hardware//electronics//analog-to-digital converter

An analog-to-digital converter (ADC) turns a voltage into a number many times per second, and it is the boundary every measurement crosses on its way into a computer: before it the signal is a continuous physical quantity, after it a stream of integers that software can store and process. Two independent choices define it, how finely it divides the voltage and how often it looks.

An analog-to-digital converter (ADC) turns a voltage into a number many times per second, and it is the boundary every measurement crosses on its way into a computer: before it the signal is a continuous physical quantity, after it a stream of integers that software can store and process. Two independent choices define it, how finely it divides the voltage and how often it looks.

The first is the number of bits. With NNN bits there are 2N2^N2N levels, and the smallest step it can tell apart (the least significant bit) is the range divided among them. A 2-bit converter over 0 to 1 V has four levels, 00 to 11, each a quarter of a volt wide, so 0.63 V comes out as 10; a 10-bit one over the same volt has 1024 levels, each 1/1024≈0.981/1024 \approx 0.981/1024≈0.98 mV. The second is the sampling rate, how many of those numbers it takes per second, which must exceed twice the highest frequency in the signal:

fs>2Bf_s > 2Bfs​>2B

Below that rate fast components fold down and pose as slow ones (aliasing, the wheel of a filmed car that seems to turn backwards), so an analog filter removes everything above fs/2f_s/2fs​/2 before the converter.

Bits are resolution in voltage, hertz are resolution in time, and both stop paying once they resolve the noise.

A step finer than the noise of the amplifier in front only writes that noise with more digits.

A bathroom scale that wobbles is the picture of too many bits.

A reading that drifts by a few grams gains nothing from a display with seven decimals; the extra digits show the wobble, never the weight.

Faint signals are amplified first. A signal of microvolts would use a sliver of the converter's range, so an amplifier multiplies it, Vout=G VinV_{out} = G,V_{in}Vout​=GVin​, until it fills the range; the gain changes the size, never the shape or the information.

The bandwidth is set by the signal and the filter, the rate by the bandwidth and the budget. The physics of the source says which frequencies matter (a spike of a millisecond carries content to about 10 kHz), the filter enforces it, and the rate is then chosen above 2B2B2B and below what power, data and the link allow.

Data grow as channels times rate times bits. A 384-channel neural probe at 30 kHz and 10 bits produces about 115 Mbit/s, which is why converters are often placed next to the sensor, on the same CMOS chip, and only digital data travel down the cable.