What must be checked before using the R-2R ladder DAC relation?

Check Nyquist, the VFS range and the bit count.

17. A/D–D/A conversion and sampling

R-2R ladder DAC

Formula

V_o=-V_{\mathrm{ref}}\sum_{k=1}^{n}\frac{b_k}{2^k}

Detail

The R-2R DAC sums binary ladder weights to reconstruct the voltage.

Explore the idea

Variables

$V_o,V_{\mathrm{ref}}$ V
$b_k$ bits
$n$ bits
$R$ ladder Ω.

Conditions

Ideal converter, band-limited in-range signal.

Intuitive explanation

For “R-2R ladder DAC”: each bit bk contributes Vref/2^k through the R and 2R network.

Worked example

For a 3-bit R-2R DAC, code

101

and

V_{\mathrm{ref}}=8\,\mathrm V

v_o=-8(1/2+1/8)=-5\,\mathrm V

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 R-2R ladder DAC 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

R-2R ladder DAC

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

Formula

V_o=-V_{\mathrm{ref}}\sum_{k=1}^{n}\frac{b_k}{2^k}

Detail

The R-2R DAC sums binary ladder weights to reconstruct the voltage.

Explore the idea

Variables

$V_o,V_{\mathrm{ref}}$ V
$b_k$ bits
$n$ bits
$R$ ladder Ω.

Conditions

Ideal converter, band-limited in-range signal.

Intuitive explanation

For “R-2R ladder DAC”: each bit bk contributes Vref/2^k through the R and 2R network.

Worked example

For a 3-bit R-2R DAC, code

101

and

V_{\mathrm{ref}}=8\,\mathrm V

v_o=-8(1/2+1/8)=-5\,\mathrm V

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 R-2R ladder DAC 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.

R-2R ladder DAC

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Conventions

Related formulas

R-2R ladder DAC

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Conventions

Related formulas