Audio Engineering 1: The Decibel - Summary Notes

The Original Decibel

• The decibel (dB) was created to quantify power losses over a given distance of telegraph cable (a logarithmic progression).
• Power gain in dB is $10log<em>{10}(P</em>1/P<em>2)$, where $P</em>1$ is the output power and $P_2$ is the input power.

Reasons to Use the Decibel

• Perceptually more relevant.
• Easier to calculate:
  • Gain (multiplication) becomes addition.
  • Attenuation (division) becomes subtraction.
  • The range of numbers is reduced.

Voltage Gain and Power Gain

• If the input and output resistances are the same, the voltage gain equals the power gain.
• Voltage gain in dB is $20log<em>{10}(V</em>1/V<em>2)$, where $V</em>1$ is the output voltage and $V_2$ is the input voltage.

Values to Remember

• Multiply power by 2 = 3dB gain, multiply power by 10 = 10dB gain.
• Multiply voltage by 2 = 6dB gain, multiply voltage by 10 = 20dB gain.
• If input and output levels are the same, the gain is 0dB.
• Losses (attenuations) are negative gain.

Decibel Calculations with a Reference Value

• Decibel calculations can be used to compare a measured value with a reference.
• Level in dBm: $10log_{10}(P/1mW)$, where P is the measured power in mW.
• Level in dBu: $20log_{10}(V/0.775V)$, where V is the measured voltage in V.
• dBm and dBu are only identical if the resistance is 600Ω.

Typical Properties to Measure

• Peak level: Maximum allowable level to avoid distortion or clipping.
• Nominal level: Designed operating level for a signal.
• Headroom: Difference between nominal level and peak level.
• Noise floor: Level of background noise with no intended signal added.
• Signal to noise ratio: Ratio between nominal level and noise floor.
• Dynamic range: Ratio between peak level and noise floor.