# How to approach the SNR needed for this electronic instrumentation

I have an issue with using concept of SNR in many instrumentation. To ask the question more clear, I want to go with a particular example.

Let's say a Wheatstone bridge type 500N nominal force transducer similar to this one signal is amplified with this special industrial amplifier(HBM-AE101). We can set the gain of the amplifier such that +/-10N force variation can be matched to +/-10V analog voltage output. +/-10V is the range of the 16-bit data acquisition board.

Now my problem is what SNR should be aimed. What determines the target SNR and what is adequate? Do we need the resolution information of the analog output and decide about the SNR needed?

I'm kind of lost what questions to be asked and how to start with this. Could you give an example how to approach such instrumentation based on the information I provided.

Let me ask this way, if I'm after a resolution of 100mV variation(coming from the transducer amplifier) what SNR is adequate?

• You are asking this question backwards. SNR is a specification. You choose the specification that you need, and then design to it. There is no way, given the information you provide, to determine what your needs are, because you don't say how the signal is being used, so this is unanswerable. May 3, 2019 at 13:35
• I mean should we start with down to what force we want to resolve. (?) May 3, 2019 at 13:39
• Absolutely. Such decisions are often best made before a sensor is selected, and before you set the gain of the amplifier. May 3, 2019 at 13:43
• The datasheets I provided dont give any analog voltage output resolution. The force transducer sensitivity is given but not resolution. So that blocks me to proceed. May 3, 2019 at 13:44
• Then you either do an experiment to figure things out, build something and hope it's "good enough", or buy a system that is specced the way you need it to be. May 3, 2019 at 13:50

You have a 20 volt full range signal going into a 16 bit resolution ADC. Therefore the minimum signal that can be resolved is 20/65536 volts = 305uV. Your system noise must be less than this to get the best theoretical performance from a single conversion.

• How about the resolution of the analog input from the force transducer? Wouldn't that limit or target SNR? I mean Im trying to figure what is the best force resolution we can obtain so to decide about SNR. May 3, 2019 at 13:41
• Let me ask this way, if Im after a resoltuion of 100mV variation(coming from the transducer amplifier) what SNR is adequate? May 3, 2019 at 13:53
• 100mV resolution gets you about 8 bits of ADC resolution over 20V at best. You need the noise to be lower than your resolution May 3, 2019 at 14:05
• Ok lets stick with that Im using only 16 bit +/-10V ADC. And lets say detecting down to 100mV pk-pk force variation is enough for my purpose.And if the rms value of the noise is less tha 100mV pk-pk is that adequate is there a rule of thumb about how smaller should the noise be from our desired amplitude(100mV in this case)? May 3, 2019 at 14:09
• @user1999 General rule is that the noise should be less than one bit of ADC resolution. Otherwise that least significant bit only measures noise. With your 16 bit ADC the least significant 8 bits or so are going to be noise May 3, 2019 at 16:09

Here is a Signal Chain model that produces 14.5 bits ENOB, or 89dB SNR in a 10Hertz bandwidth filter placed between the gain-of-1000 amplifier and the 16-bit ADC. Notice the quantization noise is 88 uVRMS (305uVPP), while the opamp/resistor/strain_gauge produce 13 uVRMS random noise..

Sensor produces 10milliVolts PP, with 200 ohms output resistance.

The chosen opamp is OPA211, gain of 130 dB and Rnoise of about 60 ohms.

The filter is 16,000 ohms and 1uF capacitor.

The lower-left plot shows the (a) frequency response and (b) amplification accuracy of the 1,000X gain stage. At 10Hertz, the accuracy is 0.03% (300 parts per million); you can see this by clicking "<" in the EF (Ending Frequency) controls.

The lower-right plot shows the end-to-end frequency response, with the 10Hz F3dB -3dB being very obvious; in other words, if you try to measure 10Hz changes in load on your straingauge, the measurements will be quite inaccurate, BUT THE NOISE WILL BE LOW and the code-spread will be low (unless you have lots of electric field, magnetic field, ground plane and VDD rail interference).

If you raise the bandwidth from 10Hz to 100Hz (use 16Kohm and 0.1uf in the filter), your random noise will increase by sqrt(10) to 280uVRMS but the total noise will increase by only 0.5dB.