Grundlagen der Elektrotechnik IIVorlesung an der Dualen Hochschule Baden-WĆ¼rttemberg, Karlsruhe
Kapitel Wellen und Antennen
Kurs: TSHE15B
16. Mai 2016
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Inhaltsverzeichnis
1 RF Basics 3
2 Antennas 82.1 Maxwellās Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Antenna Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Linear Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 Yagi Uda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6 Small Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.7 Mobile Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.8 Examples in Mobile Phones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.9 Reflector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
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1 RF Basics
What to Expect
ā¢ Gives you an overview, why RF is a little bit different than āclassicalā electronics and what thespecifics are.
ā¢ Prepares a common ground for RF engineering
ā¢ Explains important concepts in RF
ā¢ You will learn some aspects of the common language and basic concepts RF-engineers use to maketheir life easier
ā¢ Introduces dBm
ā¢ Introduces frequency usage
ā¢ Fundamentals on RF-measurements
The Spectrum
Frequency Useage IFrequency and band on a coarse scale
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Frequency Designation Example Use3-30kHz Very Low F. (VLF) Navigation, Sonar
30-300kHz Low F. (LF) Radio, Navigation Aids
300-3000kHz Medium F. (MF) AM broadcasting, āGrenzwelleā, Maritime communication
3-30MHz High F. Amateur radio, short wave, citizens Band, RFID
30-300MHz Very High F. (VHF) FM broadcasting, Television, Air traffic
300-3000MHz Ultrahigh F. (UHF) Television, satellite comm., surveillance radar, ISM-
Applications, Microwave ovens, cellular
3-30GHz Superhigh F. (SHF) Airbore Radar, Microwave links, automotive radar, satellite
TV
30-300GHz Extreme High F. (EHF) Wheather radar, automotive radar, microwave links, expe-
rimental, short range communication
Frequency Useage IITypical Communication Bands (in Europe)
Application Frequency/MHz Bandw. ModulationCar-Key (ISM) 433.05-434.79 narrow ASK/ FSKGSM (D) 880-935 200 kHz GMSKGSM (E) 1710-1880 200 kHz GMSKWLAN (802.11b,g) 2400-2483.5 to 40 MHz g:OFDM/QAMWLAN (802.11a) 5150-5725 to 40 MHz OFDM/QAMUMTS/ W-CDMA 1920-2170 5 MHz CDMA/QAMLTE 2500-2690 to 20 MHz OFDMA, SC-FDMABluetooth 2400-2483.5 ca. 1MHz FHSS/GFSK
Governed by Maxwellās EquationsAnd God said
Differential Form Integral FormAmpereās circuit law ā Ć ļæ½ļæ½ = š½ + uļæ½uļæ½
uļæ½uļæ½ ā®uļæ½uļæ½
ļæ½ļ潚š = š¼uļæ½,uļæ½ + uļæ½Ī¦uļæ½,uļæ½uļæ½uļæ½
Faradayās law ā Ć šø = āuļæ½uļæ½uļæ½uļæ½ ā®
uļæ½uļæ½
šøšš = āuļæ½Ī¦uļæ½,uļæ½uļæ½uļæ½
Gaussā law (el.) ā ā ļæ½ļæ½ = š āÆuļæ½
ļæ½ļ潚š“ = š
Gaussā law (mag.) ā ā ļæ½ļæ½ = 0 āÆuļæ½
ļæ½ļ潚š“ = 0
And there was light.
Consider High-Frequency-Effects
ā¢ Elements are not ālumpedā anymore:physical dimensions of elements (e.g. resistors, caps, sometimes transistors, most importantly cablesand interconnects) must be considered
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ā¢ Parasitics of elements must be considered
ā¢ Power is dominant measurement quantity
ā¢ Measurement equipment has effect on the device under test (DUT) (high-ohmic vs. 50 Ī©)
ā¢ Field extension and (ir)radiation must be considered (coupling and antennas)
Think like an RF-Engineer!Think in
ā¢ Waves and wavelength š (or frequency š) š = uļæ½0āuļæ½uļæ½uļæ½uļæ½
1uļæ½
š0 Free space speed of light ā 300, 000km/sšuļæ½uļæ½uļæ½ Effective dielectric coefficient (tbd later)Remember: electromagnetic wave at 10 GHz has a free space wavelength of about 30 mm, 1 GHz of30 cm...
ā¢ Wavelength in Material (e.g. ceramics with permittivity šuļæ½ > 10) much shorter
ā¢ Itās all about matching, itās all about resonance
ā¢ Power and the unit dBm (at least mostly)
ā¢ Power-Reflection and transmission versus voltage and current
Skin-Effect
ā¢ Because of induction, magnetic field pushes current to the edges of material
ā¢ With higher frequency, current is only supported at the boundaries of conductors
ā¢ Skin-depth šæ = ā 2uļæ½uļæ½0uļæ½uļæ½uļæ½ with š permeability, š conductivity of the material.
ā¢ Skin-depth defines point, where current density is decreased by 1/š
ā¢ This is why conductivity (especially at surfaces) is important
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Material Parameters, Skin-DepthSkin-depth šæ = 1/āššš0šuļ潚
Material š Ī© cm šuļæ½ šæā
š/(šmā
GHz)Aluminum 2.65 1 2.59Copper 1.7 1 2.1Iron 9.66 5000 0.07Silver 1.59 1 2Gold 2.44 1 2.5š-Metal 55 50000 0.05
Note that relative permeability for iron and uļæ½āmetal cannot be maintained at high frequencies (thatās why they are not used in RF-shielding)!
