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Voltage waves In A, B, and C -------- Voltage wave due to point of - Voltage wave due to point of Resultant voltage wave charge charge
Current waves In D, E, and F -------- Current wave due to point of - Current wave due to point of Resultant current wave charge charge
5-11 Standing waves of voltage and current
136 Fundamentals of radio antennas
T0 T2 T3 Time T4 T5 T6 T8 T16 T14 T13 T12 A T11 T10 T8 Voltage distribution Y X B
Voltage
T3 T4
T10 T11
T12 T13 T14 T15 T16
Voltage at A Voltage at Y
5-12 Standing waves of voltage at a point on the antenna
The peak amplitude of the sine wave produced at any point depends on its position on the antenna The nearer the point is to either end, the greater its peak amplitude Standing waves of current The standing waves of current occurring at various times through the RF cycle are assembled on a single axis in Fig 5-13 This axis, AB, represents the half-wave antenna If the current variations at point Y from T0 to T16 are graphed in respect to time, the result is the sine wave in Fig 5-13B This is true for any point along the antenna with the exception of the nodes at the ends The current has its greatest swing at X, the center of the antenna Comparison of the voltage variation curve (Fig 5-12A) with the current variation curve (Fig 5-13A) shows the voltage curve leading the current curve by 90 at Y This relation can be expected on any half-wave device
Antenna fundamentals 137
T4 T2 T1 T Time 0 T4 T6 T7 T8 T9 T10 T12 T16 T15 T14 T12 Current distribution A Y X B
Current
T1 T2
T4 T5
T7 T 8
T9 T10
T11 T12
T14 T15
Current at X Current at Y
5-13 Standing waves of current at a point on the antenna
Measurement of standing waves In Fig 5-14, the standing waves of voltage E and current I are indicated along the antenna There are current nodes at A and B and a voltage node at X These standing waves are found on any half-wave antenna A meter that indicates the effective value (0707 of peak) of the ac signal can be used to measure the standing waves present on the half-wave antenna
Velocity of propagation and antenna length
In free space, electromagnetic waves travel at a constant velocity of 300,000 km (or approximately 186,000 mi) per second The RF energy on an antenna, however, moves at a velocity considerably less than that of the radiated energy in free space
138 Fundamentals of radio antennas
I 5-14 Standing waves measured with a meter
because the antenna has a dielectric constant greater than that of free space Because the dielectric constant of free space (air or vacuum) is approximately 1, a dielectric constant greater than 1 retards electromagnetic-wave travel Because of the difference in velocity between the wave in free space and the wave on the antenna, the physical length of the antenna no longer corresponds to its electrical length The antenna is a half-wavelength electrically, but somewhat shorter than this physically This is shown in the formula for the velocity of electromagnetic waves, [51] V = where V is the velocity, is the frequency, and is the wavelength Since the frequency of the wave remains constant, a decrease in the velocity results in a decrease in the wavelength Therefore, the wave traveling in an antenna has a shorter wavelength than the same wave traveling in free space, and the physical length of the antenna can be shorter The actual difference between the physical length and the electrical length of the antenna depends on several factors A thin wire antenna, for example, has less effect on wave velocity than an antenna with a large cross section As the circumference of the antenna increases, the wave velocity is lowered, as compared with its free-space velocity The effect of antenna circumference on wave velocity is illustrated in the graph of Fig 5-15 Other factors are involved that lower wave velocity on the antenna Stray capacitance, for example, increases the dielectric constant and lowers wave velocity This capacitance can be caused by the line connecting the antenna to the transmitter, the insulators used to give physical support to the antenna, or nearby objects made of metallic or dielectric materials The change in velocity resulting from stray capacitance is called end effect because the ends of the antenna are made farther apart electrically than they are physically End effect is counteracted by making the physical length about 5 percent shorter than the electrical length, as expressed in the formula L = 095 = 468 492
[52]
where L is the physical length in feet and is the frequency in megahertz This formula is accurate for all practical purposes in determining the physical length of a half-wavelength antenna at the operating frequency
Antenna fundamentals 139 The capacitive end effect also slightly changes the standing waves of voltage and current When the standing waves are measured, it is found that the nodes have some value and do not reach zero, because some current is necessary to charge the stray capacitance The standing waves measured in Fig 5-16 show the results of end effect
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