**6. Dipole radiation pattern**

The antenna radiation pattern represents the radiated fields in space at a point P (r, θ, φ) as a function of θ and φ. The antenna radiation pattern is three dimensional. When φ is constant and θ varies, we get the E plane radiation pattern. When φ varies and θ is constant, usually θ = π/2, we get the H plane radiation pattern.

### **6.1 Dipole E plane radiation pattern**

The dipole E plane radiation pattern is given in Eq. (2) and presented in **Figure 4**.

$$|E\_{\theta}| = \eta\_0 \frac{l\beta I\_0 |\sin\theta|}{4\pi r} \tag{2}$$

At a given point P(r, θ, φ), the dipole E plane radiation pattern is given in Eq. (7).

**Figure 4.** *Dipole E plane radiation pattern.*

$$E\_r = \eta\_0 \frac{\text{II}\_0 \cos \theta}{2\pi r^2} \left(1 - \frac{j}{\beta r}\right) e^{j(\alpha - \beta r)}$$

$$E\_\theta = j\eta\_0 \frac{\text{I} \text{I} \text{sinc} \,\theta}{4\pi r} \left(1 - \frac{j}{\beta r} - \frac{1}{(\beta r)^2}\right) e^{j(\alpha - \beta r)}\tag{3}$$

$$\begin{aligned} H\_\theta &= j \frac{\beta \text{I} \text{I}\_0 \sin \theta}{4\pi r} \left(1 - \frac{j}{\beta r}\right) e^{j(\alpha - \beta r)}\\ H\_r &= 0 \text{ } H\_\phi = 0 \quad E\_\phi = 0\\ I &= I\_0 \cos \alpha\\ E\_r &= -j\eta\_0 \frac{\text{I} \text{I}\_0 \cos \theta}{2\pi \text{j} \theta^3} e^{j(\alpha - \beta r)}\\ E\_\theta &= -j\eta\_0 \frac{\text{I}\_0 \sin \theta}{4\pi \text{j} \theta^3} e^{j(\alpha - \beta r)}\\ H\_\theta &= \frac{\text{I}\_0 \sin \theta}{4\pi r^2} e^{j(\alpha - \beta r)}\\ E\_r &= 0\\ E\_\theta &= j\eta\_0 \frac{\text{I} \text{g} \Omega\_0 \sin \theta}{4\pi r} e^{j(\alpha - \beta r)}\\ H\_\theta &= -j\frac{\text{J} \text{g} \Omega\_0 \sin \theta}{4\pi r} e^{j(\alpha - \beta r)}\\ \frac{E\_\theta}{H\_\phi} &= \eta\_0 = \sqrt{\frac{\mu\_0}{\varepsilon\_0}}\\ |E\_\phi| &= \eta\_0 \frac{\text{J} \Omega\_0 |\sin \theta|}{4\pi r} = A|\sin \theta|\\ \text{Choose} \quad A &= 1\end{aligned}$$

$$|E\_{\theta}| = |\sin \theta|$$

Dipole E plane radiation pattern in spherical coordinate system is shown in **Figure 5**.

#### **6.2 Dipole H plane radiation pattern**

For θ = π/2, the dipole H plane radiation pattern is given in Eq. (8) and presented in **Figure 6**.

$$|E\_{\theta}| = \eta\_0 \frac{l\beta I\_0}{4\pi r} \tag{8}$$

0.707E. Half of the radiated power, �3 dB points, is concentrated in the antenna main beam. The antenna main beam is defined as the 3 dB beam width. Radiation to undesired direction is concentrated. The antenna side lobes present radiation to

> *lβI*0j j sin *θ* <sup>4</sup>*π<sup>r</sup>* <sup>¼</sup> *<sup>A</sup>* Choose *A* ¼ 1

> > j j *E<sup>θ</sup>* ¼ 1

(9)

j j *E<sup>θ</sup>* ¼ *η*<sup>0</sup>

undesired direction.

*Antenna typical radiation pattern.*

**Figure 5.**

**Figure 6.**

**Figure 7.**

**9**

*Dipole H plane radiation pattern for θ = π/2.*

*Dipole E plane radiation pattern in spherical coordinate system.*

*Introductory Chapter: Novel Radio Frequency Antennas DOI: http://dx.doi.org/10.5772/intechopen.93142*

The dipole H plane radiation pattern in xy plane is a circle with r = 1. At a given point P(r, θ, φ), the dipole H plane radiation pattern is given in Eq. (9). The radiation pattern of a vertical dipole is omnidirectional. It radiates equal power in all azimuthal directions perpendicular to the axis of the antenna.

#### **6.3 Antenna radiation pattern**

An antenna radiation pattern is shown in **Figure 7**. The antenna main beam is defined between the points that the maximum relative field level E decays to

*Introductory Chapter: Novel Radio Frequency Antennas DOI: http://dx.doi.org/10.5772/intechopen.93142*

**Figure 5.** *Dipole E plane radiation pattern in spherical coordinate system.*

**Figure 6.** *Dipole H plane radiation pattern for θ = π/2.*

**Figure 7.** *Antenna typical radiation pattern.*

0.707E. Half of the radiated power, �3 dB points, is concentrated in the antenna main beam. The antenna main beam is defined as the 3 dB beam width. Radiation to undesired direction is concentrated. The antenna side lobes present radiation to undesired direction.

$$|E\_{\theta}| = \eta\_0 \frac{l\beta I\_0 |\sin\theta|}{4\pi r} = A$$

$$\text{Choose} \quad A = \mathbf{1} \tag{9}$$

$$|E\_{\theta}| = \mathbf{1}$$

For a dipole, the power intensity varies as sin <sup>2</sup> *θ* � �. At θ = 45° and θ = 135° the radiated power equals to half the power radiated toward θ = 90°. The dipole beam width is θ = (135–45) =90°.
