Background for Studying Frequency-Based Cable Testing

Waves

A wave is energy traveling from one place to another. There are many types of waves, but all can be described with similar vocabulary.

It is helpful to think of waves as disturbances. A bucket of water that is completely still does not have waves, because there are no disturbances. Conversely, the ocean always has some sort of detectable waves due to disturbances such as wind and tide.

Ocean waves can be described in terms of their height, or amplitude, which could be measured in meters. They can also be described in terms of how frequently the waves reach the shore, using period and frequency. The period of the waves is the amount of time between each wave, measured in seconds. The frequency is the number of waves that reach the shore each second, measured in Hertz. One Hertz is equal to one wave per second, or one cycle per second. Experiment with these concepts by adjusting the amplitude and frequency in Figure .

Networking professionals are specifically interested in voltage waves on copper media, light waves in optical fiber, and alternating electric and magnetic fields called electromagnetic waves. The amplitude of an electrical signal still represents height, but it is measured in volts instead of meters. The period is the amount of time to complete one cycle, measured in seconds. The frequency is the number of complete cycles per second, measured in Hertz.

If a disturbance is deliberately caused, and involves a fixed, predictable duration, it is called a pulse. Pulses are important in electrical signals because they determine the value of the data being transmitted
Sine waves and square waves

Sine waves, or sinusoids, are graphs of mathematical functions. Sine waves have certain characteristics. Sine waves are periodic, which means that they repeat the same pattern at regular intervals. Sine waves are continuously varying, which means that no two adjacent points on the graph have the same value.

Sine waves are graphical representations of many natural occurrences that change regularly over time. Some examples of these occurrences are the distance from the earth to the sun, the distance from the ground while riding a Ferris wheel, and the time of day that the sun rises. Since sine waves are continuously varying, they are examples of analog waves.

Square waves, like sine waves, are periodic. However, square wave graphs do not continuously vary with time. The wave holds one value for some time, and then suddenly changes to a different value. This value is held for some time, and then quickly changes back to the original value. Square waves represent digital signals, or pulses. Like all waves, square waves can be described in terms of amplitude, period, and frequency
Exponents and logarithms

In networking, there are three important number systems: Base 2 – binary Base 10 – decimal Base 16 – hexadecimal Recall that the base of a number system refers to the number of different symbols that can occupy one position. For example, binary numbers have only two different placeholders, 0 and 1. Decimal numbers have 10 different placeholders, the numbers 0-9. Hexadecimal numbers have 16 different placeholders, the numbers 0-9 and the letters A-F. Remember that 10x10 can be written as 102. 102 means ten squared or ten raised to the second power. When written this way, it is said that 10 is the base of the number and 2 is the exponent of the number. 10x10x10 can be written as 103. 103 means ten cubed or ten raised to the third power. The base is still 10, but the exponent is now 3. Use the Media Activity below to practice calculating exponents. Enter x, and y is calculated, or enter y, and x is calculated. The base of a number system also refers to the value of each digit. The least significant digit has a value of base0, or one. The next digit has a value of base1. This is equal to 2 for binary numbers, 10 for decimal numbers, and 16 for hexadecimal numbers. Numbers with exponents are used to easily represent very large or very small numbers. It is much easier and less error-prone to represent one billion numerically as 109 than as 1000000000. Many calculations involved in cable testing involve numbers that are very large, so exponents are the preferred format. Exponents can be explored in the flash activity. One way to work with the very large and very small numbers that occur in networking is to transform the numbers according to the rule, or mathematical function, known as the logarithm. Logarithms are referenced to the base of the number system being used. For example, base 10 logarithms are often abbreviated log. To take the “log” of a number use a calculator or the flash activity. For example, log (109) equals 9, log (10-3) = -3. You can also take the logarithm of numbers that are not powers of 10, but you cannot take the logarithm of a negative number. While the study of logarithms is beyond the scope of this course, the terminology is used commonly in calculating decibels, a way of measuring signals on copper, optical, and wireless media

Decibels

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?

Viewing signals in time and frequency

One of the most important facts of the information age is that data symbolizing 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 patterns were graphed over time, the distinct patterns representing the voice would 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.

Analyzing signals using an oscilloscope is called time-domain analysis, because 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. Experiment with this graphic by adding several signals, and try to predict what the output will look like on both the oscilloscope and the spectrum analyzer.

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 are changing the frequency that the radio is receiving.

Analog and digital signals in time and frequency

To understand the complexities of networking signals and cable testing, examine 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. How would a spectrum analyzer display this pure tone? Next, imagine the combination of several sine waves. The resulting wave is more complex than a pure sine wave. Several tones would be heard. How would a spectrum analyzer display this? The graph of several tones shows several individual lines corresponding to the frequency of each tone. Finally, imagine a complex signal, like a voice or a musical instrument. What would its spectrum analyzer graph look like? If many different tones are present, a continuous spectrum of individual tones would be represented.

Noise in time and frequency

Noise is an important concept in communications systems, including LANS. While noise usually refers to undesirable sounds, noise related to communications refers to undesirable signals. Noise can originate from natural and technological sources, and is added to the data signals in communications systems.

All communications systems have some amount of noise. Even though noise cannot be eliminated, its effects can be minimized if the sources of the noise are understood. There are many possible sources of noise:

• Nearby cables which carry data signals
• Radio frequency interference (RFI), which is noise from other signals being transmitted nearby
• Electromagnetic interference (EMI), which is noise from nearby sources such as motors and lights
• Laser noise at the transmitter or receiver of an optical signal

Noise that affects all transmission frequencies equally is called white noise. Noise that only affects small ranges of frequencies is called narrowband interference. When detected on a radio receiver, white noise would interfere with all radio stations. Narrowband interference would affect only a few stations whose frequencies are close together. When detected on a LAN, white noise would affect all data transmissions, but narrowband interference might disrupt only certain signals. If the band of frequencies affected by the narrowband interference included all frequencies transmitted on the LAN, then the performance of the entire LAN would be compromised
Bandwidth

Bandwidth is an extremely important concept in communications systems. Two ways of considering bandwidth that are important for the study of LANs are analog bandwidth and digital bandwidth.

Analog bandwidth typically refers to the frequency range of an analog electronic system. Analog bandwidth could be used to describe the range of frequencies transmitted by a radio station or an electronic amplifier. The units of measurement for analog bandwidth is Hertz, the same as the unit of frequency. Examples of analog bandwidth values are 3 kHz for telephony, 20 kHz for audible signals, 5 kHz for AM radio stations, and 200 MHz for FM radio stations.

Digital bandwidth measures how much information can flow from one place to another in a given amount of time. The fundamental unit of measurement for digital bandwidth is bits per second (bps). Since LANs are capable of speeds of millions of bits per second, measurement is expressed in kilobits per second (Kbps) or megabits per second (Mbps). Physical media, current technologies, and the laws of physics limit bandwidth.

During cable testing, analog bandwidth is used to determine the digital bandwidth of a copper cable. Analog frequencies are transmitted from one end and received on the opposite end. The two signals are then compared, and the amount of attenuation of the signal is calculated. In general, media that will support higher analog bandwidths without high degrees of attenuation will also support higher digital bandwidths.

Cisco Systems, Inc.