Hanyang University ANTENNA THEORY by Constantine A Balanis

Hanyang University ANTENNA THEORY by Constantine A. Balanis Chapter 2. 13 – 2. 15. 2 Yun-tae Park 2018. 01. 17 1/23 Antennas & RF Devices Lab.

Hanyang University Contents 2. Fundamental Parameters of Antennas 2. 5 Beamwidth 2. 13 Input Impedance 2. 14 Antenna Radiation Efficiency 2. 15 Antenna Vector Effetive Length and Equivalent Areas 2. 15. 1 Vetor Effective Length 2. 15. 2 Antenna Equivalent Areas 2/23 Antennas & RF Devices Lab.

Hanyang University 2. 5 Beamwidth - The angular separation between two identical points on opposite side of the pattern maximum. Half-Power Beamwidth (HPBW) - In a plane containing the direction of the maximum of a beam, the angle between the two directions in which the radiation intensity is one-half value of the beam. First-Null Beamwidth (FNBW) - The angular separation between the first nulls of the pattern. 3/23 Antennas & RF Devices Lab.

Hanyang University 2. 5 Beamwidth of the antenna is used to describe the resolution capabilities of the antenna to distinguish between two adjacent radiating sources or radar targets. - distinguish - difficult to distinguish 4/23 Antennas & RF Devices Lab.

Hanyang University 2. 13 Input Impedance Input impedance - The impedance presented by an antenna at its terminals. - The ratio of the voltage to current at a pair of terminals. - The ratio of the appropriate components of the electric to magnetic fields at a point. (272) (273) Figure 2. 27 Transmitting antenna and its equivalent circuits. 5/23 Antennas & RF Devices Lab.

Hanyang University 2. 13 Input Impedance (274) (Transmitting mode) Figure 2. 27 Transmitting antenna and its equivalent circuits. (275) (2 -75 a) 6/23 Antennas & RF Devices Lab.

Hanyang University 2. 13 Input Impedance the power delivered to the antenna for radiation (276) dissipated as heat (277) (278) Figure 2. 27 Transmitting antenna and its equivalent circuits. Maximum power delivered to the antenna when conjugate matching. 7/23 Antennas & RF Devices Lab. (279) (280)

Hanyang University 2. 13 Input Impedance (when conjugate matching, ( )) (281) (282) (283) Figure 2. 27 Transmitting antenna and its equivalent circuits. (285) (284) 8/23 Antennas & RF Devices Lab.

Hanyang University 2. 13 Input Impedance (receiving mode paralles that for the transmitting mode under conjugate matching( )) (286) (287) (288) (289) Figure 2. 28 Antenna and its equivalent circuits in the receiving mode. 9/23 Antennas & RF Devices Lab.

Hanyang University 2. 13 Input Impedance (under conjugate matching, ( )) (289) 50% (287) (286) 50% (288) The most that can be delivered to the load is only half of that captured and that is only under conjugate matching and lossless transmission line. 10/23 Antennas & RF Devices Lab.

Hanyang University 2. 14 Antenna Radiation Efficiency The conduction and dielectric losses of an antenna are very difficult to compute. (276) (290) (277) 11/23 Antennas & RF Devices Lab.

Hanyang University 2. 14 Antenna Radiation Efficiency (290 a) (290 b) 12/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas An antenna in the receiving mode is used to capture(collect) electromagnetic waves and to extract power from them. For each antenna, an equivalent length and a number of equivalent areas can be defined. Equivalent quantities are used to describe the receiving characteristics of an antenna when a wave is incident upon the antenna. Figure 2. 29 Uniform plane wave incident upon dipole and aperture antennas. 13/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 1 Vector Effective Length The effective length of an antenna is a quantity that is used to determine the voltage induced on the open-circuit terminals of the antenna when a wave impinges upon it. (291) (292) 14/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 1 Vector Effective Length the effective length is a vector (293) For linear antennas 15/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 1 Vector Effective Length Effective length of a linearly polarized antenna receiving a plane wave in a given direction - The ratio of the magnitude of the open-circuit voltage developed at the terminals of the antenna to the magnitude of the electric-field strength in the direction of the antenna polarization. - It is used to determine the polarization efficiency of the antenna. Ex) a small dipole of length and with a triangular current distribution (436 a) (292) Figure 4. 4 Geometrical arrangement of dipole and current distribution. 16/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 2 Antenna Equivalent Areas Equivalent area - the power capturing characteristics of the antenna when a wave impinges on it Effective area (aperture) - the ratio of the available power at the terminals of a receiving antenna to the power flux density of a plane wave incident on the antenna from that direction, the wave being polarization-matched to the antenna (294) Effective aperture - the area which when multiplied by the incident power density gives the power delivered to the load. (295) Figure 2. 28 Equivalent circuits in the receiving mode. 17/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 2 Antenna Equivalent Areas (295) (when conjugate matching, ( )) (296) Scattering area - the equivalent area when multiplied by the incident power density is equal to the scattered or reradiated power (297) (298) 18/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 2 Antenna Equivalent Areas Capture area - the equivalent area which when multiplied by the incident power density leads to the total power captured, collected, or intercepted by the antenna (299) Capture area = Effective area + Scattering area + Loss area (2100) 19/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 2 Antenna Equivalent Areas Partial effective area of an antenna for a given polarization in a given direction - the ratio of the available power at the terminals of a receiving antenna to the power flux density of a plane wave incident on the antenna from that direction and with a specified polarization differing from the receiving polarization of the antenna The effective area of an antenna is not necessarily the same as the physical aperture. uniform amplitude and phase field distributions nonuniform field distributions The maximum effective area of wire antennas is greater than the physical area. (if taken as the area of a cross section of the wire when split lengthwise along its diameter) the wire antenna can capture much more power than is intercepted by its physical size 20/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 2 Antenna Equivalent Areas Figure 2. 29 Uniform plane wave incident upon dipole antennas. If , the effective area is only one-half of the maximum effective area given above. 21/23 Antennas & RF Devices Lab.

Hanyang University 2. 15 Antenna Vector Effective Length and Equivalent Areas 2. 15. 2 Antenna Equivalent Areas Figure 1. 16 Current distribution on linear dipoles. Typical physical diameters (widths) of wires used for dipoles the wire antenna can capture much more power than is intercepted by its physical size 22/23 Antennas & RF Devices Lab.

Hanyang University Thank you for your attention 23/23 Antennas & RF Devices Lab.