Edited on 15th,Aug

If I want to measure a very small signal with 16 bit ADCs，say 10kHz sine waves with amplitude ranging from 0 to 1uV, I have to amplify the small signal first. The signal should be amplified with peak-to-peak value equal to the range of ADC. Then the signal will be shifted up by half of the ADC range by an ADC driver(with level shifter).

My questions is: What are the trade offs between amplifier gain selection and adc range?

Should I use a 2.5V range ADC(16 bit) with 1,250,000 gain amplifier, so the peak-to-peak value of the largest sine wave(1uV) will be amplified to 2.5V?

Or should I use a 5V range ADC(16 bit) with 2,500,000 gain amplifier, so the peak-to-peak value of the largest sine wave(1uV) will be amplified to 5V?

What aspects should be concerned in the decision?

## How to choose ADC number of bits?

Also a question, how should I decide the number of bits to use? The noises are fairly large, but I am going to use signal processing techniques, which can reduce noises greatly. It means that more bits should still be useful. (Thanks to gbulmer, you made me realize that I did not really think about this question..)

• To help me understand, are you assuming the 5V ADC will have 1 more bit of resolution than the 2.5V ADC, or are you assuming both ADCs have same numbers of bits of resolution? Or is ADC resolution an aspect of your question too? Roughly, what sort of frequency is the sinewave? Are 250,000 and 500,000 typos, did you mean 2,500,000 and 5,000,000? Commented Aug 14, 2014 at 16:14
• Thanks for your reply @gbulmer, I have updated the post with more details. Commented Aug 15, 2014 at 1:05

You'll be lucky to find a 16 bit ADC where you can have a lower Vref (input range) and get better performance compared to sticking with a higher input range and choosing a better input amplifier.

For instance, the AD7687 has a specified signal-to-noise ratio of typically 95.5dB with a reference voltage of 5V - if the 5V reference is lowered to 2.5V, the typical SNR drops to 92.5dB i.e. it gets 3dB worse.

The AD7685 has a similar story, so does the AD7988-5 et cetera....

My advice is find the best ADC you can afford and operate it with Vref set to the best possible value to maximize performance (usually the highest value permissible) - then design your front-end amplifier to deliver the best performance (usually by trading-off current consumption to reduce noise.

Sampling rate - this affects perceived quantization noise, for instance, if you sample at say 30 kHz, all the relevant q-noise will be contained in that bandwidth and so if you sample at 100 kHz, the noise is spread over a wider bandwidth meaning you can use process gain to reduce the noise in your digitized 10 kHz signal - average several samples and decimate in software. Process gain is the same if you converted to analogue and used filters after the DAC - the faster the sampling rate the more noise you can remove by filtering.

I think... the more you amplify a signal, the greater the distortion and extraneous noise you're likely to introduce. I'd use the lowest-range ADC I could reasonably muster, so I could use the lowest-gain amplifier to match it.

Less introduced noise means less noise to dispose of later.

Use the highest-resolution ADC as you are prepared to handle the bits for - if you're only prepared to deal with 12 bits, only use a 12-bit ADC. Nothing is gained by throwing away bits. Some higher-resolution ADCs, too, require more sampling time than their equivalent lower-bit-count cousins, so if you're crunched for sampling time (need to sample often), a lower-resolution ADC may actually serve you better even if you lose the least-significant bits.

• Lower range of ADC also implies higher THD, as implies at page 14 for datasheet: analog.com/static/imported-files/data_sheets/AD7682_7689.pdf Is my understanding correct? Commented Aug 15, 2014 at 2:57
• I see a strong correlation between frequency and THD on page 14... but not between range and THD. The lower the frequency, the lower the THD. I don't think I'm aware of any correlation between range and THD. Commented Aug 15, 2014 at 3:45
• the red and orange curves are at vdd=2.5v, meaning operating at 2.5v range.. It has worse thd... Commented Aug 15, 2014 at 16:04