## Antenna fundamential properties

**In the design and installation of wireless communication systems, it is necessary for**

**system design engineers, operators and many times, installers, to have a fundamental knowledge of antenna performance and RF propagation characteristics. This knowledge will assist these individuals with the proper selection of system antennas and their subsequent mounting location and orientation in an effort to ensure optimum system coverage and performance.**

**A properly selected antenna system has the capability of improving overall system**

**performance and may lead to a reduction in system cost if the overall number of stations or**

**access points can be reduced. Conversely, a poorly selected antenna system may degrade system performance and may lead to an increase in system cost.**

**The following sections will provide a discussion of fundamental antenna and RF**

**propagation properties and how these affect wireless system performance. These discussions**

**are intended to provide system engineers and operators with a basic knowledge of antenna**

**properties and antenna selection criteria.**

**In addition to antenna performance, other factors that influence antenna selection include**

**cost, size, and appearance. In the selection of an antenna system, there will always be tradeoffs**

**between these four issues.**

**I) FUNDAMENTAL ANTENNA PROPERTIES**

**The first concept to understand regarding antennas is that they are passive devices. To**

**operate, they require no supply voltage. They do not alter nor process RF signals and they do**

**not amplify RF energy. If they are 100% efficient, they radiate no more power than is delivered**

**to their input terminal.**

**The basic properties that are used to describe the performance of an antenna include**

**impedance and VSWR (Voltage Standing Wave Ratio), amplitude radiation patterns, 3 dB**

**beamwidth, directivity, gain, polarization and finally, bandwidth. These properties and their**

**impact on system performance are discussed in the following sections.**

**Impedance and VSWR**

**In order to achieve maximum energy transfer between a transmission line**

**and an antenna, the input impedance of the antenna must identically match the characteristic**

**impedance of the transmission line. If the two impedances do not match, a reflected wave will be generated at the antenna terminal and travel back towards the energy source. This reflection of energy results in a reduction in the overall system efficiency. This loss in efficiency will occur if the antenna is used to transmit or receive energy.**

**The ****reflection coefficient**** Γ is defined thus:**

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**Γ is a ****complex number**** that describes both the magnitude and the phase shift of the reflection. The simplest cases, when the imaginary part of Γ is zero, are:**

**Γ = − 1: maximum negative reflection, when the line is short-circuited,****Γ = 0: no reflection, when the line is perfectly matched,****Γ = + 1: maximum positive reflection, when the line is open-circuited.**

**The resultant voltage wave on the transmission line is the combination of both the**

**incident (source) and reflected waves. The ratio between the maximum voltage and the minimum voltage along the transmission line is defined as the Voltage Standing Wave Ratio or VSWR.**

**For the calculation of VSWR, only the ****magnitude**** of Γ, denoted by ρ, is of interest. Therefore, we define**

** ρ = | Γ | . **

**At some points along the line the two waves ****interfere**** constructively, and the resulting amplitude V_{max} is the sum of their amplitudes:**

**At other points, the waves interfere destructively, and the resulting amplitude V_{min} is the difference between their amplitudes:**

**The voltage standing wave ratio is then equal to:**

**As ρ, the magnitude of Γ, always falls in the range [0,1], the VSWR is always ≥ +1.**

**The VSWR, which can be derived from the level of reflected and incident waves, is also an**

**indication of how closely or efficiently an antenna’s terminal input impedance is matched to the**

**characteristic impedance of the transmission line. An increase in VSWR indicates an increase in**

**the mismatch between the antenna and the transmission line.**

**Typically, most wireless communications systems operate with a 50 Ohm impedance and**

**therefore, the antenna must be designed with an impedance as close to 50 Ohms as possible. The antenna VSWR is then an indication of how close the antenna impedance is to 50 Ohms. A 1.0:1 VSWR would indicate an antenna impedance of exactly 50 Ohms. In many systems, the antenna is required to operate with a VSWR better than 1.5:1**

**To indicate how increased VSWR impacts overall system performance, Table 1 below**

**details the percentage of power reflected by the antenna, and the resultant overall transmission loss, for several typical VSWR values. For a 1.5:1 VSWR, the transmission loss is**

