What must be checked before using the Quantization step relation?

Check Nyquist, the VFS range and the bit count.

17. A/D–D/A conversion and sampling

Quantization step

Formula

\Delta=\frac{V_{\mathrm{FS}}}{2^n}

Detail

The quantization step Δ=VFS/2^n is the height of each digital stair.

Explore the idea

Variables

$f_s,f_{\max},f_N$ Hz
$n$ bits
$V_{\mathrm{FS}}$ V
$\Delta$ V
$\delta$ dimensionless
$t_{\mathrm{on}},T$ s.

Conditions

Ideal converter, band-limited in-range signal.

Intuitive explanation

For “Quantization step”: fs > 2 fmax avoids aliasing; n bits split VFS into 2^n levels and PWM uses duty cycle.

Worked example

With

V_{\mathrm{FS}}=5.12\,\mathrm V

and

n=10

\Delta=5.12/1024=5\,\mathrm{mV}

Common mistakes

taking fs = fmax as Nyquist
forgetting ±Δ/2 error
mixing LSB with the number of levels

Frequently asked questions

What must be checked before using the Quantization step relation?: Check Nyquist, the VFS range and the bit count.

Also known as

Nyquist, quantization, PWM, R-2R DAC, flash ADC

Conventions

Hz, V or dimensionless

Last reviewed: 2026-09-19

Found an error? Contact us.

Related formulas

17. A/D–D/A conversion and sampling

Quantization step

In 17. A/D–D/A conversion and sampling

Formula

\Delta=\frac{V_{\mathrm{FS}}}{2^n}

Detail

The quantization step Δ=VFS/2^n is the height of each digital stair.

Explore the idea

Variables

$f_s,f_{\max},f_N$ Hz
$n$ bits
$V_{\mathrm{FS}}$ V
$\Delta$ V
$\delta$ dimensionless
$t_{\mathrm{on}},T$ s.

Conditions

Ideal converter, band-limited in-range signal.

Intuitive explanation

For “Quantization step”: fs > 2 fmax avoids aliasing; n bits split VFS into 2^n levels and PWM uses duty cycle.

Worked example

With

V_{\mathrm{FS}}=5.12\,\mathrm V

and

n=10

\Delta=5.12/1024=5\,\mathrm{mV}

Common mistakes

taking fs = fmax as Nyquist
forgetting ±Δ/2 error
mixing LSB with the number of levels

Frequently asked questions

What must be checked before using the Quantization step relation?: Check Nyquist, the VFS range and the bit count.

Also known as

Nyquist, quantization, PWM, R-2R DAC, flash ADC

Conventions

Hz, V or dimensionless

Last reviewed: 2026-09-19

Found an error? Contact us.

Quantization step

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Conventions

Related formulas

Quantization step

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Conventions

Related formulas