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

Lecture IV Antennas & Propagation -4- Review The following definitions are applicable to all antennas: 1. Power Density w = Re{S} 2.Total Radiated Power P 3. Radiation Resistance R r 4. Antenna Impedance Z A 5. Equivalent Circuit 6. Load matching 7. Effective Length l e 8. Effective Area A e 9. Radiation Intensity U 10. HPBW / Bandwidth B 11. Directive Gain g 12. Directivity D 13. Radiation Efficiency e 14. (Power) Gain G

Lecture IV Antennas & Propagation -5- Review Dipole of finite length L/a > 60 : Hallén's Integral  Transmission Line

Lecture IV Antennas & Propagation -6- Review Hallén's Integral Equation Objective: (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 Z a

Lecture IV Antennas & Propagation -7- Review Pattern Factor P Radiation Power Radiation Resistance R r Directivity D

Lecture IV Antennas & Propagation -8- Extensions of the finite length Dipole

Lecture IV Antennas & Propagation -9- Problem with /2 Dipole For practical applications 2. Is there an antenna with similar radiation properties (pattern, etc) but smaller size? 1. Is there an antenna with similar geometric properties (size) but a higher radiation resistance?

Lecture IV Antennas & Propagation -10- Folded Dipole “A folded dipole has a radiation pattern the same as a dipole but with a four-fold increase in radiation resistance.” L= /2 : R r = 4*73  = 292  double strength = double amplitude = four-fold power = four-fold resistance

Lecture IV Antennas & Propagation -11- Monopole Antenna “A monopole antenna is a straight conductor above a conducting plane. It behaves like a dipole twice its length but double directivity.” L= /4 : R r = 36.5  D = 3.28 half power = half radiation resistance Tool of Analysis: Image Theory.

Lecture IV Antennas & Propagation -12- Reciprocity Theorem

Lecture IV Antennas & Propagation -13- Reciprocity Theorem (Carson) “If a voltage V A is applied to the terminal of antenna A and the current I B measured at the terminal of another antenna B, then an equal current I A will be obtained at the terminal of antenna A if the same voltage V B is applied to the terminal of antenna B.” 2 Antennas1 Antenna

Lecture IV Antennas & Propagation -14- Consequences Transmitting – Receiving Antenna All the concepts introduced for the transmitting antenna hold for the receiving and vice versa! impedance, effective length, effective area, directional pattern, etc Friis Transmission Formula

Lecture IV Antennas & Propagation -15- Mutual and Self Impedance

Lecture IV Antennas & Propagation -16- Definitions Self Impedance Mutual Impedance

Lecture IV Antennas & Propagation Pole Theory Both antennas are driven. V1V1 I1I1 I2I2 V2V2 n-pole  numerical calculations