Chapter Fundamentals of Antennas Ahmed A.Kishk enter (CEDAR) An antenna is a device that is used to transfer guided electromagnetic waves (signals)to radiating waves in an unbounded medium,usually free space,and vice versa(i.e.,in either the transmitting or receiving mode of operation).Antennas are frequency-dependent devices.Each antenna is designed for a certain frequency band.Beyond the operating band,the antenna rejects sthe signal.Therefore,we might look at the antenna as a bandpass filter and a transducer.Antennas are essential parts in communication systems.Therefore,understanding their prin- ciples is important.In this chapter,we introduce the reader to antenna fundamentals. There are many different antenn esThe isotropic point source radiator on of the basic theoretical radiators,is useful becauseitca be considered a reference to other antennas.The isotropic point source radiator radiates equally in all directions in free space.Physically,such an isotropic point source cannot exist.Most antennas'gains are mea- sured with reference to an isotropic radiator and are rated in decibels with respect to an isotropic radiator(dBi). 1.1 Basis Parameters and Definitions of Antennas must as needed,during the design process the frequency band of operation, 1
1 Chapter 1 Fundamentals of Antennas Ahmed A. Kishk Center of Electromagnetic System Research (CEDAR) Department of Electrical Engineering University of Mississippi An antenna is a device that is used to transfer guided electromagnetic waves (signals) to radiating waves in an unbounded medium, usually free space, and vice versa (i.e., in either the transmitting or receiving mode of operation). Antennas are frequency-dependent devices. Each antenna is designed for a certain frequency band. Beyond the operating band, the antenna rejects the signal. Therefore, we might look at the antenna as a bandpass filter and a transducer. Antennas are essential parts in communication systems. Therefore, understanding their principles is important. In this chapter, we introduce the reader to antenna fundamentals. There are many different antenna types. The isotropic point source radiator, one of the basic theoretical radiators, is useful because it can be considered a reference to other antennas. The isotropic point source radiator radiates equally in all directions in free space. Physically, such an isotropic point source cannot exist. Most antennas’ gains are measured with reference to an isotropic radiator and are rated in decibels with respect to an isotropic radiator (dBi). 1.1 Basis Parameters and Definitions of Antennas Some basic parameters affect an antenna’s performance. The designer must consider these design parameters and should be able to adjust, as needed, during the design process the frequency band of operation
2 Chapter One polarization,input impedance,radiation patterns,gain,and efficiency s al m power a cceptance ties.The designer should evaluate and measure all of these parameters using various means. 1.1.1 Input Impedance and Equivalent Circuits As electromagnetic waves travel through the different parts of the antenna system.from the source (device)to the feed line to the antenna and finally to free space,they may encounter differences in impedance at each interface.Depe di ng on the e impedance match,some fracti of the wave's energy will reflect back to the source,forming a standing wave in the feed line.The ratio of maximum power to minimum power in the wave can be measured and is called the standing wave ratio(SWR). An SWR of 1:1 is ideal.An SWR of 1.5:1 is considered to be marginally acc applications where po ver loss is mor e critica SWR as h as6:1 ay still be usable with the rig ght equip ment.Minimizing impedance differences at each interface will reduce SWR and maximize power transfer through each part of the system. The frequency response of an antenna at its port is defined as input impedance (Z).The input impedance is the ratio between the volt- age and curro ents at the antenna port.In e is a complex quantity that varies with frequeney as(),wheref is the frequency.The antenna's input impedance can be represented as a circuit element in the system's microwave circuit.The antenna can be represented by an equivalent circuit of several lumped elements,as shown in Figure 1.1.In Figure 1.1,the equivalent circuit of the antenna is conected toa source,V ith inter al impedance,Z.=R.+jX.The antenna has an input impedance of Zin=Ra+iXa.The real part consists 0 Xa Figure 1.1 Equivalent circuit of an antenna
