What Is a Log Periodic Antenna?

A logarithmic periodic antenna is a non-frequency-varying antenna. The so-called non-frequency-varying antenna refers to the antenna's impedance, pattern, gain, standing wave ratio and other electrical characteristics that change periodically with the logarithm of the frequency, and in a wide frequency band Remained essentially unchanged.

It is built on the theory described below: When the antenna is at a certain scale factor

After the transformation, it still has its original structure. This way appears in frequency

f and

Antenna performance will be in

f and

Repeatedly appears in the frequency range of f, and so on, the electrical performance of the antenna will change periodically over a wide frequency range. So if we can do it at f ~

The small change of the antenna performance index in the f-band, then it is possible to meet the requirements of non-frequency-variable antennas. At the same time, the log-period antenna is a linearly polarized antenna. The polarization direction of the electric field is parallel to the direction of the vibrator. Therefore, the logarithmic periodic antenna has a wide-band characteristic and a linear polarization characteristic, so it is an optimal choice for the antenna part to apply it as a corona discharge signal detection system. ^[1]

As shown in Figure 2, the logarithmic periodic antenna is composed of N symmetrical vibrators arranged in parallel according to the structural periodic rate, and has the following relationship

In the formula:

,

,

They are the distance between two adjacent oscillators, the distance from the imaginary vertex to the longest oscillator, and the vertical distance from the geometrical vertex of the antenna to the nth oscillator; the serial number of the oscillator is n.

The overall structure of a log-periodic dipole antenna is determined by the periodic rate and the structural opening angle 2. When the periodic rate and 2 are determined, the geometric structure of the log-period antenna is also determined. Since R _{n + 1} =

R _n and R _n = (l _n / 2) cot.

and so

Log-periodic antennas have extremely wide operating bandwidths, which can reach 10: 1 or wider. Its working principle is easier to understand conceptually: the directional characteristics and impedance characteristics of the antenna are functions of the electrical size. The size of each element of the logarithmic periodic antenna satisfies ln + 1 / ln = , that is, these frequencies are required to satisfy n + 1 / n = or fn + 1 / fn = 1 / . If is close to 1, the working frequency of the antenna that meets the above requirements approaches a continuous change. If the geometry of the antenna is infinitely large and infinitely fine, then the operating frequency band of the antenna can reach infinity.

The logarithmic periodic antenna radiates linearly polarized electromagnetic waves, and its polarization direction is parallel to the oscillator direction. The radiating area of the logarithmic periodic antenna is mainly a vibrator, and the vibrator length in this area is about / 2, which has strong excitation and plays a main radiating role. When the operating frequency changes, the radiating area will move back and forth on the antenna (for example, when the frequency increases, it will move to the end of the short oscillator) to maintain its electrical performance.

According to the working conditions of the symmetrical oscillator of each part of the logarithmic periodic antenna, the whole antenna can be divided into three working areas: Except the radiation area, the part from the power source to the radiation area is called the transmission area; the part after the radiation area is called the non-radiation area Incentive area. The following briefly introduces the three working areas: (a) In the transmission area, the electrical length of each symmetrical oscillator is short, the input impedance (capacitive reactance) of the oscillator is large, so the excitation current is small, so the radiation of the oscillator is weak. Acts as a transmission line. (B) In the non-excitation region, since the symmetric oscillator in the radiation area is in a resonance state, the excitation current of the oscillator is large, and most of the energy transmitted by the transmission line has been radiated out, so the excitation current of the symmetric oscillator in this area becomes very small. That is the aforementioned current cutoff phenomenon. (C) In the radiation area, it is usually defined as the area between two oscillators whose excitation current value is equal to 1/3 of the maximum excitation current. The number of oscillators N in this region is determined in principle by the geometric parameters and , which can be approximately determined by the empirical formula:

Where K ₁ and K ₂ are the truncation constants at the high and low ends of the operating band, determined by the following empirical formula

K ₁ = 1.01-0.519

The number of oscillators in the radiation area is generally not less than three. The larger the number of vibrators in the radiation area, the stronger the directivity of the antenna and the higher the gain. In order to concisely analyze the working principle of the radiation zone, here only three oscillators are taken as a representative, as shown in FIG. 3. It can be seen from the synthesis of the vector that the a and c oscillators can enhance the radiation field of the b oscillator.

The electrical characteristics of the log-period antenna mainly include input impedance, pattern and direction coefficient, polarization, and bandwidth. These aspects will be described separately below.

1.Input impedance

The input impedance of a log-period antenna is the impedance it presents at the feed point (the beginning of the collective line). When high-frequency energy is input from the antenna feed point, electromagnetic energy is transmitted forward along the collective line. The electrical length of the transducer in the transmission area is small, and the input terminal presents a large capacitive reactance, so the current at its input terminal is small. The transmission area oscillator is equivalent to adding an additional capacitor in parallel at the corresponding point of the collective line, which changes the distribution parameters of the collective line and reduces the characteristic impedance of the collective line (the characteristic impedance of the transmission line is inversely proportional to the square root of the distributed capacitance).

The radiating area is the main load of the collective line. The high-frequency energy transmitted by the collective line is almost completely absorbed by the oscillators in the radiating area and radiates to space. The non-resonant region oscillator behind the radiating area is much larger than the resonance length. Because the high-frequency energy obtained by it is very small, the energy reflected from the terminal of the collective line is also very small. If the terminal of the collective line is connected with a proper short-circuit branch length, the reflected wave component on the collective line can be reduced to a minimum. At this time, the collective line can be considered to carry traveling waves. Therefore, the input impedance of the logarithmic periodic antenna is approximately equal to the characteristic impedance of the collective line after considering the influence of the transmission area oscillator, which is basically resistive and has a small reactance component.

2.Pattern and direction coefficient

The log-period antenna is an end-fire antenna, and the maximum radiation direction is the direction from the longest oscillator to the shortest oscillator along the collective line. When the operating frequency changes, the radiating area of the antenna moves back and forth on the antenna to maintain similar characteristics, so its directional pattern changes less with frequency. In addition to the log-period antenna pattern, its half-power angle also has a certain relationship with the geometric parameters and . The larger , the more the number of oscillators in the radiation area, the stronger the directivity of the antenna, and the half-power of the pattern The smaller the angle.

At any operating frequency, only some of the oscillators in the radiating area play a major role in the radiation, and not all oscillators have an important contribution to the radiation, so its directivity is not strong. The beam width of the pattern is generally tens of degrees, and the directivity coefficient or antenna gain is generally about 10 dBi, which belongs to the category of medium gain antennas.

3.Polarization

Similar to the directional antenna, the log-period antenna is a linearly polarized antenna. When the vibrator plane of a log-period antenna is placed horizontally, it radiates or receives a horizontally polarized wave; when its vibrator plane is placed vertically, it radiates or receives a vertically polarized wave.

4.Bandwidth

The radiation area of a log-periodic antenna has certain requirements for the length of the vibrator, so its operating bandwidth will be basically limited by the longest and shortest vibrator size. ^[2]