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I don't understand this paragraph about flash ADC.

A flash converter can produce a non-linear output which is an additional advantage. The voltage divider network consists of equal-value resistors which provide a proportional response. But for special applications, the value of the resistors can be changed which will give a non linear response.

How type is non-linear output? What is the meaning of first sentence? What kind of relationship is value of the resistor's change and nonlinear response? Please, give the example.

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Flash ADCs normally use a set of comparators, one per LSB, that use equally-spaced reference voltages developed from a string of equal-value resistors. What the author is saying is that the spacing of the reference voltages can be modified to implement a non-linear input-to-digital mapping.

A good example of a possible use of non-linear spacing is for a camera ADC, that implements gamma correction (tone mapping) at the ADC itself. There are many papers about this idea. It seemed popular about 5 years ago, but never really caught on. Probably because making unequally-spaced resistances with precision and repeatability in silicon posed some difficulty.

At any rate, instead of analog non-linear sampling, what's done for sensors now is to use higher resolution linear ADCs, and re-map their levels in the digital domain using a technique called piecewise linear mapping, or PWL. The overall result is the same however: tones are mapped more usefully to match human visual response, that makes maximum use of the numerical range available.

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A flash ADC consists of a string of resistors to create the voltage levels the analog comparators use to compare the input voltage against. The typical ADC would have equaly spaced values to get a linear response from the ADC.
But sometimes you want a very high dynamic range, meaning you want to be able to see very small signals as well as very large signals. In many cases you don't really need a very high resolution for your large input signals, but you still need a high resolution to see the small signals with your large input range. And this is where non-linear ADCs come to stage. The voltage divider string uses small values at the bottom, to get small voltage steps for small inputs. And the higher you go, the larger the resistors become. This makes the voltage step a little bit larger with every step and gives you a logarithmic response from the ADC.

Overall, this technique gives you the resolution you need to see small signals, but still let's you see large signals as well (but with lower absolute resolution. The relative resolution typically will stay the same over the complete input range).

Your eyes for example are doing the same thing: They have a logarithmic response. You can see in very low light and still make out details. But you can also see in extremely bright environments, but the "resolution" for different brightness levels is reduced in the brighter environment.

enter image description here
Source: https://en.wikipedia.org/wiki/File:Flash_ADC.png

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A flash converter can produce a non-linear output which is an additional advantage. The voltage divider network consists of equal-value resistors which provide a proportional response. But for special applications, the value of the resistors can be changed which will give a non linear response.

Would have phrased that differently:

Usually, we want ADCs to be very linear, i.e. the digital output is a linear function of the analog input (e.g. voltage).
In fact, in many ADC architectures, it's hard to do anything else! That's what's special about the flash converter: a simple modification of the resistor values in the resistors involved allows us to set the quantization steps for individual input ranges arbitrarily.

That makes it easy to build ADCs for applications where you don't need to digitize the whole analog range in a nice, fixed raster, but where e.g. a logarithmic resolution is better for the application, for example in power detection.

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