Chapter 2: Radio Wave Propagation Fundamentals
M.Sc. Sevda Abadpour Dr.-Ing. Marwan Younis
INSTITUTE OF RADIO FREQUENCY ENGINEERING AND ELECTRONICS
KIT – The Research University in the Helmholtz Association www.ihe.kit.edu Scope of the (Today‘s) Lecture
D Effects during wireless transmission of signals: A . physical phenomena that influence the propagation analog source & of electromagnetic waves channel decoding . no statistical description of those effects in terms digital of modulated signals demodulation
filtering, filtering, amplification amplification Noise
Antennas Propagation Time and Frequency Phenomena Selective Radio Channel
2 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Phenomena
refraction reflection zR zT path N diffraction
transmitter receiver QTi path i QRi yT xR y Ti yRi xT path 1 yR scattering
reflection: scattering: free space - plane wave reflection - rough surface scattering propagation: - Fresnel coefficients - volume scattering - line of sight - no multipath diffraction: refraction in the troposphere: - knife edge diffraction - not considered
In general multipath propagation leads to fading at the receiver site
3 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics The Received Signal
Signal fading Fading is a deviation of the attenuation that a signal experiences over certain propagation media.
It may vary with time, position Frequency
and/or frequency Time
Classification of fading: . large-scale fading (gradual change in local average of signal level) . small-scale fading (rapid variations
large-scale fading due to random multipath signals) small-scale fading
4 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Models
Propagation models (PM) are being used to predict: . average signal strength at a given distance from the transmitter . variability of the signal strength in close spatial proximity to a particular location
Severe multipath conditions in PM can be divided into: urban areas (small-scale fading) . large-scale models (mean signal strength for large transmitter receiver separation) . small-scale models (rapid fluctuations of the received signal over very short travel distances)
5 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Large-Scale Propagation
Free Space Propagation
6 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Free Space Propagation
T R x x Assumptions: Pt Pr . unobstructed line of sight (LOS) Gt Gr . no multipath propagation r no (influence of) ground
Received power: Power density at Rx site: Antenna effective area:
Friis free space equation:
7 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Received Power and Path Loss
Using:
i i
Assumptions: . polarization matched receiving antenna . conjugate complex impedance matching of the receiver
Path loss:
Isotropic path loss (no antenna gains):
8 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization
Orientation of Field Vectors and Reference Planes
9 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization of the EM Waves
Every elliptically polarized EM wave can be decomposed into a horizontal and a vertical component.
Elliptical Circular Linear
10 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization: II, T , V or H?
Plane of incidence: formed by the normal vector to the reflecting surface and Poynting vector of the incidence wave
EII or EV
E T or EH
Polarization (E-field vector) with Polarization (E-field vector) with respect to the plane of incidence: respect to the earth coordinates: . parallel (II) . vertical (V)
. perpendicular ( )T . horizontal (H)
11 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Reflection and Transmission
Dielectric Boundary
12 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Snell’s Law of Reflection
. surface large compared to the wave length θi θr 1 . smooth surface (otherwise scattering) . three angles: - incidence 2 - reflection - transmission / refraction θt
. Relation between angles through Fermat’s principle (principle of least time): - “the rays of light (EM-waves) traverse the path of stationary optical length” . This results in* Snell’s laws: - “ratio of the sines of the angles of incidence and refraction is equivalent to the opposite ratio of the indices of refraction” - “the incidence and reflection angles are equal and they are in the same plane”
sin(i ) n2 nx r,x r,x i r sin(t ) n1 *full derivation in Arthur Schuster: “An Introduction to the Theory of Optics”
13 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Which Part is Transmitted / Reflected?
