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5-15 Effect of antenna circumference on wave velocity
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002 001 0 2 4 6 8 10 Wave velocity Free-space velocity
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E 5-16 Impedance along half-wave antenna I 73 ohms (center)
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The antenna is a circuit element having distributed constants of inductance, capacitance, and resistance, which can be made to form a resonant circuit The half-wave antenna is the shortest resonant length of antenna However, antennas which are two or more half-wavelengths can also be resonant Such antennas are said to operate on harmonics If an antenna is four half-wavelengths at the transmitter frequency, it is being operated at the fourth harmonic of its lowest resonant frequency In other words, this antenna is a half-wavelength at one-quarter of the frequency of operation An antenna operating on the third harmonic is shown in Fig 5-7 Resistance A current flowing in the antenna must contend with three kinds of resistance With the antenna considered as a radiator of energy, the power expended in the form of radiation can be thought of as an I 2Rt loss Rt is called the radiation resistance With the antenna considered as a conductor, a certain amount of energy is dissipated in the form of heat In this I 2R0 loss, R0 is the ohmic resistance There is also an I 2R loss because of the leakage resistance of dielectric elements, such as insulators This R usually is included in the ohmic resistance The purpose of the antenna is to dissipate as much energy as possible in the form of radiation The energy dissipated by the radiation resistance, therefore, is the useful part of the total power dissipated Because the actual power loss depends on the ohmic resistance, this resistance should be kept as low as possible In the halfwave antenna, the radiation resistance is large compared to the ohmic resistance, and most of the available energy is radiated The half-wave antenna is, therefore, a very efficient radiator for most purposes For a half-wave antenna fed at the center point, the radiation resistance is equal to 73 The reference point is the center of the antenna at the time of peak current flow Ohmic resistance is referred to this point The total resistance is of importance in matching the antenna to a transmission line Impedance Because the half-wave antenna has different conditions of voltage and current at different points, and because impedance is equal to the voltage across a circuit divided by the current through it, the impedance will vary along the length of the antenna If E is divided by I at each point of the voltage and current curves in Fig 5-16, the result is the impedance curve, Z The impedance is about 73 at the center point and rises to a value of about 2500 at the ends The impedance of the half-wave antenna usually is considered to be the impedance as seen by the transmitter at the input terminals This impedance consists of both resistance and reactance If the antenna is cut to a length of exact resonance, the reactance is zero and the impedance is purely resistive However, if the antenna is longer or shorter than resonance, reactance is present When the antenna is made shorter, capacitive reactance is present; when the antenna is made longer, inductive reactance is present The impedance at the antenna input terminals is important in terms of power efficiency If the transmitter is feeding a nonresonant antenna, a power loss is caused by the reactive component of the antenna impedance Conversely, if the frequency of the transmitter is changed, the electrical length of the antenna also changes If the frequency is made somewhat higher, the electrical length is made greater, and inductive reactance is added to the impedance If the frequency is lowered, the electrical length is shortened, and capacitive reactance is added to the impedance
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