# Understanding electromagnetic fields and antenna radiation takes (almost) no math

Ron Schmitt, Sensor Research and Development Corp -March 02, 2000

Understanding antennas and electromagnetic fields is obviously important in RF engineering, in which capturing and propagating waves are primary objectives. An understanding of RF fields is also important for dealing with the electromagnetic-compatibility (EMC) aspects of every electronic product, including digital systems. EMC design is concerned with preventing circuits from producing inadvertent electromagnetic radiation and stray electromagnetic fields. EMC also involves preventing circuits from misbehaving as a result of ambient radio waves and fields. With digital systems' ever-increasing frequencies and edge rates, EMC is becoming harder to achieve and is no longer a topic just for experts. The seemingly mystical processes by which circuits radiate energy are actually quite simple. To understand them, you don't even need to know Maxwell's equations.

Consider the following fictitious disagreement. An electrical engineer is telling a lawyer friend about a new home-electronics project. The engineer lives near some high-voltage power lines and is working on a device for harnessing the power of the 60-Hz electromagnetic field that permeates his property. The lawyer immediately states that what the engineer plans to do would, in effect, be stealing from the utility company.

This statement angers the engineer, who replies, "That's the trouble with you lawyers. You defend laws without regard to the truth. Even without my device, the stray electromagnetic energy from the power lines is radiated away and lost, so I might as well use it." The lawyer stands his ground and says that the engineer will still be stealing.

Who is right? The lawyer is correct, even though he probably doesn't know the difference between reactive and radiating electromagnetic fields. The field surrounding the power lines is a reactive field, meaning that it stores energy as opposed to radiating energy, so the engineer's device would in fact be "stealing" energy from the power lines. But why? Why do some circuits produce fields that only store energy, whereas others produce fields that radiate it?

The energy goes back and forth

To further examine this situation, consider the circuit of Figure 1a. It is a simple circuit consisting of an ac power source driving an inductor. If the inductor is ideal, no energy is lost from the power supply. The inductor does, however, produce an electromagnetic field. Because no energy is lost, this field is purely a storage field. The circuit pumps power into the field, which then returns energy to the circuit. Because of this energy cycling, the current and voltage of the inductor are out of phase by 90°, thus producing a reactive impedance, ZL =jωL. The reactive nature of the impedance explains why such storage fields are called reactive fields.

Figure 1
An inductor creates a reactive field that stores energy (a). Adding a second inductor harnesses the reactive field to transfer energy to a load without metallic contact (b).

Referring to Figure 1b, when you place a second circuit consisting of an inductor and a resistor near the first circuit, the field from L1 couples to L2 and causes current to flow in the resistor. (The coupled fields create a transformer.) The reactive field transfers energy from the source to the resistor even though the original circuit has not changed. This action suggests that a reactive field can store or transfer energy, depending upon what other electrical or magnetic devices are in the field. So the reactive field "reacts" with devices that are within it. Similarly, a capacitor creates a reactive field that can store energy, transfer energy, or do both (Figure 2).

Figure 2
A capacitor creates a reactive field that stores energy (a). Adding a second capacitor harnesses some of the reactive field to transfer energy to a load without metallic contact (b).

Now consider the circuits of Figure 3. An ac voltage source drives two types of ideal antennas, a half-wavelength loop and a half-wavelength dipole. Unlike the previous circuits, the antennas launch propagating fields that continuously carry energy away from the source. The energy is not stored but propagates from the source regardless of whether there is a receiving antenna. This energy loss appears as resistance to the source in a similar manner to how loss in a resistor corresponds to heat loss.

Figure 3
The two most basic antennas are a loop antenna whose circumference is equal to the source wavelength divided by 2 (a) and a dipole antenna whose length is equal to the source wavelength divided by 2 (b).

Now back to the engineer and the lawyer. The engineer thought that the power-transmission line near his house was radiating energy the way an antenna does and that he was just collecting the radiating energy with a receiving antenna. However, when the engineer measured the field on his property, he measured the reactive field surrounding the power lines. When he activates his invention, he is coupling to the reactive field and removing energy that is stored in the field surrounding the power lines—energy that would otherwise be cycled to the loads. The circuit is analogous to the transformer circuit in Figure 1b, so the engineer is, in fact, stealing the power.

These examples illuminate the characteristics of reactive and radiating electromagnetic fields, but they still do not answer the question of why or how radiation occurs. To understand radiation, it is best to start with the analysis of the field of a point charge.