Derivation procedure: . Definition of the electric field strength of the incident wave . Reflected and transmitted field strengths . Faraday’s law of induction . Boundary conditions at the border between two dielectric media . Decomposition of the incident waves on parallel and normal components
14 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Fresnel Reflection & Transmission Coefficients
parallel
perpendicular
where:
Fresnel coefficients are frequency dependent and in general complex
15 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Brewster‘s Angle (I)
Angle, where no reflection occurs is Brewster’s Angle: . exists only for parallel (II / V) polarization . calculation by comparing the reflection coefficient to zero . calculation by using “physical limitations”
16 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Brewster‘s Angle (II)
Air (less dense) Glass (dense)
17 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics
Brewster‘s Angle (III) phasein degree
18 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Brewster‘s Angle (IV)
Operation principle of Brewster window: . used for windows in optical or quasi optical systems . window with normal incidence reflection loses at window . window tilted at Brewster’s angle no reflection loses at window
Microwave gyrotron Brewster window
19 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Total Internal Reflection (I)
When does the total internal reflection appears? ni sini nt sint t 90 . a ray must strike the medium’s boundary
at an angle larger than the critical angle nt c arcsin . calculation by comparing the ni transmission angle to 90 degree critical angle exists only for nt < ni
Increasing the incidence angle Total reflection of red laser light in PMMA
20 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Total Internal Reflection (II)
Operation principle of rain sensors: . IR-beam projected on the glass-air interface at a specific angle . total inner reflection in dry conditions . partial transmission to the second medium if windshield is wet . reduced receive power triggers the sensor
Rain sensor in the rear view mirror
21 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Visualization Parallel Pol – E-Field
Parallel Pol – Air to Glass Parallel Pol – Glass to Air
22 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Visualization Perpendicular Pol – E-Field
Perpendicular Pol – Air to Glass Perpendicular Pol – Glass to Air
23 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Reflection and (no) Transmission
Perfect Electric Conductor (PEC)
24 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Orthogonal PEC Reflection
Boundary conditions:
Etan Etan,i Etan,r 0
Hnorm Hnorm,i Hnorm,r 0 reflected wave incident wave
Ey Ey SR S SR
Hx Hx H HxR E xR EyR yR
y
z
x
25 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics PEC Reflection, Orthogonal Polarization H incident reflected wave Ey wave Hxi H i S S
Plane of incidence Eyi ai Ey
Hzi H Hzr
Eyr PEC reflector
PEC reflection: Hxr Hr
x
. RII = +1 y T z . R = -1 (to ensure E = 0) tan ai ar
26 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics PEC Reflection: Applications
Reflection in the direction of incidence: Radar calibration with metallic: . dihedral . trihedral (corner reflector)
Buoy with dihedral
Radar image with corner reflectors
Satellite radar calibration
27 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Two-Ray Propagation Model
28 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Geometry
T
d1 R
zT
zR d2 air (휺풓 = ퟏ) j j r ground (휺 ) 풓 d
Two-Ray model is based on geometrical optics and predicts large-scale fading
29 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Assumptions
Assumptions in two-ray model: . ground is PEC
. d >> zT,zR
d
Observations:
2 2 . the received power PR oscillates like a sin or cos with distance
. the minimum value of PR is 0
. the maximum value of PR is 4 · PR,freespace (+ 6 dB)
30 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Large Distances
Conditions:
. d >> k0zTzR . cos2x 1 . sin2x x2
Observations: . parallel pol: 20 dB / decade, perpendicular pol: 40 dB / decade . perpendicular pol: independent on frequency
. perpendicular pol: antenna height gain (double zT or zR quadruple PR)
31 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Breakpoint
Definition: The breakpoint is the distance where the argument of the sin2 and cos2 terms equals 0.5
1
0.5
Beyond the 0 1 breakpoint there are no oscillations!
