Section 17

A/D–D/A conversion and sampling

viz

f_s>2f_{\max}

Nyquist requires fs>2 fmax to sample without aliasing.

Ideal converter, band-limited in-range signal.

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Nyquist frequency

f_N=\frac{f_s}{2}

Computes Nyquist frequency from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

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Quantization step

viz

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

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

Ideal converter, band-limited in-range signal.

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Quantization error

-\frac{\Delta}{2}\le e_q<\frac{\Delta}{2}

Computes Quantization error from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

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PWM duty cycle

viz

\delta=\frac{t_{\mathrm{on}}}{T}

PWM duty δ=ton/T is the fraction of the period spent high.

Ideal converter, band-limited in-range signal.

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R-2R ladder DAC

viz

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

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

Ideal converter, band-limited in-range signal.

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Least-significant-bit weight

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

Computes Least-significant-bit weight from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

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Number of digital levels

N=2^n

Computes Number of digital levels from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

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Flash-ADC comparators

N_{\mathrm{comp}}=2^n-1

Computes Flash-ADC comparators from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

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Successive-approximation conversion

D_k=\operatorname{SAR}(V_{\mathrm{in}},V_{\mathrm{DAC}})

Computes Successive-approximation conversion from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

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Section 17

A/D–D/A conversion and sampling

Nyquist criterion

viz

f_s>2f_{\max}

Nyquist requires fs>2 fmax to sample without aliasing.

Ideal converter, band-limited in-range signal.

View detail →

Nyquist frequency

f_N=\frac{f_s}{2}

Computes Nyquist frequency from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

View detail →

Quantization step

viz

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

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

Ideal converter, band-limited in-range signal.

View detail →

Quantization error

-\frac{\Delta}{2}\le e_q<\frac{\Delta}{2}

Computes Quantization error from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

View detail →

PWM duty cycle

viz

\delta=\frac{t_{\mathrm{on}}}{T}

PWM duty δ=ton/T is the fraction of the period spent high.

Ideal converter, band-limited in-range signal.

View detail →

R-2R ladder DAC

viz

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

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

Ideal converter, band-limited in-range signal.

View detail →

Least-significant-bit weight

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

Computes Least-significant-bit weight from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

View detail →

Number of digital levels

N=2^n

Computes Number of digital levels from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

View detail →

Flash-ADC comparators

N_{\mathrm{comp}}=2^n-1

Computes Flash-ADC comparators from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

View detail →

Successive-approximation conversion

D_k=\operatorname{SAR}(V_{\mathrm{in}},V_{\mathrm{DAC}})

Computes Successive-approximation conversion from the circuit model and the stated conditions.

Ideal converter, band-limited in-range signal.

View detail →