2 Chapter One polarization, input impedance, radiation patterns, gain, and efficiency. An antenna in the transmitting mode has a maximum power acceptance. An antenna in the receiving mode differs in its noise rejection properties. The designer should evaluate and measure all of these parameters using various means. 1.1.1 Input Impedance and Equivalent Circuits As electromagnetic waves travel through the different parts of the antenna system, from the source (device) to the feed line to the antenna and finally to free space, they may encounter differences in impedance at each interface. Depending on the impedance match, some fraction of the wave’s energy will reflect back to the source, forming a standing wave in the feed line. The ratio of maximum power to minimum power in the wave can be measured and is called the standing wave ratio (SWR). An SWR of 1:1 is ideal. An SWR of 1.5:1 is considered to be marginally acceptable in low-power applications where power loss is more critical, although an SWR as high as 6:1 may still be usable with the right equipment. Minimizing impedance differences at each interface will reduce SWR and maximize power transfer through each part of the system. The frequency response of an antenna at its port is defined as input impedance (Zin). The input impedance is the ratio between the voltage and currents at the antenna port. Input impedance is a complex quantity that varies with frequency as Zin( f ) = Rin( f ) + jXin(f), where f is the frequency. The antenna’s input impedance can be represented as a circuit element in the system’s microwave circuit. The antenna can be represented by an equivalent circuit of several lumped elements, as shown in Figure 1.1. In Figure 1.1, the equivalent circuit of the antenna is connected to a source, Vs, with internal impedance, Zs = Rs + jXs. The antenna has an input impedance of Zin = Ra + jXa. The real part consists Rr Rs Rl Xa Zin Vs Xs Figure 1.1 Equivalent circuit of an antenna
Fundamentals of Antennas 3 of the radiation resistance (R)and the antenna losses(R).The input impedance can then be used to determine the reflection coefficient ( and related param (1.1) Zi +Z where Z is the normalizing impedance of the port.IfZ is complex,the reflection coefficient can be modified to be (12) Zm+Z。 where Z is the conjugate of the nominal impedance.The VSWR is given as vswR=1-可 1+Γ (13) And the return loss is defined as RL=-20l0gTI (1.4) Input impedance is usually plotted using a Smith chart.The Smith oo that shows the reflectio coefficient 出et品号h(nductve any of the antenna's resonance frequencies.These frequencies are those at which the input impedance is purely real;conveniently,this corre- sponds to locations on the Smith chart where the antenna's impedance locus crosses the real axis. Impedance f an antenna is complex and a function of frequency.The impedance of adjusted through the design process to be matched with the feed line and have less reflection to the source. If that is not possible for some antennas,the impedance of the antenna can be matched to the feed line and radio by adjusting the feed line's impedance,thus using the feed line as an impedance transformer. 1.1.2 Matching and Bandwidth In some cases,the impedance is adjusted at the load by inserting a matching trans mer,ma tch composed of lumped ele mentuasindutors and capacitors for requen catio or implementing such a matching circuit using transmission-line tech- nology as a matching section for high-frequency applications where lumped elements cannot be used
Fundamentals of Antennas 3 of the radiation resistance (Rr) and the antenna losses (Rl). The input impedance can then be used to determine the reflection coefficient (Γ) and related parameters, such as voltage standing wave ratio (VSWR) and return loss (RL), as a function of frequency as given in1–4 Γ = − + Z Z Z Z o o in in (1.1) where Zo is the normalizing impedance of the port. If Zo is complex, the reflection coefficient can be modified to be Γ = − + ∗ Z Z Z Z o o in in (1.2) where Z* o is the conjugate of the nominal impedance. The VSWR is given as VSWR = + − 1 1 Γ Γ (1.3) And the return loss is defined as RL = −20 log| |Γ (1.4) Input impedance is usually plotted using a Smith chart. The Smith chart is a tool that shows the reflection coefficient and the antenna’s frequency behavior (inductive or capacitive). One would also determine any of the antenna’s resonance frequencies. These frequencies are those at which the input impedance is purely real; conveniently, this corresponds to locations on the Smith chart where the antenna’s impedance locus crosses the real axis. Impedance of an antenna is complex and a function of frequency. The impedance of the antenna can be adjusted through the design process to be matched with the feed line and have less reflection to the source. If that is not possible for some antennas, the impedance of the antenna can be matched to the feed line and radio by adjusting the feed line’s impedance, thus using the feed line as an impedance transformer. 1.1.2 Matching and Bandwidth In some cases, the impedance is adjusted at the load by inserting a matching transformer, matching networks composed of lumped elements such as inductors and capacitors for low-frequency applications, or implementing such a matching circuit using transmission-line technology as a matching section for high-frequency applications where lumped elements cannot be used