Skin-Depth
1Eā1
1E+0
1E+1
1E+2
1E+00 1E+02 1E+04 1E+06 1E+08 1E+10
Sk
inād
ep
th/
mm
Frequency/ Hz
Aluminum Copper
Iron Silver
Gold muāMetal
1Eā4
1Eā3
1Eā2
1Eā1
1E+0
1E+1
1E+2
1E+00 1E+02 1E+04 1E+06 1E+08 1E+10
Sk
inād
ep
th/
mm
Frequency/ Hz
Aluminum Copper
Iron Silver
Gold muāMetal
Skin-depth vs. frequency (logarithmic!) for various materials
THE Unit: dB (dezi-Bel)Measure of relative quantities
ā¢ Power-relation: šuļæ½ = 10 log uļæ½1uļæ½2
ā¢ Voltage-relation: šuļæ½ = 20 log uļæ½1uļæ½2
(equal impedance levels on Port 1 and 2)
For absolute quantities a reference level must be introduced:
ā¢ Power (relative to 1mW): š [dBm] = 10 log uļæ½1mW
ā¢ Voltage (relative to 1šV): š[dBš] = 20 log uļæ½1uļæ½V
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dB: Whatās the Ratio?dB Power Scale Amplitude Scale100 10000000000.0 100000.090 1000000000.0 31620.080 100000000.0 10000.070 10000000.0 3162.060 1000000.0 1000.050 100000.0 316.240 10000.0 100.030 1000.0 31.6220 100.0 10.10 10.0 3.1620 1 1
dB: Whatās the Ratio?dB Power Scale Amplitude Scale0 1 1
-10 0.1 0.3162-20 0.01 0.1-30 0.001 0.03162-40 0.0001 0.01-50 0.00001 0.003162-60 0.000001 0.001-70 0.0000001 0.0003162-80 0.00000001 0.0001-90 0.000000001 0.00003162-100 0.0000000001 0.00001
Calculate dB in your HeaddB Sum/Difference of 10,5,3 Mult., Div. Linear0 Memorize 11 10 ā 3 ā 3 ā 3 10/2/2/2 1.252 5 ā 3 3/2 1.53 Memorize 24 10 ā 3 ā 3 10/2/2 2.55 Memorize 36 3 + 3 2 ā 2 47 10 ā 3 10/2 58 5 + 3 3 ā 2 69 3 + 3 + 3 2 ā 2 ā 2 810 Memorize 10
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2 Antennas
Antennas
How to Send and Receive: Antennas and ElectromagneticWaves in Free Space
Antennas
Different antennae pictures GPL, http://de.wikipedia.org
Antennas at DHBW in Karlsruhe
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What you Learn
ā¢ Understand the basic concepts of antennas
ā¢ Have terminology and characteristics of antennas at hand
ā¢ Understand the mechanism of irradiation
ā¢ Know different types (families) of antennas
ā¢ Know basic electromagnetism
ā¢ Be able to understand and judge different antenna (full wave) simulation schemes and know how touse them
2.1 Maxwellās Equations
Governed by Maxwellās EquationsAnd God said
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Differential Form Integral FormAmpereās circuit law ā Ć ļæ½ļæ½ = š½ + uļæ½uļæ½
uļæ½uļæ½ ā®uļæ½uļæ½
ļæ½ļ潚š = š¼uļæ½,uļæ½ + uļæ½Ī¦uļæ½,uļæ½uļæ½uļæ½
Faradayās law ā Ć šø = āuļæ½uļæ½uļæ½uļæ½ ā®
uļæ½uļæ½
šøšš = āuļæ½Ī¦uļæ½,uļæ½uļæ½uļæ½
Gaussā law (el.) ā ā ļæ½ļæ½ = š ā®uļæ½uļæ½
ļæ½ļ潚š“ = š
Gaussā law (mag.) ā ā ļæ½ļæ½ = 0 ā®uļæ½uļæ½
ļæ½ļ潚š“ = 0
And there was light.
Maxwellās EquationsMaxwellā equations [14, 4, 10] for time-harmonic fields (i.e. š(š”) ā šāuļæ½uļæ½uļæ½, š circular frequency 2šš
Three dimensions One dimension (z)ā Ć ļæ½ļæ½ = jšļæ½ļæ½ + š½ āuļæ½uļæ½uļæ½
uļæ½uļæ½ = jšš·uļæ½ + š½uļæ½uļæ½uļæ½uļæ½uļæ½uļæ½ = jšš·uļæ½ + š½uļæ½
ā Ć šø = ājšļæ½ļæ½ ā ļæ½ļæ½ āuļæ½uļæ½uļæ½uļæ½uļæ½ = ājššµuļæ½ ā šuļæ½
uļæ½uļæ½uļæ½uļæ½uļæ½ = ājššµuļæ½ ā šuļæ½
ā ā ļæ½ļæ½ = š uļæ½uļæ½uļæ½uļæ½uļæ½ = š
ā ā ļæ½ļæ½ = 0 uļæ½uļæ½uļæ½uļæ½uļæ½ = 0
ā ( uļæ½uļæ½uļæ½ , uļæ½
uļæ½uļæ½ , uļæ½uļæ½uļæ½)
uļæ½ šø electric fieldļæ½ļæ½ electric flux density ļæ½ļæ½ magnetic fieldļæ½ļæ½ magnetic flux density š½ electric current densityļæ½ļæ½ magnetic current density š electric charge density
Material EquationsConstants from mother nature
š0 8.85418 10ā12 As/(Vm) Permittivityā 10ā9/(36š) As/(Vm)
šuļæ½ 2 ā¦ 12 PCB, Semiconductorā¦ 80 (usual) Ceramicsā¦ 1000š (high Diel.Const.) Ceramicsā 80 Water (in GHz range)ā 1000š Metal
š0 4š 10ā7 Vs/(Am) Permeability1.25664 10ā6 Vs/(Am)
šuļæ½ 1 Mostly for us700 Steel20, 000 šāmetal
ļæ½ļæ½ = š0šuļæ½(š) šø, ļæ½ļæ½ = š0šuļæ½(š)ļæ½ļæ½Continuity equation (from MWeq.) jšš + ā ā š½ = 0.
