What is Frequency and Wavelength?

The Electromagnetic Spectrum

Electromagnetic waves are signals that oscillate; i.e., the amplitudes of the electric and magnetic fields vary at a specific crate. The field intensities fluctuate up and down, and the polarity reverses a given number of times per second. The electromagnetic waves very sinusoidally. Their frequency is measured in cycles per second (cps) or Hertz (Hz). These oscillations may occur at a very low frequency or at an extremely high frequency. The range of electromagnetic signals encompassing all frequencies is referred to as the electromagnetic spectrum. All electrical and electronic signals that radiate into free space fall into the electromagnetic spectrum. Not included are signals carried by cables. Signals carried by cable may share the same frequencies of similar signals in the spectrum, but they are not radio signals. Fig. 1-13 shows the entire electromagnetic spectrum, giving both frequency and wavelength. Within the middle ranges are located the most commonly used radio frequencies for two-way communication, TV, cell phones, wireless LANs, radar, and other applications. At the upper end of the spectrum are infrared and visible light. Fig. 1-14 is a  listing of the generally recognized segments in the spectrum used for electronic communication.

What is Frequency and Wavelength?

A given signal is located on the frequency spectrum according to its frequency and wavelength.


Frequency is the number of times a particular phenomenon occurs in a given period of time. In electronics, frequency is the number of cycles of a repetitive wave that occurs in a given time period. A cycle consists of two voltage polarity reversals, current reversals, or electromagnetic field oscillations. The cycles repeat, forming a continuous but repetitive wave. Frequency is measured in cycles per second (cps). In electronics, the unit of frequency is the hertz, named for the German physicist Heinrich Hertz, who was a pioneer in the field of electromagnetics. One cycle per second is equal to one hertz, abbreviated (Hz). Therefore, 440 cps 5 440 Hz. Fig. 1-15(a) shows a sine wave variation of voltage. One positive alternation and one negative alternation form a cycle. If 2500 cycles occur in 1 s, the frequency is 2500 Hz.

What is Frequency and Wavelength?


In 1887 German physicist Heinrich Hertz was the fi rst to demonstrate the effect of electromagnetic radiation through space. The distance of transmission was only a few feet, but this transmission proved that radio waves could travel from one place to another without the need for any connecting wires. Hertz also proved that radio waves, although invisible, travel at the same velocity as light waves.

What is Frequency and

Prefi xes representing powers of 10 are often used to express frequencies. The most frequently used prefi xes are as follows:

Prefi xes representing powers of 10 are often used to express frequencies. The most frequently used prefi xes are as follows:

Thus, 1000 Hz 5 1 kHz (kilohertz). A frequency of 9,000,000 Hz is more commonly expressed as 9 MHz (megahertz). A signal with a frequency of 15,700,000,000 Hz is written as 15.7 GHz (gigahertz).

Wavelength. Wavelength is the distance occupied by one cycle of a wave, and it is  usually expressed in meters. One meter (m) is equal to 39.37 in (just over 3 ft, or 1 yd). Wavelength is measured between identical points on succeeding cycles of a wave, as Fig. 1-15(b) shows.

Wavelength is the distance occupied by one cycle of a wave, and it is  usually expressed in meters. One meter (m) is equal to 39.37 in (just over 3 ft, or 1 yd). Wavelength is measured between identical points on succeeding cycles of a wave, as Fig. 1-15(b) shows.

If the signal is an electromagnetic wave, one wavelength is the distance that one cycle occupies in free space. It is the distance between adjacent peaks or valleys of the electric and magnetic fields making up the wave. Wavelength is also the distance traveled by an electromagnetic wave during the time of one cycle. Electromagnetic waves travel at the speed of light, or 299,792,800 m/s. The speed of light and radio waves in a vacuum or in air is usually rounded off to 300,000,000 m/s (3x 10 power 8 m/s), or 186,000 mi/s. The speed of transmission in media such as a cable is less. The wavelength of a signal, which is represented by the Greek letter λ (lambda), is computed by dividing the speed of light by the frequency f of the wave in hertz: λ = 300,000,000/f. For example, the wavelength of a 4,000,000-Hz signal is