4 Chapter One The bandwidth is the antenna operating frequency band within which antenna matching band if its radiation patterns do not change within this band.In fact,this is the case for small antennas where a fundamen- tal limit relates bandwidth,size,and efficiency.The bandwidth ofother antennas might be affected by the radiation pattern's characteristics. and the radiation characteristics might change although the matching of the antenna is accep table.We can define antenna bandwidth in sev eral ways.Ratio bandwidth(BW)is BW.=fo (1.5) where fu and fi are the upper and lower frequency of the band,respec- tively.The other definition is the percentage bandwidth (WB.)and is related to the ratio bandwidth as Bw,=20%=20- W阳+行% (1.6) fu+f 1.1.3 Radiation Patterns Radiation pattersare graphical representations of theeerom the antenna.The fields are measured in the spherical coordinate system,as shown in Figure 1.2,in the 6and o directions.For the ideal isotropic antenna,this would be a sphere.For a typical dipole,this would be a toroid.The radiation pattern of an antenna is typically rep- resented by a three-dimensional (3D)graph,as shown in igure 1.3 or polar plots of the horizontal and vertical ros section.The graph should show sidelobes and backlobes.The polar plot can be considered as a planer cut from the 3D radiation pattern,as shown in Figure 1.4. 2 Figure12 Spherical coordinates
4 Chapter One The bandwidth is the antenna operating frequency band within which the antenna performs as desired. The bandwidth could be related to the antenna matching band if its radiation patterns do not change within this band. In fact, this is the case for small antennas where a fundamental limit relates bandwidth, size, and efficiency. The bandwidth of other antennas might be affected by the radiation pattern’s characteristics, and the radiation characteristics might change although the matching of the antenna is acceptable. We can define antenna bandwidth in several ways. Ratio bandwidth (BWr) is BWr U L f f = (1.5) where fU and fL are the upper and lower frequency of the band, respectively. The other definition is the percentage bandwidth (WBp) and is related to the ratio bandwidth as BW WB WB p U L U L r r f f f f = − + = − + 200 200 1 1 % % (1.6) 1.1.3 Radiation Patterns Radiation patterns are graphical representations of the electromagnetic power distribution in free space. Also, these patterns can be considered to be representative of the relative field strengths of the field radiated by the antenna.1–4 The fields are measured in the spherical coordinate system, as shown in Figure 1.2, in the q and f directions. For the ideal isotropic antenna, this would be a sphere. For a typical dipole, this would be a toroid. The radiation pattern of an antenna is typically represented by a three-dimensional (3D) graph, as shown in Figure 1.3, or polar plots of the horizontal and vertical cross sections. The graph should show sidelobes and backlobes. The polar plot can be considered as a planer cut from the 3D radiation pattern, as shown in Figure 1.4. Figure 1.2 Spherical coordinates x y z q f
Fundamentals of Antennas 5 Color scale magnitude 0.00☐ -4.44 Main lobe -8.89 -13.33 -17.78 -22.22 -26.67 -31.11 356 -40.00 Figure 1.3 3D radiation pattern 20 210 240 270 Figure 14 Polar plot radiation The same pattern can be presented in the rectangular coordinate system,as shown in Figure 1.5.We should point out that these pat- terns are normalized to the pattern's peak,which is pointed to =0 in this case and given in decibels. 1.1.3.1 Beamwidth The beamwidth of the antenna is usually considered to be the angular width of the half power radiated within a certain cut through the main beam of the antenna where most of the power is radi- ating from the peak radiation intensity of the radiation pattern.which is the peak of the main beam,the half power level is3dB below such a peak where the two points on the main beam are located;these points are on two sides of the peak,which separate the angular width of the half power.The angular distance between the half power points is defined as the beamwidth.Half the power expressed in decibels is-3 dB,so the
Fundamentals of Antennas 5 Backlobe Sidelobes Main lobe Nulls 0.00 Color scale magnitude -4.44 -8.89 -13.33 -17.78 -22.22 -26.67 -31.11 -35.56 - 40.00 Figure 1.3 3D radiation pattern Figure 1.4 Polar plot radiation 120° 90° 60° 30° 0° 330° 300° 270° 240° 210° 180° 150° -10 -20 -30 -40 0 The same pattern can be presented in the rectangular coordinate system, as shown in Figure 1.5. We should point out that these patterns are normalized to the pattern’s peak, which is pointed to q = 0 in this case and given in decibels. 1.1.3.1 Beamwidth The beamwidth of the antenna is usually considered to be the angular width of the half power radiated within a certain cut through the main beam of the antenna where most of the power is radiating. From the peak radiation intensity of the radiation pattern, which is the peak of the main beam, the half power level is −3 dB below such a peak where the two points on the main beam are located; these points are on two sides of the peak, which separate the angular width of the half power. The angular distance between the half power points is defined as the beamwidth. Half the power expressed in decibels is −3 dB, so the