Antennas and Wave Propagation

Transcription

1 Antennas and Wave Propagation Chapter 1: Introduction Chapter 2: Fundamental Concepts and Theorems Dr.-Ing. Thomas Bertuch Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR) Wachtberg, Germany Version: WS 2016/17, Aachen University of Applied Sciences

2 Fraunhofer Institute for High Frequency Physics and Radar Techniques Founded 1957 approx. 300 employees Budget approx. 30 Mio Since August 2009 member of Fraunhofer- Gesellschaft Preface

3 Radar Research in Wachtberg since 1957 First objective: Radar observation of space. State of TIRA in Preface

4 Fraunhofer Institute for High Frequency Physics and Radar Techniques Defense technology research in the area of high frequency physics and radar technology Installation of commercial research areas, opening of civil market Consulting during installation of defense systems, contribution to industry projects Linked with research institutes, universities, companies, and institutions Core competences: EM fields, microwave and millimeter wave technology, signal processing RF technology and signal processing education Preface

5 First demonstration of radar in Cologne (1904) by Christian Hülsmeyer Radar indicating Rhine ships Hohenzollern Bridge Preface

6 First demonstration of radar in Cologne (1904) by Christian Hülsmeyer Radar indicating Rhine ships Hohenzollern Bridge Preface

7 Course Organization Lessons Examples / exercises Practical exercise in CEM Repetition during last appointment Oral exam Preface

8 Lecture Goals Several different antenna types and configurations Principle of operation Technological aspects Advantages / disadvantages Typical antenna parameters Measurement techniques Theoretical background Preface

9 Requirements Motivation and enthusiasm Complex characterization of circuits consisting of linear, time-invariant, and passive components in case of time harmonic excitation Discrete resonators and matching of source and load Transmission line theory including hollow waveguides Fundamentals of vector calculus in different coordinate systems Preface

10 Lecture Overview 1. Introduction 3. Antenna Parameters 4. Individual Antenna Types 5. Array Antennas 6. Antenna Far-Field Measurements Preface

11 Preliminary Time Schedule Number Date Topic (preliminary) Introduction, Fundamental Concepts and Theorems Fundamentals Concepts and Theorems Fundamentals Concepts and Theorems Antenna Parameters Antenna Parameters Individual Antenna Types Individual Antenna Types Individual Antenna Types CEM Example CEM Example CEM Example Array Antennas Measurement Techniques Repetition Preface

12 Introduction Antennas are the eyes and the ears of wireless communication and electromagnetic remote sensing systems. The antenna performs a transformation between guided electromagnetic waves or alternating voltages and currents and electromagnetic waves propagating in free space (electromagnetic transducer). U oc ~ Z i I U 1. Introduction

13 Radiation Mechanism The radiation from balanced alternating currents (close by and in opposite direction) cancels out. Un-balanced alternating currents radiate. Z i I - U oc ~ + Z i I U oc ~ 1. Introduction

14 Antenna vs. Transmission Line Compared to a transmission line, for large distances, the transmitted power by an antenna system decays less rapidly with increasing distance. Line of sight! Atmospheric attenuation, multi path! Z i U oc ~ r Z l ~e 2αl Z i l U oc ~ Z l ~r 2 1. Introduction

15 Atmospheric Attenuation Additional exponential term: transmitted power Introduction

16 Some Highlights of Antenna History Date Name Achievement 1831 Michael Faraday (Englishman) 1873 James Clerk Maxwell (Scotsman) 1886 Heinrich Rodolf Hertz (German) Electromagnetic (EM) induction (two coils around iron ring: one attached to battery via switch, one attached to galvanomenter) Unification of the theories of electricity and magnetism, postulation of EM nature of light EM theory of light, demonstration of EM waves (transmitter: electric spark in gap of dipole antenna, receiver: loop antenna) 1901 Guglielmo Marconi (Italian) First transatlantic transmission (transmitter in Poldhu, Cornwall, England: several vertical wires attached to ground, receiver in St. John s, Newfoundland: 200 meter wire held up by kite), array antenna, wireless WW I 1928 Hidetsugu Yagi, Shintaro Uda (Japanese) 1931 Karl Guthe Jansky (American) Before: long wave lengths (2000 to m) with spark or arc generators; after: 200 to 600 m with continuous waves generated by vacuum tubes Yagi-Uda antenna Cosmic static coming from the center of our galaxy, father of radio astronomy 1943 Grote Reber (American) First radio map of the sky (Parabolic reflector antenna) WW II 1950s 1960s 1970s Before: single elements or array of wires, dipoles, helices, rhombuses, fans, etc.; during and after: many aperture type antennas such as open-ended waveguides, slots, horns, reflectors, lenses and others, phased array antennas (1944: Mammut) Frequency independent antennas (e.g. self-complimentary antennas), leaky and surface wave antennas Log periodic antennas, reflect arrays 1. Introduction Microstrip patch antenna, Vivaldi antenna