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The Wave Equation (Derivation)
ā¢ Assume for derivation: All space is free of sources except for electrical current (and subsequently thecharge)
ā¢ Curl (āĆ) of second MWEq: ā Ć (ā Ć šø) = ājššā Ć ļæ½ļæ½
ā¢ Put in first ā Ć ļæ½ļæ½ = jšš šø + š½ : ā Ć (ā Ć šø) = ājšš (jšš šø + š½)
ā¢ Reorganize and use vector identity ā Ć (ā Ć š ) = ā (ā ā š ) ā ā2š
ā¢ And another of MWEq ā ā šø = uļæ½uļæ½ ā ā Ć (ā Ć šø) = āā uļæ½
uļæ½ ā ā2 šø = āā uļæ½uļæ½ ā ā³ šø
Wave-equation ā³ šø + š2šš šø = jšš š½ + āā uļæ½uļæ½
Or in only z-dimension uļæ½2
uļæ½uļæ½2šø + š2šš šø = jšš š½ + 1
uļæ½uļæ½uļæ½uļæ½uļæ½
Solution of the Wave EquationOnly consider the one-dimensional wave-equation.
ā¢ āGuessā the solution to be šøuļæ½ = šuļ潚Ā±juļæ½uļæ½uļæ½ (other vector components similar)
ā¢ Put into the wave-equation (no sources. š½ = 0)
ā¢ āš2uļ潚uļæ½ + š2šššuļæ½ = 0 and all other components equally.
ā¢ Hence, equation fulfilled, if only šuļæ½ = Ā±šāšš, Dimension of it is m (length) and so is š = 1āuļæ½0uļæ½0=
299, 792, 458 m/s the speed of light (in vacuum)
The Plane Wave
ā¢ Suppose the wave is travelling in z-direction, so there is only a variation in z-direction and thusuļæ½
uļæ½uļæ½ = uļæ½uļæ½uļæ½ = 0, then šā ā šø = uļæ½uļæ½uļæ½
uļæ½uļæ½ = 0 and so šøuļæ½ = 0
ā The electric field is transversal, it has only vector components perpendicular to the propagationdirection.
ā¢ Further ā Ć šø = ājššļæ½ļæ½ =āāāāā
uļæ½uļæ½uļæ½uļæ½uļæ½
āuļæ½uļæ½uļæ½uļæ½uļæ½0
āāāāā
= ājšāāāāā
šøuļæ½
āšøuļæ½
0
āāāāā
And so the magnetic field is also
transversal and can be calculated directly from the components of the electric field.
ā¢ This kind of wave is called a transversal electro-magnetic or TEM wave.
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Wave-ImpedanceConsider electrical field only in y-direction (šøuļæ½ ā 0, šøuļæ½ = 0 ā š»uļæ½ = j 1
uļæ½uļæ½uļæ½uļæ½uļæ½uļæ½uļæ½ )
ā¢ With a z-propagating wave šøuļæ½ = šuļ潚ājuļæ½uļæ½ do partial derivative
ā¢ š»uļæ½ = āuļ潚ājuļæ½uļæ½ = ājš 1uļæ½uļæ½ jšuļ潚ājuļæ½uļæ½
ā¢ We already know š = šāšš
ā¢ And so uļæ½uļæ½āuļæ½
= āuļæ½uļæ½ = š
ā¢ Wave-Impedance of free space š0 = āuļæ½0uļæ½0
= 120š Ī© ā 377 Ī©
ā¢ All equally valid for other constellations of field components
Polarization
ā¢ Linear Polarization: uļæ½uļæ½uļæ½uļæ½
= š š is a real quantity
ā Two waves with linear polarization are orthogonal (practical use: law-enforcement radio (old),terrestrial satellite TV (channel separation)
ā Drawback: If you happen to have a receiver (geometrically) turned to receive the other pola-rization, you are out of luck
ā¢ Circular polarization: Field components āturnā around the propagation vector. Field componentsuļæ½uļæ½uļæ½uļæ½
= Ā±j are Ā±90ā out of phase (i.e. šøuļæ½ = 0 ā šøuļæ½ =max, and vice versa) [9]
ā Two kinds: Right-handed (āj) and Left-handed (j) circular polarized waves
ā There is also some power in some component of the electric (or magnetic) field
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Flow of Energy
ā¢ We already know: In plane waves, where there is electric field, there is magnetic, and they are inphase!
ā¢ For many applications (antennas are one of them) in the end we are interested in the energy flow,not particularly in electric or magnetic field.
ā¢ Poynting-Vector š = šø Ć ļæ½ļæ½ā defines the snapshot of the energy density.
