# HOW RADIO WAVES ARE BORN

One of the least-understood phenomena in electrical engineering is how electric and magnetic fields allow a transmission antenna to form what we know as radio waves. This overview (which makes certain assumptions to eliminate the need for calculus) describes how electromagnetic fields behave to provide propagated radio signals. (An expanded version can be found at www.jphawkins.com/radio.shtml or at *MRT*‘s Web site at www.mrtmag.com.)

The electromagnetic field equations developed by 19th-century physicist James Clerk Maxwell lead us to begin with the premise that a changing magnetic field causes the existence of an electric field, and a changing electric field causes the existence of a magnetic field. We move from there to establish that electromagnetic waves can exist in space without the presence of a conductor. Finally, based on these two phenomena, the transition from conduction electromagnetic fields (those bound to the conductor) to those existing in free space becomes apparent, as well as the mechanism of propagation of these fields as waves.

### Changing magnetic fields creates electric fields in space

In a straight wire, the total voltage can be calculated by multiplying the electric field intensity that is parallel to the wire by the length of the wire:

*Vc = E × L*

where

*L* = the length of the wire (m)

*E* = electric field strength (V/m)

*Vc* = the resulting potential between the ends of the wire (V)

To find the relationship of the total voltage to the magnetic flux density *B*, we use Faraday’s Law, which states that the voltage induced in a loop of wire is directly proportional to the number of magnetic flux lines, (measured in *Webers*) passing through the wire per unit of time. So, the number of volts is proportional to Webers per second.

If we assume that all the flux lines are perpendicular to the wire, we can write that the total flux, in Webers, is *B × A,* where *B* is the flux density in Webers/m^{2} and *A* is the area in square meters. To express this in terms of Faraday’s Law, let’s say that the flux density changes from *B = B _{0}* to

*B = B*. We express the voltage developed as the flux changes from time “0” (

_{1}*t*) to time “1” (

_{0}*t*) as:

_{1}*Vc = A(B _{1} – B_{0}) ÷ (t_{1} – t_{0})*

Taking the voltage due to the electric field, *E*, and substituting, we now have:

*E × L = A(B _{1} = B_{0}) ÷ (t_{1} – t_{0})*

which is the mathematical equivalent to the statement that a changing magnetic field, *B*, will create an electric field, *E*, in space.

### Create a magnetic field in space

The idea of *displacement current* is the key to developing a mathematical explanation that a magnetic field is born out of a changing electric field in space. Displacement current is an abstract idea that there is an electric current flowing in space. By assuming that a “current is flowing,” certain assumptions can be made to develop the necessary equations. (For more on the development of the displacement current concept, see the previously referenced Web site.)

First, we introduce *dielectric displacement, D,* which represents the electrical strain that occurs in a dielectric medium, when an electric field is present:

*D* = ε*E*

*B* = μ*H*

*D* is analogous to magnetic flux density, *B*; hence *D* is really the *electric* flux density. It is related to the electric field by ε, which is the *permittivity,* or dielectric constant, of the material between the plates of a capacitor. The magnetic flux density, *B,* is related to the magnetic field strength, *H,* by μ, which is the permeability of the material within the magnetic field.

A capacitor is a useful model to explore the displacement current concept. When a voltage is applied to the leads of an uncharged capacitor, a current flows until the capacitor is fully charged. What is happening between the plates of the capacitor (that, for this example we assume is filled with space)?

First, as current flows into the capacitor, an electric charge accumulates on the plates, with excess electrons on one plate and positive ions on the other. As the charge builds up, an electric field, *E,* builds between the plates, causing the dielectric displacement, or electric field density, to also increase. To satisfy Kirchoff’s law (the total current flowing *into* a volume must flow *out* of the volume), there must be some sort of current flowing in the dielectric, and it must be proportional to the rate of change of dielectric displacement. This current is called *displacement*. We can think of it as an inflow (displacement) of additional flux, as required, as the electric flux density increases. This total displacement current equals the conduction current flowing into and out of the capacitor.

Maxwell made the assumption that a magnetic field was associated with the displacement current. In considering this, he developed the following relationship, assuming that the displacement current is perpendicular to the area and the area is flat:

*H × L = A (D _{1} – D_{0}) ÷ (t_{1} – t_{0})*

where

*A × D* = the total flux across the capacitor space

*(D _{1} – D_{0}) ÷ (t_{1} – t_{0})* = the change in flux density with a change in time.

The displacement current is the rate of change of the electric flux across the capacitor space.

### We have radiation

We have finally arrived at two simplified versions of the principal field equations of Maxwell:

*E × L = A(B _{1} – B_{0}) ÷ (t_{1} – t_{0})*

*H × L = A(D _{1} – D_{0}) ÷ (t_{1} = t_{0})*

If we make the substitutions from *B* = μ*H* and *D* = ε*E*, we have the following non-calculus simplification of Maxwell’s free-space equations:

*E × L* = μ*A(H _{1} – H_{0}) ÷ (t_{1} – t_{0})*

a changing magnetic field, *H,* will produce an electric field, *E*, and

*H × L* = ε*A(E _{1} – E_{0}) ÷ (t_{1} – t_{0})*

a changing electric field, *E,* will produce a magnetic field, *H*.

These equations are the keys to electromagnetic radiation. Most important is the fact that no conduction current need exist and, therefore, no physical conductor is required.

### The concept of radiation

The concept of radiation, therefore, can be described as: *If there is an alternating current in a conductor, an alternating magnetic field will be created surrounding the wire. The alternating magnetic field, due to the current in the wire, will create an alternating electric field in space farther out from the conductor*.

We have liftoff. The first transition from conduction fields to space fields has been made. Carrying it further, the alternating electric field, which was just born in space, will create a magnetic field (due to the corresponding displacement current in space) farther away from the conductor. The alternating magnetic field will then create another alternating electric field. This process, which continues on away from the conductor, is called electromagnetic wave propagation, and that gives us *radio*.

Hawkins, a writer in Middleton, NJ, with a background in electrical engineering and computer science, develops fiber-optic test-and-measurement software for Tycom Laboratories, Eatontown, NJ. He is a member of the Radio Club of America. For more detailed information on this subject, visit his broadcast technology Web site at www.jphawkins.com/radio.shtml.

### FURTHER READING

Griffith, Benjamin Whitfield, *Radio-Electronic Transmission Fundamentals,* McGraw-Hill, 1962.

Hayt, William H. Jr., *Engineering Electromagnetics,* 5th ed., McGraw Hill, 1989.

Kaplan, Wilfred, *Advanced Calculus,* 1st ed., 5th printing, Addison Wesley, 1959.

Kraus, John D., *Electromagnetics,* 4th ed., McGraw Hill, 1992.

MacLeish, Kenneth, “Why an Antenna Radiates,” *QST,* Nov. 1992.

Schev, H. M., *Div, grad, curl, and all that: an informal text on vector calculus*, 3rd ed., Norton, 1997.

Sears, Francis Weston and Mark W. Zemansky, *University Physics,* 3rd ed., Addison Wesley, 1964.