17 Source: Internet (e.g. Wikipedia) M. Faraday J.C. Maxwell H.R. Hertz G. Marconi H. Yagi & S. Uda K.G. Jansky G. Reber Mammut 1. Introduction

18 UWB Frequency Bands and Allocation Wavelength 10 m EU neu Communication Band HF Radar Band Frequency 20 MHz 5 m 2 m 1 m 50 cm 20 cm 10 cm 5 cm 2 cm 1 cm A B C D E F G H I J K VHF UHF SHF GSM 900 GPS L1 (1,23 GHz) GPS L2 (1,58 GHz) GSM 1800/1900, UMTS WLAN (2,4 GHz) WLAN (5,15-5,725 GHz) L 1-2 GHz S 2-4 GHz C 4-8 GHz X (8-12 GHz) Ku (12-18 GHz) K (18-27 GHz) Ka (27-40 GHz) 50 MHz 100 MHz 200 MHz 500 MHz 1 GHz 2 GHz 5 GHz 10 GHz 20 GHz 5 mm 2 mm 1 mm L M EHF sub-mm / IR V GHz W GHz KFZ-Radar (24 GHz) KFZ-Radar (77-79 GHz) 50 GHz 100 GHz 200 GHz 500 GHz 1. Introduction

19 Literature and Sources (1) C. A. Balanis, Antenna Theory: Analysis and Design. 3rd edition, Hoboken: John Wiley & Sons, (2) C. A. Balanis (ed.), Modern Antenna Handbook. John Wiley & Sons, (3) P. W. Hannan, The element-gain paradox for a phased-array antenna, IEEE Trans. Antennas Propag., vol. 12, no. 4, pp , July (4) R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, (5) J.R. James, P.S. Hall (ed.), Handbook of Microstrip Antennas. London: Peter Peregrinus, (6) Y. T. Lo, S. W. Lee (ed.), Antenna Handbook Vol. II: Antenna Theory. New York: Van Nostrand Reinhold, (7) H. Meinke, F. W. Gundlach (ed.), Taschenbuch der Hochfrequenztechnik Band 2: Komponenten. Berlin: Springer, (8) Y. Mushiake, "A report on Japanese development of antennas: from the Yagi-Uda antenna to selfcomplementary antennas," Antennas and Propagation Magazine, IEEE, vol.46, no.4, pp , Aug (9) D.M. Pozar, The Active Element Pattern, IEEE Trans. Antennas and Propagat., vol. 42, no. 8, Aug. 1994, S (10) W. L. Stutzman and G. A. Thiele, Antenna Theory and Design. New York: John Wiley & Sons, (11) H.-G. Unger, Hochfrequenztechnik in Funk und Radar. Stuttgart: Teubner, (12) J. L. Volakis (ed.), Antenna Engineering Handbook. 4th ed., New York: McGraw-Hill, (13) O. Zinke, H. Brunswig (ed.), Hochfrequenztechnik 1. Berline: Springer, Introduction

20 Notation Symbol Meaning Symbol Meaning a Scalar quantity curl a Curl (= a) Re a, Im{a} Real, imaginary part a Conjugate complex Definition, Much larger, smaller as a a a b a b (a, b) A grad a div a Vector Unit vector Scalar product Vector product Angle between vectors Matrix Nabla operator Gradient (= a) Divergence (= a) Approximately the same as ~ Proportional to a 2 a 2 a Partial derivative with respect to a Second partial derivative with respect to a Derivative with respect to time

