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.
4.1.5 One of the most important facts of the information age is that characters, words, pictures, video, or music can be represented electrically by voltage patterns on wires and in electronic devices. The data represented by these voltage patterns can be converted to light waves or radio waves, and then back to voltage waves. Consider the example of an analog telephone. The sound waves of the caller’s voice enter a microphone in the telephone. The microphone converts the patterns of sound energy into voltage patterns of electrical energy that represent the voice.
If the voltage is graphed over time, the patterns that represent the voice will be displayed. An oscilloscope is an important electronic device used to view electrical signals such as voltage waves and pulses. The x-axis on the display represents time and the y-axis represents voltage or current. There are usually two y-axis inputs, so two waves can be observed and measured at the same time.
The analysis of signals with an oscilloscope is called time-domain analysis. The x-axis or domain of the mathematical function represents time. Engineers also use frequency-domain analysis to study signals. In frequency-domain analysis, the x-axis represents frequency. An electronic device called a spectrum analyzer creates graphs for frequency-domain analysis.
Electromagnetic signals use different frequencies for transmission so that different signals do not interfere with each other. Frequency modulation (FM) radio signals use frequencies that are different from television or satellite signals. When listeners change the station on a radio, they change the frequency that the radio receives.
The next page examines the variations of network signals.
4.1.6 This page will explain how analog signals vary with time and with frequency.
First, consider a single-frequency electrical sine wave, whose frequency can be detected by the human ear. If this signal is transmitted to a speaker, a tone can be heard.
Next, imagine the combination of several sine waves. This will create a wave that is more complex than a pure sine wave. This wave will include several tones. A graph of the tones will show several lines that correspond to the frequency of each tone.
Finally, imagine a complex signal, like a voice or a musical instrument. If many different tones are present, the graph will show a continuous spectrum of individual tones.
The Interactive Media Activity draws sine waves and complex waves based on amplitude, frequency, and the phase.
The next page will discuss noise.
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