Chapter 3
Antenna Theory and Engineering
This chapter explains the field generated by the alternating electric dipole, which is closely related to EMC research in the antenna theory and engineering [1, 7, 8]. Through this chapter, our readers will learn the basic characteristics of the near field, far field, and transition zone and understand that the EMC problems usually happens with the coexistence in the near field, far field, and transition zone. This chapter also explains the radiation characteristics of the antenna. Our readers will get the knowledge of some basic concepts of the antenna, including the antenna pattern and gain. In the last section, an example is provided to illustrate that the out-of-band characteristics of the antenna have become an important factor in the EMC design and antenna layout analysis of the whole aircraft.
3.1 Field of Alternating Electric Dipole
The field generated by the alternating electric dipole is closely related to EMC problems due to the leakage of fields from slots, apertures, and cables.
An alternating electric dipole refers to two alternating point charges +q(t) and −q(t), with the same value but opposite signs. The distance between the two point charges is dl(dl → 0), generally represented by qdl˙ . From the view of the law of charge conservation, alternating electric dipole qdl˙ can also be regarded as current element I˙dl
Let the time change factor be e− jωt , and then the electromagnetic field generated by the alternating dipole is [1]:
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H (r )
i ϕ |
˙ 4π |
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I dl sin θ |
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jβ |
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˜ ˙ ˙
E(r) i rS ErS + i θ Eθ (r )
(3.1a)
(3.1b)
© National Defense Industry Press and Springer Nature Singapore Pte Ltd. 2019 |
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D. Su et al., Theory and Methods of Quantification Design on System-Level Electromagnetic Compatibility, https://doi.org/10.1007/978-981-13-3690-4_3
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3 Antenna Theory and Engineering |
where
˙ r ( )
E S r
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Eθ (r )
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I˙dl cos θ |
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β |
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j |
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jβrS |
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jβ |
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2π ωε |
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rS2 − rS3 e− |
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V m |
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4π ωε |
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+ rS2 |
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rS |
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I˙dl sin |
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jβrS |
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For the sake of convenience, formulas (3.1a) and (3.1c) can be rewritten as
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I˙dl |
β2 sin θ |
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e− jβrS A m |
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H˙ ϕ (r ) |
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4π |
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jβrS |
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I˙dlβ |
2η2 cos θ |
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e− jβrS V m |
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E˙ rS |
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( jβrS ) |
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2η sin θ |
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E˙ θ (r ) |
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I˙dlβ |
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e− jβrS V m |
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4π |
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jβr |
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where η μ ε is the wave impedance of the medium.
(3.2a)
(3.2b)
(3.2c)
The electromagnetic field excited by the alternating current elements represented by (3.1a)–(3.1c) is very important in the discussion of radiation problems. Next, we will analyze these three equations, which will lead to some basic concepts of radiation problems.
3.1.1 Near Field
The region that satisfies βrS << 1 is called the near-field region of the electric dipole. In the near-field region, there is
(βrS )−3 >> (βrS )−2 >> (βrS )−1
e−jβrS ≈ 1
Therefore, the magnetic field in the near-field region can be expressed as
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4π rS2 |
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H (r ) |
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i ϕ I dl |
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The electric field in the near-field region can be expressed as:
E(r ) |
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i rS |
2 cos θ + i θ sin θ |
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4π εrS3 |
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3.1 Field of Alternating Electric Dipole |
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It should be noted that the near-field magnetic field is exactly the same as the static magnetic field and the near-field electric field is identical with respect to the field excited by static electric dipole. Therefore, the near-field region is called as “quasistatic field.” From the Poynting vector of electromagnetic field, it can be concluded that the complex Poynting vector of the static field is a pure imaginary number with zero active power density. Therefore, the electromagnetic energy of the static field is not radiated, as if this part of the energy was trapped in the near zone. Therefore, the static field is usually called the “bounded field.” Based on this fact, we can say that the main component of the near-field region generated by the alternating electric dipole is the bounded field.
3.1.2 Far Field
The region which satisfies βrS >> 1 is the far-field region of the electric dipole. In the far field, since βrS >> 1, there is
(βrS )−1 >> (βrS )−2 >> (βrS )−3
Therefore, the magnetic field in the far-field region can be expressed as:
H˜ (r ) ≈ i φ jI˙dl |
sin θ e−jβrS |
A m |
2λrS |
The electric field in the far-field region can be expressed as:
E˜ (r ) ≈ i θ jη I˙dl |
sin θ e−jβrS |
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It is not difficult to find that the main components of H |
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region have the same phase, and their Poynting vector shown below is real. |
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S˜ (r ) E˜ (r ) × H˜ (r ) 2 i rS η ˙φ |
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It indicates that there is an active power flow in the i rS direction, and the electromagnetic energy is propagating outward. In addition, from the expression of the electromagnetic field in the far field, the main part of the far field is inversely proportional to rS . Thus, their Poynting vector should be inversely proportional to rS2. Then, we can make a flux integral on the Poynting vector on the surface A of a sphere with the radius rS , and we will get a constant unrelated with rS , i.e.,
A S˜ (r ) · da |
π η I 2dl2 |
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