#### 2. Optimization of the Midload Whip Antenna

##### 2.1. Calculation of Resonance Shortening Length

In order to calculate the effect of the middle loading on the resonant length of the whip antenna, the structure of the antenna needs to be analyzed. Figure 1 shows a schematic diagram of the middle loading whip antenna.

As shown in Figure 1, the antenna is divided into three parts: the first part is the part from the intersection point M of the loading part to the top of the antenna, the length is and the radius is and the second part is the part from the intersection point M of the loading part to the feeding point 0, the length is and the radius is . The third part is the part of the loaded radiator, the length of the radiator is and the radius is .

First, the input impedance of each part of the antenna should be analyzed.

According to the transmission line theory, it is well known that the characteristic impedance of a uniform dual transmission line is given by .where is the distance between the uniform double transmission lines and is the wire radius of the uniform double line. For a symmetric element with a single side length and a radius , its input impedance can be regarded as a function of the antenna characteristic impedance , the antenna radius , and the antenna single arm length , that is ,

According to the radiation segment theory of the antenna, is the attenuation constant of the antenna, is the phase shift constant, where and .

Part 1 of the antenna and its mirror image can be regarded as a lossy uniform double transmission line, so the average characteristic impedance of part 1 of the antenna is as follows:

Among them, z is the distance from the antenna unit element to the feeding point . Substituting the average characteristic impedance , wire radius and antenna length of part 1 of the antenna into formula (2), the input impedance of part 1 can be obtained as .

Similarly, the average characteristic impedance of the antenna part 2 can be obtained, but different from the antenna part 1, its integral range for the antenna is , which can obtain as follows:

Similarly, part 3 can be regarded as an elevated monopole antenna, forming a standard uniform dual transmission line with a distance from its mirrored part, and the average characteristic impedance of the loaded part is as follows:

We substitute this into formula (2) as well, and the input impedance of the three parts can be obtained as .

The input impedance of point M can be regarded as the parallel connection of part 1 and part 3, the antenna of part 2 can be regarded as a uniform lossy dual transmission line , and its termination is connected to the total input impedance of point M. The equivalent circuit is shown in Figure 2.

Total input impedance at point M is as follows

At this time, the total input impedance of the antenna at the feeding point can be obtained .

If the midload antenna is in a resonant state, the reactance part of the antenna needs to be zeroed, that is, the imaginary part of is . At this time, the resonance length at the frequency can be obtained. We explain that when the impedance part of the total input impedance at the feeding point 0, the length that needs to be shortened can be expressed as ; then, this part should be shortened by due to the current and impedance distribution of the antenna.

##### 2.2. Radiation Field Strength Calculation

The polar coordinate system as shown in Figure 3 is established, and the antenna is also divided into part 1, part 2, and part 3.

Part 1 of the antenna is mainly used to adjust the resonant frequency of the antenna, so that the antenna can have a smaller reflection coefficient when it operates at the preset frequency and can also radiate energy together with part 2. Part 3 is mainly used to improve the radiation null problem of whip antenna and increase the omnidirectionality of antenna.

Let the current at the antenna feed point 0, the current at point M is approximately expressed as follows:

At this time, the input current of part 1 is as follows:

The input current of part 3 is as follows:

The field strength contribution of the antenna part 1 to a certain point in the far field can be approximately calculated as follows:

The field strength contribution of antenna part 2 to this point is as follows:

The field strength contribution of antenna part 3 to this point is as follows:

Therefore, it can be concluded that the superimposed field strength of the midload whip antenna to a certain point in the far field is as follows::

The magnitude of the superimposed field strength can effectively reflect the omnidirectionality of the midload whip antenna in the far field and solve the radiation blind area problem of the traditional whip antenna.

#### 3. Simulation

It can be seen that when the length of the whip antenna loaded in the middle is not shortened, its resonant frequency is 69.97 MHz, and the reflection coefficient is −12.606 dB. At this time, if it works at the ideal resonant frequency of 75 MHz, its reflection coefficient is about −8 dB. Compared with the reflection coefficient of −12.606 dB, there is a large mismatch loss of about 4.606 dB; when the antenna is shortened by 6.94 cm, the resonance frequency of the antenna rises to 74.52 MHz and the reflection coefficient is −12.417 dB, which is basically equal to the ideal resonance frequency. This shows that shortening the antenna after theoretical calculation can better make the antenna close to the resonance state at the preset frequency and has a smaller reflection coefficient than when the antenna is not shortened. To a certain extent, the correctness of the above calculation derivation is verified.

