Practical_Antenna_Handbook_0071639586
C h a p t e r 2 : r a d i o - W a v e P r o p a g a t i o n 15 90 Electric field E Magnetic field B Direction of travel Figure 2.3 A transverse electromagnetic (TEM) wave consists of electric and magnetic fields at right angles to each other and to the direction of wave propagation. all directions from the source. When a radio wave encounters a receiving antenna, it delivers energy to that antenna and to any associated load. If the load impedance includes a real, or resistive part, real power is dissipated in it—power that can only have come from the arriving wave! Radio-Wave Intensity In free space, a radio wave expanding outward over an ever-growing spherical surface centered on the source (accelerated electrons on a conductor) neither gains nor loses energy. Thus, with the passage of time and distance, the original amount of energy is spread over a larger and larger surface (the wavefront). A helpful analogy is to visualize the process of blowing up a balloon. The total energy in the wavefront is analogous to the total rubber in the skin of the balloon. Of course, as you blow into the balloon, the balloon expands and the skin becomes thinner. Similarly, as the radio wavefront occupies a larger and larger spherical surface, the power per unit area of the surface anywhere on the sphere is smaller and smaller. Thus, even though there are no obstacles in free space to dissipate the energy in the wavefront, if we could measure the amplitude of the passing wavefront at points progressively farther from the source we would see that it decreases with distance from the source. In common radio lingo, we say the radio wave is attenuated (i.e., reduced in apparent power) as it propagates from the transmitter to the receiver, but this can be misleading unless we understand that the so-called attenuation we are referring to is not the same as when we attenuate a signal in a resistive voltage divider. Because a fixed amount of power in the wavefront is spread over a larger and larger surface area, the amplitude of the wave is inversely proportional to the total area of the sphere’s surface. That area is, of course, proportional to the square of the radius of the surface from the source, so radio waves at all frequencies suffer losses according to the inverse square law. Let’s take a look at that phenomenon.
16 p a r t I I : F u n d a m e n t a l s Electric fields (E-fields) are measured in units of volts per meter (V/m), or in the subunits millivolts per meter (mV/m) or microvolts per meter (µV/m). Thus, if a vertically oriented E-field of 10 mV/m crosses your body from head to toe, and you are about 2 m tall, a voltage of (2 m) × (10 mV/m), or 20 mV, is generated. As a radio wave travels outward from its source, the electric field vector falls off in direct proportion to the distance traveled. The reduction of the E-field is linearly related to distance (i.e., if the distance doubles, the E-field voltage vector halves). Thus, a 100-mV/m E-field that is measured 1 mi from the transmitter will be 50 mV/m at 2 mi. The power in any electrical system is related to the voltage by the relationship P = V 2 R (2.4) where P = power in watts (W) R = resistance in ohms (Ω) V = electrical potential in volts (V) In the case of a radio wave, the R term is replaced with the impedance (Z) of free space, which happens to be 377 Ω. If the E-field intensity is, for example, 10 V/m, then the power density of the signal is (10 V / m) P = 377Ω 2 2 2 = 0.265 W / m = 26.5 mW / m (2.5) The power density, measured in watts per square meter (W/m 2 ) or subunits thereof, falls off according to the square of the distance, for the “stretched balloon” reasons described previously. This phenomenon is shown graphically in Fig. 2.4. Here, you can see a lamp emitting a light beam that falls on a surface (A), at distance L, with a given intensity. At another surface (B) that is 2L from the source, the same amount of energy is Lamp A B L 2L Figure 2.4 Wave propagation obeys the inverse square law.
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16 p a r t I I : F u n d a m e n t a l s<br />
Electric fields (E-fields) are measured in units of volts per meter (V/m), or in the<br />
subunits millivolts per meter (mV/m) or microvolts per meter (µV/m). Thus, if a vertically<br />
oriented E-field of 10 mV/m crosses your body from head to toe, and you are<br />
about 2 m tall, a voltage of (2 m) × (10 mV/m), or 20 mV, is generated. As a radio wave<br />
travels outward from its source, the electric field vector falls off in direct proportion to<br />
the distance traveled. The reduction of the E-field is linearly related to distance (i.e., if<br />
the distance doubles, the E-field voltage vector halves). Thus, a 100-mV/m E-field that<br />
is measured 1 mi from the transmitter will be 50 mV/m at 2 mi.<br />
The power in any electrical system is related to the voltage by the relationship<br />
P =<br />
V 2<br />
R<br />
(2.4)<br />
where P = power in watts (W)<br />
R = resistance in ohms (Ω)<br />
V = electrical potential in volts (V)<br />
In the case of a radio wave, the R term is replaced with the impedance (Z) of free<br />
space, which happens to be 377 Ω. If the E-field intensity is, for example, 10 V/m, then<br />
the power density of the signal is<br />
(10 V / m)<br />
P =<br />
377Ω<br />
2<br />
2 2<br />
= 0.265 W / m = 26.5 mW / m<br />
(2.5)<br />
The power density, measured in watts per square meter (W/m 2 ) or subunits thereof,<br />
falls off according to the square of the distance, for the “stretched balloon” reasons described<br />
previously. This phenomenon is shown graphically in Fig. 2.4. Here, you can see<br />
a lamp emitting a light beam that falls on a surface (A), at distance L, with a given intensity.<br />
At another surface (B) that is 2L from the source, the same amount of energy is<br />
Lamp<br />
A<br />
B<br />
L<br />
2L<br />
Figure 2.4 Wave propagation obeys the inverse square law.
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