# An Antenna Radiates Energy Engineering Essay

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In this chapter, the fundamental concepts of an antenna are provided and explained. Next, some important performance parameters of antennas are reviewed. Afterwards the microstrip patch antenna is explained.

Electromagnetic energy is radiated and received by metallic structures known as Antennas. An antenna acts as an intermediate structure between the channelling device such as a transmission line and the free space. The official IEEE definition of an antenna as given by Stutzman and Thiele [14] "The part of a transmitting or receiving system that is designed to radiate or receive electromagnetic waves".

To understand how an antenna radiates, first it must be known how radiation takes place. A metallic wire emits radiation mainly due to time-varying current or an acceleration or deceleration of charge. If there is no movement of charge in the wire, no radiation is emitted, since no flow of current occurred. Radiation does not occur even if the charges are moving with constant velocity along the wire. If the charge is oscillating with respect to time, then radiation occurs as explained by Balanis [15].

The radiation from an antenna can be understood with the use of figure 2.1 which illustrates a voltage source connected to a two conductor transmission line. When a sinusoidal voltage is connected across the transmission line, an electric field is generated which is also in sinusoidal form and this causes the generation of electric lines of force. These electric lines of force are tangential to the electric field. The electric field's magnitude is indicated by the grouping of the electric lines of force. The free electrons in the conductor are displaced by the electric lines of force and the motion of these electrons causes the flow of current which in turn leads to the generation of a magnetic field.

Fig.2.1 - Radiation emitted from the Antenna [15]

The time varying electric and magnetic fields cause electromagnetic waves to be created and the latter waves travel between the conductors. As these waves approach the open space, free space waves are formed by linking the open ends of the electric lines. The sinusoidal source constantly creates the electric disturbance and hence electromagnetic waves which are sustained by the charges are continuously generated. These travel through the transmission line and the Antenna, form closed loops and are finally radiated into free space [15].

## 2.4 Near and Far Field Regions

The field patterns change with distance and are related with two energy types and these are reactive and radiating energy. Hence, the space enclosing the antenna can be divided into three sections as depicted in figure 2.2.

Fig.2.2 - Field regions around an Antenna [16]

The most significant region is the far field region [17], as this field determines the antenna's radiation pattern. Also, antennas are utilised to communicate wirelessly from long distances, so most antennas operate in this region.

## 2.4.1 Reactive Near Field Region

In the closest vicinity of the antenna [17], the reactive near field is found. In this region, the fields consist mostly of reactive fields, which mean that the electric and magnetic fields are out of phase by ninety degrees to each other. Propagating or radiating fields are orthogonal and in phase and hence reactive near fields do not propagate.

If the maximum linear dimension of an antenna is D, then the limit of this region is given by:

(2.1)

## 2.4.2 Far Field (Fraunhofer) Region

The far field is the region furthest from the antenna [17]. The radiation pattern does not change shape with distance even though the fields still attenuate with 1/R2. Also, this region consists mostly of radiated fields, with the electric and magnetic fields orthogonal to each other and the direction of propagation similar to plane waves.

The limit of this region is given by:

(2.2)

## 2.4.3 Radiating Near Field (Fresnel) Region

The radiating near field also known as the Fresnel region resides between the near and far fields [17]. The reactive fields start to diminish and the radiating fields begin to increase. Contrary to the Far Field region, the shape of the radiation pattern varies substantially with distance.

The boundary is given by:

(2.3)

Depending on the values of the wavelength and R, this field may or may not exist.

Finally, the above can be summarised via figure 2.3:

Fig.2.3 - Summarisation of Field regions [17]

## 2.5 Far field radiation given by a Hertzian dipole

The far field radiation given by a Hertzian dipole can be described with the help of the spherical co-ordinate system as shown in figure 2.4. The z axis is taken in the vertical direction and the xy plane is taken in horizontal direction. Î¸ represents the elevation angle and Ï† represents the azimuthal angle. The xy plane is called the azimuthal plane (Î¸ = Ï€ / 2) or the H-plane which is the plane containing the magnetic field vector and the direction of maximum radiation. The xz plane is called the elevation plane (Î¸ = 0) or the E-plane which is the plane containing the electric field vector and the direction of maximum radiation [15].

Fig. 2.4 - Spherical co-ordinate system for a Hertzian dipole [15]

The far field radiation can be described with the help of the Hertzian dipole also known as the infinitesimal dipole. This consists of a piece of straight wire whose diameter and length L and are both very small compared to one wavelength. Moreover, a uniform current I (0) is assumed to travel along its length. If this dipole is placed at the origin along the z axis, then as given by [15], it can be written as:

For far field radiation purposes, terms in r2 and r3 can be ignored and the above equations can be modified and written as :

where Î· = intrinsic free space impedance

k = 2Ï€ /Î» = wave propagation constant

r = radius for the spherical co-ordinate system.

