Noise & Signal Quality#

Every real signal coexists with noise — unwanted energy that limits how much useful information can be extracted. Signal quality is ultimately about the ratio between what’s wanted and what isn’t: the signal-to-noise ratio. Understanding noise sources, how they combine, and how measurement bandwidth affects what’s observed is fundamental to designing systems that work well rather than just work.

Signal-to-Noise Ratio#

SNR is the ratio of signal power to noise power, expressed in dB:

SNR = 10 × log₁₀(P_signal / P_noise) dB

Or equivalently, for voltage measurements across the same impedance:

SNR = 20 × log₁₀(V_signal / V_noise) dB

What the numbers mean practically:

SNR is always measured over a defined bandwidth. An amplifier with 80 dB SNR over 20 kHz bandwidth will show a different (usually worse) number if measured over 100 kHz. Always check what bandwidth an SNR spec refers to.

Dynamic Range vs SNR#

These terms are related but not identical:

• SNR — Ratio of a specified signal level (often full scale or nominal operating level) to the noise floor
• Dynamic range — The ratio between the largest undistorted signal and the smallest detectable signal. This accounts for both noise (at the bottom) and distortion/clipping (at the top)

In a well-designed system, dynamic range ≈ SNR when the signal is at full scale. But if distortion rises before clipping (common in analog circuits), the maximum clean signal may be below full scale, and dynamic range is less than the full-scale SNR.

For converters, SFDR (Spurious-Free Dynamic Range) is often more relevant — it’s the ratio between the signal and the largest spurious component (harmonic, intermodulation product, or digital artifact). SFDR can be larger or smaller than SNR depending on the dominant limitation.

Noise Sources#

Noise has different origins, and each type has characteristic behavior:

Thermal noise (Johnson-Nyquist) — Generated by random thermal motion of electrons in any resistor. V_noise = √(4kTRB), where k is Boltzmann’s constant, T is temperature in Kelvin, R is resistance, and B is bandwidth. This is fundamental — it cannot be eliminated, only minimized by reducing R, T, or B. Thermal noise is white (equal power per Hz across all frequencies).

Shot noise — Caused by the discrete nature of charge carriers crossing a junction. Appears in diodes, transistors, and photodetectors. Also white noise. I_noise = √(2qIB), where q is electron charge and I is DC current.

Flicker noise (1/f) — Power spectral density increases at lower frequencies. Present in all active devices, especially MOSFETs. Dominates at low frequencies (below the “corner frequency” where 1/f noise equals white noise). This is why DC and low-frequency precision measurements are harder than they look.

Interference — Not fundamental noise but unwanted signals coupled from external sources: power line hum (50/60 Hz and harmonics), switching regulator spurs, RF pickup, ground loops. Unlike fundamental noise, interference can theoretically be eliminated through shielding, filtering, and proper grounding. See Noise, Stability & Reality for analog circuit noise topics.

Noise and Bandwidth#

Total noise power is the integral of noise spectral density over the measurement bandwidth. For white noise with density N₀:

Total noise power = N₀ × B

This has a critical practical consequence: reducing bandwidth reduces noise. A filter that halves the bandwidth reduces white noise power by 3 dB (noise voltage by 1.4×). This is why narrowband receivers are more sensitive than wideband ones, and why a lock-in amplifier can extract signals buried far below the broadband noise floor.

For 1/f noise, the relationship is different — the noise power depends on the ratio of the upper to lower frequency bounds (each decade contributes equal noise power). Narrowing the bandwidth helps less when 1/f noise dominates.

Noise Floor and Sensitivity#

The noise floor is the minimum detectable signal level — anything below it is lost in noise. It depends on:

1. The intrinsic noise of the front-end device (noise figure)
2. The measurement bandwidth
3. External interference

Noise figure (NF) quantifies how much noise a device adds beyond the thermal noise floor. NF = 0 dB means the device adds no noise (ideal). A low-noise amplifier (LNA) might have NF = 1-2 dB; a general-purpose op-amp might have NF = 5-15 dB depending on source impedance.

The first stage in a signal chain dominates the system noise figure (Friis formula). This is why preamplifier design is critical — see Microphone & Sensor Preamps.

Tips#

• Reduce measurement bandwidth to improve SNR when the full bandwidth isn’t needed
• Use a low-noise preamplifier as the first stage — the first stage dominates total system noise
• For precision low-frequency measurements, beware of 1/f noise in active devices

Caveats#

• SNR specs without bandwidth are meaningless — A “90 dB SNR” spec means nothing without knowing the measurement bandwidth. An audio DAC measured over 20 Hz-20 kHz and a wideband amplifier measured over 20 Hz-1 MHz are not comparable
• A-weighting inflates audio SNR numbers — A-weighted measurements apply a filter that emphasizes frequencies where human hearing is most sensitive (~2-4 kHz) and attenuates low and very high frequencies. A-weighted SNR is always higher than unweighted. Some datasheets only give the A-weighted number
• Averaging reduces noise, but slowly — Averaging N measurements improves SNR by √N (10 × log₁₀(N) dB). Getting 20 dB improvement requires 100 averages. Getting 40 dB requires 10,000 averages. This gets impractical fast
• Noise adds as power, not voltage — Two uncorrelated noise sources of 1 mV RMS each produce √(1² + 1²) = 1.41 mV total, not 2 mV. Correlated signals (interference) can add as voltage in the worst case
• The quietest stage is not the most important — The stage with the worst noise contribution referred to the input is what matters. A noisy gain stage followed by a quiet one is fine; a quiet first stage followed by a noisy second stage might not be — it depends on the gain distribution (see Gain Staging)

In Practice#

• A noise floor that changes with bandwidth setting confirms the noise is broadband (thermal or quantization), not discrete interference
• Noise that appears at specific frequencies (60 Hz, switching frequencies) is interference, not fundamental noise — look for coupling paths
• SNR that degrades at low signal levels faster than expected suggests 1/f noise or ADC quantization noise dominating
• A system that meets SNR specs on the bench but fails in the field often has interference problems that weren’t present in the lab environment