1. Hanyang University 1/22 Antennas & RF Devices Lab. MODERN ANTENNA HANDBOOK by CONSTANTINE A.BALANIS chap 1.6 – 1.11 Jeong Gu Ho

2. Hanyang University 2/23 Contents 1.6 DIRECTIVITY - 1.6.1 Directional Patterns - 1.6.2 Omnidirectional Patterns 1.7 NUMERICAL TECHNIQUES 1.8 ANTENNA EFFICIENCY 1.9 GAIN 1.10 BEAM EFFICIENCY 1.11 BANDWIDTH

3. Hanyang University 3/23 1.6 DIRECTIVITY –The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions –If the direction is not specified, it implies the direction of maximum radiation intensity(maximum directivity) express as

4. Hanyang University 4/23 –For antennas with orthogonal polarization components, the partial directivity of an antenna for a given polarization in a given direction is defined as “that part of the radiation intensity corresponding to a given polarization divided by the total radiation intensity averaged over all directions” –Then in a given direction “the total directivity is the sum of the partial directivities for any two orthogonal polarizations.”

5. Hanyang University 5/23 –A more general expression for the directivity can be developed to include sources with radiation patterns that may be functions of both spherical coordinate angles Ɵ and ϕ.

6. Hanyang University 6/23 –The maximum value expressed as, –The maximum directivity can be written,

7. Hanyang University 7/23 1.6.1 Directional patterns –For antennas with one narrow major lobe and very negligible minor lobes Half-power beamwidths of the E and H-planes Kraus equation

8. Hanyang University 8/23 –For narrow beam patterns, the directivity is expressed in terms of the half-power beam width of the E and H-plane patterns. The better approximation of the formula is the geometrical mean formula. [10] C.-T. Tai and C. S. Pereira, An approximate formula for calculating the directivity of an antenna, IEEE Trans. Antennas Propag., Vol. 24, No. 2, pp. 235–236, March 1976. Arithmetic-mean formula Half-power beamwidths of the E and H-planes Tai-Pereira equation

9. Hanyang University 9/23 Tai-Pereira equationKraus equation Exact equation

10. Hanyang University 10/23 1.6.2 Omnidirectional Patterns –Some antennas (such as dipoles, loops, and broadside arrays) exhibit omnidirectional patterns, as illustrated by the three- dimensional patterns –Approximate directivity formulas have been derived [11, 12].

11. Hanyang University 11/23 1.6.2 Omnidirectional Patterns using half-wave dipole [11]. N. A. McDonald, Approximate relationship between directivity and beamwidth for broadsidecollinear arrays, IEEE Trans. Antennas Propag., Vol. 26, No. 2, pp. 340–341, March 1978. More accurate for omnidirectional patterns with minor lobes McDonald’s approximation In our book ; 101 for isotropic

12. Hanyang University 12/23 1.6.2 Omnidirectional Patterns [12] D. M. Pozar, Directivity of omnidirectional antennas, IEEE Antennas Propag. Mag., Vol. 35, No. 5, pp. 50–51, October 1993. Curve-fit equation Pozar’s approximation More accurate for omnidirectional patterns with minor lobes of very low intensity (ideally no minor lobes)

13. Hanyang University 13/23 1.6.2 Omnidirectional Patterns Specify the desired directivity and determine the value of n and half- power beamwidth of the omnidirectional antenna pattern Comparison of expression

14. Hanyang University 14/23 1.7 numerical techniques A MATLAB and FORTRAN computer program called Directivity has been developed to compute the maximum directivity

15. Hanyang University 15/23 1.8 Antenna Efficiency –The total antenna efficiency is used to take into account losses at the input terminals and within the structure of the antenna. –Reflections because of the mismatch between the transmission line and the antenna –Conduction and dielectric losses

16. Hanyang University 16/23 –In general, the overall efficiency can be written

17. Hanyang University 17/23 1.9 Gain –A measure that takes into account the efficiency of the antenna as well as its directional capabilities. –Relative gain : the ratio of the power gain in a given direction to the power of a reference antenna in its referenced direction. In most cases, the reference antenna is a lossless isotropic source. When the direction is not stated, the power gain is usually taken in the direction of maximum radiation.

18. Hanyang University 18/23 –The total radiated power is related to the total input power by –The maximum gain is related to the maximum directivity P rad = e cd P in

19. Hanyang University 19/23 1.9 Gain –It does not take into account the losses when the antenna element is connected to a transmission line (referred to as reflections (mismatch) losses) –Absolute gain(G abs ) : takes into account the reflection/mismatch losses (due to the connection of the antenna element to the transmission line)

20. Hanyang University 20/23 –Similarly, the maximum absolute gain G 0abs is related to the maximum directivity D 0 by –In practice, whenever the term “gain” is used, it usually refers to the maximum gain G 0abs = G abs (θ, ϕ )| max = e r G(θ, ϕ )| max = (1 − |Γ| 2 )G(θ, ϕ )| max = e r e cd D(θ, ϕ )| max = e o D(θ, ϕ )| max = e o D 0 G 0 (dB) = 10 log 10 [e cd D 0 (dimensionless)]

21. Hanyang University 21/23 1.10 Beam efficiency –Another parameter that is frequently used to judge the quality of transmitting and receiving antennas. –Radiometry, astronomy, radar High beam efficiency is necessary Minor lobes must be minimized

22. Hanyang University 22/23 1.11 Bandwidth –The range of frequencies within which the performance of the antenna, with respect to some characteristic, conforms to a specified standard. –For broadband antennas, the bandwidth is usually expressed as the ratio of the upper-to-lower frequencies of acceptable operation Ex) 10:1 –For narrowband antennas, the bandwidth is expressed as a percentage of the frequency difference (upper minus lower) over the center frequency of the bandwidth. Ex) 5% Pattern bandwidth Directivity/Gain Side lobe level Beamwidth Polarization Beam direction Impedance bandwidth Input impedance Radiation efficiency

23. Hanyang University 23/22 Antennas & RF Devices Lab. Thank you for your attention Antennas & RF Devices Lab.