In all the above equations, the phase term ejÏ‰t has been omitted and it is being assumed that every field is sinusoidally varying with time. It can be seen from the above equations that the only non-zero fields are EÎ¸ and HÏ†, and that they are transverse to each other. The ratio EÎ¸ / HÏ† = Î·, such that the wave impedance is 120Ï€ and the fields are in phase and inversely proportional to r. The directions of E, H and r create a right handed set such that the Poynting vector is in the r direction. The Poynting vector indicates the direction of propagation of the electromagnetic wave. Hence the time average poynting vector given by [15] can be written as:

(2.13)

where E and H correspond to the peak values of the electric and magnetic fields respectively.

The average power radiated by the antenna can be written as:

(2.14)

where ds is the vector differential surface area element = r2 sin(Î¸)dÎ¸dÏ†

Wrad is the magnitude of the time average poynting vector (Watts /m2)

The radiation intensity is defined as the power radiated from an antenna per unit solid angle and is given by:

(2.15)

where U is the radiation intensity in Watts per unit solid angle.

## 2.6 Antenna Performance Parameters

The performance of an antenna can be determined from a number of parameters. Certain important parameters are discussed below.

## 2.6.1 Antenna Radiation Pattern

The antenna's radiation pattern is a plot of the far-field radiation of an antenna as a function of the spatial co-ordinates which are specified by the azimuth angle Ï† and the elevation angle Î¸. Moreover it is a plot of the power radiated from an antenna per unit solid angle which is also known as the radiation intensity [15]. Consider the case of an isotropic antenna which radiates equally in all directions. If the total power radiated by an isotropic antenna is P and the power is spread over a sphere of radius r, then the power density S at this distance in any given direction is given by [15]:

(2.16)

Hence, the radiation intensity for this isotropic antenna Ui can be written as:

(2.17)

An isotropic antenna cannot be realised in practice and it is solely used for comparison purposes. A practical type of antenna is the directional antenna. It radiates more power in certain directions and less power in other directions. The omnidirectional antenna is a special case of the directional antenna whose radiation pattern may be constant in one plane varies in the orthogonal plane. The radiation pattern of a general directional antenna is shown in Figure 2.5.

Fig. 2.5 - Radiation pattern of a generic directional antenna [15]:

Figure 2.5 shows the following points, namely:

HPBW: The half power beamwidth (HPBW) is defined as the angle subtended at the antenna by the half power points of the main lobe.

Main Lobe: The radiation lobe containing the maximum radiation.

Minor Lobe: All the lobes except the main lobe are called minor lobes. These lobes correspond to radiation in undesired directions. The level of minor lobes is expressed as a ratio of the power density in the lobe in question to that of the major lobe. This ratio is called the side lobe level and is expressed in decibels.

Back Lobe: This is the minor lobe exactly opposite to the main lobe.

Side Lobes: These are the minor lobes nearby the main lobe and are separated by radiation nulls. Side lobes are usually the largest of the minor lobes.

## 2.6.2 Antenna Directivity

The directivity of an antenna has been defined by [15] as "the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions". This means that the directivity of a non isotropic source equates to the ratio of its radiation intensity in a given direction, with respect to that of an isotropic source.

(2.18)

where D is the directivity of the antenna

U is the radiation intensity of the non isotropic antenna

Ui is the radiation intensity of an isotropic source

P is the total power radiated

If the direction of the directivity is not specified, the direction of the maximum radiation intensity is implied and the maximum directivity is given by [15] as:

(2.19)

where D max is the maximum directivity

U max is the maximum radiation intensity

Directivity is a dimensionless quantity because it is the ratio of two radiation intensities and is usually given in dBi. The directivity of an antenna can be easily deduced from the radiation pattern of the antenna. An antenna with a narrow main lobe would be more directive than an antenna with a broader main lobe.

## 2.6.3 Antenna Input Impedance

The input impedance of an antenna is defined by [15] as "the impedance given by an antenna at its terminals or the ratio of the voltage to the current at the terminals or the ratio of the appropriate components of the electric and magnetic fields at a point". Hence the impedance of the antenna can be written as:

Z in = R in + jX in (2.20)

where Zin is the antenna impedance at the terminals

R in is the antenna resistance at the terminals

Xin is the antenna reactance at the terminals

The power stored in the near field of an antenna corresponds to the imaginary part, Xin of the input impedance. The resistive part, Rin, consists of two components, the loss resistance RL and the radiation resistance Rr. The actual power radiated by the antenna is related with the radiation resistance. The power lost as heat by the antenna due to dielectric or conducting losses is related with the loss resistance.