**approximately 0.2 dB or a 4.0% reduction in efficiency. It is also important to note that some**

**transmitter circuits decrease their output power with increasing antenna VSWR. This factor**

**varies with each transmitter and is not quantified in this discussion.**

**Table 1. Percent Reflected Power and Transmission Loss as a Function of VSWR.**

**Radiation Patterns and 3 dB beamwidth**

**The radiation patterns of an antenna provide the information that describes how the**

**antenna directs the energy it radiates. As stated earlier, an antenna cannot radiate more total**

**energy than is delivered to its input terminals. All antennas, if 100% efficient will radiate the**

**same total energy, for equal input power, regardless of pattern shape.**

**Antenna radiation patterns are typically presented in the form of a polar plot for a 360**

**degree angular pattern in one of two sweep planes. The most common angular sweep planes**

**used to describe antenna patterns are a horizontal or azimuth sweep plane and a vertical or**

**elevation (zenith) sweep plane. A graphical representation of these planes and a typical polar**

**pattern are presented in Figure 1. Radiation patterns are generally presented on a relative power dB scale.**

**Figure 1. Graphical Representation of the Horizontal and Vertical Sweep Planes and a**

**Typical Polar Pattern Plot.**

**In many cases, the convention of an E-plane and H-plane sweep or pattern is used in the**

**presentation of antenna pattern data. The E-plane is the plane that contains the antenna’s**

**radiated electric field potential while the H-plane is the plane that contains the antenna’s radiated magnetic field potential. These planes are always orthogonal. For dipole and Yagi antennas, the E-plane is always in the plane parallel to the linear antenna elements.**

**Once the antenna pattern information is detailed in a polar plot, some quantitative aspects**

**of the antenna pattern properties can be described. These quantitative aspects generally include the 3 dB beamwidth (1/2 power level), directivity, side lobe level and front to back ratio. To further understand these concepts, we first consider the fundamental reference antenna, the point source. A point source is an imaginary antenna that radiates energy equally in all directions such that the antenna pattern is a perfect sphere as shown in Figure 2. This antenna is said to be an omnidirectional isotropic radiator and has 0 dB directivity. In practice, when an antenna is said to be omnidirectional, it is inferred that this is referenced only to the horizontal or azimuth sweep plane.**

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**Figure 2. Spherical Radiation Pattern of a Point Source Antenna.**

**For any practical antenna, there will always be some specific direction of maximum**

**radiated energy as shown in Figure 3. The relative level of the maximum radiated energy to that**

**of an isotropic radiator is termed directivity. This is a relative measure of how an antenna**

**focuses or directs the energy it radiates. The higher the directivity, the more focused the antenna pattern. It is important to note that no antenna can have a directivity less than 0 dB.**

**The 3 dB beamwidth of antenna is simply a measure of the angular width of the –3 dB**

**points on the antenna pattern relative to the pattern maximum. These –3 dB points on the**

**pattern represent the point on the pattern where the power level is half of the value at the pattern maximum. Generally, the 3 dB beamwidth is expressed separately for each of the individual pattern sweep planes.**

**Figure 3. A Typical Radiation Pattern of a Practical Antenna.**

**The antenna side lobe level and front to back ratio are measures of how much energy the**

**antenna radiates outside of its main beam. The side lobe level describes the relative level of minor pattern lobes outside the main beam while the front to back ratio describes the level of radiation directly opposite the main beam. Ideally, these levels should be as low as possible since they reduce the directivity and hence efficiency of the main beam. Energy radiated outside of the main beam of the antenna reduces the overall antenna efficiency. For transmit antennas, the presence of side and back lobes may also cause interference to other nearby receive sites. For receive antennas, the presence of side and back lobes may generate interference into the receive systemfrom surrounding transmit sites.**