ā¢ For our TEM-wave in z-direction this is
š =āāāāā
šøuļ潚»āuļæ½ ā šøuļ潚»ā
uļæ½
šøuļ潚»āuļæ½ ā šøuļ潚»ā
uļæ½
šøuļ潚»āuļæ½ ā šøuļ潚»ā
uļæ½
āāāāā
=āāāāā
00
šøuļ潚»āuļæ½ ā šøuļ潚»ā
uļæ½
āāāāā
ā¢ So generally energy flow is only in the direction of propagation
ā¢ Power transmitted through a surface (or even closed surface) is š = Re {12 ā®
uļ潚ø Ć ļæ½ļæ½ā}
2.2 Antenna Parameters
The First Antenna
Electrically small linear antenna (š āŖ š) (Hertzās Dipol) with current feed.
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Coordinate System, or What is šøuļæ½?
(a) (b)
Cartesian and spherical coordinate system (b) and the earth (a) GPL, de.wikipedia.org
ā¢ Local orthogonal coordinate system [14, 3]
ā¢ Transformation of a location vectorāāāāā
š„š¦š§
āāāāā
āāāāāā
ššš
āāāāā
Coordinate System, or What is šøuļæ½? II
ā¢ Local orthogonal coordinatesystem [14, 3]
ā¢ Transformation of a location
vectorāāāāā
š„š¦š§
āāāāā
āāāāāā
ššš
āāāāā
šāš„2 + š¦2 + š§2 š„ = š sin š cos šš = arctan (uļæ½
uļæ½ ) š¦ = š sin š sin šš = arccos ( uļæ½
āuļæ½2+uļæ½2 ) š§ = š cos š
Coordinate System, or What is šøuļæ½? III
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(a) (b)
(a) Vector with only š-component at different locations in x-z- (š = 0 or š)-plane, (b) One vector withš-components in x-y (š = š/2 or š)-plane and another vector at another location with only š-(radial)
component
Coordinate System, or What is šøuļæ½? IV
ā¢ Transformation of a vector likeāāāāā
šøuļæ½
šøuļæ½
šøuļæ½
āāāāā
āāāāāā
šøuļæ½
šøuļæ½
šøuļæ½
āāāāā
ā¢ Into Cartesian coordinatesšøuļæ½ = šøuļæ½ sin š cos š ā šøuļæ½ sin š + šøuļæ½ cos š cos ššøuļæ½ = šøuļæ½ sin š sin š + šøuļæ½ cos š + šøuļæ½ cos š sin ššøuļæ½ = šøuļæ½ cos š ā šøuļæ½ sin š
ā¢ Into Spherical coordinatesšøuļæ½ = šøuļæ½ sin š cos š + šøuļæ½ sin š sin š + šøuļæ½ cos ššøuļæ½ = šøuļæ½ cos š cos š + šøuļæ½ cos š sin š ā šøuļæ½ sin ššøuļæ½ = āšøuļæ½ sin š + šøuļæ½ cos š
ā¢ Note: š, š are related to the LOCATION, where the vector is present, not the angles between com-ponents of the vector.
And Now Again: The First Antenna
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Electrically small antenna (š āŖ š) with current feed. Current is constant on the wire. ... And itās far fieldpattern
Radiation Pattern
ā¢ Radiation Pattern: [6] radiation pattern: 1. The variation of the field intensity of an antenna as an angular function with
respect to the axis. (188) Note: A radiation pattern is usually represented graphically for the far-field conditions in either horizontal
or vertical plane.
Radiation Pattern II
ā¢ Radiation Pattern (continued)
ā Describes the strength of the field at certain points in space.ā Sometimes 3-dimensional (very nice, but difficult to quantify)ā Most often as 2-dimensional cuts (e.g. x-y-plane, x-z-plane)ā We are most concerned with far-field radiation patternā Often given in (dB), in this case relative to isotropic radiator (dBi). So this is relative to the
antenna that radiates its power equally to all directions
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E & H-Plane
ā¢ E-plane: The plane that is parallel to the vector of electric field (here this is any vertical plane (e.g.x-z-plane))
ā¢ H-plane: The plane that is parallel to the vector of the magnetic field (here this is the horizontal(x-y)-plane)
Nice, But Not-existing: Isotropic Antenna
ā¢ Imagine an antenna that radiates equally in all directions
ā¢ Its electrical field would be like šøuļæ½ = šøuļæ½ ā uļæ½āuļæ½uļæ½uļæ½
4uļæ½uļæ½
ā¢ Standard antenna to compare all the others to
ā¢ Radiates its power š equally distributed to all directions, so that power density is š = uļæ½4uļæ½uļæ½2
Further Parameters: Gain & Directivity
ā¢ Directivity, Gain [6, 13]antenna gain: The ratio of the power required at the input of a loss-free reference antenna to the power supplied to the input ofthe given antenna to produce, in a given direction, the same field strength at the same distance. Note 1: Antenna gain is usuallyexpressed in dB. Note 2: Unless otherwise specified, the gain refers to the direction of maximum radiation. The gain may beconsidered for a specified polarization. Depending on the choice of the reference antenna, a distinction is made between:
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ā absolute or isotropic gain (uļæ½uļæ½), when the reference antenna is an isotropic antenna isolated in space;
ā gain relative to a half-wave dipole (uļæ½uļæ½) when the reference antenna is a half-wave dipole isolated in space and with anequatorial plane that contains the given direction;
ā gain relative to a short vertical antenna (uļæ½uļæ½), when the reference antenna is a linear conductor, much shorter than onequarter of the wavelength, normal to the surface of a perfectly conducting plane which contains the given direction. [RR](188) Synonyms gain of an antenna, power gain of an antenna.
