Measurement Units
dB, gain, and noise — the fundamental language of audio engineering. Understanding these concepts is essential before approaching any circuit design or measurement.
The Decibel
A logarithmic ratio because human hearing is logarithmic. Doubling perceived loudness requires roughly +10 dB.
The decibel is always a ratio between two quantities. For power: dB = 10×log₁₀(P₂/P₁). For voltage (same impedance): dB = 20×log₁₀(V₂/V₁). The factor of 20 comes from power being proportional to voltage squared.
dBm — Referenced to 1 mW. Into 600Ω: 0 dBm = 0.775 V
dBu — Referenced to 0.775 V regardless of impedance (unloaded)
dBV — Referenced to 1 V. Note: 0 dBV = +2.218 dBu
dBFS — Digital full scale. 0 dBFS = maximum before digital clipping
| Signal | Level | Voltage |
|---|---|---|
| Pro line level | +4 dBu | 1.228 V |
| Consumer line level | -10 dBV | 0.316 V |
| Typical clip point | +24 dBu | 12.3 V |
| Mic level (typical) | -40 dBu | 7.75 mV |
| Phono cartridge (MM) | -44 dBu | 4.9 mV |
Thermal Noise (Johnson-Nyquist)
Every resistor generates random noise from thermal electron agitation. This is the absolute noise floor — it cannot be eliminated.
k = Boltzmann constant = 1.38 × 10−23 J/K
T = Temperature in Kelvin (room temp = 300 K)
B = Bandwidth in Hz (audio: 20 Hz – 20 kHz)
R = Resistance in ohms
At room temperature (300 K), a 1 kΩ resistor across a 20 kHz bandwidth produces about 0.57 µV of noise. Practical implication: keep grid resistors as low as possible to minimize noise.
Shot Noise & 1/f Noise
Beyond thermal noise: random electron emission (shot noise) and low-frequency fluctuations (flicker noise) in vacuum tubes.
Random electron emission from cathode to anode creates noise. In triodes, the space charge provides partial smoothing. The equivalent noise resistance:
In pentodes, the cathode current splits between anode and screen grid. This random partition adds significant noise — typically 3–5× the triode equivalent noise resistance. This is why triode input stages are preferred for low-noise designs.
Power spectral density increases at lower frequencies. Dominant below ~100 Hz. Worse in old or contaminated tubes. Modern JFETs have much lower 1/f noise than tubes, making them attractive for phono preamp input stages.
Excess Noise in Resistors
Beyond thermal noise, current flowing through a resistor generates additional noise dependent on resistor type and construction.
Measured in µV/V or as a noise index in dB. A noise index of -20 dB means the excess noise is 10 µV per volt of DC across the resistor. In a 100 kΩ anode resistor with 200 V across it, a -20 dB excess noise index means 2 mV of added noise — significant in an audio circuit.
| Type | Noise Index |
|---|---|
| Carbon composition | -10 to -20 dB |
| Carbon film | -25 dB |
| Metal film | -35 to -40 dB |
| Wire-wound | Lowest (but inductive) |
→ Always use metal film resistors in the audio signal path. Carbon composition should only be used where their specific sonic character is desired (e.g., guitar amps).
Dynamic Range
The ratio between the loudest and quietest signals a system can handle, measured in dB.
16-bit (CD) → 96.3 dB
24-bit (Studio) → 144.5 dB
32-bit float → ~1528 dB (theoretical)
SNR — Signal-to-noise ratio
SINAD — Signal to noise and distortion
THD+N — Total harmonic distortion + noise
A-wtd — A-weighting for psychoacoustic relevance
A well-designed tube amplifier achieves 90–110 dB of dynamic range. 16-bit digital (96 dB) matches this well. 24-bit recording (144 dB) exceeds the performance of any analog stage, providing comfortable headroom for mixing and processing.
Modern Measurement
FFT analysis, sound card test instruments, and practical test bench setup for tube amplifier characterization.
The Fast Fourier Transform converts a time-domain signal into its frequency components, revealing harmonics, noise floor, and spurious signals. The resolution depends on sample rate and FFT length: Δf = fs / N.
An FFT assumes the signal repeats infinitely. Discontinuities at block edges create spectral leakage. Window functions taper the signal to zero at the edges, trading frequency resolution for reduced leakage.
A quality audio interface (e.g., Focusrite, RME, MOTU) can serve as an affordable test instrument. Limitations: noise floor (-100 to -115 dBFS), maximum input level (may need attenuator for high-voltage tube circuits), sample rate (bandwidth limited to fs/2).
Key measurements: THD (total harmonic distortion), IMD (intermodulation distortion), frequency response, output impedance (via two-load method), noise floor, and phase response. Always use a dummy load on the output transformer — never run a tube amp without a load.
Measurement Units — Full Quiz
Test your knowledge of decibels, noise, and dynamic range
Professional line level is +4 dBu. What voltage does this correspond to?