## The Field Of An Alternating Current

If we allow the voltage source across a wire to slowly oscillate in time at frequency, fo, the accompanying electric field will take the same form as that of the DC charge, except that the magnitude will vary between positive and negative values (see Figure 5.8).

Relating frequency to wavelength by l = c/f, we define "slow oscillation" as any frequency whose corresponding wavelength is much greater than the length of the wire. This condition is often called quasi-static. In this case, the current in the wire will vary sinusoidally, and the effective charge will experience a sinusoidal acceleration. Consequently, the oscillating charge will radiate electromagnetic energy at frequency, fo. The power (energy per time) radiated is proportional to the magnitude of current squared and the length of the wire squared, because both parameters increase the amount of moving charge. The radiation power is also proportional to the frequency squared since the charge experiences a greater acceleration at higher frequencies. (Imagine yourself on a spinning ride at an amusement park. The faster it spins, the greater the acceleration you and your lunch feel.)

Expressed algebraically:

Figure 5.9 Electric field surrounding a wire carrying a rapidly varying AC current. A) Electric field at time t = 0. B) Electric field at time t = T/2, a half-cycle later.

VRadiated power ~ current x length x frequency

This expression shows clearly why RF signals radiate more readily than signals at lower frequencies such as those in the audio range. In other words, a given circuit will radiate more at higher frequencies. Because wavelength is inversely proportional to frequency (l = c/f), an equivalent expression is

VRadiated power ~ (current) x (electrical length)

Hence, at a given source voltage and frequency, the radiated power is proportional to the length of the wire squared. In other words, the longer you make an antenna, the more it will radiate.

Up until now we have considered only slowly oscillating fields. When the frequency of the voltage source is increased such that the wavelength approaches the length of the wire or greater, the quasi-static picture no longer holds true. As shown in Figure 5.9, the current is no longer equal throughout the length of wire. In fact, the current is pointing in different directions at different locations. These opposing

Figure 5.10 The root-mean-square radiation power versus electrical length for a dipole antenna driven by 1 ampRMS of current. The radiation resistance follows the same curve. At one-half wavelength the resistance is 73 ohms.

 i ) 05 1 1.5 2 2.5 3 Antenna Length [wavelengths]

currents cause destructive interference just as water waves colliding from opposite directions tend to cancel each other out. The result is that the radiation is no longer directly proportional to the wire or antenna length squared.

Figure 5.10 shows a plot of radiated power as a function of antenna length. When the antenna is much smaller than a wavelength, the radiated power is proportional to the length squared. However, for wire lengths near or above the wavelength, the radiated power relates as a slowly increasing and oscillating function. This "diminishing returns" of the radiation power versus wire length is one of the reasons that 1/2 is usually chosen as the length for a dipole antenna (1/4 for a monopole). The other reasons being that at l = 1/2, the electrical impedance of the antenna is purely real (electrically resonant), and the radiation pattern is simple (single lobed) and broad.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

Get My Free Ebook