Gain, Directivity, & Power
ā¢ Mostly used: isotropic gain, relative to theisotropic antenna
ā¢ Potential loss of antenna included in gain.
ā¢ Gain of small dipole: šŗuļæ½ = 1.76 dB= 1.5,for 100% radiation efficiency
ā¢ Gain of half wave dipole: šŗuļæ½ = 2.16 dB=1.64,
ā¢ EIRP Effectively isotropic radiated power:Power delivered to an isotropic antenna togenerate the same field strength: šøš¼š š =šuļ潚ŗuļæ½, šuļæ½: total power delivered to the an-tenna.
ā¢ ERP as above but referenced to half wavedipole
Parameters for Power and Circuits I
ā¢ Two kinds of power make the total power šuļæ½ (e.g. [9])
1. Power radiated šuļæ½uļæ½uļæ½
2. Power lost in the antenna (network) šuļæ½
šuļæ½ = šuļæ½uļæ½uļæ½ + šuļæ½
ā¢ Antenna efficiency š = uļæ½uļæ½uļæ½uļæ½uļæ½uļæ½
(for our simulated small dipole š = 89% reached).
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Parameters for Power and Circuits II
ā¢ Definition of power allows definition of resistors:
1. Radiation resistance š uļæ½uļæ½uļæ½ = 2uļæ½uļæ½uļæ½uļæ½uļæ½2 = 2 uļæ½2
uļæ½uļæ½uļæ½uļæ½
2. Loss resistance š uļæ½ = 2uļæ½uļæ½uļæ½2 = 2uļæ½2
uļæ½uļæ½
3. Total Antenna resistance is thus š uļæ½ = š uļæ½ + š uļæ½uļæ½uļæ½ + jš and this is the one we need to matchthe circuit to
What is Wrong with the Small Antenna?Why does not everybody just use the small linear antenna? It radiates, it is small, so what is wrong withit?
- It is more an open than an antenna (very low real part of the antenna impedance, but very high(negative) imaginary
- You almost get no power into it
- Very ineffective, impossible to match, very high reactance since it is essentially an open
2.3 Linear Antennas
š/2-DipoleWhat can be better than a small antenna stub?
ā¢ Resonance.....
ā¢ Simply remember from transmission line theory: An open transformed over a š/4 line turns out tobe an open... (this at least brings the reactance into manageable regions)
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Pattern of the š/2-Antenna
Parameter of the uļæ½2 ā dipole are š = (77.4+j45.4) Ī©, Gain šŗuļæ½ = 2.16 dBi, vertical polarization. This thing
is matchable.
More on the Wire-Antenna
Simulation on wire antenna with length š=1.5 m (š/2 at 100 MHz)
ā¢ Note distinct (and sharp) resonances
ā¢ Granted, also reflection of -2.4 dB (at 100 MHz) is not good, but here, we can easily design a matchingnetwork
ā¢ Note, how the forward gain changes.
ā¢ See NEC-Simulation of lambda_2.nec over 30 to 800 MHz, browse through the gain-pattern vs. frequency
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Patterns of Wire Antennae
Radiation patterns for a 2 Ć 1.5 m long symmetrical wire antenna for various frequencies.
2.4 Wave Propagation
A Communication System
ā¢ Power received at Antenna 2 (and used in the resistor) is uļæ½2uļæ½1
= šŗ1šŗ2 ( uļæ½4uļæ½uļæ½)2
ā¢ Or in dB uļæ½2uļæ½1
ā£uļæ½uļæ½
= šŗ1|uļæ½uļæ½ + šŗ2|uļæ½uļæ½ ā 20 log10 ( uļæ½1 uļæ½uļæ½) ā 20 log10 ( uļæ½
1 uļæ½uļæ½uļæ½) ā 92.44 ššµ The lastterm includes the 4š and speed of light.
System Examples
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Parameter Bluetooth GSM Astra 1Eš1 10 dBm 2 W 85 Wšŗ1/dB 0 0 32EIRP 10 dBm 33 dBm 51 dBWšŗ2/dB 0 11 35š/GHz 2.4 0.9 12š/cm 12.5 33.3 2.7š 10 m 35 km 36,000 km( uļæ½
4uļæ½uļæ½)2 /dB -60 -122.4 -204š2/š1/dB -60 -111.4 -137š2 -50.0 dBm -78,4 dBm 1.6 pW
Colored quantities are input Comments
ā¢ GSM: (Free space) received power does not limit range (Sens. BTS -104 dBm)
ā¢ Sat-TV: Note the exceptionally low received power! Noise power in 10 MHz band is -104 dBm=0.04 pW (SNR=16 dB) in best case scenario.
Wave-Propagation in Not-So Free Space
ā¢ Wave propagation disturbed by
ā Obstacles
ā Fringing
ā Reflection etc.
