Chapter 2. Fundamental Properties of Antennas. ECE 5318/6352 Antenna Engineering Dr. Stuart Long

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1 Chapter Fundamental Properties of Antennas ECE 5318/635 Antenna Engineering Dr. Stuart Long 1

2 IEEE Standards Definition of Terms for Antennas IEEE Standard IEEE Transactions on Antennas and Propagation Vol. AP-31, No. 6, Part II, Nov. 1983

3 Radiation Pattern (or Antenna Pattern) The spatial distribution of a quantity which characterizes the electromagnetic field generated by an antenna. 3

4 Distribution can be a Mathematical function Graphical representation Collection of experimental data points 4

5 Quantity plotted can be a Power flux density W [W/m²] Radiation intensity U [W/sr] Field strength E [V/m] Directivity D 5

6 Graph can be Polar or rectangular 6

7 Graph can be Amplitude field E or power E ² patterns (in linear scale) (in db) 7

8 Graph can be -dimensional or 3-D most usually several -D cuts in principle planes 8

9 Radiation pattern can be Isotropic Equal radiation in all directions (not physically realizable, but valuable for comparison purposes) Directional Radiates (or receives) more effectively in some directions than in others Omni-directional nondirectional in azimuth, directional in elevation 9

10 Principle patterns E-plane Plane defined by E-field and direction of maximum radiation H-plane Plane defined by H-field and direction of maximum radiation (usually coincide with principle planes of the coordinate system) 10

11 Coordinate System Fig..1 Coordinate system for antenna analysis. 11

12 Radiation pattern lobes Major lobe (main beam) in direction of maximum radiation (may be more than one) Minor lobe - any lobe but a major one Side lobe - lobe adjacent to major one Back lobe minor lobe in direction exactly opposite to major one 1

13 Side lobe level or ratio (SLR) (side lobe magnitude / major lobe magnitude) - 0 db typical < -50 db very difficult Plot routine included on CD for rectangular and polar graphs 13

14 Polar Pattern Fig..3(a) Radiation lobes and beamwidths of an antenna pattern 14

15 Linear Pattern Fig..3(b) Linear plot of power pattern and its associated lobes and beamwidths 15

16 Field Regions Reactive near field energy stored not radiated R D λ= wavelength D= largest dimension of the antenna 16

17 Field Regions Radiating near field (Fresnel) radiating fields predominate pattern still depend on R radial component may still be appreciable D R D λ= wavelength D= largest dimension of the antenna 17

18 Field Regions Far field (Fraunhofer( Fraunhofer) field distribution independent of R field components are essentially transverse R D 18

19 Radian radians in full circle arc length of circle r Fig..10(a) Geometrical arrangements for defining a radian 19

20 Steradian one steradian subtends an area of A r 4π steradians in entire sphere da r sin d d d da r sin d d Fig..10(b) Geometrical arrangements for defining a steradian. 0

21 Radiation power density Instantaneous Poynting vector W E H [ W/m ² ] Total instantaneous Power P W s s [-3] d [ W ] [-4] Time average Poynting vector W avg 1 Re E H Average radiated Power Prad Wavg d s s [ W/m ² ] [-8] [ W ] [-9] 1

22 Radiation intensity Power radiated per unit solid angle Note: This final equation does not have an r in it. The zero superscript means that the 1/r term is removed. U r Wavg [W/unit solid angle] r U (, ) E ( r,, ) r 1 E E ( r,, ) o far zone fields without 1/r factor E ( r,, ) o E (, ) (, ) [-1a]

23 Directive Gain Ratio of radiation intensity in a given direction to the radiation intensity averaged over all directions Directivity Gain (Dg) -- directivity in a given direction D g U U o U 4 P rad [-16] U 0 P rad 4 (This is the radiation intensity if the antenna radiated its power equally in all directions.) Note: U 1 0 U, sin d d 4 S 3

24 Directivity Directivity -- Do value of directive gain in direction of maximum radiation intensity D o U U max o U 4 P max rad Do (isotropic) = Dg Do 4

25 Beamwidth Half power beamwidth Angle between adjacent points where field strength is times the maximum, or the power is 0.5 times the maximum (-3dB below maximum) First null beamwidth Angle between nulls in pattern Fig..11(b) -D power patterns (in linear scale) of U()=cos²()cos³() 5

