Practical_Antenna_Handbook_0071639586
C h a p t e r 3 : A n t e n n a B a s i c s 93 A B Figure 3.6 Electric field between wires at various angles. cifically, for the thin rod geometry we’ve been using, accelerating charges along the rods create previously unpredicted magnetic fields and those “new” magnetic fields similarly create “new” electric fields, which in turn create . . . well, you get the picture. Suppose we now attempt to observe the effects of these accelerating charges at a point in space far from the region around the rods. The acceleration of the electrons on the rods, coupled with the finite speed of light and all EM waves, causes us to detect an E-field that is at right angles to the radius line drawn between the rods and our observation point. Similarly, we detect a magnetic field that is also at right angles to the line between the rods and us, and at right angles to the E-field. In other words, both the E-field and the H-field are at right angles to the direction of travel from the antenna to the receiving point. These fields are not the static and quasi-static fields of high school science classes, and they were totally unknown prior to Maxwell’s treatise discovery of them! They can only be explained by the existence of a transverse electromagnetic wave originating from the region of the rods and traveling through space at the speed of light. It’s as if the E- and H-fields associated with the accelerating electrons are detached from the rods and pushed out into space each time electrons slam against the end of either rod. Further examination of the behavior of these fields at distant receiving points discloses the fact that these fields are an exact reproduction of the frequency and phase of the source voltage applied to the rods except for a delay that is proportional to the distance from the rods to the observation point. That delay is caused, of course, by the finite speed of light. Perhaps more surprising, however, is that if we attach a resistive load to our receiving antenna, we observe real power being dissipated! The E- and H-fields we are monitoring are two components of an electromagnetic wave propagating through space, and that wave is a real entity. That is, it carries energy with it and can do useful work wherever it goes, just as the sun’s rays warm you by delivering energy in the form of heat when you lie out in them at the beach.
94 P a r t I I : F u n d a m e n t a l s The received E-field at a point far from a very short (relative to wavelength) pair of rods oriented vertically and driven by a sine wave at frequency f 0 is described in spherical coordinates by 60πI ⎧ ⎛ ⎞⎫ 0h r E θ = sin θsin ⎨2πf ⎜t − ⎟⎬ (3.19) 0 λr ⎩ ⎝ c ⎠⎭ and the corresponding H-field is H φ I ⎧ ⎛ ⎞⎫ 0h r = sin θsin ⎨2πf ⎜t − ⎟⎬ (3.20) 0 2 λ r ⎩ ⎝ c ⎠⎭ These equations are not as complicated as they may seem; let’s break them down piece by piece, looking at each term: • 60 is the result of combining a bunch of physical constants into a single number. We’ll say more about it shortly. • I 0 is the amplitude of the drive current at the center of the two rods; it simply tells us the obvious: Any field we measure at a distant point is going to be directly proportional to the drive current at the source. • h is the total height, or length, of the antenna formed by the two rods, expressed as a fraction of the wavelength, l. Implicit in the approximations allowing us to use this equation is the constraint that h is small with respect to l. A good value might be l/20 or less. • r is the distance from the center of the two rods to our distant point. • q (pronounced “thay-ta”) is the angle from the axis of the antenna. The sinq term tells us that the E-field drops to zero off the ends of the antenna and is maximum broadside to the antenna, where sinq = 1. (See App. A for derivations and meaning of sine and cosine functions.) • sin{2pf 0 (t – r/c)} identifies the instantaneous amplitude of the E-field as a function of the drive signal frequency and the distance of the receiving point from the rods. Because this is an argument of a sine function, as it increases the resulting sine function simply goes through multiple cycles from –1 to +1 and back again. • The subscript q for the E-field means the only component of the E-field that has any amplitude far from the two rods is an E-field lying in the same direction as the axis of the rods. Although the axis of the rods is typically described as lying on the z axis of a cartesian coordinate system, the radiated wave is best analyzed in spherical coordinates. If not, we run the risk of E q becoming replaced by complicated equations for E x , E y , and E z . An E-field comprised of solely E q is consistent with our earlier statement that the E- and H-fields are always at right angles to the direction of wave propagation. • Similarly, the subscript f for the H-field tells us that the only detectable component of the magnetic field at a distant point is in the f direction as defined in
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C h a p t e r 3 : A n t e n n a B a s i c s 93<br />
A<br />
B<br />
Figure 3.6 Electric field between wires at various angles.<br />
cifically, for the thin rod geometry we’ve been using, accelerating charges along the<br />
rods create previously unpredicted magnetic fields and those “new” magnetic fields<br />
similarly create “new” electric fields, which in turn create . . . well, you get the picture.<br />
Suppose we now attempt to observe the effects of these accelerating charges at a<br />
point in space far from the region around the rods. The acceleration of the electrons on<br />
the rods, coupled with the finite speed of light and all EM waves, causes us to detect an<br />
E-field that is at right angles to the radius line drawn between the rods and our observation<br />
point. Similarly, we detect a magnetic field that is also at right angles to the line<br />
between the rods and us, and at right angles to the E-field. In other words, both the<br />
E-field and the H-field are at right angles to the direction of travel from the antenna to<br />
the receiving point.<br />
These fields are not the static and quasi-static fields of high school science classes,<br />
and they were totally unknown prior to Maxwell’s treatise discovery of them! They can<br />
only be explained by the existence of a transverse electromagnetic wave originating from<br />
the region of the rods and traveling through space at the speed of light. It’s as if the<br />
E- and H-fields associated with the accelerating electrons are detached from the rods<br />
and pushed out into space each time electrons slam against the end of either rod.<br />
Further examination of the behavior of these fields at distant receiving points discloses<br />
the fact that these fields are an exact reproduction of the frequency and phase of<br />
the source voltage applied to the rods except for a delay that is proportional to the distance<br />
from the rods to the observation point. That delay is caused, of course, by the finite<br />
speed of light. Perhaps more surprising, however, is that if we attach a resistive<br />
load to our receiving antenna, we observe real power being dissipated! The E- and<br />
H-fields we are monitoring are two components of an electromagnetic wave propagating<br />
through space, and that wave is a real entity. That is, it carries energy with it and can<br />
do useful work wherever it goes, just as the sun’s rays warm you by delivering energy<br />
in the form of heat when you lie out in them at the beach.
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