ā¢ Free space model just seen represents a best case scenario
ā¢ For e.g. IEEE 802.15.4 communication systems the scenario is usually adopted like
uļæ½2uļæ½1
ā£uļæ½
= {šš(1m) ā 10š¾1 log(š) š ā¤ 8mšš(8m) ā 10š¾8 log(š/8) š > 8m
, šš(1m) = 20 log(4uļæ½uļæ½uļæ½0
) With values
Parameter 900 MHz 2400 MHzšš(1m) -31.53 dB -40.2 dBšš(8m) -49.59 dB -58.5 dBš¾1 2 dB 2 dBš¾8 3.3 dB 3.3 dB
Path-Loss Models at GHz CommunicationExample: Take the path-loss models that base ZigBee (IEEE 802.15.4) [1]
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2.5 Yagi Uda
Yagi-Uda AntennaCommonly used directive antenna for radio and TV reception
ā¢ Composed of (roughly) three sections
1. Feed antenna (folded, or š/2-dipole)
2. Directors šæuļæ½ < šæ, act as transmission line structure, that guides a surface wave
3. Reflector šæuļæ½ > šæ, usually only one, can also be build as a reflecting grid
ā¢ Homogeneous (all directors equally) and in-homogeneous (directors individually optimized)
Yagi Antenna DesignSome designs for in-homogeneous Yagi-Uda antennas after classical paper [16] āYagi Antenna Designā
uļæ½ uļæ½/uļæ½ uļæ½uļæ½/uļæ½ uļæ½/uļæ½ uļæ½uļæ½1/uļæ½ uļæ½uļæ½2/uļæ½ uļæ½uļæ½3/uļæ½ uļæ½uļæ½4/uļæ½ uļæ½uļæ½5/uļæ½ uļæ½uļæ½6/uļæ½ uļæ½uļæ½7/uļæ½ uļæ½uļæ½8āuļæ½/uļæ½0 0.2 0.482 0.4531 0.2 0.482 0.453 0.4243 0.2 0.482 0.455 0.428 0.424 0.4284 0.25 0.482 0.455 0.428 0.42 0.42 0.42810 0.2 0.482 0.457 0.432 0.415 0.407 0.398 0.39 0.39 0.39 0.3915 0.2 0.482 0.455 0.428 0.42 0.407 0.398 0.394 0.39 0.386 0.38613 0.308 0.475 0.4495 0.424 0.424 0.42 0.407 0.403 0.398 0.394 0.39
Simulation done at š = 100 MHz (š = 2.99 m). Wire radius (this is critical!) is 1.3 mm
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uļæ½ uļæ½/uļæ½ uļæ½/dB0 0.2 6.381 0.4 9.073 0.8 11.24 1.25 12.410 2.2 14.115 3.2 15.413 4.312 15.4
Pattern of Yagi Antennas
Radiation patterns for the afore mentioned design values
Yagi: Results
ā¢ Gain of a Yagi-Antenna depends much on size (length of the structure), less on actual number ofelements
ā¢ Radius of wire is important (as reactance of directors is used to adjust the phase velocity of thesurface waves on the director section)
ā¢ Length of feeding antenna does not much influence the overall directivity and my thus be chosen foroptimum match
2.6 Small Antennas
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Small AntennasWouldnāt it be nice to have an antenna of no physical extend (or at least well integrated on a chip)?
ā¢ Goal for antennas is to have a moderately high radiation resistance
ā Low Q (Quality factor) is desired but not by means of losses to the network! [2]
ā¢ Fundamental limit š ā 1uļæ½uļæ½ for šš = 2uļæ½
uļæ½ š āŖ 1 š radius of encloding shere
ā¢ Even this has never been reached or exceeded
Small Antenna LimitsConsequences on the limit to small antennas
ā¢ High Q = high reactive part = low (radiation) resistive part
ā¢ Difficult to match (need to compensate reactance, and increase to resistive level of driver/ receiver)
ā¢ š = Īš/š so low band-width
ā¢ Conductor losses are still there: Small antenna with low input resistance have low efficiency!
ā¢ Bottom-line: No matter what: Effective Antennas will have some size! [at best they even resonate]
Fold the Dipol
ā¢ Folding the Dipol retains the electrical lengths and resonance by reducing extend (9 cm compared to16 cm)
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ā¢ But adds currents in opposite directions (fields cancel)
ā¢ Adds inductance (through bends) and capacitance (through couplings)
ā Sonewhat more compact than the linear dipol, but
ā¢ Performance inbetween smaller and resonant dipol (even though this thing is at resonance)
Complete electrical length of dipol is 18.1 cm
Antennas at DHBW in Kalrsruhe
Inverted F-AntennaSmall and somewhat more broadband.
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Inverted F-Antenna
ā¢ More on the design is found in [15]
ā¢ Height š» determines input impedance (0.1 ā¦ 0.11 ā š for 50 Ī©)
ā¢ Parameters for a.m. IFA:š, š 1250 MHz 239 mm š» 33 mm 0.138ššæuļæ½ 46.5 mm 0.195š šæuļæ½ 20 mm 0.084š
Comments on Inverted F-Antenna
ā¢ Function:
ā In effect the IFA is a monopole-antenna (š/4-antenna over conducting ground)
ā Folded down (šæuļæ½ ) (to reduce height of the antenna)
ā Folding, and then parallel to ground adds capacitance
ā Compensation of this capacitance done by short stub (šæuļæ½) (i.e. inductance)
ā¢ Application
ā Popular in cellular phones
ā Can be printed (micro-strip technology), then Planar Inverted F-Antenna (PIFA)
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2.7 Mobile Antennas
Antenna Design for Mobile CommunicationSome Design requirements
ā¢ Small in size, fitting into design (marketing)
ā¢ Small in price, easy to manufacture
ā¢ Effective, good SAR (specific absorption ratio) (= do not radiate into the brain!)
