Antennas 1. Antennas

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1 Antennas Antennas 1! Grading policy. " Weekly Homework 40%. " Midterm Exam 30%. " Project 30%.! Office hour: 3:10 ~ 4:00 pm, Monday.! Textbook: Warren L. Stutzman and Gary A. Thiele, Antenna Theory and Design, 2 nd Ed.! Matlab programming may be needed.! Contents " Electromagnetics and Antenna Fundamentals " Simple Antennas " Arrays " Resonant Antennas " Broadband Antennas " Aperture Antennas " Antenna Synthesis " Numerical Techniques

2 Antennas 2

3 Overview of Antennas Antennas 3! Antenna performance parameters " Radiation pattern: Angular variation of radiation power or field strength around the antenna, including: directive, single or multiple narrow beams, omnidirectional, shaped main beam. " Directivity : ratio of power density in the direction of the pattern maximum to the average power density at the same distance from the antenna. " Gain : Directivity reduced by the losses on the antenna. " Polarization: The direction of electric fields. - Linear - Circular - Elliptical " Impedance

4 " Bandwidth Antennas 4

5 Antennas 5! Antenna types " Electrically small antennas: The extent of the antenna structure is much less than a wavelength. - Properties # very low directivity # Low input resistance # High input reactance # Low radiation efficiency - Examples # Short dipole # Small loop

6 Antennas 6 " Resonant antennas: The antenna operates well as a single of selected narrow frequency bands. - Properties # Low to moderate gain # Real input impedance # Narrow bandwidth - Examples # Half wave dipole # Microstrip patch # Yagi

7 Antennas 7 " Broadband antennas: - Properties # Low to moderate gain # Constant gain # Real input impedance # Wide bandwidth - Examples # Spiral # Log periodic dipole array

8 " Aperture antennas: has a physical aperture (opening) through which waves flow. - Properties # High gain # Gain increases with frequency # Moderate bandwidth - Examples # Horn # Reflector Antennas 8

9 Maxwell Equations Antennas 9! Important Laws in Electromagnetics " Coulomb s Law " Gauss s Law " Ampere s Law " Ohm s Law " Kirchhoff s Law " Biot-Savart Law " Faradays Law James Clerk Maxwell ! Maxwell Equations (1873) : electric field intensity. : electric flux density : magnetic field intensity

10 Antennas 10 : magnetic flux density : electric current density : magnetic current density : electric charge density : magnetic charge density : permittivity : permeability! Constituent Relationship! Continuity Equations! Boundary Conditions

11 Antennas 11! Time-Harmonic Fields Time-harmonic: : a real function in both space and time. : a real function in space. : a complex function in space. A phaser. Thus, all derivative of time becomes. For a partial deferential equation, all derivative of time can be replace with, and all time dependence of can be removed and becomes a partial deferential equation of space only. Representing all field quantities as, then the original Maxwell s equation becomes

12 Antennas 12! Power Relationship! Poynting vector:! Solution of Maxwell s Equations Note all the field and source quantities are functions of space only. The wave equations of potentials becomes, where is called the wave number. The above equations are called nonhomogeneous Helmholtz s equations. The Lorentz condition becomes Also

13 Antennas 13 The wave functions for electric and magnetic fields in source free region becomes

14 The Ideal Dipole Antennas 14 Purpose: Investigate the fundamental properties of an antenna. Short Dipole: Therefore Since

15 Antennas 15 We have. And As or, then

16 Antennas 16 E-plane pattern: plane containing E-fields. H-plane pattern: plane containing H-fields. Radiated power, To sum up, at far field 1. Spherical TEM waves. 2. Wave impedance equal the intrinsic impedance. 3. Real power flow. Radiation from Line Currents For a general straight line source located at origin, At far field, and, thus.

17 Antennas 17. Since, At neglecting high order terms of, Similarly, and. Far Field Conditions To sum up:

18 Antennas At fixed frequency,. 2. At fixed antenna size, 3. At various frequency and antenna size scaled, Example 1-1 Radiation Pattern Definitions Normalized field pattern: Power pattern:

19 Antennas 19 In db scale Examples Ideal dipole: Line current: Main lobe (major lobe, main beam) Side lobe (minor lobe) Maximum side lobe level: Half-power beamwidth: Pattern types: Broadside, Intermediate, Endfire.

20 Antennas 20 Directivity Solid angle: Radiation intensity: where Directivity: Beam solid angle: Example 1-2 Directivity of an Ideal Dipole

21 Antennas 21 or Example 1-3 Directivity of a Sector Omnidirectional Pattern Power Gain (Gain) or Radiation efficiency:

22 Antennas 22 Referenced Gain: dbi: referenced to isotropic antenna. dbd: referenced to dipole antenna. Antenna Impedance Ideal dipole: When the conductor is thicker than skin depth where Considering the effect of continuity at the end of the dipole, use triangular current distribution

23 Antennas 23 Example 1-4: Radiation Efficiency of an AM Car Radio Antenna. Radius Dipole Length Frequency 1 MHz. For short dipole, Example 1-5: Input Reactance of an AM Car Radio Antenna of Example 1-4.

