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I have an Atmel SAM4S MCU with a 12-bit internal ADC. I would like to achieve 16-bit resolution at a sample rate of 500 Hz. The input to the ADC is fairly low-frequency (about 20 Hz max frequency content), and low noise (less than one 12-bit lsb RMS).

How can I achieve 16-bit resolution with this processor's ADC?

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You can increase the effective resolution by intentionally oversampling the input signal. Here is brief summary of the idea from an application note on the topic provided by Atmel:

The theory behind ‘Oversampling and decimation’ is rather complex, but using the method is fairly easy. The technique requires a higher amount of samples. These extra samples can be achieved by oversampling the signal. For each additional bit of resolution, n, the signal must be oversampled four times. Which frequency to sample the input signal with, is given by Equation 3-1. To get the best possible representation of a analog input signal, it is necessary to oversample the signal this much, because a larger amount of samples will give a better representation of the input signal, when averaged.

The full application note can be obtained here: http://www.atmel.com/images/doc8003.pdf.

In your specific case, you would need to sample at about 8KHz to get the equivalent of 16 bits of resolution out of your 12-bit ADC.

Here's how I arrived at this number:

f_oversample_rate = f_current_sample_rate * (4 * (desired_bits - current_bits))
f_oversample_rate = 500Hz * (4 * (16 - 12))
f_oversample_rate = 500Hz * (4 * 4)
f_oversample_rate = 500Hz * 16
f_oversample_rate = 8KHz
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  • $\begingroup$ Does this require some noise to work? We've been given a max value for the noise, which would be enough, but no minimum. $\endgroup$
    – Simon Jenkins
    Commented Jul 31, 2015 at 19:45
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    $\begingroup$ @SimonJenkins Yes it does. Section 3.2 of the application notes cover noise, and it specifies that the noise level should be a minimum of 1 LSB, but just over 0.5LSB is the hard minimum because that will be enough to toggle the LSB. If your system doesn't meet that spec, you can add artificial noise with dithering. $\endgroup$
    – skrrgwasme
    Commented Jul 31, 2015 at 20:04

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