Antenna Basics (Frequency)

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Frequency is one of the most important concepts in the universe and to antenna theory, which we will see. But fortunately, it isn’t too complicated.

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Beginner Level (or preliminaries):

Antennas function by transmitting or receiving electromagnetic (EM) waves. Examples of these electromagnetic waves include the light from the sun and the waves received by your cell phone or radio. Your eyes are basically “receiving antennas” that pick up electromagnetic waves that are of a particular frequency. The colors that you see (red, green, blue) are each waves of different frequencies that your eyes can detect.

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your eye is an antenna

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All electromagnetic waves propagate at the same speed in air or in space. This speed (the speed of light) is roughly 671 million miles per hour (1 billion kilometers per hour). This is roughly a million times faster than the speed of sound (which is about 761 miles per hour at sea level). The speed of light will be denoted as c in the equations that follow. We like to use “SI” units in science (length measured in meters,time in seconds,mass in kilograms), so we will forever remember that:

speed of light is a constant function of frequency times wavelength

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Before defining frequency, we must define what a “electromagnetic wave” is. This is an electric field that travels away from some source (an antenna, the sun, a radio tower, whatever). A traveling electric field has an associated magnetic field with it, and the two make up an electromagnetic wave.

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The universe allows these waves to take any shape. The most important shape though is the sinusoidal wave, which is plotted in Figure 1. EM waves vary with space (position) and time. The spatial variation is given in Figure 1, and the the temporal (time) variation is given in Figure 2.

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sinusoidal wave, plotted as a function of space

Figure 1. A Sinusoidal Wave plotted as a function of position.

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electromagnetic wave plotted versus time

Figure 2. A Sinusoidal Wave plotted as a function of time.

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The wave is periodic, it repeats itself every T seconds. Plotted as a function in space, it repeats itself every wavelength meters, which we will call the wavelength. The frequency (written f ) is simply the number of complete cycles the wave completes (viewed as a function of time) in one second (two hundred cycles per second is written 200 Hz, or 200 “Hertz”). Mathematically this is written as:

frequency is the number of cycles per second (Hertz)

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How fast someone walks depends on the size of the steps they take (the wavelength) multipled by the rate at which they take steps (the frequency). The speed that the waves travel is how fast the waves are oscillating in time (f ) multiplied by the size of the step the waves are taken per period (wavelength). The equation that relates frequency, wavelength and the speed of light can be tattooed on your forehead:

frequency times wavelength gives the speed of propagation for all waves

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Basically, the frequency is just a measure of how fast the wave is oscillating. And since all EM waves travel at the same speed, the faster it oscillates the shorter the wavelength. And a longer wavelength implies a slower frequency.

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This may sound stupid, and actually it probably should. When I was young I remember scientists discussing frequency and I could never see why it mattered. But it is of fundamental importance, as will be explained in the “more advanced” section on frequency.