λ = 300,000,000/4,000,000 = 75m

If the frequency is expressed in megahertz, the formula can be simplified to λ(m) 300/f(MHz) or λ(ft) = 984 f(MHz). The 4,000,000-Hz signal can be expressed as 4 MHz. Therefore λ = 300/4 =75m. A wavelength of 0.697 m, as in the second equation in

Example 1-1, is known as a very high frequency signal wavelength. Very high frequency wavelengths are sometimes expressed in centimeters (cm). Since 1 m equals 100 cm, we can express the wavelength of 0.697 m in Example 1-1 as 69.7, or about 70 cm.

Example 1-1 Find the wavelengths of (a) a 150-MHz, (b) a 430-MHz, (c) an 8-MHz, and (d) a 750kHz signal.

is known as a very high frequency signal wavelength. Very high frequency wavelengths are sometimes expressed

If the wavelength of a signal is known or can be measured, the frequency of the signal can be calculated by rearranging the basic formula f = 300/λ. Here, f is in megahertz and λ is in meters. As an example, a signal with a wavelength of 14.29 m has a frequency of f = 300/14.29 = 21 MHz.

Example 1-2 A signal with a wavelength of 1.5 m has a frequency of

f = 300/1.5 = 200 MHz

Example 1-3 A signal travels a distance of 75 ft in the time it takes to complete 1 cycle. What is its frequency?

A signal travels a distance of 75 ft in the time it takes to complete 1 cycle. What is its frequency?

Example 1-4 The maximum peaks of an electromagnetic wave are separated by a distance of 8 in. What is the frequency in megahertz? In gigahertz?

The maximum peaks of an electromagnetic wave are separated by a distance of 8 in. What is the frequency in megahertz? In gigahertz?

Frequency Ranges from 30 Hz to 300 GHz

For the purpose of classification, the electromagnetic frequency spectrum is divided into segments, as shown in Fig. 1-13. The signal characteristics and applications for each segment are discussed in the following paragraphs.

Extremely Low Frequencies

Extremely low frequencies (ELFs) are in the 30- to 300-Hz range. These include ac power line frequencies (50 and 60 Hz are common), as well as those frequencies in the low end of the human audio range.

Voice Frequencies

Voice frequencies (VFs) are in the range of 300 to 3000 Hz. This is the normal range of human speech. Although human hearing extends from approximately 20 to 20,000 Hz, most intelligible sound occurs in the VF range.

Very Low Frequencies

Very low frequencies (VLFs) extend from 9 kHz to 30 kHz and include the higher end of the human hearing range up to about 15 or 20 kHz. Many musical instruments make sounds in this range as well as in the ELF and VF ranges. The VLF range is also used in some government and military communication. For example, VLF radio transmission is used by the navy to communicate with submarines.

Low Frequencies

Low frequencies (LFs) are in the 30- to 300-kHz range. The primary communication services using this range are in aeronautical and marine navigation. Frequencies in this range are also used as subcarriers, signals that are modulated by the baseband information. Usually, two or more subcarriers are added, and the combination is used to modulate the final high-frequency carrier.

Medium Frequencies

Medium frequencies (MFs) are in the 300- to 3000-kHz (0.3- to 3.0-MHz) range. The major application of frequencies in this range is AM radio broadcasting (535 to 1605 kHz). Other applications in this range are various marine and amateur radio communication.

High Frequencies

High frequencies (HFs) are in the 3- to 30-MHz range. These are the frequencies generally known as short waves. All kinds of simplex broadcasting and half duplex two-way radio communication take place in this range. Broadcasts from Voice of America and the British Broadcasting Company occur in this range. Government and military services use these frequencies for two-way communication. An example is diplomatic communication between embassies. Amateur radio and CB communication also occur in this part of the spectrum.

Very High Frequencies

Very high frequencies (VHFs) encompass the 30- to 300-MHz range. This popular frequency range is used by many services, including mobile radio, marine and aeronautical communication, FM radio broadcasting (88 to 108 MHz), and television channels 2 through 13. Radio amateurs also have numerous bands in this frequency range.