21 Time Harmonic Quantities Relation between real time harmonic and complex quantities a: instantaneous quantity A: complex quantity (peak value!) = 2 p f : angular frequency Suppression of time factor e j t from most of the formulations! Im{A} a 0 t A t+j a Re{A}

22 Power and db Z i I I U oc ~ Z l U I sc Y i Z l U Real power dissipated by load Z l = 1/Y l Maximum available power of a source (Z l = Z i ) Ratio of physical quantities in logarithmic decibel (db) scale Power: Circuit or field quantities:

23 Coordinate Systems Coordinate Transformations Kartesian: x, y, z z r Cylindrical: r, j, z J r j y Spherical: r, J, j x

24 Coordinate Systems Unit Vectors Kartesian: x, y, z z r z r φ Cylindrical: ρ(φ), φ(φ), z x J r θ ρ y Spherical: r (θ, φ), θ(θ, φ), φ(φ) j y x

25 Field Quantities vs. Circuit Quantities Circuit Quantities: U: Voltage [V] I : Electric Current [A] Q: Electric Charge [As] : Magnetic Flux [Vs] e : Electric Flux [As] Field Quantities: E: Electric (Field) Intensity [V/m] H: Magnetic (Field) Intensity [A/m] D: Electric Flux Density [As/m²] B: Magnetic Flux Density [Vs/m²] J: Electric Current Density [A/m²] Q v : Electric Charge Density [As/m³]

26 Maxwell s Equations: Integral Representation B a c A c s, E a J, D c A c s, H a B a A A Q D Axioms!

27 Maxwell s Equations: Differential Representation Harmonic time dependence via e j t : Faraday s law: Generalized Ampere s law: Gauss law: Continuity of magn. flux: Continuity law: Differential/Nabla Operator, del: Gradient: Divergence: Curl: Laplacian:

28 Application of Differential Operator in Different Coordinate Systems Rectangular coordinates Cylindrical coordinates Source and Notation: R.F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961

29 Application of Differential Operator in Different Coordinate Systems Spherical coordinates Source and Notation: R.F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961

30 Some Useful Vector Identities Addition and Multiplication Differentiation Source and Notation: R.F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961

31 Material Equations Isotropic materials e : Permittivity [As/(Vm)] m : Permeability [Vs/(Am)] s : Electric Conductivity [A/(Vm)] Free space Nonmagnetic metals Nonmagnetic dielectrics Ferromagnetic matter Extremely lossy and nonlinear with respect to m r.

32 Boundary Conditions Region (1) Impressed sources along interface: Jump condition J s M s Region (2) S J s or M s =0: Continuity of tangential field components across the interface. Region (2) perfect electric conductor (s ) and no impressed sources on surface: J s : Electric surface current [A/m] M s : Magnetic surface current [V/m] Tangential electric field vanishes at PEC (perfect electric conducting) surface. (M s = 0)

33 Radiation from Electric Current Element Maxwell: Any divergenceless vector is the curl of some other vector. A is called a magnetic vector potential. Helmholtz equation or complex wave equation. Solutions are called wave potentials. (k: intrinsic wave constant) E and H as a function of A: Advantage: Rectangular components of A have corresponding rectangular components of J as their sources!

34 Radiation from Electric Current Element Source: z-directed current I at origin extending over incremental length dl (point source). z A z = A z (r) r q dl/2 -dl/2 x I y Intrinsic wave impedance:

35 Field Regions r λ = 1 f εμ, : wavelength Field regions Very close: Quasi-static o E: static charge dipole o H: constant current element Intermediate: Induction field Far away: Radiation field o E and H perpendicular and in phase

36 Field Magnitudes

37 Field Vectors Near field

38 Field Vectors Near Far field

39 Field Vectors Power transport: (E H) direction of propagation E, H in phase Near Far field

40 Field Vectors Electric and magnetic field lines Power transport: (E H) direction of propagation E, H in phase Near Far field

41 Radiation from Electric Current Distribution x z I dl r' y r - r' r Superposition of solutions for each element r: field coordinates r : source coordinates Direction of vector potential is that of the current element Problem Current distribution generally unknown Solution Estimation of current distribution Analytical/numerical computation of current distribution

42 Complex Poynting Vector, Radiated Power, and Radiation Resistance Complex Poynting Vector flux [W/m²]: Time average power density vector [W/m²]: Time average radiated (real) power [W]: Time average reactive power [VA]: Radiation Resistance [ ]: (with I 0 being an arbitrary reference current)

43 Radiated Power of Electric Current Element Re Im

44 Radiated Power of Electric Current Element Independent of distance! Re Im Negative: Excess of electric over magnetic energy in near field!