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**Gain**

**The gain of an antenna is essentially a measure of the antenna’s overall efficiency. If an**

**antenna were 100% efficient, it would have a gain equal to its directivity. There are many factors that affect and reduce the overall efficiency of an antenna. Some of the most significant factors that impact antenna gain include the following: Impedance/VSWR: As mentioned in previous sections, the VSWR provides an indication of how closely the impedance of an antenna matches the impedance of the connecting transmission line. If an impedance mismatch exists, a reflected wave will be generated towards the energy source. This reflected wave reduces the level of energy transferred between the transmission line and the antenna. This effectively reduces the total level of radiated energy relative to the energy incident at the antenna’s input terminal. This loss of energy reduces the effective gain of the antenna. **

**Antenna Gain is defined as the ratio of the ****radiation**** intensity of an ****antenna**** in a given direction, to the intensity of the same antenna as it radiates in all directions (isotropically). Since the radiation intensity of an isotropically radiated power is equal to the power into the antenna divided by 4п (360 degrees) we can express the following equation: The terms U_{θ} and U_{φ} represent the radiation intensity in a given direction contained in their respective E field component.**

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**The formulas above show the relationship between antenna gain and directivity, where ε_{cd} is the antenna efficiency factor, D the directivity of the antenna and G the antenna gain**

**Antenna Absolute Gain is another definition for antenna gain. However, Absolute Gain does include the reflection or mismatch losses.**

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**In this equation, ε_{refl} is the reflection efficiency, and ε_{cd} includes the dielectric and conduction efficiency. The term ε_{eff} is the total antenna efficiency factor.**

**Matching Network Losses: In general, the terminal impedance of an antenna will not exactly match the characteristic impedance of the connecting transmission line to the required VSWR level. In order to align or match these impedances, a matching circuit or network is constructed at the antenna terminals. This matching network may typically consist of lumped circuit elements (inductors and/or capacitors), transformers (coaxial or microstrip) and microstrip circuitry. In any such matching circuit, energy is delivered to both the matching components and the antenna. Additionally, some of the matching components may be inherently lossy and will dissipate energy delivered to the antenna. The losses in these matching components may be minimal but do reduce the effective gain of the antenna. **

**Material (metal/dielectric) Losses: All antennas are constructed of discrete materials which include both metallic and non metallic components. If these components are used as part of the actual radiating structure, such as wire elements or dielectric substrates, they will dissipate some energy as heat rather than radiating it. The energy lost as heat in these components reduces the effective gain of the antenna.**

**Radome Losses: In many cases, the radiating structure of the antenna is housed inside a**

**radome for protection from the operating environment. In this case, the energy radiated by the**

**antenna must pass through the radome. In most cases, some amount of radiated energy is**

**dissipated as it passes through the antenna radome. This dissipated energy reduces the effective gain of the antenna. Considering all of these factors, it would appear that the antenna must overcome a lot of adversity in order to achieve acceptable gain performance. These loss factors are well known to antenna design engineers and can be eliminated or minimized with proper antenna design.**

**Typically, efficiency levels of 85% to 95% are not uncommon and are reflected in the calibrated**

**gain curves provided with antenna performance data.**

**Polarization**

**The polarization of an antenna describes the orientation and sense of the radiated wave’s**

**electric field vector. **

**Mathematically, the electric field of a plane wave can be written as,**

**or alternatively,**

**where A_{x} and A_{y} are the amplitudes of the x and y directions and φ is the relative phase between the two components The shape traced out in a fixed plane by the electric vector as such a plane wave passes over it is a description of the polarization state. The following figures show some examples of the evolution of the electric field vector (blue), with time(the vertical axes), at a particular point in space, along with its x and y components (red/left and green/right), and the path traced by the tip of the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.**

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**All radiated waves are generally defined as elliptically polarized. In this general case, the antenna’s total electric field (E-field) has two components that lie in the same plane. These two E-field components may be of different strength and are oriented at different angles (phase relationship). The two most known and common cases of elliptical polarization are circular; in which the two E-field components are equal in magnitude and oriented at 90 degrees to each other (90 degrees out of phase), and linear; in which the wave has a single E-field component. These concepts are graphically depicted in Figure 4. The term axial ratio is used to define the relative strength of the two E-field components in an elliptically polarized wave. For pure circular polarization the axial ratio is 0 dB and for linear polarization the axial ratio is Infinite. **

