RADIO WAVE FREQUENCY and WAVELENGTH

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Radar is a variant of radio technology and shares many of the same basic elements. It is useful to discuss fundamental concepts of radio operation to provide a basis for discussing fundamental concepts of radar operation.

Late in the 19th century, researchers discovered that if an alternating electric current were run through a wire or rod, it emitted an invisible form of radiation that could generate an alternating electric current in a remote wire or rod with no wired electrical connection between the two. This invisible radiation was quickly realized to be a form of “electromagnetic (EM) radiation”, a disturbance of electric and magnetic fields that propagated through space.

Electromagnetic radiation is in the form of waves propagating at a speed of 300,000,000 meters per second (186,000 miles per second). The waves could be generated at varying “frequencies”, defined by the number of cyclical variations of the wave that passed every second through a plane perpendicular to the motion of the wave. Frequencies were once measured in “cycles per second (CPS)”, but now are universally defined in terms of “hertz (Hz)”, after Heinrich Hertz, a pioneering radio researcher.

The frequencies of electromagnetic radiation are usually large numbers, and so it is useful to use “metric prefixes” as shorthand. For example:

kilohertz (kHz): 1,000 hertz
megahertz (MHz): 1,000,000 hertz
gigahertz (GHz): 1,000,000,000 hertz
terahertz (THz): 1,000,000,000,000 hertz

The full range of frequencies of EM radiation is known as the “electromagnetic spectrum”. Radio waves only take up part of this spectrum, in practice generally in the form of kilohertz, megahertz, or gigahertz radio emissions. Above about 300 GHz, EM radiation moves into a region of the spectrum known as “infrared”; and then with increasingly higher frequencies (and incidentally, higher energies) into the region of visible light that we can see with our eyes; and finally into energetic radiation defined as the “ultraviolet”, “X-ray”, and (at the very highest frequencies) “gamma ray” regions of the spectrum.
Put more simply, radio waves are the same thing as visible light, both being forms of EM radiation. The only real difference is that radio waves have lower frequencies. Incidentally, electromagnetic waves are entirely different from sound waves, which are mechanical disturbances propagating through the air, water, or a solid medium. The two kinds of waves can be confused because very low frequency EM waves are sometimes said to be at “audio” frequencies, matching the frequencies of the sound waves we can hear, and of course EM waves can be used to transmit audio, as turning on a household radio receiver shows.

• This document focuses only on radio waves. Sometimes it is easier to talk about radio waves in terms of their “wavelength” in meters instead of their frequency. There is a simple relationship between the wavelength and frequency of a wave:

wavelength = wave_propagation_speed / frequency

Since the propagation speed of EM radiation in free space is 300,000,000 meters per second, then for EM radiation this is:
wavelength = 300,000,000 / frequency

If frequency and wavelength are given in the appropriately scaled units of measurement kilohertz and kilometers, megahertz and meters, or gigahertz and millimeters this simplifies to:
wavelength = 300 / frequency

The list below gives the wavelengths at various frequencies:
1 kHz = 300 kilometers
3 kHz = 100 kilometers
10 kHz = 30 kilometers
30 kHz = 10 kilometers
100 kHz = 3 kilometers
300 kHz = 1 kilometer

1 MHz = 300 meters
3 MHz = 100 meters
10 MHz = 30 meters
30 MHz = 10 meters
100 MHz = 3 meters
300 MHz = 1 meter

1 GHz = 300 millimeters = 30 centimeters
3 GHz = 100 millimeters = 10 centimeters
10 GHz = 30 millimeters = 3 centimeters
30 GHz = 10 millimeters = 1 centimeter
100 GHz = 3 millimeters
300 GHz = 1 millimeter

Frequency and wavelength are two sides of the same coin, with frequency being a useful term in some cases and wavelength being more convenient in others. This document switches back and forth between them at will.
Various frequency / wavelength ranges, or “bands”, have been defined for radars, with general classes of equipment usually operating in one or a few bands. The band names as defined by the International Telecommunications Union (ITU), an electronic standards body, with the frequency / wavelength corresponding to the lower or base end of each band, are as follows:

