Fast Circuit Boards

Appendix CThe Decibel

There are many parameters in engineering that extend in value over many decades. As an example, useful voltages extend from well below a microvolt to megavolts. That is over 12 orders of magnitude. Often it is convenient to consider a logarithmic scale rather than a linear scale to discuss parameters. In the early days of telephony, engineers needed a logarithmic scale for discussing sound levels. Noise levels, for example, were millivolts while signal levels were volts. The power ratio here is a million to one. It was convenient to use a logarithmic scale, where a just discernable change in loudness was 1 unit.¹ This unit had to work for noise as well as voice signals. It turned out that the logarithm of the ratio of power from two signals when multiplied by 10 was just such a scale. It worked at all signal levels. The unit was called the decibel to honor Mr. Bell, the telephone inventor. The definition of the decibel is

(C1)

where P₁ and P₂ are power levels. If the signal levels are measured as voltage on one resistor, then the ratio can be written as

(C2)

The decibel is abbreviated as dB and in conversation it is pronounced “deebee.” For those that use this measure on a regular basis, they know that 6 dB is a factor of 2, 20 dB is a factor of 10, and ...