ADC resolution and effective number of bits

Question

As I understand it, if I have a 3-bit ADC with 2-bits effective resolution, and a full scale range of 7V, this means that instead of my LSB being 1V (7V / 2^3 - 1 = 1), my LSB is actually 2.33V (7V / 2^2 - 1 = 2.33).

Is that correct?

The ADC can still output any 3 bit value though can't it? So does this mean that if my input is 1V, instead of constantly getting an ADC output of 001 which I would expect for an ideal 3-bit ADC, I would instead get varying output that averages out over time to 2.3333V?

Answer 1

A 3 bit ADC means you have 3 physical bits, and can output up to 8 different codes. It doesn't say anything about how accurately those voltages represent any particular coding, or whether any will be missing.

Two effective bits means that when using some specified measurement method, the ADC behaves as well as a perfect ADC with 2 bits would.

Usually, the method is to drive a nearly full scale sinewave into the ADC, spectrum analyse the result, and calculate the SNR, the signal to noise ratio. The effective number of bits (ENOB) is the size of theoretically perfect ADC (could be fractional) that produces the same SNR. Or the sum could be done for SINAD, the signal to noise and distortion ratio, which would produce a slightly different answer.

As you can see, this definition produces essentially no useful information about what the average code would be for any specific DC input, or the 'size' of the LSB when measured with a DC input.

Answer 2

In a correctly dithered quantiser the system as a whole is LINEAR, there is no notion of the size of the LSB any more, just a clipping threshold and a noise floor, just like an analogue system.

With a DC input a correctly dithered quantiser will switch between output codes such that the mean value when taken over a sufficient number of samples converges to the input voltage. Correct dither in this context means adding 1 LSB of trangular probability distribution noise before quantising such that the probability of the sample exceeding the quantiser threshold is equal to the amount by which the signal value exceeds the next lower threshold.