Nyquist criterion

Tags

• conversion
• A/D–D/A conversion and sampling
• Digital
• Electronics
• physics
• Electronics formula
• physics formula

Detail

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

Worked example

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 Nyquist criterion relation?

Check Nyquist, the VFS range and the bit count.

Also known as

• Nyquist
• sampling theorem

Conventions

• Hz, V or dimensionless

Related formulas

• Related

  Successive-approximation conversion

  $$D_k=\operatorname{SAR}(V_{\mathrm{in}},V_{\mathrm{DAC}})$$
  Open formulaOpen in section

• Related

  Nyquist frequency

  $$f_N=\frac{f_s}{2}$$
  Open formulaOpen in section

• Related

  Angular frequency

  $$\omega=2\pi f$$
  Open formulaOpen in section

• Related

  RC low-pass filter

  $$H(j\omega)=\frac{1}{1+j\omega RC}$$
  Open formulaOpen in section