## 2.6.4 Antenna Voltage Standing Wave Ratio (VSWR)

For efficient antenna operation, maximum power transfer must take place between the transmitter and the antenna. Maximum power transfer can take place only when the impedance of the antenna (Zin) is matched to that of the transmitter (Zs) and this implies that the impedance of the transmitter is a complex conjugate of the impedance of the antenna or vice-versa. Thus, the condition for successful matching is:

Zin = Zs* (2.21)

where Zin = Rin + jXin

Zs = Rs + jXs as shown in figure 2.6

Fig.2.6 Equivalent circuit of a transmitting antenna []

If matching is not accomplished, some power may be reflected back and this leads to the generation of standing waves, which are characterised by a parameter called the Voltage Standing Wave Ratio (VSWR).

The VSWR is given by [18] as :

where Î“ is called the reflection coefficient

Vi is the amplitude of the incident wave

Vr is the amplitude of the reflected wave

The VSWR is a measure of the impedance mismatch between the transmitter and the antenna. A greater mismatch yields a higher VSWR. A VSWR of unity corresponds to a perfect match. A antenna design should have an input impedance of either 50Î© or 75Î© since most RF Systems are built for this impedance.

## 2.6.5 Antenna Return Loss (RL)

The Return Loss (RL) is a parameter which indicates the amount of power that has been absorbed by the antenna and does not return to the transmitter as a reflection. Hence the RL is a parameter similar to the VSWR to indicate how well the transmitter and antenna are matched. The RL is given by [18]:

RL = -20log10 Î“ (dB) (2.24)

Perfect matching between the transmitter and the antenna implies Î“ = 0 and RL = âˆž. This means no power was reflected back. Conversely, Î“ = 1 equivalent to RL = 0 dB, implies that all incident power towards the antenna was reflected back towards the transmitter. For wideband applications, a RL of -6.00 dB is acceptable, equivalent to a VSWR of 3:1.

## 2.6.6 Antenna Efficiency

The antenna efficiency is a parameter which sums up the amount of losses incurred by the antenna. These losses are given by [15] as:

Mismatch losses between the transmitter and the antenna

Conduction and dielectric losses (I2R losses)

Hence the total antenna efficiency can be written as:

et = er ec ed (2.25)

where et = total antenna efficiency

er = (1âˆ’Î“ 2 ) = reflection (mismatch) efficiency

ec = conduction efficiency

ed = dielectric efficiency

ec and ed are difficult to separate and hence they are lumped together to form the ecd efficiency which is given as:

(2.26)

ecd is called as the antenna radiation efficiency. It is defined as the ratio of the power delivered to the radiation resistance Rr, to the power delivered to Rr and RL.

## 2.6.7 Antenna Gain

Antenna gain is a parameter directly related to the directivity of the antenna. Directivity is how much an antenna concentrates energy in one direction in preference to radiation in other directions. Since all antennas will radiate more in a particular direction than in another direction, the gain is the amount of power that can be achieved in one direction at the expense of the power lost in the others as explained by [19]. The gain is always referenced with respect to the main lobe and is specified in the direction of the main lobe unless indicated. It is given by:

G(Î¸ ,Ï† ) = ecd D(Î¸ ,Ï† ) (dBi) (2.27)

## 2.6.8 Antenna Polarisation

Polarisation of a radiated wave is defined by [15] as "that property of an electromagnetic wave describing the time varying direction and relative magnitude of the electric field vector". The position and direction of the electric field referenced to the ground determines the radiated wave and antenna polarisation. Some types of polarisations are horizontal and vertical linear polarisations as well as right hand and left hand circular polarisation.

Figure 2.7 shows a linearly polarised wave.

Fig.2.7 - A vertically polarised wave []

## 2.6.9 Antenna Bandwidth

The bandwidth of an antenna is defined by [15] as "the range of usable frequencies within which the performance of the antenna, with respect to some characteristic, conforms to a specified standard." The bandwidth is defined as the range of frequencies on either side of the center frequency when the input impedance is close to the value which has been obtained at the center frequency. Such impedance is also known as the impedance bandwidth.

The bandwidth of a broadband antenna can be defined as the ratio of the upper to lower frequencies with respect to a predefined return loss level.

The bandwidth of a narrowband antenna can be defined as the percentage of the frequency difference over the center frequency with respect to a predefined return loss level [15].

According to [14] these definitions can be written in terms of the following equations:

where fH = upper frequency

fL = lower frequency

fC = center frequency

An antenna is broadband if fH / fL = 2. A method of evaluating how much an antenna is operating efficiently over the required range of frequencies is by measuring its VSWR and the consequent return loss. A VSWR â‰¤ 3 (RL â‰¤ âˆ’6.00 dB) ensures good performance as depicted in figure 2.8.

Fig.2.8 - Measuring bandwidth from the return loss plot