24 Antennas 24 Polarization Cases 1. Linear polarization: 2. Circular polarization: 3. Others: Ellipse.

25 Antennas 25

26 Half-wave Dipole Antennas 26 Image Theory

27 Antennas 27 Monopole Small Loop Antenna

28 Antennas 28 Duality: due to symmetry of Maxwell s Eqs. For a magnetic dipole Ferrite rod antenna: Inductance: Small circular loop of radius b for :

29 Small rectangular loop of : Antennas 29 Example 2-1: A Small Circular Loop Antenna Loop circumference Wire radius Frequency

30 Antenna in Communication Systems Antennas 30 Open circuit voltage: for ideal dipole receiving antenna and polarization match. When Maximum power transfer: Power density: Maximum effective aperture For an ideal dipole In general, or Effective aperture: Available power: In general, Aperture efficiency:, where is the physical

31 aperture size. Antennas 31 Communication Links Power delivered to the load : polarization mismatch factor, : impedance mismatch factor, In db form or where dbm is power in decibels above a milliwatt. EIRP: effective (equivalent) isotropically radiated power ERP: effective radiated power by a half-dipole Example 2-3: Direct Broadcast Satellite Reception Receiving disk antenna: size 0.46 m in diameter,

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33 Antennas 33 Arrays Phased array: electronic scan. Radars, smart antennas. Active array: each antenna element is powered individually. Passive array: all antenna elements are powered by one source. Array type by positioning: 1. Linear arrays, 2. Planar arrays, 3. Conformal arrays. Examples

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36 Array Factor Antennas 36 In general the radiation pattern is where is the excitation current of n-th antenna, the location vector, and the field pattern. If all antenna elements are the same AF is called array factor. It is determine only by two parameters: the excitations and the locations of the antennas. Equal Space Linear Array

37 Antennas 37 If the excitation has a linear phase progression, i.e. Then where. If the amplitude of the excitation is the same, that is, then Neglecting the phase factor,

38 Antennas 38 Normalized AF:. Maximum at Main beam at. This is the scanning effect. Broadside: Endfire: Summary: N increases as the main lobe beamwidth decreases. Number of side lobes: N-2. Number of nulls: N-1. Side lobe width:. Main lobe width:. Side lobe peaks decrease with increasing N. is symmetric about.

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40 Antennas 40 BWFN of Broadside Array ( ) First null occurs when, or Then, for long array Similarly, half power beamwidth near broadside. BWFN of Endfire Array First null occurs when, or Similarly, half power beamwidth

41 Antennas 41 Example 3-5 Four-Element Linear Array Parameters:,, Main beam

42 Single Mainbeam Oridinary Endfire Array Oridinary Endfire: main beam at exactly or. Range of : Half-width of a grating lobe: Antennas 42 Choose to eliminate most of the grating lobe, or Example 3-6 Five-Element Ordinary Endfire Linear Array Parameters:

43 Antennas 43 Hansen-Woodyard Endfire Array Purpose: increase directivity by increasing to reduce the visible region of the main beam. Choose to reduce main beam width. Choose to prevent back lobe to become larger than main lobe. Maximum directivity for large array:. Simpler Formula for : Example 3-7 Five-Element Hansen-Woodyard Endfire Linear Array Parameters:,

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45 Antennas 45 Pattern Multiplication Example 3-8 Two-Collinear, Half-Wavelength Spaced Short Dipoles Parameters:

46 Example 3-9 Two Parallel, Half-Wavelength Spaced Short Dipoles Antennas 46 Since

47 Directivity of Uniformly Excited, Equal Spaced Linear Arrays Antennas 47 For and, For broadside, isotropic array, for. For ordinary endfire, isotropic array, for. For Hansen-Woodyard endfire, isotropic array

48 Directivity as a function of scan angles Combining element pattern: Antennas 48

49 Nonuniformly Excited, Equally Spaced Linear Arrays Antennas 49 Let, then the array factor is a polynomial of 1. Binomial distribution: Properties: no sidelobe, broader beam width, lower directivity. 2. Dolph-Chebyshev distribution: Properties: equal sidelobe levels, narrower beam width, higher directivity. Sidelobe level can be specified.

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51 Antennas 51 General expression of directivity of non-equal spaced and non-uniform excitation: where is the current amplitude of k-th element, the position, and. For equal space, broadside array,,, we have Furthermore, if, we have

52 Antennas 52 Issue of Array 1. Mutual Coupling a. Effect impedances b. Effect radiation patterns c. Scan Blindness 2. Feed network a. Increase loss b. Effect bandwidth c. Increase space Feed Network

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54 2-Dimensional Equal Space Progressive Phase Arrays Antennas 54 From the general equation, where Thus, where

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Antenna Theory and Design

Antenna Theory and Design SECOND EDITION Warren L. Stutzman Gary A. Thiele WILEY Contents Chapter 1 Antenna Fundamentals and Definitions 1 1.1 Introduction 1 1.2 How Antennas Radiate 4 1.3 Overview of