nature and revealed a set of striking equations that encompassed the various laws of electricity derived by Fscaday, Ampere, Ohm, and others. Maxwell's unified field equations of electric and magnetic behavior form today's basis of electromagnetic theory. Not only did Maxwell's equations describe all known electromag- tromagnetic waves may be found in Electromagnetics, by John D. Kraus McGraw-Hill Book Co., New York.
Radiation from an Antenna Radiation and interception of eleetromagnetic energy is explained by Maxwell's equations. The equations pro-
The abstract concept of a radio wave travelling through space is difficult to comprehend without the assistance of Maxwell's equations. Viewed from the simple concept of electron flow in a conductor there is no suggestion of radiation of energy into space in the form of electromagnetic waves. Maxwell's assumptions that an electric field changing in time is a form of current which sets up a magnetic field about itself, and the latter, also changing in time, sets up the electric field, is the basis for the further assumption that the two interact and propagate energy from one place to another. These assumptions provide the necessary bridge between simple electron flow and an electromagnetic field about the conductor.
Maxwell's equations (above) form the basis of modern electromagnetic theory. The first equation states that, in the absence of electric charges, electric lines of force can neither be created nor destroyed. The second equation states the same principle for magnetic lines of force and, in addition, states that magnetic charges do not exist. The third equation is a generalized statement of Faraday's Law that a changing magnetic field produces an electric field and that the ratio of the electrostatic units to the electromagnetic units is a constant (c) related to the speed of light. The fourth equation is derived from Ampere's Law and states that a changing electric field produces a magnetic field by virtue of the sum of the conduction and displacement currents and that the time rate of change of the electric field has properties related to the displacement current. E and H represent the electric and magnetic field strengths. Div (divergence) and curl (an abbreviation for rotation) represent mathematical operations expressing rate of change and vorticity. The symbol E indicates a partial differentiation with respect to time, t. Maxwell showed that an electric charge which is accelerated or decelerated is accompanied by a magnetic field which pulsates and, with the passage of time is propagated outward through the surrounding medium. The increase of energy, of course, has been supplied by the force responsible for the acceleration of the charge. During acceleration and deceleration, the magnetic field energy does not simply flow outward and again inward. Rather, this energy is radiated and permanently lost to the charge and its field. The electromagnetic feld thus created is in the form of an energy wave travelling radially outward from the source, with electric and magnetic components identical in form and mutually perpendicular. The electric and magnetic components become weaker as the wave travels outward because both are inversely proportional to the radius of the wave from the point of origin.
Figure 3. Maxwell's Famous Equations
netic phenomena, but in the broader sense predicted eleetromagnetic radiation, simultaneously introducing i4to physics the general concept of fields to describe interactions between one body and another. Maxwell's equations (Figure 3) picture the interplay ot' energy between electric and magnetic fields which is elf-maintained, with the energy radiating outward hom the point of origin. The equations express the continuous nature of the fields and define how changes in one field bring about changes in the other. The com- pound disturbance described by Maxwell's equations was proven in fact by Hertz, who generated, radiated and intercepted electromagnetic waves in 1888, fifteen years after Maxwell had predicted their existence. A mmplete discussion of Maxwell's equations and elec- vide the link between electron motion in a conductor and electromagnetic waves in space. In addition, the equations show that the electromagnetic field, in ebb and flow, provides a quantity of energy which is propa- gated outward and is detached from the field of the moving electron, or charge, in the antenna. The somewhat obscure concept of radiation from a current-carrying conductor may be pictured with the aid of an imaginary bit of antenna termed an oscillating doublet (Figure 4). Two equal electric charges of oppo- site polarity spaced a fixed distance apart in space com- prise this configuration. This concept allows for the regular, periodic linear displacement of charges along the axis of the doublet when excited by an alternating current. If the charges move up and down along the
RADIATION AND PROPAGATION
Figure 4. The Oscillating Doublet The creation of a closed eledric field about an oscillating doublet is illustrated here. The radiation of eledromag- netic energy takes place from an oscillating doublet composed of charges moving sinusoidally with respect to each other along a common axis. Current flow (move- ment of charges) causes a magnetic field to be created, which is perpendicular to the page and not shown. Sep- aration of charges causes an eledric field to be set up, which is shown here by eledric lines of force in the plane of the page. Since the currents and charges pro- ducing these fields are out of phase, the fields are also out of phase and constitute an indurtion field, the en- ergy of which cannot be detached from the doublet. The eledric field, however, in a radiated wave, does not terminate on a charge, and when the charges move together (C), the field closes upon itself in the polar regions. The independent electric field, in turn, gener- ates a magnetic field and both fields constitute a radi- ated eledromagnetic wave flowing outward from the doublet.
