LECTURE NOTES OF ANTENNAS Mário G. Silveirinha Lisboa, May 2020 Antennas ii Antennas Index 1. Radiating systems ................................................................................................................ 1 1.1 Fields radiated by a generic current distribution ..................................................... 1 1.2 Far-field region ........................................................................................................ 2 1.3 Radiation intensity ................................................................................................... 6 2. Linear antennas ................................................................................................................... 9 2.1 The dipole antenna ................................................................................................... 9 2.2 Hallén’s integral equation ...................................................................................... 10 2.3 Sinusoidal current approximation .......................................................................... 13 2.4 Far-field of the dipole ............................................................................................ 15 2.5 Effective height with the sinusoidal current approximation .................................. 15 2.6 Radiated power and radiation resistance ............................................................... 18 2.7 Input impedance ..................................................................................................... 19 2.8 The half-wavelength dipole ................................................................................... 21 2.9 Further discussion about the resonant condition ................................................... 22 2.10 Image method ......................................................................................................... 24 2.11 The monopole antenna ........................................................................................... 28 3. Receiving antenna ............................................................................................................. 31 3.1 The receiving antenna ............................................................................................ 31 3.2 Simultaneous excitation ......................................................................................... 32 3.3 Equivalent circuit of the receiving antenna ........................................................... 35 3.4 Power delivered to a load and impedance matching .............................................. 36 3.5 Polarization matching, available power and effective area ................................... 37 3.6 Reciprocity theorem ............................................................................................... 40 3.7 Application of the reciprocity theorem to antenna theory ..................................... 43 3.8 Relation between the effective area and power gain ............................................. 46 3.9 Friis formula........................................................................................................... 47 3.10 Antenna polarization .............................................................................................. 48 3.11 Optimal polarization for the incident wave ........................................................... 50 3.12 The Poincaré sphere ............................................................................................... 52 3.13 Examples with the dipole antenna ......................................................................... 54 4. Mutual and self impedances .............................................................................................. 57 iii Antennas 4.1 Antenna coupling ................................................................................................... 57 4.2 Reciprocity constraint on the mutual impedances ................................................. 60 4.3 Mutual impedance with perturbation theory .......................................................... 63 4.4 Application to linear antennas ............................................................................... 65 4.5 Accepted power ..................................................................................................... 67 5. Thermal noise .................................................................................................................... 69 5.1 Thermal radiation ................................................................................................... 69 5.2 Equipartition law .................................................................................................... 69 5.3 The natural modes .................................................................................................. 71 5.4 Spectrum of the thermal energy ............................................................................. 73 5.5 Thermal energy captured by an antenna ................................................................ 73 5.6 Antenna noise temperature .................................................................................... 76 5.7 Equivalent circuit ................................................................................................... 78 6. Balancing devices.............................................................................................................. 81 6.1 Balanced lines ........................................................................................................ 81 6.2 Baluns .................................................................................................................... 82 7. Antenna arrays .................................................................................................................. 85 7.1 Introduction ............................................................................................................ 85 7.2 Principle of pattern multiplication ......................................................................... 86 7.3 Linear arrays .......................................................................................................... 89 7.4 Progressive phaseshift array .................................................................................. 92 7.5 Electronic beam steering ........................................................................................ 95 7.6 Uniform array ......................................................................................................... 96 7.7 Graphical construction of the array radiation pattern .......................................... 100 7.8 The Dolph-Chebyshev array ................................................................................ 101 7.9 Planar arrays ........................................................................................................ 111 7.10 Power gain and gain in field intensity ................................................................. 115 8. Wire-type antennas .......................................................................................................... 119 8.1 Introduction .......................................................................................................... 119 8.2 Corner reflector .................................................................................................... 119 8.3 Yagi-Uda .............................................................................................................. 124 8.4 The turnstile antenna ............................................................................................ 130 8.5 Loop antenna ........................................................................................................ 138 8.6 The helical antenna .............................................................................................. 142 iv Antennas 9. Frequency independent antennas .................................................................................... 155 9.1 Transformation of scale ....................................................................................... 155 9.2 Biconical antenna ................................................................................................. 158 9.3 Log-periodic antennas .......................................................................................... 164 9.4 Spiral antennas ..................................................................................................... 168 10. Aperture antennas ..................................................................................................... 173 10.1 Introduction .......................................................................................................... 173 10.2 The equivalence principle .................................................................................... 173 10.3 Fields radiated by the equivalent currents ........................................................... 177 10.4 Uniform rectangular aperture ............................................................................... 179 10.5 Open-ended rectangular waveguide ..................................................................... 182 10.6 Horn antenna ........................................................................................................ 185 v Antennas 1. Radiating systems 1.1 Fields radiated by a generic current distribution Consider a generic source (antenna) described by the electric current density