Ultrahigh Frequencies

Ultrahigh frequencies (UHFs) encompass the 300- to 3000-MHz range. This, too, is a widely used portion of the frequency spectrum. It includes the UHF TV channels 14 through 51, and it is used for land mobile communication and services such as cellular telephones as well as for military communication. Some radar and navigation services occupy this portion of the frequency spectrum, and radio amateurs also have bands in this range.

Microwaves and SHFs

Frequencies between the 1000-MHz (1-GHz) and 30-GHz range are called microwaves. Microwave ovens usually operate at 2.45 GHz. Superhigh frequencies (SHFs) are in the 3- to 30-GHz range. These microwave frequencies are widely used for satellite communication and radar. Wireless local-area networks (LANs) and many cellular telephone systems also occupy this region.

Extremely High Frequencies

Extremely high frequencies (EHFs) extend from 30 to 300 GHz. Electromagnetic signals with frequencies higher than 30 GHz are referred to as millimeter waves. Equipment used to generate and receive signals in this range is extremely complex and expensive, but there is growing use of this range for satellite communication telephony, computer data, short-haul cellular networks, and some specialized radar.

Frequencies Between 300 GHz and the Optical Spectrum

This portion of the spectrum is virtually uninhabited. It is a cross between RF and optical. Lack of hardware and components limits its use.

The Optical Spectrum

Right above the millimeter wave region is what is called the optical spectrum, the region occupied by light waves. There are three different types of light waves: infrared, visible, and ultraviolet.


The infrared region is sandwiched between the highest radio frequencies (i.e., millimeter waves) and the visible portion of the electromagnetic spectrum. Infrared occupies the range between approximately 0.1 millimeter (mm) and 700 nanometers (nm), or 100 to 0.7 micrometer (μm). One micrometer is one-millionth of a meter. Infrared wavelengths are often given in micrometers or nanometers. Infrared radiation is generally associated with heat. Infrared is produced by light-bulbs, our bodies, and any physical equipment that generates heat. Infrared signals can also be generated by special types of light-emitting diodes (LEDs) and lasers. Infrared signals are used for various special kinds of communication. For example, infrared is used in astronomy to detect stars and other physical bodies in the universe, and for guidance in weapons systems, where the heat radiated from airplanes or missiles can be picked up by infrared detectors and used to guide missiles to targets. Infrared is also used in most new TV remote-control units where specially coded signals are transmitted by an infrared LED to the TV receiver for the purpose of changing channels, setting the volume, and performing other functions. Infrared is the basis for all fiberoptic communication. Infrared signals have many of the same properties as signals in the visible spectrum. Optical devices such as lenses and mirrors are often used to process and manipulate infrared signals, and infrared light is the signal usually propagated over fiber-optic cables.

The Visible Spectrum

Just above the infrared region is the visible spectrum we ordinarily refer to as light. Light is a special type of electromagnetic radiation that has a wavelength in the 0.4- to 0.8-μm range (400 to 800 nm). Light wavelengths are usually expressed in terms of angstroms (Å). An angstrom is one ten-thousandth of a micrometer; for example, 1 Å = 10 power -10 m. The visible range is approximately 8000 Å (red) to 4000 Å (violet). Red is low-frequency or long-wavelength light, whereas violet is high-frequency or short-wavelength light. Light is used for various kinds of communication. Light waves can be modulated and transmitted through glass fibers, just as electric signals can be transmitted over wires. The great advantage of light wave signals is that their very high frequency gives them the ability to handle a tremendous amount of information. That is, the bandwidth of the baseband signals can be very wide. Light signals can also be transmitted through free space. Various types of communication systems have been created using a laser that generates a light beam at a specifi c visible frequency. Lasers generate an extremely narrow beam of light, which is easily modulated with voice, video, and data information.