ā¢ Work in vicinity of head, hand, housing, battery
ā¢ Multi-band ā¦or broadband
ā GSM (824-894, 890-960, 1710-1880, 1850-1990 MHz) and more
ā UMTS (1900-2170 MHz) and growing (see also GSM)
ā WLAN/ WPAN (2400-2485, 5150-5350, 5725-5875 MHz)
ā GPS (1575 MHz) (RHCP)
ā Video (DVB-T, -H) (170-230, 470-862, 1452-1492 MHz)
ā¢ Multiple-Antennas: Diversity and MIMO [Multi-In-Multi-Out]
General Concepts
ā¢ Combination of above ātricksā
ā¢ Loading (parasitic elements)
ā¢ Reducing physical size (folding/ meandering)
ā¢ Combining many antennas (for same or different task)
ā¢ Printed technology, LTCC-technology (chip antennas)
PIFA
Geometry of a Planar Inverted F-Antenna [5, 11]
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ā¢ More degrees of freedom: (šæ/š), (š/š) compared to IFA
ā¢ Resonance at šuļæ½uļæ½uļæ½ ā uļæ½4(uļæ½+uļæ½+uļæ½ā) š¾ determines influence of grounding strip (š¾ = 1 for š āŖ š¤, 0
otherwise)
ā¢ š Large, bandwidth large (up to 10 %), š small BW down to 1 %
ā¢ Modifications to put slots in the radiating element will meander the current, thus increasing electrical length
Meandered Patch
After [5]
Combining PIFA, PIFA, and IFA
(a) (b)
After [7, 8]
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2.8 Examples in Mobile Phones
Examples of Antennas in Mobile Phones
Siemens C35
GSM Helix
Antenna
and
Bluetooth IFA
Examples of Antennas in Mobile Phones
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Blackberry 7130,
Multiband printed Antenna
and
Bluetooth
Examples of Antennas in Mobile Phones
Motorola Wire Antenna (left) and
Wirelike HTC TRIN100 Antenna
Battery
Examples of Antennas in Mobile Phones
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Apple
IPhone 4
Bluetooth, WiFi, GPS
GSM/ UMTS
Effective Area
ā¢ Effective Area
ā For large antennas determined by (ā) the geometrical size
ā For small antenna can be viewed as the area that the antenna draws the field lines upon itself
ā¢ Effective Aperture (Area) of an antenna: š“uļæ½ = uļæ½uļæ½uļæ½uļæ½uļæ½ with (total) power received by a (receiving)
antenna šuļæ½uļæ½uļæ½ and power density š at the location of the antenna
ā¢ Effective area is proportional to for all antennas and all antenna types
ā¢ Relation to gain is calculated to uļæ½uļæ½uļæ½ = uļæ½2
4uļæ½
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Antenna FactorParameters especially for EMC-measurements [12], where you want to know the field strength (and power)at a certain point.
ā¢ Antenna Factor: š“š¹ = uļæ½uļæ½uļæ½
dimension (1/m) with electrical field šø and voltage at antenna ports š .in dB: š“š¹uļæ½uļæ½/uļæ½ = šøuļæ½uļæ½uļæ½uļæ½ /uļæ½ ā šuļæ½uļæ½uļæ½uļæ½
ā¢ Ohmās gives us šuļæ½uļæ½uļæ½ = uļæ½2uļæ½
uļæ½ delivered to a load
ā¢ In free space Ohmās law is used to š = uļæ½2
uļæ½0š0 = 120š Ī©
ā¢ Putting it together (also with previous slide) š“š¹ = ā uļæ½0uļæ½uļæ½uļæ½
= 2.745āuļæ½uļæ½
= 9.734uļæ½
āuļæ½ = 2uļæ½
uļæ½ ā120 Ī©uļæ½uļæ½ in dB
š“š¹uļæ½uļæ½/uļæ½ = 19.8 ā 20 log10(š/š) ā uļæ½uļæ½uļæ½2 ; all for š = 50 Ī©
Transmit Antenna Factor
ā¢ Now to relate the input voltage to a (transmit) antenna to the resulting field strength at a certaindistance
ā¢ Define Transmit Antenna Factor š š“š¹ = uļæ½uļæ½uļæ½
as the field-strength šø that the given antenna generates,when the voltage šuļæ½ is applied to it, at a distance š
ā¢ Again Power density š = uļæ½uļæ½uļæ½uļæ½4uļæ½uļæ½ and šuļæ½ = uļæ½2
uļæ½uļæ½ , š = uļæ½2
uļæ½0
ā¢ Then uļæ½2
uļæ½0= uļæ½uļæ½uļæ½uļæ½
4uļæ½uļæ½
Transmit Antenna Factor II
ā¢ And so the field strength at distance š is šø = ā30 Ī© šuļ潚ŗuļæ½1uļæ½ = ā30 Ī©
uļæ½ šŗuļæ½uļæ½uļæ½uļæ½ = ā0.6šŗuļæ½
uļæ½uļæ½uļæ½ for
š = 50 Ī©
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ā¢ Finally uļæ½uļæ½uļæ½
= š š“š¹ = ā30 Ī©uļæ½ šŗuļæ½
1uļæ½ in dB: š š“š¹uļæ½uļæ½/uļæ½ = uļæ½uļæ½,uļæ½uļæ½
2 ā 2.22dB ā 20 log10(š/m)
ā¢ Relation between š“š¹ and š š“š¹ is found by solving both for šŗ and equation (Gain is reciprocal!)
ā¢ š š“š¹ = 120uļæ½ Ī©uļæ½
1uļæ½uļæ½uļæ½uļæ½ in dB (50 Ī©): š š“š¹uļæ½uļæ½/uļæ½ = 17.54āš“š¹uļæ½uļæ½/uļæ½ā20ā [log10 (š/m) + log10 (š/m)]
ā¢ š š“š¹, š“š¹ measured valid under matching and radiation conditions. Thus, not 1-1 reciprocal!
