Decibels (Optional)

Decibels (Optional)
4.1.4 The study of logarithms is beyond the scope of this course. However, the terminology is often used to calculate decibels and measure signals on copper, optical, and wireless media. The decibel is related to the exponents and logarithms described in prior sections. There are two formulas that are used to calculate decibels:


dB = 10 log10 (Pfinal / Pref)
dB = 20 log10 (Vfinal / Vref)

In these formulas, dB represents the loss or gain of the power of a wave. Decibels can be negative values which would represent a loss in power as the wave travels or a positive value to represent a gain in power if the signal is amplified.

The log10 variable implies that the number in parentheses will be transformed with the base 10 logarithm rule.

Pfinal is the delivered power measured in watts.
Pref is the original power measured in watts.
Vfinal is the delivered voltage measured in volts.
Vref 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). The power formula is often used to measure light waves on optical fiber and radio waves in the air. The voltage formula is used to measure electromagnetic waves on copper cables. These formulas have several things in common.

In the formula dB = 10 log10 (Pfinal / Pref), enter values for dB and Pref to discover the delivered power. This formula could be used to see how much power is left in a radio wave after it travels through different materials and stages of electronic systems such as radios. Try the following examples with the Interactive Media Activities:

• If the source power of the original laser, or Pref is seven microwatts (1 x 10-6 Watts), and the total loss of a fiber link is 13 dB, how much power is delivered?

• If the total loss of a fiber link is 84 dB and the source power of the original laser, or Pref is 1 milliwatt, how much power is delivered?

• If 2 microvolts, or 2 x 10-6 volts, are measured at the end of a cable and the source voltage was 1 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?

The next page will explain how an oscilloscope is used to analyze and view signals.