RF Wavelength Calculations for Wireless Networks

The wavelength of a RF wave is calculated as the distance between two adjacent identical points on the wave. The wavelength is frequently measured as the distance from one crest of the wave to the next.

The wavelength is an important factor in wireless networking. The wavelength dictates the optimum size of the receiving antenna and it determines how the RF wave will interact with its environment. For example, an RF wave will react differently when it strikes an object that is large in comparison to the wavelength than when it strikes an object that is small in comparison to the wavelength.

The wavelength and the frequency are interrelated. For a given medium, if you know the wavelength, you can calculate the frequency and if you know the frequency, you can calculate the wavelength. The wavelength is directly related to the frequency and the speed of light. If you know the frequency, you can calculate the wavelength. If you know the wavelength, you can calculate the frequency.

One of the great discoveries in the history of electromagnetism is that electromagnetic waves travel at the speed of light. Since we know the speed of light to be 299,792,458 meters per second (or the simple 300,000,00 meters per second, if you prefer), we also know that this is the speed at which electromagnetic waves travel in a vacuum. This was theorized by James Clerk Maxwell and proved through experimentation by Heinrich Hertz.

You are probably familiar with measurements like 100 megahertz and 3.6 gigahertz. These measurements refer to the number of cycles per second. When we say that the access point is using the 2.45 GHz (gigahertz) spectrum, we say it is using the spectrum that uses a wave cycle rate of 2,450,000,000 times per second. This measurement is named for Heinrich Hertz and his research in electricity and magnetism. A kilohertz is 1,000 hertz or cycles per second. A megahertz is 1,000,000 hertz and a gigahertz is 1,000,000,000 hertz. A terahertz is one trillion hertz, but these frequencies are not commonly found in today’s wireless communications.

Since we know that RF waves travel at the speed of light we can calculate the frequency when we know the wavelength or the wavelength when we know the frequency. The following formula can be used to calculate the wavelength in meters when the frequency is known:

w = 299,792,458 / f

Where w is the wavelength in meters and f is the frequency in hertz and the medium is a vacuum. Therefore, the 2.45 GHz spectrum would have a wavelength that is calculated with the following formula:

w = 299,792,458 / 2,450,000,000

The result is .123 meters or approximately 12.3 centimeters in length. This translates to about 4.8 inches. To calculate inches from centimeters, just multiple the number of centimeters times 0.3937. The formal character used to represent a wavelength is the Greek lambda (λ), and the symbol for the speed of light is c. Therefore, the formal representation of the previous formula would be:

λ = c / f

The calculation for frequency is just the opposite. You will divide the speed of light by the wavelength in meters to discover the frequency. Keep in mind that the numbers we’ve been using have been rounded and that impacts the results of the following formula; however, the results are close enough to recognize that a wavelength of .123 meters would indicate a RF wave in the 2.45 GHz spectrum:

f = 299,792,458 / .123
f = 2437337056.91

Due to the complex measurement number that is the speed of light, this number is often rounded to 300 billion meters per second. While this will change formula results, the findings are close enough for understanding the behavior of RF waves; however, engineers developing RF systems must use more precise measurements. Additionally, formulas like the following simplify matters:

wavelength in inches (λ) = 11.811 / f (in GHz)
wavelength in centimeters (λ) = 20 / f (in GHz)

Because wireless networks use such high frequency ranges, formulas like this make the calculations easier.
 

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