26 Approximate directivity for omnidirectional patterns For example U sin n π π [-3] McDonald Pozar Do HPBW HPBW Do HPBW [-33a] Better if no minor lobes [-33b] (HPBW in degrees) Results shown with exact values in Fig..18 6

27 Approximate directivity for directional patterns Antennas with only one narrow main lobe and very negligible minor lobes For example D o Kraus 4 41,53 1r r 1d d [-7] U cos n Do π/ π Tai & Pereira.18 1r r [-30b] [-31] 7,815 1d d,, 1r r 1d ( ) HPBW in two perpendicular planes in radians or in degrees) d Note: According to Elliott, a better number to use in the Kraus formula is 3,400 (Eq. -71 in Balanis). In fact, the 41,53 is really wrong (it is derived assuming a rectangular beam footprint instead of the correct elliptical one). 7

28 Approximate directivity for directional patterns Can calculate directivity directly (sect..5), can evaluate directivity numerically (sect..6) (when integral for P rad cannot be done analytically, analytical formulas cannot be used ) 8

Gain Like directivity but also takes into account efficiency of antenna (includes reflection, conductor, and dielectric losses) G oabs e o D o e o 4 Umax 4 Umax Prad Pin (lossless,

29 Gain Like directivity but also takes into account efficiency of antenna (includes reflection, conductor, and dielectric losses) G oabs e o D o e o 4 Umax 4 Umax Prad Pin (lossless, isotropic source) [-49c] Efficiency eo erec ecd ec e ed d eo : overall eff. er : reflection eff. ec : conduction eff. ed : dielectric eff. Zin Zo 1 in o ; Z Z e o P P rad inc e cd P rad P in 9

30 Gain By IEEE definition gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches (losses) G o e cd D o P in 4 Umax (lossless, isotropic source) [-49a] 30

31 Bandwidth frequency range over which some characteristic conforms to a standard Pattern bandwidth Beamwidth, side lobe level, gain, polarization, beam direction polarization bandwidth example: circular polarization with axial ratio < 3 db Impedance bandwidth usually based on reflection coefficient under to 1 VSWR typical 31

32 Bandwidth Broadband antennas usually use ratio (e.g. 10:1) Narrow band antennas usually use percentage (e.g. 5%) 3

33 Polarization Linear Circular Elliptical Right or left handed rotation in time 33

34 Polarization Polarization loss factor w a p ˆ ˆ [-71] PLF cos p is angle between wave and antenna polarization 34

35 Input impedance Ratio of voltage to current at terminals of antenna ZA = RA + jxa RA = Rr + RL ZA = antenna impedance at terminals a-b Rr = radiation resistance RL = loss resistance 35

36 Input impedance Antenna radiation efficiency e cd Power Radiated by Antenna P Power Delivered to Antenna ( Pr PL) r 1 Ig 1 1 R g r g L I R I R r e cd R r R r R L [-90] Note: this works well for those antennas that are modeled as a series RLC circuit like wire antennas. For those that are modeled as parallel RLC circuit (like a microstrip antenna), we would use G values instead of R values. 36

37 Friis Transmission Equation Fig..31 Geometrical orientation of transmitting and receiving antennas for Friis transmission equation 37

38 Friis Transmission Equation P P r t e t e r D t (, ) t t D r 4 R (, ) r [-117] r et = efficiency of transmitting antenna er = efficiency of receiving antenna Dt = directive gain of transmitting antenna Dr = directive gain of receiving antenna = wavelength R = distance between antennas assuming impedance and polarization matches 38

39 39 Radar Range Equation Radar Range Equation Fig..3 Geometrical arrangement of transmitter, target, and receiver for radar range equation ), ( ), ( R R D D e e P P r r r t t t t r cdr cdt [-13]

40 Radar Cross Section RCS Usually given symbol U W r 4 inc Far field characteristic Units in [m²] Winc incident power density on body from transmit direction U r scattered power intensity in receive direction Physical interpretation: The radar cross section is the area of an equivalent ideal black body absorber that absorbs all incident power that then radiates it equally in all directions. 40

41 Radar Cross Section (RCS)( Function of Polarization of the wave Angle of incidence Angle of observation Geometry of target Electrical properties of target Frequency 41

42 Radar Cross Section (RCS)( 4

S=E H ANTENNA RADIATION

S=E H ANTENNA RADIATION ANTENNA RADIATION Antennas radiate spherical waves that propagate in the radial direction for a coordinate system centered on the antenna. At large distances, spherical waves can be approx imated by plane