Why is quantization error unavoidable?

A finite number of codes cannot represent every continuous voltage exactly. Any input within a bin maps to one code, so the reconstructed value differs from the true signal by up to about ±½ LSB in a uniform mid-rise quantizer, plus systematic nonlinearity in real hardware.

What is the Nyquist limit?

When uniformly sampling a baseband signal, the sample rate must exceed twice the highest frequency component you need to preserve, otherwise spectra overlap and aliases appear in-band. Practical systems sample higher than this minimum to allow analog anti-alias filtering.

Does a DAC output a smooth sine wave directly?

A zero-order-hold DAC emits a piecewise-constant waveform; images appear at multiples of the sample rate. A reconstruction filter smooths those steps. The simulator may emphasize the discrete levels before filtering.

Are ENOB and bit width the same?

No. Effective number of bits (ENOB) folds in noise and distortion. A 16-bit converter might behave like 13 ENOB at a given frequency because of jitter and nonlinearity.

ADC / DAC (sampling & quantization)

Analog-to-digital (ADC) and digital-to-analog (DAC) converters bridge continuous physical signals and discrete binary words. An ADC maps a voltage interval to a finite set of codes, introducing quantization error on the order of one least significant bit (LSB) for a uniform quantizer; a DAC reconstructs a staircase or filtered waveform from those codes. Key figures of merit include resolution (number of bits n), full-scale range, sampling rate for ADCs, and settling time for DACs. This educational simulator stresses the *structure* of the conversion—reference levels, code bins, reconstruction levels, and aliasing intuition when sampling is involved—without replacing a full mixed-signal electronics course. Idealizations omit comparator metastability, aperture jitter, differential nonlinearity, and thermal noise so the discrete mathematics remains clear. Students see why more bits shrink quantization noise, why exceeding the Nyquist limit folds high-frequency content, and why real systems add anti-alias filters and dither.

Who it's for: Introductory signals-and-systems or electronics labs where students meet sampling, quantization, and reconstruction before diving into datasheet-level ADC/DAC design.

Key terms

ADC
DAC
Quantization
Sampling
Nyquist frequency
Resolution (bits)
Full-scale range
Aliasing

How it works

Ideal sampling, then uniform quantization with 2^N levels (N = bit depth on the slider). ZOH reconstruction holds each sample until the next. When f_signal exceeds f_s/2, the spectrum folds (aliasing) — try the demo toggle.

Frequently asked questions

Why is quantization error unavoidable?: A finite number of codes cannot represent every continuous voltage exactly. Any input within a bin maps to one code, so the reconstructed value differs from the true signal by up to about ±½ LSB in a uniform mid-rise quantizer, plus systematic nonlinearity in real hardware.
What is the Nyquist limit?: When uniformly sampling a baseband signal, the sample rate must exceed twice the highest frequency component you need to preserve, otherwise spectra overlap and aliases appear in-band. Practical systems sample higher than this minimum to allow analog anti-alias filtering.
Does a DAC output a smooth sine wave directly?: A zero-order-hold DAC emits a piecewise-constant waveform; images appear at multiples of the sample rate. A reconstruction filter smooths those steps. The simulator may emphasize the discrete levels before filtering.
Are ENOB and bit width the same?: No. Effective number of bits (ENOB) folds in noise and distortion. A 16-bit converter might behave like 13 ENOB at a given frequency because of jitter and nonlinearity.