axis with equal and opposite velocities so that the sys- tem is in a continuous state of acceleration or decelera- tion, a current is said to flow in the doublet and the system must radiate energy. The principles of radiation of electromagnetic energy are based on Maxwell's laws that a moving electric charge creates an electric field. The created field at any instant is in step with the parent field, but is perpendic- ular to it in space. These laws hold true whether a conductor is present or not. At the start of oscillation (Figure 4A) the doublet is neutral and the charges are just beginning to move apart. Flux lines are drawn between the charges. An electromagnetic field is created with the direction of the magnetic field in a loop around the doublet, perpendic- ular to the page. The electric field is in the plane of the page. As the doublet moves toward its full displacement (Figure 4B) energy in both magnetic and electric fields is propagated outward. The intensity of the electromag- netic field is approximately E X H, showing that as the charges separate, stored energy is increasing in the
space around the doublet. Maxwell's first equation, moreover, states that the electric lines of force in a radiated wave do not terminate on a charge but are closed curves (div E = 0) in the polar regions of the doublet, as shown in Figure 4C. An instant after the independent field has been formed, the doublet charges start to move together, producing lines of force oppositc tu the recently formed independent electric field (Figure 4D). At first thought it would appear as though the periodic reversal of charge would result in a periodic reversal of the energy flow and no net energy would flow outward. This would be so if the field at a point away from the doub- let at a given instant depended on the charge distribu- tion of the doublet at that instant. However, there is a time Iag between the creation of a particular current in the doublet, the charge distribution, and the conse- quent electromagnetic field at a given point. It is this time lag that allows some of the energy in the region around the doublet to continue to travel outward in a closed electric field even when conditions of charge at the doublet indicate a flow of energy directed inward toward the doublet. The closed, moving electric field generates a magnetic field in accord with Maxwell's third law and the detached electromagnetic field moves away from the doublet at the speed of light. The cycle starts to repeat itself with the collapse of the field when the charges move together and then separate once again. With sinusoidal doublet motion there must, there- fore, be a continuous radiation of energy over and above the amount required to establish a steady-state field. Maxwell's equations describe a beautifully simple electromagnetic wave traveling radially outward from the doublet, becoming weaker with distance since the two component fields are inversely proportional in strength to the distance traveled from the doublet. There is no loss of energy, it is merely dissipated in area as the wave spreads. Once having been produced,the expanding wave travels and propagates itself for an unlimited time, as do the light waves reaching the earth from an extragalactic nova, millions of years after the start that created them has ceased to exist.
The Standing Wave
A previous paragraph touched on the voltage standing-
wave ratio (SWR) and its relation to antenna system
discontinuity, and to the coefficient of reflection. This
is an important concept and deserves additional elabo-
ration.
When an electromagnetic wave travels through space,
there is a balance between the electric and magnetic
fields, with half the energy in each field (Figure 5). If
the wave enters a new medium, or encounters a discon-
tinuity in the medium, there must be a new redistribu-
tion of energy. Whether the new medium is a
conducting, semiconducting, or nonconducting mate-
rial, there will have to be a readjustment of energy
RADIATION AND PROPAGATION
Figure 5. Oblique View of Traveling Wave The traveling eledromagnetic wave is represented in terms of its eledric and magnetic components, identical in form, and perpendicular in diredion to each other and to the diredion of travel of the wave. The fields vary sinusoidally along the axis of travel and at any fixed point, the fields vary sinusoidally with time. As the wave travels, the whole pattern moves to the right with the velocity of light.
relations as the wave reaches the surface of the disconti- nuity. Sina no new energy can be added to the wave as it pmsa through the boundary surface, the only way that t new balance may be achieved is for some of the nergy to be rejected. The rejected energy constitutes a I/lected wave. In this manner, the observer sees reflec- ti0n of light from a conducting metal surface or from a aonconducting glass surface. The electromagnetic wave, if unimpeded, will travel definitely in free space. In the hypothetical case of an f'mitely long conducting medium, the traveling wave COuld voyage onward forever. But if the medium is bfoken at a point, and a load, or absorptive device (a dintinuity) of the correct magnitude replaces the rest of the medium, the energy is completely absorbed and oonverted to heat in the load. If the medium is termi- 0lted by a discontinuity having reflective properties, tke discontinuity will reflect energy back through the edium toward the source. The reflected energy will Combine with the forward energy in such a way as to produce a pattern in the medium known as a standing woYo.
Wave Reflection An example of a simple discontinuity is a perfectly oonducting plane surface (Figure 6). A wave falling on tbe surface is totally reflected. Both the electric and magnMic components of the traveling wave are re- , but while the electric component is reflected rith reversal of sign (A) thus leaving the electric field at the retlecting surface zero, the magnetic component is retlected with unchanging sign (B) and is so doubled at the reflecting surface. The sum of the forward and
reflected traveling waves is a standing wave which is continually changing in magnitude but is fixed in space, resembling the vibration of a string on a musical instru- ment. The total electric intensity at the reflecting sur- face is always zero, and also zero at distances that are multiples of half-wavelengths from the surface. These points of zero electric field are termed nodes. There are also nodes in the intensity of the magnetic field, at i/a wavelength and odd muftiples thgrgof from the reflec- tor. If there were no loss of energy, for example, in the form of friction in the case of the vibrating string, or energy lost in the traveling wave, the standing wave would persist indefinitely. Derivations of Maxwell's equations show that where there are nodes of magnetic fields, maximum electric fields (loops) occur. In addition, the standing waves of magnetic and electric fields pulse out of phase in time, so that when the magnetic field is zero, the electric field is maximum, and vice versa. Thus, the standing wave has a very different appearance from a traveling wave, although it is nothing more than the sum of two travel- ing waves.
The Reflection Coefficient When an electromagnetic wave falls on the surface of a dielectric or insulating material, or meets a discontinu- ity, there is a partial reflection and partial transmission of the incident energy. That fraction of the incident wave that is reflected, when expressed as a ratio of the original wave, is termed the reflection coefficient. If the reflection coefficient is low (the discontinuity of the medium possessing poor reflective qualities), there is very little reflected energy, and the total field about the reflecting surface is only slightly modified from that of a traveling wave. If, on the other hand, the reflection coefficient is near unity (the discontinuity possessing good reflective qualities), the maximum field strength will vary as a function of the distance from the surface, with well-defined nodes and loops. The resulting wave bears a definite relationship to the amplitude of the reflected wave and to the reflection coefficient, as ex- pressed by:
Finally, it should be noted that if the medium is terminated by a load of the proper magnitude, no dis- continuity or reflection will exist in the medium, and the medium is considered to be matched. The degree of mismatch between the medium and the load can be defined in terms of the amplitude of the reflected wave, or in terms of the standing-wave ratio (SWR), which may be readily measured by inexpensive instruments.
, I',I.