**Figure 4. Graphical Depiction of Polarization Orientation.**

**The important performance issue relative to signal polarization is that maximum energy**

**transfer between a transmitting and receiving antenna will only occur if both antennas have**

**identical axial ratio, identical polarization sense and the same spatial orientation. It is assumed**

**that nothing in the propagation path causes the signal polarization to change (polarization**

**distortion). With linearly polarized transmit and receive antennas, the polarization of each must be of the same orientation to achieve maximum energy transfer between the two antennas. If the two linearly polarized antennas are not identically oriented, there will be a reduction in energy transfer due to polarization mismatch. Table 2 on the following page provides a summary of polarization mismatch loss between two linearly polarized waves (antennas) that do not have the same angular orientation.**

**Table 2. Polarization Mismatch Between Two Linearly Polarized Waves as a Function of**

**Angular Orientation.**

**One common misconception in the communication industry is that there is always a 3 dB**

**polarization mismatch between linearly and circularly polarized antennas. This will only be true**

**if one antenna is purely circularly polarized and the other is purely linearly polarized. In most**

**cases, it is unlikely that the circularly polarized antenna will have an axial ratio of 0 dB and field**

**components exactly 90 degrees out of phase. Similarly, it is possible that the linearly polarized**

**antenna may have another minor field component.**

**Table 3 provides a summary of the polarization mismatch between a linearly polarized**

**and a circularly polarized wave as a function of the circularly polarized wave’s axial ratio. It is**

**assumed that the circularly polarized wave’s field components are orthogonal.**

**Table 3. Polarization Mismatch between a Linearly and Circularly Polarized Wave as a**

**Function of the Circularly Polarized Wave’s Axial Ratio.**

**Minimum polarization loss occurs when the strongest linear field component of the circularly polarized**

**wave is identically aligned with the linearly polarized wave.**

**Maximum polarization loss occurs when the weakest linear field component of the circularly polarized**

**wave is aligned with the linearly polarized wave.**

**Bandwidth**

**The term bandwidth simply defines the frequency range over which an antenna meets a**

**certain set of specification performance criteria. The important issue to consider regarding**

**bandwidth is the performance tradeoffs between all of the performance properties described**

**above. These tradeoffs will be described in more detail in the following sections.**

**TRP (Total Radiated Power)**

**To determine exactly how to apply the range calibration, it is important to make a comparison between the desired measurement quantities and what will actually be measured by the test system. The primary quantity of interest is the TRP, which can be obtained by integrating the time-averaged power density of the radiated signal across the entire spherical surface enclosing the AUT.**

**The time-averaged power density of a radiating signal is given by the real part of the Poynting vector:**

**where r is the time-averaged power density, E is the peak electric field strength, H is the peak magnetic field strength, E_{rms} is the root-mean-square (rms) electric field strength, and h is the impedance of free space (120p).^{3, 4}**

**The factor of 1/2 in the definition of the power density originates from the time averaging of the power across a complete period. Although most reference materials and numerical analysis tools refer to wave magnitudes by their peak values,**

**most measurement instrumentation reports rms values,**

**Therefore, when determining the power density from the rms electric field, the factor of 1/2 has already been accounted for. The difference between rms and peak field values can result in an immediate 3-dB error in reported measurement results if it is not treated correctly.**

**The TRP is given by integrating the power density across the surface of the reference sphere:**

**where TRP is the total radiated power, r is the time-averaged power density, r is the radius of the sphere (the range length), q is the elevation angle, and f is the azimuth angle.**

**The electric field generated at a point in the far field as a function of the transmitted power is given by**

**where E is the electric field generated at the distance r from the transmit antenna, P_{t} is the power measured at the transmit antenna input port, G_{t} (q, f) is the angle-dependent gain of the transmit antenna, and r is the distance from the transmit antenna to the test point (the range length).^{1}**

**Combining the equation for the power density with that of the electric field gives**

**Combining this result with the equation for TRP gives**

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