0.5
0 0 0.5 1 1.5 2 2.5
32 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization Dependence
perpendicular polarization parallel polarization
1/d2 1/d2 6 dB 6 dB
dependent on frequency 1/d2 6 dB 6 dB
1/d4 independent on frequency
33 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Frequency Dependence
f = 900 MHz f = 4 GHz
dbreakpoint
dbreakpoint
distances of notches >> l
34 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Path Loss Prediction
80dB 200m height z vertical (parallel)
polarization
path path loss (above ground) (above 50m
0m 130dB 0m range coordinate r (distance from transmitter) 2000m
80dB 200m
horizontal (perpendicular) height z
polarization
path path loss (above ground) (above 50m
0m 130dB 0m range coordinate r (distance from transmitter) 2000m
35 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Diffraction
Diffraction on Absorbing Half-Plates
36 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Geometry
z secondary spherical waves
z = H rT rR H>0
y x d d transmitter T R receiver
. obstacle: semi-infinite, infinitely thin, absorbing plate . calculate behavior behind the plate: Huygens’ principle . wave propagation behind the plate: sum of secondary waves
37 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Model
Assumptions in knife edge model: . cylindrical waves (2D problem)
. Tx and Rx at same height
. |H| << dT,dR
Fresnel Integrals Field-strength relative to free space (no obstacle):
2 2 E 1 1 1 C( ) S( ) E H 2 2 2
2 1 1 H l dT dR
38 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Electric Field (I)
shadow region
- 6 dB
lit region
2 1 1 H l dT dR
39 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Electric Field (II)
shadow region
- 6 dB
lit region
0 if 0.78 dB E 6.9 20log 0.1 0.1 2 1 E H if 0.78
40 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Frequency Dependence (I)
• field strength normalized to free space level • isotropic Tx antenna • semi-infinite, absorbing plate • f = 1 GHz, 3 GHz, 10 GHz
diffraction loss increases with frequency f for 1
41 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Frequency Dependence (II)
SINGLE KNIFE EDGE DIFFRACTION , FREQUENCY DEPENDENCE shadow / lit region
-6 dB
f ∞
transmitter height = obstacle height distance transmitter to knife edge = 1000m distance knife edge to receiver = 100m
42 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Fresnel Ellipsoids
Nth Fresnel zone is bounded by an ellipsoid, where
the Tx-Rx-path is N half wavelengths longer than dFN dT dR N l 2
the direct Tx-Rx-path dT + dR between Tx and Rx
rF1 Tx Rx dT dR
1st Fresnel ellipsoid Nth Fresnel ellipsoid
Radius of Nth Fresnel ellipsoid
43 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics When to Neglect the Knife Edge Diffraction?
Relate Fresnel radius RFN with diffraction parameter :
-1
2
If the knife edge does not extend into 1st Fresnel zone, then the error compared to free space propagation is less than 1.1 dB:
If the knife edge does not extend into the 1st Fresnel zone, then knife edge diffraction can be neglected
44 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Fresnel Ellipsoids: Example
Tx Rx
dT dR
RF1
dT+dR+l0/2
45 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Scattering
Scattering of Incident Energy on Rough Surfaces
46 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Different Types of Scattering
point scattering distributed scattering
Simple targets (plate, sphere, rough surface scattering volume scattering cylinder, etc.)
47 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics From Specular Reflection to Incoherent Scattering
specular reflection coherent scattering diffuse scattering
Roughness criteria: Roughness paremeter: s : RMS height l h i s Rayleigh: s 0 L: correlation length h 8cosi L l Fraunhofer: 0 s h sh 32cosi
48 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Multipath Propagation
Combination of all Wave Propagation Effects
49 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Phenomena
refraction reflection zR zT path N diffraction
transmitter receiver QTi path i QRi yT xR y Ti yRi xT path 1 yR scattering
reflection: scattering: free space - plane wave reflection - rough surface scattering propagation: - Fresnel coefficients - volume scattering - line of sight - no multipath diffraction: refraction in the troposphere: - knife edge diffraction - not considered
In general multipath propagation leads to fading at the receiver site
50 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Path Loss Prediction over Natural Terrain
70 dB 80 m
• f = 435 MHz
height path path loss 16.4 m
0 m • Tx height = 16.4 m 150 dB 0 km distance 7.95 km • vertical polarization 80 dB 80 m
height • f = 1900 MHz path path loss
16.4 m
0 m 160 dB 0 km distance 7.95 km
51 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics