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Introduction to Antennas Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W: www.eee.bham.ac.uk/ConstantinouCC/ E: [email protected] Recommended textbook • Constantine A. Balanis, Antenna Theory: Analysis and Design, 3rd Edition, WileyInterscience, 2005; ISBN:0-471-66782-X – Chapters 1 & 2 2 Antennas • An antenna can be thought of as a transition / transducer device • Two ways of describing antenna operation – Field point of view – Circuit point of view 3 Antenna examples • Wire antennas – Monopoles – Dipoles – Arrays 4 Antenna examples • Aperture Antennas – – – – – Reflectors Lenses Horns Patches Planar inverted F 5 Antennas • Most antennas are resonant structures – Narrowband – Size is inversely proportional to frequency of operation • Travelling wave antennas also important 1000 ft diameter; 50 MHz to 10 GHz – Wideband – Size dictates lowest frequency of operation chip size = 2 x 1 mm2; 60 GHz antenna 6 How does it work? – radiation 7 How does it work? – radiation 8 How does it work? – radiation 9 How does it work? – radiation 10 How does it work? – radiation B A Sphere grows with time (i.e. delay increases with distance) 11 How does it work? – radiation 12 How does it work? – radiation Source: MIT Open Courseware 13 How does it work? – radiation Source: MIT Open Courseware 14 Antennas – TV aerial • Radiation of power in space can be controlled by carefully arranging the patterns of electron motion • This is the same as their sensitivity to received signals from different directions in space 15 Fundamental antenna parameters • Radiation pattern; radiation power density; radiation intensity • Beamwidth; directivity; sidelobe levels • Efficiency; gain • Polarisation • Impedance • Bandwidth • Vector effective length and equivalent area • Antenna temperature 16 Radiation pattern • A mathematical and/or graphical representation of the properties of an antenna, usually the radiation intensity vs. spatial direction coordinates sufficiently far from the antenna • Is polarisation specific • Spherical polar coordinates are always used Source: C.A. Balanis© 17 Radiation pattern Linear pattern Polar pattern Source: C.A. Balanis© 18 Radiation pattern Linear pattern E plane is plane of electric field H plane is plane of magnetic field If field direction not known, do not use E or H plane Source: C.A. Balanis© 19 Omnidirectional antenna radiation pattern H-plane E-plane λ/2 dipole antenna radiation pattern Source: C.A. Balanis© 20 Radiation pattern definitions • Isotropic antenna – Radiates equally in all directions in space; physically unrealisable • Omnidirectional antenna – Radiates equally in all directions in one plane only; e.g. dipoles, monopoles, loops, etc. • Directional antenna – Radiates strongly in a given direction; has a principal or main lobe, the maximum of which point in the direction of the antenna’s boreside – Can you guess what is meant by front-to-back ratio? 21 Field regions • Reactive near-field – Phases of electric and magnetic fields are often close to quadrature – High reactive wave impedance – High content of non-propagating stored energy near the antenna • Radiative near-field (Fresnel) – Fields are predominantly in-phase – Wavefronts are not yet spherical; pattern varies with distance • Radiative far-field (Fraunhofer) – Electric and magnetic fields are in-phase – Wavefront is spherical; field range dependence is e-jkr/r – Wave impedance is real (Eθ/Hφ = 120π = 377 Ω) – Power flow is real; no stored energy • Field regions have no sharp boundaries Source: C.A. Balanis© 22 Reminder on angular units Radians Steradians For the whole sphere, 2 2 0 0 0 0 sin d d d sin d 2 cos 0 2 1 1 4 Sr Source: C.A. Balanis© 23 Radiation power intensity and density • Poynting vector S E H Wm2 1 • Time-averaged Poyting vector S Re E H* Wm 2 2 • Radiation power density W , S Wm 2 • Radiation intensity U , r 2W W/Sr • Total radiated power Prad Pavg 2 Prad 0 S.dA 2 ˆ S . e r r d 1 * 2 ˆ Re E H . e r 0 2 r sin d d 24 Directivity U , 4 U , D , U avg Prad Dmax U max 4 U max U0 Prad D dB 10log10 Dmax dimensionless 25 Directivity • Isotropic antenna U max U avg D 1 or D 0dB • Current element L << λ U , Umax sin2 Prad 2 0 0 0 3 2 U sin d d 2 U sin sin d max max 8 2 U max 1 u du U max 3 1 1 2 Dmax 4 U max 4 U max 3 Dmax or D 1.76dB 8 Prad 2 U max 3 26 Directivity cos 2 cos • Half wave dipole L = λ/2 U , U max sin 2 cos 2 cos Prad U max sin d d sin 0 0 cos2 2 cos 2 U max d sin 0 2 2 2 U max 1.22 Dmax 4 U max 4 U max Dmax 1.64 or D 2.15dB Prad 1.22 2 U max 27 Beamwidth • Current element L << λ U , Umax sin2 • The half-power angles in E-plane are given by, 1 U 3dB , U max U max sin 2 3dB 2 1 3 sin 3dB 3dB,1 , 3dB,2 4 4 2 HPBW 3dB,2 3dB,1 90 • Halfwave dipole – a similar numerical calculation for the two roots of cos 2 cos 3dB 1 HPBW 78 sin 3dB 2 28 Beamwidth vs. directivity • The narrower the beamwidth of an antenna, the bigger its directivity • For a single main beam antenna Dmax 4 A where ΩA is the main lobe half power beam solid angle • Kraus approximation for nonsymmetrical main lobes 4 41, 253 Dmax 1r 2 r 1d 2 d • Tai & Pereira approximation for non symmetrical main lobes 32 ln 2 72,815 Dmax 2 2 2 1r 2 r 1d 22d Source: C.A. Balanis© 29 Antenna efficiency, ηant • In an antenna, we experience reduction in radiated power due to – Reflection at the input terminals (impedance mismatch) – Ohmic conductor losses (c) in the antenna conductors – Dielectric losses (d) in the antenna dielectrics ant 1 in cd 2 Typical antenna efficiency values Dipole ηant ~ 98% Patch antenna ηant ~ 90% Mobile phone PIFA ηant ~ 50% – The latter two are grouped Prad under the term antenna rad cd Pin radiation efficiency Source: C.A. Balanis© 30 Antenna Gain 4 U , G , a D , Pin Gmax a Dmax G dB 10log10 Gmax dimensionless Antenna Absolute Gain G , 1 D , 2 abs in a 31 Bandwidth • Many properties vary with frequency and deteriorate in value from their optimum values: – Pattern bandwidth • • • • • Directivity/gain Sidelobe level Beamwidth Polarisation Beam direction – Impedance bandwidth • Input impedance • Radiation efficiency 32 Polarisation • Antenna polarisation refers to the orientation of the far-field radiated electric field vector from the antenna – A vertical dipole radiates a vertical electric field – A horizontal dipole radiates a horizontal electric field – A general (e.g. horn) antenna with a vertical aperture electric field radiates a vertical electric field in the E-plane and H-plane only; everywhere else the electric field vector is inclined to the vertical and changes with angular direction 33 Polarisation • The polarisation of an electromagnetic wave can be – Linear (as in all previously discussed examples) – Circular (e.g. using a helical antenna to transmit) – Elliptical (e.g. circular after reflection from a lossy interface) • Circular and elliptical polarisations have a sense of rotation – Positive helicity (or right hand, clockwise) – Negative helicity Source: C.A. Balanis© 34 Polarisation Axial ratio, AR OA OB 1 AR Source: C.A. Balanis© 35 Polarisation • Linearly polarised uniform plane wave (E0x and E0y real) E x, y, z, t Re E0 xeˆ x E0 y eˆ y e jt e jk0 z • Circularly polarised uniform plane wave (+/- corresponding to positive/negative helicity) E x, y, z, t Re E0 eˆ x jeˆ y e jt e jk0 z • Elliptically polarised uniform plane wave (+/- corresponding to positive/negative helicity; E0x and E0y real) E x, y, z, t Re E0 xeˆ x E0 y e j eˆ y e jt e jk0 z E0 x E0 y , n , or E0 x E0 y , 2n 1 2 36 Polarisation • The radiation pattern performance of antennas is often specified in terms of its co-polar and cross-polar components – – – Detailed mathematical definition is Ludwig’s 3rd definition of cross-polarisation (A. Ludwig (1973), “The definition of cross polarization,” IEEE Transactions on Antennas and Propagation, 21(1)) Co-polar radiation pattern of an antenna is measured with a suitably polarised probe antenna which is sensitive to the “wanted” polarisation Cross-polarised pattern is measured for linear polarisation by rotating the probe antenna by π/2 around the line joining the two antennas, or for circular/elliptical polarisation by changing the probe antenna helicity sign 37 Impedance • Transmitting operation • Receiving operation generator receiver (Zg = Rg + jXg) (Zrx) a Vg RL Ig Rg Rr Xg b Gg Bg Gr b GL BA Norton equivalent circuit (suitable for magnetic radiators, e.g. loop, etc.) Va Ia Rrx Rr Xrx b XA a Ig Thevenin equivalent circuit (suitable for electric radiators, e.g. monopole, dipole, etc.) RL a XA a Grx Gr Brx GL Ia BA b 38 Impedance • The antenna operation is characterised by an impedance ZA – An equivalent radiation resistance, Rr – A loss (ohmic and dielectric) resistance, RL – A reactance, XA • When connected to a generator, usually via a transmission line, the usual transmission line and circuit theories apply 2 1 • Radiated power Pr 2 I g Rr • Maximum power transferred from generator to antenna (maximum power transfer theorem) RA Rr RL Rg & X A X g • Half of generator power is consumed intenally, other half is shared between antenna losses and antenna radiation 39 Impedance Pr PL Vg 2 Rr Rr RL 8 Vg 8 2 2 RL Rr RL 2 Since Rr RL Rg ; Vg X A Xg 2 1 Pr PL Pg 8 Rr RL Total PT Pg Pr PL Vg 2 4 Rr RL 40 Radiation efficiency • We have come across radiation efficiency before, but now we express it in circuit theory equivalent terms • Describes how much power is radiated vs. dissipated in the antenna Rr rad Rr RL 41 Antenna effective length • The voltage at the antenna terminals is determined from the incident field • The effective length is a vector Va VOC Ei .dl Ei .l e , C • When taking the maximum value over θ,φ this becomes Va Ei .l e • For linear antennas l e physical Source: C.A. Balanis© 42 Effective aperture area Ae • This is usually assumed to refer to the co-polar radiation pattern on the boreside of an antenna • The antenna effective aperture area is defined as a ratio PT Ae Wi – PT is the power delivered to a matched load in W – Wi is the incident wave power density in Wm–2 – Ae is the antenna effective aperture area in m2 • For any passive antenna we can invoke the principle of reciprocity to show that G Tx 4 2 Rx Ae 43 Antenna aperture efficiency • For all aperture antennas Ae Aphysical • This allows us to introduce the concept of antenna aperture efficiency Ae a Aphysical • For aperture antennas a 1 • For wire antennas a 1 where the physical aperture is taken to be the cross sectional area of the wire 44 Friis free-space transmission • From your propagation lectures, assuming matched antennas, PRx 4 d GTxGRx PTx • This expression is a statement of the principle of conservation of energy coupled with the notions of antenna gain and antenna effective aperture area 2 45