45 Wave Impedance Characteristic impedance [ ]: (transmission lines) Directed wave impedance [ ]: (with respect to an arbitrary direction r ) Intrinsic wave impedance [ ]: (corresponds to directed wave impedance of TEM wave with respect to direction of propagation) Free space intrinsic wave impedance [ ]: TEM: Transverse electromagnetic (plane wave in free space, homogeneously filled transmission line with two conductors) E r = k H E H E, H direction of propagation E / H = E, H in phase (lossless material)

46 Some Examples of Characteristic Impedances Source: R.F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961

47 Radiation from Infinitesimal Loop of Electric Current z Magnetic vector potential: da q r I y Electromagnetic field components: Electric current element: x

48 Duality Concept If the equations describing two different phenomena are of the same mathematical form, also solutions to them will take the same mathematical form. Dual equations (all sources of electric type / all sources of magnetic type): Dual quantities: Electric vector potential (in analogy to A, the magnetic vector potential)

49 El. Current element Magn. Current element El. Current loop Radiation from Magnetic Current Element z da q r I y x z q r dl/2 -dl/2 K y x z q r Duality dl/2 -dl/2 I y x

50 Uniqueness Theoreme Concept A solution is said to be unique when it is the only one possible among a given class of solutions. A field within a region is uniquely specified by the sources within the region plus the tangential components of either E over the boundary or H over the boundary or E over a part of the boundary and H over the rest of the boundary Example E, H Sources

51 Uniqueness Theoreme Concept A solution is said to be unique when it is the only one possible among a given class of solutions. A field within a region is uniquely specified by the sources within the region plus the tangential components of either E over the boundary or H over the boundary or E over a part of the boundary and H over the rest of the boundary Example E, H n S Sources E tan H tan

52 The Equivalence Principle Concept Many source distributions outside a given region can produce the same fields inside the region. Two sources producing the same field within a region of space are said to be equivalent within that region. Simple application The equivalent (surface) currents J s and M s produce the same field external to S as do the original sources. E, H E, H n E, H n S Sources S Zero field

53 The Equivalence Principle Concept Many source distributions outside a given region can produce the same fields inside the region. Two sources producing the same field within a region of space are said to be equivalent within that region. Simple application The equivalent (surface) currents J s and M s produce the same field external to S as do the original sources. Computation E, of H fields outside S n assuming homogeneously filled space (as outside S) everywhere: E, H E, H n S Sources S Zero field

54 The Equivalence Principle General Formulation E a, H a E a, H a S E a, H a E b, H b n n J s E b, H b S E b, H b E b, H b E a, H a n n -J s Typically, no homogenously filled space anymore! Here we use the tangential components of both E and H to set up the equivalent problem! S M s S -M s Note: In each case we must keep the original sources and media in the region for which we keep the field!

55 The Equivalence Principle General Formulation E a, H a n E b, H b E a, H a S S E a, H a n E b, H b E b, H b J s E b, H b E a, H a n n -J s Typically, no homogenously filled space anymore! Here we use the tangential components of both E and H to set up the equivalent problem! S M s S -M s Note: In each case we must keep the original sources and media in the region for which we keep the field!

56 The Equivalence Principle Uniqueness: Tangential components of only E or H should be sufficient to determine the field. E, H n n Zero E, H field E, H S Sources S Electric conductor E tan = 0 Radiation of impressed M s in presence of el. conducting body. J s E, H n E, H n Zero field Radiation of impressed J s in presence of magn. conducting body. M s S Zero field S Magnetic conductor H tan = 0

57 The Equivalence Principle Uniqueness: Tangential components of only E or H should be sufficient to determine the field. Radiation of E, H E, H n impressed M s in n Zero presence of el. E, H field conducting body. Electric J s S conductor S E tan = 0 Sources E, H n Zero field S E, H n Zero field S Magnetic conductor H tan = 0 Radiation of impressed J s in presence of magn. conducting body. M s