Ultraviolet light (UV) covers the range from about 4 to 400 nm. Ultraviolet generated by the sun is what causes sunburn. Ultraviolet is also generated by mercury vapor lights and some other types of lights such as fluorescent lamps and sun lamps. Ultraviolet is not used for communication; its primary use is medical. Beyond the visible region are the X-rays, gamma rays, and cosmic rays. These are all forms of electromagnetic radiation, but they do not figure into communication systems and are not covered here.


Although it is expensive to build a fiber-optic or wireless network, servicing each additional user is cost-effective. The more users a network has, the lower the overall cost.


Bandwidth (BW) is that portion of the electromagnetic spectrum occupied by a signal. It is also the frequency range over which a receiver or other electronic circuit operates. More specifi cally, bandwidth is the difference between the upper and lower frequency limits of the signal or the equipment operation range. Fig. 1-16 shows the bandwidth of the voice frequency range from 300 to 3000 Hz. The upper frequency is f2 and the lower frequency is f1. The bandwidth, then, is

BW = f2 – f1

Example 1-5 A commonly used frequency range is 902 to 928 MHz. What is the width of this band?

Example 1-6 A television signal occupies a 6-MHz bandwidth. If the low-frequency limit of channel 2 is 54 MHz, what is the upper-frequency limit?

Channel Bandwidth

When information is modulated onto a carrier somewhere in the electromagnetic spectrum, the resulting signal occupies a small portion of the spectrum surrounding the carrier frequency. The modulation process causes other signals, called sidebands, to be generated at

frequencies above and below the carrier frequency by an amount equal to the modulating frequency. For example, in AM broadcasting, audio signals up to 5 kHz can be transmitted. If the carrier frequency is 1000 kHz, or 1 MHz, and the modulating frequency is 5 kHz, sidebands will be produced at 1000 – 5 = 995 kHz and at 1000 + 5 = 1005 kHz. In other words, the modulation process generates other signals that take up spectrum space. It is not just the carrier at 1000 kHz that is transmitted. Thus the term bandwidth refers to the range of frequencies that contain the information. The term channel bandwidth refers to the range of frequencies required to transmit the desired information. The bandwidth of the AM signal described above is the difference between the highest and lowest transmitting frequencies: BW = 1005 kHz – 995 kHz = 10 kHz. In this case, the channel bandwidth is 10 kHz. An AM broadcast signal, therefore, takes up a 10-kHz piece of the spectrum. Signals transmitting on the same frequency or on overlapping frequencies do, of course, interfere with one another. Thus a limited number of signals can be transmitted in the frequency spectrum. As communication activities have grown over the years, there has been a continuous demand for more frequency channels over which communication can be transmitted. This has caused a push for the development of equipment that operates at the higher frequencies. Prior to World War II, frequencies above 1 GHz were virtually unused, since there were no electronic components suitable for generating signals at those frequencies. But technological developments over the years have given us many microwave components such as klystrons, magnetrons, and traveling-wave tubes, and today transistors, integrated circuits, and other semiconductor devices that routinely work in the microwave range.

More Room at the Top

The benefit of using the higher frequencies for communication carriers is that a signal of a given bandwidth represents a smaller percentage of the spectrum at the higher frequencies than at the lower frequencies. For example, at 1000 kHz, the 10-kHz-wide AM signal discussed earlier represents 1 percent of the spectrum:


The Federal Communications Commission (FCC) was formed in 1934 to regulate interstate and foreign communication. A primary function of the FCC is to allocate bands of frequencies and set limitations on broadcast power for different types of radio and TV operations. The FCC also monitors broadcasts to detect unlicensed operations and technical violations. In addition to TV and radio stations, the FCC licenses about 50 million transmitters operated by individuals, businesses, ships and airplanes, emergency services, and telephone systems. FCC policy is set by fi ve commissioners who are appointed by the President for fi ve-year terms

