Understanding Audio Calculations Excerpt from Electronic Systems Technician Level 4 Trainee Guide

Most audio measurements are presented in decibels. A decibel is one-tenth of a bel. A bel is the logarithm of electrical, acoustic, or other power ratios. A decibel is the unit used to express the relative difference in power or intensity between two acoustic or electric signals.

A logarithm is the power to which a base, such as 10, must be raised to produce a given number. The term logarithm is shortened to log when used as part of a formula. For example, the log of 100 is 2 (10 × 10); the log of 1,000 is 3 (10 × 10 × 10). When working with audio calculations we always assume the base is 10.

It is important to recognize that decibels represents a specific ratio: the ratio of two different wattages, the ratio of two different voltages, or the ratio of two different sound pressure levels. It is also important to recognize that as a ratio, we are expressing a relative difference; the ratio is relative to the specific thing we are measuring: voltage, wattage, or sound pressure.

Decibels for sound pressure levels are mathematically expressed with the equation dB = 10 × Log (P1/P2). P1 and P2 are power values represented in watts.

A watt is a measurement of power. It is defined as 1 joule per second. A joule is a measurement of energy. A watt therefore is the rate of energy transfer. This is the same as saying a watt is the rate of doing work.

Notice in the formula above that the log of P1 divided by P2 is then multiplied by 10. This is true for all power calculations.

When performing calculations for voltage and current you multiply by 20. The formula for determining the ratio of two voltages is dB = 20 × Log (E1/E2). E1 and E2 are voltages.

Power ratings are limited mainly to amplifiers. Most audio equipment is rated based on voltage. As we explore various audio concepts, different decibel measurements are used:

 dBm – Electrical power level, assuming a 600 ohm impedance, 0dBm = 1mw  dBu – Electrical voltage level, the impedance level must be stated  dBV – 0dBV = 1.0 volts  dBv – 0dBv = 0.775 volts  dBu – 0dBu = 0.775 volts at 600 ohms

You can convert between dBV and dBu (dBv) by adding or subtracting 2.2dB. For example, to convert dBV to dBu, subtract 2.2dB. To convert from dBu to dBV, add 2.2dB.