect on the reading.
Measure the voltage at the junction with the converter.
16-bits should give more than a 12-bit resolution over the resistance range of the sensor.

#### sagi4422

Joined Aug 29, 2009
34
I do have DMM, arduino and Osc
What do you have available in the way of measurement tools?

DMM?
Oscilloscope?
Frequency Counter?
Arduino?
Dmm

#### sagi4422

Joined Aug 29, 2009
34
In case of Arduino, it has 10bit ADC (Uno has 12BIT) so I do need to introduce the Arduiono a new 16bit ADC

#### Alec_t

Joined Sep 17, 2013
11,739
Be aware that any ADC will require a low impedance signal source, so an appropriate buffering op-amp will be needed for the sensor signal.

#### #12

Joined Nov 30, 2010
18,210
The quest here is to measure the above resistance values and even expend it to 1MOhm to 70MOhm with at least 5% of accuracy
I'm not all that good with bits and bytes, but has any body thought, "Five percent is about 1 part in 20 for accuracy (5 bits will describe that). Why do we need 12 bit precision (4096 counts) in the ADC?"

#### sagi4422

Joined Aug 29, 2009
34
Be aware that any ADC will require a low impedance signal source, so an appropriate buffering op-amp will be needed for the sensor signal.

Where do I find this information in the ADC's datasheet - what is the minimum signal source impedance?
Any sophisticated buffer op-amp should I need or I can use standard voltage follower design ?

#### crutschow

Joined Mar 14, 2008
25,651
I'm not all that good with bits and bytes, but has any body thought, "Five percent is about 1 part in 20 for accuracy (5 bits will describe that). Why do we need 12 bit precision (4096 counts) in the ADC?"
Sometimes signal resolution is more important than absolute accuracy.

• #12

#### #12

Joined Nov 30, 2010
18,210
Where do I find this information in the ADC's datasheet - what is the maximum signal source impedance?
Name the part.
or post the datasheet.

#### #12

Joined Nov 30, 2010
18,210
Sometimes signal resolution is more important than absolute accuracy.
Oh. Finding small changes in the signal. OK.
Thanks.

#### #12

Joined Nov 30, 2010
18,210
Any sophisticated buffer op-amp should I need or I can use standard voltage follower design ?
You have to choose a method first. If you start with an inverting stage as in my first post, input impedance will be very important. Second consideration is input noise levels, but they also depend on the gain of the stage. Almost any op-amp configuration can be considered to be a buffer compared to a million ohms. #### MikeML

Joined Oct 2, 2009
5,444
Expanding a bit on Alec's (post #3) suggestion:

I show what could be done using a measurement of the period of an ideal oscillator. Unfortunately, Alec's circuit would have to be calibrated, but the one I develop is self-calibrating. This method relies on using an Arduino or a frequency-counter to measure the period or frequency of a pulse train. Time measurement is usually much more precise than measuring analog voltages/currents..

This approach relies on the RC time-constant created between R1, the unknown multi-MegΩ resistor, and a precision, low-leakage 1nF (1000pF) capacitor C1. The precision of this measurement scheme depends primarily on the known accuracy of C1. Checking with DigiKey, you can buy several types of capacitors (dipped mica, polypropoline film, ceramic) that are +-1% of marked value that also have very low leakage. The goal is make an oscillator where other factors do not degrade the +-1% accuracy determined from the capacitor accuracy.

Here is a idealized oscillator whose period is controlled by R1*C1. It is the classic multi-vibrator which switches on as the voltage across the timing capacitor V(rc) decreases below Vdd/3 = 1.667V and switches off as V(rc) increases above 2*Vdd/3 = 3.333V. I model the hysteretic switch using LTSpice's voltage-controlled switch, which draws no current to sense the voltage, and has trip points explicitly defined at 1.667V and 3.333V. It's off resistance is essentially , and it's on resistance is set to 1mΩ.

The oscillation is caused by C1 alternatively charging through R1 (in series with R2) when the switch is off, and then discharging through R1 (to ground) when the switch is on. Note that R2 is such a tiny fraction of R1 that the error caused is tiny compared to the 1% uncertainty in C1.

I plot V(rc) at four different values of R1, R1=80megΩ (green), 40megΩ (dark blue) , 20megΩ (red) and 10megΩ (lt. blue). Note that the period of oscillation is proportional to R1, so that it halves each time as R1 steps from 80megΩ to 10megΩ. Note that the period is 110.89ms @ 80megΩ. Using Period = k*R1*C1, and solving for k, I get k=Period/(R1*C1) = 0.11098/(80e6*e-9) = 0.11098/0.08 = 1.387. Transposing and substituting, I get R1= Period/(k*C1) = Period/(1.387*e-9) = 0.721e9*Period = (721*Period) megΩ. Note that this expression can be derived from the classic exponential RC charging/discharging equation.

To implement this measurement scheme using real-world parts, we must consider other accuracy-degrading factors besides the accuracy of C1. For example, the circuit that senses the voltage V(rc) must have have an input bias (leakage) current less than 1% of the current that flows in R1. With R1 = 100meg, the minimum current in R1 is 16nA, so the input bias current of whatever is used to sense V(rc) should be less than 150pA. Think about an opamp voltage follower...

I have a design in mind that would do this with only two critical parts, namely an accurate capacitor C1, and a low-input bias current opamp. I will present it only if Sagi wants to pursue this approach.

He would have to learn how to use the Arduino to measure periods in the 10s to 100s of ms, or use a laboratory frequency counter (in period measurement mode). Last edited:
• Alec_t