2.9 Reflector
Reflector Antennas
ā¢ Known: The higher the efficient area,the higher the gain: uļæ½uļæ½uļæ½ = uļæ½2
4uļæ½
ā¢ For large antennas (š“uļæ½ > š2) the effective area is in the range of about the geometrical area
ā¢ In this case quasi-optical approaches can be used
ā¢ Focusing of radiation with lens or parabolic mirror
Parabolic Mirror
Heinrich Hertz Turm in Hamburg (Photo GPL, de.wikipedia.org)
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Parabolic mirror, classical approach and feed as in shell antenna
ā¢ Description is parabolic with š¦ = šš„2
ā¢ Focal point š = 1/(4š), where all rays have the same length
ā¢ Area (geometric) of course š“uļæ½ = šš2
ā¢ And gain is šŗ = 4š uļæ½uļæ½uļæ½2 = š (2uļæ½uļæ½
uļæ½ )2
ā¢ Area-efficiency š = uļæ½uļæ½uļæ½uļæ½
ā 0.5 ā¦ 0.6 < 1
Parabolic Mirror II
ā¢ Area efficiency always < 1. Determined by
ā Illumination (best: spherical wave with homogeneous illumination of the mirror)
ā Shadowing through mechanical structure and feeding network (horn). ā Remedy shell configu-ration (off-center feed)
ā¢ Homogeneous illumination: Higher side-lobes (rect ā ā14 dB)
ā¢ Backward (off angle) radiation determined by fringing/ diffraction at edges, radiation over the edges,secondary radiation from feeding structure
ā¢ Required accuracy of mirror about š/100 ā¦ š/50
35
Practical Results on Parabolic Mirror
ā¢ Gain 30...40 dB
ā¢ HWBW š3uļæ½uļæ½ ā 70ā uļæ½uļæ½
ā¢ Simple satellite Dish (Kathrein CAS06), 2š = 0.57 m, š = 11.7 ā¦ 12.75 GHz ā š ā 0.027 m
šŗ = 34.9 ā¦ 35.9 dBi š3uļæ½uļæ½ < 2.8ā
ā¢ Linear: šŗ = 3161 Calculate Area-efficiency š = šŗ/ (2uļæ½uļæ½uļæ½ )2 = 71%
Reflector Antennas Advanced
ā¢ Offset Feed
ā¢ Folded Mirrors (e.g. Cassegrain-Antenna with Hyperboloid)
ā¢ Polarization and frequency selective reflecting surfaces
References
[1] IEEE Computer Society. Part 15.4: Wireless Medium Access Control (MAC) and Physical Layer (PHY)Specifications for Low-Rate Wireless Personal Area Networks (WPANs). Techn. Ber. 802.15.4. IEEE,2006.
[2] Constantine A. Balanis. Antenna Theory, Analysis and Design. 3. Aufl. New York: Wiley Interscience,2005.
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[3] I. N. Bronstein und K.A. Semendjajew. Taschenbuch der Mathematik. 23. Aufl. Leipzig: BSB B.G.Teubner Verlagsgesellschaft, 1987.
[4] R. E. Collin. Foundations for Microwave Engineering. 2. Aufl. McGraw Hill, 1991.
[5] N. P. Cummings. āLow Profile Integrated GPS and Cellular Antennaā. Magisterarb. Virginia Polytech-nic Institute und State University, 2001. url: http://scholar.lib.vt.edu/theses/available/etd-11132001-145613/unrestricted/etd.pdf.
[6] Federal Standard 1037C, Telecommunications: Glossary of Telecommunication Terms. ITS Institutefor Telecommunication Siences. 1996. url: http:// www.its. bldrdoc.gov/ fs- 1037/ fs-1037c.htm.
[7] Rafal Glogowski und Custodio Peixeiro. āMultiple Printed Antennas for Integration Into Small Mul-tistandard Handsetsā. In: IEEE Antennas and Wireless Propagation Letters 7 (2008), S. 632ā635.
[8] D. Manteufel u. a. āDesign Consideration for Integrated Mobile Phone Antennasā. In: InternationalConference on Antennas and Propagation. Bd. 11. Apr. 2001.
[9] H. Meinke und F.W. Grundlach. Taschenbuch der Hochfrequenztechnik. 5. Aufl. Berlin: Springer,1992.
[10] G. Oberschmidt. Waveletbasierte Simulationswerkzeuge fĆ¼r planare Mikrowellenschaltungen. Bd. 293.9. DĆ¼sseldorf: VDI Fortschritt-Berichte, 1998.
[11] K. Ogawa und T. Uwano. āA Diversity Antenna for Very Small 800-MHz Band Portable Telephonesā.In: IEEE Trans. Antennas Propagat. 42.9 (Sep. 1994), S. 1342ā1345.
[12] J.D. Osburn. EMC Antenna Parameters and Their Relationships. EMC-Test Systems. 1997. url:http://www.ets-lindgren.com/page/?i=WhitePaper-I0196.
[13] K. Rothammel. Antennenbuch. 10. Aufl. Stuttgart: MilitƤrverlag der DDR, 1984.
[14] J. A. Stratton. Electromagnetic Theory. McGraw Hill, 1941.
[15] SuperNEC- Inverted F Antenna. SuperNEC. 2008. url: http://www.supernec.com/ifa.htm.
[16] P.P. Viezbicke. Yagi Antenna Design. National Institute of Standards amd Technology. 1976. url:http://tf.nist.gov/timefreq/general/pdf/451.pdf.
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