Nyquist Sampling Rate, Folded Alias Frequency & ADC SNR / ENOB formulas

Prevent phantom aliased tones and size A/D converter bit depth!

For a band-limited baseband signal, the sampling rate must exceed twice its highest frequency to avoid the Nyquist-boundary ambiguity. Real designs also need transition bandwidth for an analog anti-alias filter. The folded-frequency formula identifies a nonnegative apparent tone frequency, not its amplitude, phase or original frequency.

The ideal 6.02*N+1.76 dB approximation assumes a full-scale sinusoid, uniform quantization and the usual quantization-noise model over the Nyquist band. It is not an unconditional dynamic-range specification. Real noise, distortion, clipping, jitter and bandwidth change performance.

ENOB uses measured SINAD, including distortion, rather than SNR alone. The simple conversion here assumes a full-scale referenced sine test; reduced-amplitude tests require attention to amplitude correction. A negative numerical ENOB is not a negative physical bit count, and a computed value above nominal resolution is a reason to inspect bandwidth and measurement conventions.

Exact Nyquist-Zone Folded Alias Frequency (Hz)

Use a nonnegative tone frequency and a positive sample rate in the same unit. Half-integer ratios fold to the Nyquist boundary regardless of which neighboring integer ROUND chooses; an exact Nyquist sine can vanish at certain sampling phases. Floating-point arithmetic limits precision at extreme ratios.

=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<0,B3<=0),"Invalid inputs",ABS(B2 - B3 * ROUND(B2 / B3, 0))))

Ideal N-Bit ADC SNR (dB) & Real-World ENOB

Relates bit resolution N (B4) and measured signal-to-noise-and-distortion SINAD (B5) via 6.02 dB/bit + 1.76 dB sine-crest constant.

=IF(NOT(ISNUMBER(B4)),"Invalid inputs",IF(OR(B4<1,B4<>INT(B4)),"Invalid inputs",ROUND(6.02 * B4 + 1.76, 2)))

ENOB from full-scale referenced SINAD

The result is rounded only for display. Nominal integer bit depth and measured effective bit depth are different quantities.

=IF(NOT(ISNUMBER(B5)),"Invalid inputs",ROUND((B5 - 1.76) / 6.02, 2))

Twice-bandwidth Nyquist boundary

B6 is the highest baseband frequency, not the sampling rate. The returned boundary is not a recommended practical sample rate; choose a higher rate and design the anti-alias filter.

=IF(NOT(ISNUMBER(B6)),"Invalid inputs",IF(B6<0,"Invalid inputs",2*B6))

Further reading

• Microsoft Support — ROUND function
• Analog Devices — ENOB for ADC dynamic performance measurement