The decibel (dB) is a measurement unit important in describing networking signals. The decibel is related to the exponents and logarithms described in prior sections. There are two formulas for calculating decibels:

• dB = 10 log₁₀ (P_final / P_ref)
• dB = 20 log₁₀ (V_final / V_reference)

The variables represent the following values:

• dB measures the loss or gain of the power of a wave. Decibels are usually negative numbers representing a loss in power as the wave travels, but can also be positive values representing a gain in power if the signal is amplified
• log₁₀ implies that the number in parenthesis will be transformed using the base 10 logarithm rule
• P_final is the delivered power measured in Watts
• P_ref is the original power measured in Watts
• V_final is the delivered voltage measured in Volts
• V_reference is the original voltage measured in Volts

The first formula describes decibels in terms of power (P), and the second in terms of voltage (V). Typically, light waves on optical fiber and radio waves in the air are measured using the power formula. Electromagnetic waves on copper cables are measured using the voltage formula. These formulas have several things in common.

Enter values for dB and P_ref to discover the correct power. This formula could be used to see how much power is left in a radio wave after it has traveled over a distance through different materials, and through various stages of electronic systems such as a radio. To explore decibels further, try the following examples using the flash activities: 

• If P_final is one microWatt (1 x 10^-6 Watts) and P_ref is one milliWatt (1 x 10^-3 Watts), what is the gain or loss in decibels? Is this value positive or negative? Does the value represent a gain or a loss in power?
• If the total loss of a fiber link is -84 dB, and the source power of the original laser (P_ref) is one milliWatt (1 x 10^-3 Watts), how much power is delivered? 
• If two microVolts (2 x 10^-6 Volts) are measured at the end of a cable and the source voltage was one volt, what is the gain or loss in decibels? Is this value positive or negative? Does the value represent a gain or a loss in voltage?

Interactive Media Activity Interactivity: Calculating Gain This activity allows the user  to enter the final voltage and the reference voltage to get gain in decibels.

Interactive Media Activity Interactivity: Using Decibels This activity allows the user to enter a value for the decibels and a value for the reference power resulting in the final power.

Web Links Decibels http://arts.ucsc.edu/ems/music/ tech_background/TE-06/teces_06.html