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ELF (Extremely Low Frequency) 30 Hz 10,000 kilometers
VF (Voice Frequency) 300 Hz 1,000 kilometers
VLF (Very Low Frequency) 3 kHz 100 kilometers
LF (Low Frequency) 30 kHz 10 kilometers
MF (Medium Frequency) 300 kHz 1 kilometer

HF (High Frequency) 3 MHz 100 meters
VHF (Very High Frequency) 30 MHz 10 meters
UHF (Ultra High Frequency) 300 MHz 1 meter

L 1 GHz 30 centimeters
S 2 GHz 15 centimeters
C 4 GHz 7.5 centimeters
X 8 GHz 3.75 centimeters
Ku 12 GHz 2.5 centimeters
K 18 GHz 1.67 centimeters
Ka 27 GHz 1.1 centimeters

V 40 GHz 7.5 millimeters
W 75 GHz 4 millimeters
mm 110 GHz 2.73 millimeters
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The VLF through UHF band definitions were inherited from radio engineering. The band names above UHF don’t follow any apparent logical pattern, which was apparently done by intent, as a military security measure. The K band originally also included the Ku and Ka bands, but it turned out that the center portion of the K-band was useless for most military purposes since water vapor in the atmosphere soaked up and blocked radio waves in that range. The portion of the K-band “above” the absorption range became the “Ka-band”, while the portion “under” the absorption range became the “Ku-band”. About the only way to remember the order of these bands is with a mnemonic, for example: “Lincoln State College eXplorer’s Kit”. Gear operating in the V and W bands is usually just referred to as “millimeter wave”.
To make things more confusing, different band definitions are used in other electronic fields. Radio engineers retain the ELF through UHF definitions, but take the UHF band up to 3 GHz, and then cover the higher frequencies with the “Super High Frequency (SHF)” band from 3 to 30 GHz, covering the centimetric / microwave region; and then the “Extremely High Frequency (EHF)” band from 30 to 300 GHz:

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ELF (Extremely Low Frequency) 30 Hz 10,000 kilometers
VF (Voice Frequency) 300 Hz 1,000 kilometers
VLF (Very Low Frequency) 3 kHz 100 kilometers
LF (Low Frequency) 30 kHz 10 kilometers
MF (Medium Frequency) 300 kHz 1 kilometer

HF (High Frequency) 3 MHz 100 meters
VHF (Very High Frequency) 30 MHz 10 meters
UHF (Ultra High Frequency) 300 MHz 1 meter

SHF (Super High Frequency) 3 GHz 10 centimeters
EHF (Extremely High Frequency) 30 GHz 1 centimeter
300 GHz 10 millimeters
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There is also a completely different NATO band scheme, with the bands much more conveniently arranged from “A” to “M” in order of increasing frequency. There isn’t a one-to-one correspondence between the NATO and traditional band schemes. The table below gives the NATO bands, with the frequency / wavelength given in each entry for the low end of the band:
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A 0 Hz –
B 250 MHz 1.2 meters
C 500 MHz 60 centimeters
D 1 GHz 3 centimeters
E 2 GHz 15 centimeters
F 3 GHz 10 centimeters
G 4 GHz 7.5 centimeters
H 6 GHz 5.0 centimeters
I 8 GHz 3.75 centimeters
J 10 GHz 3.0 centimeters
K 20 GHz 1.5 centimeters
L 40 GHz 7.5 millimeters
M 60 GHz 5 millimeters (up to 100 GHz / 3 millimeters)
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The NATO band scheme seems to be more popular in Europe, and is used worldwide for “electronic countermeasures?” systems that is, radio / radar jamming gear. In some publications it can be very unclear which scheme is being used, since the ITU and NATO schemes share some of the same designation letters, applied to entirely different ranges for instance, there are “C”, “L”, and “K” bands in both schemes that don’t have the matching definitions. Fortunately, the NATO scheme ends at “M”, so “S” and “X” bands can always be recognized as ITU definitions as can the “Ku” and “Ka” bands, since the NATO bands are all one letter. Since there’s no clear standard, this document uses the ITU band definitions