If there is reflection from the end of, a wire, the number of standing waves on the wire will be equal to length of the wire divided by a half wavelength. Thus,if the wire is two half wave long there will be two standing waves, and so on. There longer wires,each multiples of a half wave in length,will also be resonant,therefore,at the same frequency as the single half-- wire. When an antenna is two or more half waves in length at the operation frequency it is said to be harmonically resonant,or to operate at a harmonic. The number of the harmonic is the number of standing waves on the wire. For example, a wire two half waves long is said to be operating on its second harmonic ; one three half waves long on its third harmonic, and so on.

Harmonic operation is often utilized in antenna work because it permits operating the same on several harmonically related amateur bands. It is also an important principle in the operation of certain types of directive antenna.

Fig.2. Harmonic operation of along enough to contain several half waves. The current and voltage curves cross.

The heavy line representing the wire to indicate that there is reversal in the direction of the current,and a reversal, in the polarity of the voltage,at intervals of a half wavelength. The reversals or current and voltage do not coincide,but occur at point a quarter wavelength a part.



If the wire in the first illustration had been infinitely long the charge (voltage) and the current (an electric current is simply a charge in motion ) would both slowly decrease would result from dissipation of energy in the form of radio waves and in heating the wire because of its resistance. However , when the wire is short the charge is reflected when it reaches the far end, just as the ball bounced back from the barrier. With radio –frequency exitantion of a half –wave antenna, there is of course not just a single charge but a continuous supply of energy, varying in voltage according to a sine—wive cycle. We might consider this a series of charge, each of slightly different amplitude than the preseding one. When a charge is now haveling in the opposite direction. However, the next charge is just reaching the end of the antenna, so we have two current of practically the same amplitude flowing in opposite direction. The resultant current at the end of the antenna there fore is zero. As we move father back from the end of the antenna the magnetudes of the out going and returning current are no longer the same because the charge causing them have been supplied to the antenna at different part of the Rf cycle. There is cancellation, therefore,and a measurable current exist. The greatest different – that is, the largest resultant current--- Will be found to exist a quarter wavelength away from the end of antenna. as we move back still father from this point the current will decrease until, a half wavelength away from the antenna, it will reach zero again. Thus, in a half-- wave antenna the current is zero at the end and maximum at the center. This current distribution along a half-- wave wire is shown in Fig.1.

Fig.1.Current and voltage distribution on a half--wave wire . In this conventional representation the distance at any point ( x , for instance ) from the wire , represented be heavy line, to the curve gives the relative intensity of current or voltage at the point. The relative direction of current flow ( or polarity of voltage ) is indicated by drawing the curve either above or bellow the line that represent the antenna. The curve above, for example, show that the instantaneous polarity of the voltage in one half of the antenna is opposite to that in the other half .
this distance measured vertically from the antenna wire to the curve marked “ current “, at any point a long the wire represent the relative amplitude of the current as measured by an ammeter at the point . This is called a standing wave of current. The instantaneous value of current of at any point varies sinusoidally at the applied frequency, but is amplitude is different at every point along the wire as shown by the curve. The standing wave curve it self has the shape of a half sine wave , at least to a good approximation.

The voltage along the wire will behave differently ; it is obviously greatest at the end since at this point we have two practically equal charge adding. As we move back along the wire , however,the out going and returning charges are not equal are their sum is smaller. At the quarter-wave point the returning charge is of equal magnitude but of opposite sign to the out going charge, since at this time the polarity of the voltage wave from the source has reversed ( one-half cycle ). The two voltage therefore cancel each other end the resultant voltage is zero . Beyond the quarter- wave point, away from the end of the wire,the voltage again increases,but this time with the opposite polarity.

It will be observed, therefore, that the voltage is maximum at every point wire the current is minimum,and vise versa. The polarity of the current or voltage reverses every half wavelength along the wire , but the reverses do not occur, at the same point for both current and voltage ; the respective reversals do not occur, in fact, at point a quarter wave a part .A maximum point on standing wave is called a loop ( or antinode ) ;a minimum point is called a node.



The shortest length of wire that will resonate to a given frequency is one just long enough to permit an electric charge to travel from one end RF cycle. If the speed at which the charge travel is equal to the velocity of light,approximately 300,000,000 meters per second, the distance it will cover in one cycle or period will be equal to this velocity divided by the frequency in hertz, or = 300,000,000/f

note: ==> wavelength

f ==> frequency in meter

Since the charge traverses the wire twice , the length of wire needed to permit the charge to travel a distance in one cycle is / 2 , or one—half wavelength. Therefore the shortest resonant were will be a half wavelength long.

The reason for this length can be made clear by a simple example. Imagine a trough with barriers at each end. If an elastic ball is started along the trough from one end,it will strike the far barrier,bounce again,and continue until the energy imported to it originally is all dissipated. if however,whenever it returns to the near barrier it is given a new push just as it starts a way, its back-and-forth motion can be kept up indefinitely. The impulses, however must be timed properly ; in other words, the rate or frequency of the impulses and the speed of the ball are fixed, the length of the trough must be adjusted to “ Fit “.

In the case of the antenna, the speed is essentially constant, so we have the alternatives of adjusting the frequency to a given length of wire,or the length of wire to a given operating frequency. The latter is usually practical condition.

By changing the units in the equation just given and dividing by 2, the formula : l =492/f(MHz) is obtained. In this case “ l “ is the length in feet of a half wavelength for a frequency “ f “ , given in megahertz, when the wave travels with length in antenna work are developed. It represents the length of a half wavelength in space, When no factors that modify the speed of propagation exist.
To determine a half wavelength in meters.
The relationship is ; l =150/ f (Mhz)



An antenna is an electric circuit of a special kind. In the ordinary type of circuit the dimension of coils,capacitors and connections usually are small compared with the wavelength that corresponds to the frequency in use.when this is the case most of the electromagnetic energy escapes by radiation in the form of electromagnetic waves. when the circuit is intentionally designed so that the major portion of the energy is radiated,we have an antenna.
Usually,the antenna is a straight section of conductor,or a combination of such conductor.Very frequently the conductor is a wire,although rods and tubing also are used .in this chapter we shall use the term “WIRE”to mean any type of conductor having across section that is small compared with its length.

The strength of the electromagnetic field radiated from a section of wire carrying radio-frequency current depends on the length of the wire and the amount of current flowing.( it would also be true to say that the field strength depend on the voltage across the section of wire, but it is generally more convenient to mean sure current. The electromagnet field, consist of both magnetic and electric energy, but it is generally more convenient to mean sure current. The electromagnetic filed consist of both magnetic and electric energy, with the total energy equally divided between the two one cannot exist without the other in a electromagnetic waves, and the voltage in an antenna is just as much a mean sure of the field intensity as the current ). other things being equal,the field strength will be directly proportional to the current .It is therefore desirable to make the current as large as possible,considering the power available. In any circuit that contains both resistance and reactance , the largest current will flow ( for given a mount of power ) when the reactance is “ Tuned out “-- in other words, when the circuit in made resonant at the operating frequency. So it is with the common type of antenna ; the current in it will be largest, and the radiation therefore greatest,when the antenna is resonant.
In an ordinary circuit the inductance is usually concentrated in a coil, the capacitance in a capacitor , and the resistance is principally concentrated in resistors, although some may be distributed around the circuit wiring and coil conductor. Such circuits are said to have lumped constant. In an antenna, on the other hand, the inductance, capacitance,and resistance are distributed along the wire. Such a circuit is said to have distributed constant. Circuits with distributed constant are so frequently straight-line conductor that they are customarily called linear circuits.

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