58 Image Theory Electric and magnetic current elements in front of an infinite perfectly conducting plane Boundary conditions at a perfect electric conductor are vanishing tangential components of E. An element of source plus an image element of source, radiating in free space, produce zero tangential components of E over the plane bisecting the line joining the two elements. Matter also can be imaged. Perfectly conducting plane Zero field Original sources and matter

59 Image Theory Electric and magnetic current elements in front of an infinite perfectly conducting plane Boundary conditions at a perfect electric conductor are vanishing tangential components of E. An element of source plus an image element of source, radiating in free space, produce zero tangential components of E over the plane bisecting the line joining the two elements. Matter also can be imaged. Solution is valid only above the image plane! Original sources and matter E tan = 0 Tangential el. and normal magn. currents very close to a metal plane do not radiate! Total radiated power varries with distance of original source from metal plane. Imaged sources and matter

60 The Induction Theorem Incident field: E i, H i produced by sources without obstacle Total field: E, H produced by sources with obstacle Scattered field: E s, H s Produced by conduction and polarization currents on obstacle Original Problem: Induction Equivalent: E = E i + E s H = H i + H s Sources S E H n E s H s S E H n

61 The Induction Theorem Incident field: E i, H i produced by sources without obstacle Total field: E, H produced by sources with obstacle Scattered field: E s, H s Produced by conduction and polarization currents on obstacle Original Problem: E = E i + E s H = H i + H s S Sources E H n perfect conductor E s H s Induction Equivalent: n perfect E conductor H S

62 Scattered Field from Metal Obstacles via Electric Surface Current Distribution Original Problem: Equivalent Problem for Scattered Field: E = E i + E s H = H i + H s Sources S n perfect conductor E s H s S -E i -H i n

63 Scattered Field from Metal Obstacles via Electric Surface Current Distribution Physical optics approximation Obstacle: Large with respect to wavelength, smooth, gently curved Total field (E and H) negligible in shadow region Approximate n H s on illuminated portion by locally applying image theory assuming infinite and flat ground plane with same n : n H s n H i E = E i + E s H = H i + H s Incident Plane Wave Original Problem: S n perfect conductor Physical optics approximation for scattered Field: E s H s S -E i -H i n

64 Scattered Field from Metal Obstacles via Electric Surface Current Distribution Radiation from metallic antenna Original Problem: Equivalent Problem for Scattered Field: Metal Antenna E = E i + E s H = H i + H s E s H s Source S

65 The Reciprocity Theorem Simple formulation The response of a system to a source is unchanged when source and measurer are interchanged. Circuit theory statement of reciprocity In a network constructed of linear isotropic matter is the voltage at port 2 due to a current source at port 1 equal to the voltage at port 1 due to the same current source at port 2. port 1 port 2 port 1 port 2 I U U I Impedance matrix representation: Reciprocity:

66 The Reciprocity Theorem Antennas a and b The receiving pattern of any antenna constructed of linear isotropic matter is identical to its transmitting pattern. o If the b antenna is infinitely remote from the a antenna, its field will be a plane wave in the vicinity of a, and vice versa. o The receiving pattern of an antenna is defined as the voltage at the antenna terminals due to a plane wave incident upon the antenna. Antenna a Antenna b I U

67 Waves in Lossy Matter Wave number k = ω εμ and intrinsic impedance η = μ ε are complex numbers Wave is attenuated in direction of propagation Magnetic field is no longer in phase with electric field. Source: R.F. Harrington, Time- Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961

68 Waves in Lossy Matter Good dielectrics (ε ε ) Good conductors (σ ωε) Skin depth or depth of penetration Surface Copper (σ = m/ω) at 10 MHz: δ = 21 μm

69 Reflection/Transmission of Plane Wave at Planar Interface (m 1 = m 2 ) e 1, m 1 e 2, m 2 Brewster angle (63,4 ) J i J r J t

70 Reflection/Transmission of Plane Wave at Planar Interface (m 1 = m 2 ) e 1, m 1 e 2, m 2 Brewster angle (26,6 ) J i J r J t Critical angle (30 )