Dynamic range and the noise floor
Dynamic range is the span between the quietest and loudest signals a system can handle. Understanding where noise enters the signal chain — and how bit depth, analogue design, and converter quality each contribute — is fundamental to getting clean recordings.
What dynamic range means
Dynamic range is the ratio between the maximum undistorted signal level and the minimum discernible signal level in a system. It is expressed in decibels:
Dynamic range (dB) = 20 × log₁₀(V_max / V_min)
In practice, V_min is determined by the noise floor — the level at which noise and the signal become indistinguishable. A system with a noise floor of −90 dBFS and a clip point of 0 dBFS has a dynamic range of 90 dB.
Sources of noise
Thermal noise
All resistive components generate thermal noise (also called Johnson–Nyquist noise) due to random electron motion. The RMS noise voltage is:
V_n = √(4kTRΔf)
Where k is Boltzmann's constant (1.38 × 10⁻²³ J/K), T is temperature in Kelvin, R is resistance in ohms, and Δf is the bandwidth of interest. This noise is unavoidable and sets an absolute floor for any analogue system.
In a well-designed microphone preamplifier, careful management of source impedance and first-stage gain keeps thermal noise below audible thresholds. Equivalent input noise (EIN) is a common preamplifier specification — a good mic pre will achieve −128 dBu EIN or better.
Quantisation noise
In a digital audio system, the analogue signal is rounded to the nearest available binary value at each sample. The error introduced by this rounding is quantisation noise. For a full-scale sine wave encoded at n bits, the theoretical signal-to-noise ratio is approximately:
SNR ≈ 6.02n + 1.76 dB
For 16-bit audio (CD format), this gives approximately 98 dB. For 24-bit audio, the theoretical figure is around 146 dB — far beyond what any analogue circuit can achieve in practice. The practical dynamic range of a 24-bit converter is typically 115–120 dB, limited by analogue noise in the converter's input stage.
Noise in context
| Format / system | Approximate dynamic range |
|---|---|
| Vinyl record | 55–65 dB |
| Compact Cassette | 50–60 dB (with Dolby NR) |
| CD (16-bit) | ~96 dB theoretical, ~90 dB practical |
| 24-bit digital | ~120 dB practical |
| Human hearing (threshold to pain) | ~120–130 dB |
Signal-to-noise ratio vs dynamic range
SNR (signal-to-noise ratio) and dynamic range are related but not identical:
- SNR compares a specific signal level to the noise floor. It depends on the operating level chosen.
- Dynamic range describes the full usable range of the system, from noise floor to clip point.
A system with 120 dB of dynamic range might have an SNR of only 80 dB if the signal is running 40 dB below the clip point. This is one reason gain structure matters — see the companion article.
Noise floor in a DAW
Inside a 32-bit or 64-bit floating-point DAW, mathematical operations are essentially noiseless — the effective dynamic range of floating-point arithmetic vastly exceeds any real-world source. Noise accumulates at the boundaries: when audio is recorded through a converter, and when it is played back through one. The noise floor of the final mix is therefore determined primarily by the quality of the converters and the gain structure used during tracking.
Dither
When reducing bit depth — for example, when exporting a 24-bit mix to 16-bit for CD — quantisation noise increases. Dither is a small amount of low-level noise (typically noise-shaped to push energy above the audible range) added before truncation. Dither converts the harsh, signal-correlated nature of truncation distortion into gentler, steady-state noise. It should always be applied when reducing bit depth for distribution.