Polarization

According to the concept of displacement current, James C. Maxwell got agreement with other electromagnetic equations and predicted the existence of electromagnetic wave since more than a century ago. In the far-field region, energy radiation caused by current distribution on antennas can be seen as a transverse electromagnetic (TEM) wave - the components of electric field (E), magnetic field (H) and propagating direction are perpendicular each other none the loss because they vary with time. The term Polarization can only use the trajectory of time-varying E in space to identify behavior of microwave radiation due to the relation between E and H as (2.1.11).

Generally, infinitesimal current I with ∆z ≪ λ in length on the antenna can be seen as an equal length ideal dipole possesses both uniform magnitude and phase[19].

Such an ideal dipole illuminates in free space to form a doughnut-like radiation pattern without inner hollow and hence polar plots with omni-direction and figure-of-eight are revealed through the cross-section vertical and horizontal to the dipole separately. In a practical sense, H plane presents the vertical cutting mentioned above as it contains H vector and E-plane indicates the other for the same reason. The wave is referred as to a planer wave while observation point is stationed adequately far from radiating source, and its E vector and H vector are co-located on the constant phase plane. Selecting any constant phase plane as an observation plane with time-varying condition, a trajectory constructed by the tip of E vector can be obtained.

E_θ

H_φ

=

^ωμ

β

=

^ωμ

ω μϵ

=

^μ

ε

= η

(2.1.11) where η is the intrinsic impedance of the medium, and

E = E

_θ

θ =

^I∆z ground and the wave is so-called vertical polarization. Horizontal polarization presents time-varying E vector which varies with the straight line parallel to ground by the same token. The situation a wave polarized in the x-direction is traveling along the +z-axis can be written as following:

E = x E

_x

e

^−jkz (2.1.14) To deserve to be mentioned, 45-degrees polarization is obtained as the included angle of 45 degrees between dipole and ground plane is illustrated. It would be obtained in the situation such as dual-polarized application. After the discussion of three kinds of the polarization type, it can be attached the triple to linear polarization because of the orbits caused by them are linearity.

A coordinate system is further established on an observation plane to describe the behaviors of polarization through two orthogonal bases - E_v and E_H, which means that the electric field distribution in free space would be composed of Ev and EH even through it varies with time. The classifications of polarization are completed according to combinations of the bases and hence circular polarization and elliptical polarization will be considered.

Elliptical Polarization

The elliptical polarization will be produced while the E vectors against time on

vectors. In other words, the tips of vectors on the observation plane depict an ellipse with respect to time varying. It would be judged which is a left polarization or right polarization according to phase relation between these two components. Take a simple example: it is a left polarized wave as observer faces the incoming wave and the vector combined by generating sets rotates clockwise. It can be considered the situation a wave of component leads y-component by +90 degrees is traveling along the z-axis forms the right hand elliptically polarized wave. It would be expressed as following:

E = x E

_x

e

^−jkz

− y jE

_y

e

^−jkz (2.1.15) The expression gives a good account of the fact that an elliptical polarized wave can be decomposed to a couple of linear polarized waves which are perpendicular each other in space as well as are 90 degrees out of phase. In physical sense, it presents this phenomenon obviously and hints elliptically polarization can be as a general solution to derive other polarized types. Generally speaking, elliptical polarization is a kind of conventional polarization type in everyday life.

Circular Polarization and Axial Ratio

Circular polarization would be constructed as imposing a restriction of generating components with equal quantity on the elliptical polarization. As implied by the name, the vector remains constant in length and rotates around in a circular path. Similarly, the discrimination between left-hand circular polarization (LHCP) and right-hand circular polarization (RHCP) will be done through the rotational sense by vector as the wave travels toward the observer.

After the discussion, it would be derived to the question which one parameter could identify the types of polarization. It should be concentrated on the interpretation of axial ratio and the extended discussion of elliptical polarization will be considered.

Y

Fig. 2.3 RHEP with traveling direction in the +z-axis and tilt angle τ with respect to the principle axis

As shown in Fig. 2.3, at first, the spatial configuration attracts more attention about that coordinate transformation would be employed to simply analysis just because the bases are non-unique and it leads into Fig.2.4. Turning to the observation on time domain, the elliptical trajectory is formed along the time with angular frequency ω .

Fig. 2.4 Modified-axis RHEP presentation

The H-component equals to E1 and no V-component as point A lies on the H-axis, similarly, the V-component equals to E₂ and no H-component as point A lies on the

V-axis. The H-component leads V-component by 90 degrees according to the pasting angle is about 90 degrees. Polarized behavior can be described in terms of space and time and axial ratio can be written as following:

AR = 20log ^Emax

E_min (2.1.16) Where E_max means maximum value of E along major axis and E_min means maximum value of E along minor axis.

In conclusions,

(1) Linear polarization:(AR → ∞) Uni-axis or bi-axial with in phase (2) Elliptical Polarization:(AR ≥ 0dB)

Bi-axis with quadrature phase (3) Circular Polarization:(AR = 0dB)

Bi-axis with identical magnitude and quadrature phase

In this work, we defined the axial ratio specification is small than 3dB could be used.

2.2 2.5/5.2GHz Dual-Band Circularly-polarized Antenna Design

In this chapter, a 2.5/5.2GHz dual-band circularly-polarized of a monopole antenna fed through microstrip line is proposed. The proposed antenna is achieved using microstrip-fed with two circular strips and two circular patches. One circular strip radiates lower band, the other one covers higher band. By adding the circular patch on the back of the substrate, the left-hand circular polarization (LHCP) gain at the positive z axial of this proposed antenna has been improved. The antenna operates in two bands which are 2.5GHz and 5.2GHz. These two operating bands can be applied for the WiMax and WLAN application. Fig.2.5 shows the configuration of our proposed dual band circularly polarized antenna. The antenna is fabricated on an FR4 substrate with a dielectric constant of 4.4 and a loss tangent of 0.02. The thickness of the substrate is 1.6 mm. The size of the antenna is ( G × G ) 50 mm × 50 mm which is suitable for most mobile devices. Experimental results show the proposed antenna has good return loss and circular polarization characteristics. The 10 dB return loss impedance bandwidths for the lower band (2.5GHz) and higher band (5.2GHz) are 50% and 23%, respectively. The 3dB axial-ratio bandwidths are 14.8%and 4.0% with respect to 2.5GHz and 5.2GHz, respectively.

在文檔中 雙頻帶圓極化天線及雙頻帶高隔離度多重輸入多重輸出天線設計 (頁 24-30)