Decibel (dB)

The decibel (dB) is a dimensionless logarithmic unit used to express the ratio between two quantities, typically power or amplitude. Named after Alexander Graham Bell, it simplifies comparisons by converting multiplication into addition and is widely used in electronics, acoustics, and signal processing.

How to Calculate Decibels

The decibel is calculated differently depending on the type of quantity:

• Power ratio:
  dB = 10 × log₁₀(P₁ / P₂)
  (P₁ and P₂ are power values)

• Amplitude ratio (voltage, current, sound pressure):
  dB = 20 × log₁₀(A₁ / A₂)
  (A₁ and A₂ are amplitude values)

The factor of 20 arises because power is proportional to the square of amplitude (P ∝ A²).

Common Decibel Variants

When referenced to standard values, decibels are expressed with specific suffixes:

• dBm: Power relative to 1 milliwatt

• dBW: Power relative to 1 watt

• dBV: Voltage relative to 1 volt

• dBA: Sound pressure weighted for human hearing sensitivity

These variants provide context-specific interpretations of dB measurements.

Example: Interpreting dB Values

• An increase of 3 dB ≈ doubling of power

• An increase of 10 dB = tenfold power increase

Example:
A 100 W amplifier delivers 20 dB more power than a 1 W amplifier:
10 × log₁₀(100 / 1) = 20 dB

This shows how dB simplifies large-scale comparisons.

Applications in Engineering and Science

The decibel is widely used in:

• Acoustics: Sound pressure level measurements (dBA)

• Electronics: Gain, attenuation, and signal loss in circuits

• Telecommunications: Signal-to-noise ratio (SNR), link margin analysis

• Audio and RF Engineering: Filter performance and dynamic range

• Signal Processing: Simplifies system modeling and scaling

Because human perception of sound and brightness is approximately logarithmic, the decibel aligns naturally with sensory response curves and engineering design needs.