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Lecture IV Antennas & Propagation -1- Antennas & Propagation Mischa Dohler King’s College London Centre for Telecommunications Research Lecture IV Antennas & Propagation -2- Overview of Lecture IV - Review of Lecture III - Extensions of the finite length Dipole - Definitions Mutual and Self Impedance Lecture IV Antennas & Propagation -3- Review The following definitions are applicable to all antennas: 1. Power Density w = Re{S} 2.Total Radiated Power P 3. Radiation Resistance Rr 4. Antenna Impedance ZA Lecture IV Antennas & Propagation -4- Review 5. Equivalent Circuit 6. Load matching 7. Effective Length le 8. Effective Area Ae 9. Radiation Intensity U 12. Directivity D 10. HPBW / Bandwidth B 13. Radiation Efficiency e 11. Directive Gain g 14. (Power) Gain G Dipole of finite length jk Hφ I 0 e jkr le θ 4πr E H φ Lecture IV Antennas & Propagation -5- Review sin jkzcos le I ( z ) e dz I ( 0) L I ( z ) I max 1 sin k L z , 2 I max 1 I (0) / sin kL 2 L/a > 60 : Hallén's Integral Transmission Line Hallén's Integral Equation Objective: Lecture IV Antennas & Propagation -6- Review (1) Current distribution I along a wire (2) Input impedance Proceedings: (Derivation on blackboard!) (1) Obtain magnetic vector potential A inside a wire due to driven voltage V. (2) Obtain magnetic vector potential A outside a wire due to current I. (3) Equate the tangential component of both at the surface of the wire. (4) Solve the equation to obtain I and Za Pattern Factor P Lecture IV Antennas & Propagation -7- Review cos 1 kL cos cos 1 kL 2 2 P sin Radiation Power Radiation Resistance Rr Directivity D Lecture IV Antennas & Propagation -8- Extensions of the finite length Dipole 1 2 Pradiated I max feeding Rr geometry 2 Lecture IV Antennas & Propagation -9- Problem with /2 Dipole For practical applications 1. Is there an antenna with similar geometric properties (size) but a higher radiation resistance? 2. Is there an antenna with similar radiation properties (pattern, etc) but smaller size? “A folded dipole has a radiation pattern the same as a dipole but with a four-fold increase in radiation resistance.” Lecture IV Antennas & Propagation -10- Folded Dipole double strength = double amplitude = four-fold power = four-fold resistance L=/2 : Rr = 4*73 = 292 “A monopole antenna is a straight conductor above a conducting plane. It behaves like a dipole twice its length but double directivity.” Lecture IV Antennas & Propagation -11- Monopole Antenna Tool of Analysis: Image Theory. half power = half radiation resistance L=/4 : Rr = 36.5 D = 3.28 Lecture IV Antennas & Propagation -12- Reciprocity Theorem “If a voltage VA is applied to the terminal of antenna A and the current IB measured at the terminal of another antenna B, then an equal current IA will be obtained at the terminal Lecture IV Antennas & Propagation -13- Reciprocity Theorem (Carson) of antenna A if the same voltage VB is applied to the terminal of antenna B.” 2 Antennas VA ( z1 0) VB ( z2 0) I B ( z2 0) I A ( z1 0) 1 Antenna VA ( z1 0) VA ( z1 z ) I A ( z1 z ) I A ( z1 0) Transmitting – Receiving Antenna All the concepts introduced for the transmitting antenna hold for the receiving and vice versa! Lecture IV Antennas & Propagation -14- Consequences impedance, effective length, effective area, directional pattern, etc Friis Transmission Formula Preceived GA GB Ptransmitted 4r 2 Lecture IV Antennas & Propagation -15- Mutual and Self Impedance Self Impedance Lecture IV Antennas & Propagation -16- Definitions V (0) Za I (0) Mutual Impedance V21 V12 Z 21 Z12 I1 I2 Both antennas are driven. I2 I1 Lecture IV Antennas & Propagation -17- 2-Pole Theory V2 V1 V1 I1 Z11 I 2 Z12 V2 I1 Z 21 I 2 Z 22 n-pole numerical calculations Z a Z11