In practice, this means that there are many more 10-kHz channels at the higher frequencies than at the lower frequencies. In other words, there is more spectrum space for information signals at the higher frequencies. The higher frequencies also permit wider-bandwidth signals to be used. A TV signal, e.g., occupies a bandwidth of 6 MHz. Such a signal cannot be used to modulate a carrier in the MF or HF ranges because it would use up all the available spectrum space. Television signals are transmitted in the VHF and UHF portions of the spectrum, where suffi cient space is available. Today, virtually the entire frequency spectrum between approximately 30 kHz and 30 GHz has been spoken for. Some open areas and portions of the spectrum are not heavily used, but for the most part, the spectrum is fi lled with communication activities of all kinds generated from all over the world. There is tremendous competition for these frequencies, not only between companies, individuals, and government services in individual carriers but also between the different nations of the world. The electromagnetic spectrum is one of our most precious natural resources. Because of this, communication engineering is devoted to making the best use of that fi nite spectrum. A considerable amount of effort goes into developing communication techniques that will minimize the bandwidth required to transmit given information and thus conserve spectrum space.This provides more room for additional communication channels and gives other services or users an opportunity to take advantage of it. Many of the techniques discussed later in this book evolved in an effort to minimize transmission bandwidth.

Spectrum Management

Governments of the United States and other countries recognized early on that the frequency spectrum was a valuable and fi nite natural resource and so set up agencies to control spectrum use. In the United States, Congress passed the Communications Act of 1934. This Act and its various amendments established regulations for the use of spectrum space. It also established the Federal Communications Commission (FCC), a regulatory body whose function is to allocate spectrum space, issue licenses, set standards, and police the airwaves. The Telecommunications Act of 1996 has also greatly infl uenced the use of spectrum. The FCC controls all telephone and radio communications in this country and, in general, regulates all electromagnetic emissions. The National Telecommunications and Information Administration (NTIA) performs a similar function for government and military services. Other countries have similar organizations. The International Telecommunications Union (ITU), an agency of the United Nations that is headquartered in Geneva, Switzerland, comprises 189 member countries that meet at regular intervals to promote cooperation and negotiate national interests. Typical of these meetings are the World Administrative Radio Conferences, held approximately every two years. Various committees of the ITU set standards for various areas within the communication fi eld. The ITU brings together the various countries to discuss how the frequency spectrum is to be divided up and shared. Because many of the signals generated in the spectrum do not carry for long distances, countries can use these frequencies simultaneously without interference. On the other hand, some ranges of the frequency spectrum can literally carry signals around the world. As a result, countries must negotiate with one another to coordinate usage of various portions of the high-frequency spectrum to prevent mutual interference.


Standards are specifi cations and guidelines that companies and individuals follow to ensure compatibility between transmitting and receiving equipment in communication systems. Although the concepts of communication are simple, there are obviously many ways to send and receive information. A variety of methods are used to modulate, multiplex, and otherwise process the information to be transmitted. If each system used different methods created at the whim of the designing engineer, the systems would be incompatible with one another and no communication could take place. In the real world, standards are set and followed so that when equipment is designed and built, compatibility is ensured. The term used to describe the ability of equipment from one manufacturer to work compatibly with that of another is interoperability. Standards are detailed outlines of principles of operation, blueprints for construction, and methods of measurement that defi ne communication equipment. Some of the specifi – cations covered are modulation methods, frequency of operation, multiplexing methods, word length and bit formats, data transmission speeds, line coding methods, and cable and connector types. These standards are set and maintained by numerous nonprofi t organizations around the world. Committees made up of individuals from industry and academia meet to establish and agree upon the standards, which are then published for others to use. Other committees review, revise, and enhance the standards over time, as needs change. In working in the communication fi eld, you will regularly encounter many different standards. For example, there are standards for long-distance telephone transmission, digital cell phones, local-area networks, and computer modems. Listed below are organizations that maintain standards for communication systems. For more details, go to the corresponding website.

A Survey of Communication Applications

The applications of electronic techniques to communication are so common and pervasive that you are already familiar with most of them. You use the telephone, listen to the radio, and watch TV. You also use other forms of electronic communication, such as cellular telephones, ham radios, CB and Family radios, home wireless networks for Internet access, texting, electronic mail, and remote-control garage door openers. Fig. 1-17 lists all the various major applications of electronic communication.

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