Figure 6 shows the comparison of the directivity of the midload whip antenna and the traditional whip antenna. Because the pattern of the whip antenna is symmetrical, the XOZ plane is intercepted, which is representative.

It can be seen that the closer the traditional whip antenna is to , the worse its directivity is, and it can hardly work when receiving or transmitting signals. When it is loaded in the middle, the middle loading body radiates energy outward, which can not only maintain the good directivity of the original whip antenna in other directions but also reduce the blind area of the traditional whip antenna to a certain extent. This shows that the directivity of the whip antenna loaded in the middle is better than that of the traditional whip antenna, which is in good agreement with the theoretical derivation.

#### 4. Field Test

In order to better verify the theoretical derivation and simulation results, the shortening effect and radiation performance of the midload antenna will be tested. Figure 7 shows an experimental diagram of the reflection coefficient test of the self-made midload whip antenna. In order to be consistent with the simulation experiments, the radius of the conductor is 3 mm, the preset frequency is 75 MHz, and the initial length of the whip antenna is 1 m, which is the ideal resonance length. The middle loading body has a radius of 3 mm and a length of 20 cm and is loaded at a position 0.5 m away from the antenna feeding point. The bottom of the antenna is placed in the salt water that simulates the seawater environment prepared in the figure, and a network analyzer is used to collect data on the resonant frequency and reflection coefficient of the antenna. First, we measure the parameters of the antenna without shortening, and the measurement results are shown in Figure 8.

It can be seen that its resonant frequency is 67.19 MHz, the reflection coefficient is −25.62 dB, and its reflection coefficient is about −5.35 dB at the preset frequency of 75 MHz. The operating frequency is about 68.6 MHz–79.4 MHz and the bandwidth is 10.8 MHz.

Then, we test the parameters of the antenna shortened by 6.94 cm, and the measurement results are shown in Figure 9.

It can be seen that its resonant frequency is 74.35 MHz, the reflection coefficient is −26.02 dB, and its reflection coefficient is −24.44 dB at the preset frequency of 75 MHz.

It can be seen from the experimental results that the resonant frequency of the nonshortened midload whip antenna has a large deviation from the ideal resonant frequency, and the reflection coefficient is large at the preset frequency. After the antenna is shortened, the resonant frequency of the antenna gradually approaches the ideal resonant frequency and the reflection coefficient at the preset frequency decreases accordingly. At 75 MHz, the reflection coefficient of the shortened antenna is improved by 19.09 dB compared with the nonshortened antenna. This shows that shortening the antenna to a certain length changes the impedance distribution of the antenna, which is also in high consistency with the theoretical calculation and simulation experiments and further proves the correctness of the derivation process.

The omnidirectional test of the antenna is carried out in the external field, and the test is carried out by loading the whip antenna in the middle and the traditional whip antenna in the direction (because theoretically, this direction is the radiation blind area of the traditional whip antenna), because the directivity cannot be obtained well. Therefore, the receiving field strength of the far field is used to indirectly prove the radiation capability of the antenna. The directions of 10 m, 20 m, and 30 m were selected for testing. The experimental results are shown in Table 1.

Obviously, the centrally loaded whip antenna solves the radiation blind area problem of the traditional whip antenna. Theoretically, in the blind area, the signal transmitted by the traditional whip antenna should not be received, but the receiver may still receive a very small signal due to the diffraction ability of electromagnetic waves.

#### 5. Conclusions

This paper solves the difference between the ideal resonant length and the actual resonant length of a midload whip antenna at the ideal operating frequency. In engineering, this error is mainly achieved by direct measurement and no literature has disclosed this method to calculate the length of shortening. Second, the middle loading body not only realizes the miniaturization of the whip antenna but also solves the blind area problem of the whip antenna to a certain extent, which is the omnidirectionality especially required for the offshore antenna. The article analyzes the antenna from three aspects: calculation, simulation, and field test. The results all show that the shortening of the midload antenna is beneficial to reduce the reflection coefficient of the antenna, make the antenna resonant frequency closer to the preset frequency, and avoid large energy loss. The simulation and experimental results show that under the preset frequency of 75 MHz, the reflection coefficient of the shortened midload whip antenna decreases by 4.414 dB and 19.09 dB, respectively. Compared with the traditional whip antenna, the simulation gain of the midload whip antenna at the radiation null point is increased to −26.7 dBi. At the same time, it provides a certain omnidirectionality for the whip antenna and provides a theoretical basis for the design and radiation analysis of the offshore surface antenna.

#### Data Availability

The data of the simulation and experimentation used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This work was supported by National Natural Science Foundation of China (41774021, 41874091, and 42074074) and National Natural Science Foundation of China Youth Fund (62101579).