An analog-to-digital converter (ADC) measures a voltage many times a second and reports each measurement as a binary number. A digital-to-analog converter (DAC) does the reverse, turning numbers back into a voltage. They are the doorway between the analog world of antennas, microphones and speakers and the digital world of processors and software.
Two choices: how often and how finely
The input is rounded down to the nearest step. The leftover, up to one step (1 LSB), is quantization error.
Quantization error202.75 mV
An ADC makes two independent decisions. How often to measure is the sample rate: too slow and fast signals are misread as slower ones (aliasing, covered in Sampling and the Nyquist limit). How finely to measure is the resolution in bits. An n-bit converter can only report one of 2ⁿ values, so every sample is rounded to one of those steps, and the rounding error is heard or seen as a low level of noise.
Bits set the number of levels (2 to the power of the bits). The filter removes the sampling steps, not the level error.
Levels2^3 = 8
Each extra bit halves the step and adds about 6 dB of ideal signal-to-noise ratio:
Bits
Levels
Step at 3.3 V reference
Ideal SNR
8
256
12.9 mV
49.9 dB
10
1,024
3.22 mV
62.0 dB
12
4,096
0.806 mV
74.0 dB
16
65,536
0.050 mV
98.1 dB
Real converters fall short of the ideal figure through their own noise and distortion, so datasheets quote an "effective" number of bits.
Converters in ham gear
Sound cards and codecs turn the receiver's audio into numbers for digital modes, and numbers back into audio tones to transmit, typically at 44.1 or 48 thousand samples per second.
SDR receivers put the ADC early in the signal path, in some designs right at the antenna end, so the radio becomes software:
After the ADC the signal is just numbers for software to process. Direct sampling skips the mixer and oscillator.
Microcontrollers use a small built-in ADC to read a battery voltage, a rotator's position potentiometer, or the forward and reflected voltages of an SWR meter. See Microcontrollers.
A DAC's output is a staircase, one step per sample. A low-pass filter after it (the reconstruction filter) smooths the stairs into a clean wave and removes the sampling products. Common designs are a resistor ladder (R-2R), where each bit switches a binary-weighted current, and a fast PWM (pulse-width modulated) output followed by a filter, where the average voltage follows the pulse width.