For a single charged particle, such as an electron, the electric field forms a simple radial pattern (Figure 4). By convention, the field lines point outward for a positive (+) charge and inward for a negative (–) charge. The field remains the same over time; hence, it is called a static field. The field stores the particle's electromagnetic energy. When another charge is present, the field imparts a force on the other object, and energy is transferred. When no other charged particles are present, the field has no effect but to store energy. The fact that energy is transferred from the field only when another charged particle is present is a defining characteristic of the static field. As you will soon learn, this fact does not hold true for a radiating field.

Figure 4
You can show the electric field of a static charge (a) or a dipole (b) as a vector plot, a streamline plot, and a log-magnitude contour plot.

Now consider the same charged particle moving at a constant velocity, much lower than the speed of light. The particle carries the field wherever it goes, and, at any instant, the field appears the same as in the static case (Figure 5a). In addition, because the charge is now moving, a magnetic field also surrounds the charge in a cylindrical manner, as governed by Lorentz's law. This magnetic field is a consequence of the fact that a moving electric field produces a magnetic field and vice versa. As with a static charge, both the electric and magnetic fields of a constant-velocity charge store energy and transmit electric and magnetic forces only when other charges are present. To make the description easier, the rest of this article ignores the magnetic field.

Figure 5
The electric field follows a particle moving to the right with constant velocity (a); the electric field follows a particle moving to the right with constant acceleration (b); the electric field follows a particle coming into motion from a resting condition (c). Particle locations and field lines at earlier times appear in gray.

When a charged particle accelerates, the lines of the electric field start to bend (Figure 5b). A review of Einstein's theory of relativity helps to explain why the bending occurs: No particle, energy, or information can travel faster than the speed of light, c. This speed limit holds for fields as well as particles. For that matter, a field is just a group of virtual particles (see sidebar "Quantum physics and virtual photons"). For instance, if a charged particle were suddenly created, its field would not instantly appear everywhere. The field would first appear immediately around the particle and then extend outward at the speed of light. For example, light takes about eight minutes to travel from the sun to earth. If the sun were to suddenly extinguish, people on earth would not know until eight minutes later. Similarly, as a particle moves, the surrounding field continually updates to its new position, but this information can propagate only at the speed of light. Points in the space surrounding the particle actually experience the field corresponding to where the particle used to be. This delay is known as time retardation . It seems reasonable to assume that even a charge moving at constant velocity should cause the field lines to bend because of time retardation. However, nature (that is, the electromagnetic field) gets around the delay by predicting where the particle will be based on its past velocity. Therefore, field lines of particles moving at constant velocities do not bend. This behavior stems from Einstein's theory of special relativity, which states that velocity is a relative—not an absolute—measurement. Furthermore, the bent field lines of the charge correspond to radiating energy. Therefore, if the field lines are straight in one observer's reference frame, conservation of energy requires that all other observers perceive them as straight.

A curious kink

To understand why the bent field lines of a charge correspond to radiated energy, consider a charged particle that starts at rest and is "kicked" into motion by an impulsive force. When the particle accelerates, a kink appears in the field immediately surrounding the particle. This kink propagates away from the charge, updating the rest of the field that has lagged behind (Figure 5c). Part of the energy exerted by the driving force is expended to propagate the kink in the field. Therefore, the kink carries with it energy that is electromagnetic radiation. Fourier analysis shows that because the kink is a transient, it consists of a superposition of many frequencies. Therefore, a charge accelerating in this manner simultaneously radiates energy at many frequencies.

You can also analyze this phenomenon from a kinetic-energy perspective. In freshman physics, you learned that it takes a force to accelerate a particle and that the force transfers energy to the particle, thus increasing its kinetic energy. The same analysis holds true for the particle's field. Energy is required to accelerate the field. This energy propagates outward as a wave, increasing the field's kinetic energy (Figure 6a).

Figure 6
These log-magnitude plots show the electric field of accelerated charges. A charge starts at rest and is accelerated by a short impulsive force (a). A charge starts at rest and is sinusoidally accelerated along the horizontal axis (b).

All electromagnetic radiation—be it RF, thermal, or optical—is created by changing the energy of electrons or other charged particles. This general statement applies not only to free-electron-energy changes that result from acceleration and deceleration, but also to quantum-energy-state (orbital) changes of electrons bound into atoms.