WIRELESS COMMUNICATIONS
RANGE
ACTIVE
PASSIVE
Arm’s
Length
Pills, hearing aids, computer
peripherals
Faucets, CD’s,
thermometers,
<100 m
Wireless phones, remote
controllers, computer links
Cameras, doors
<100 km
Radio, television, cell phones,
UWB, 802.11
Multispectral remote
sensing
Global
Ham radio, communications
satellites, radar, lidar
Weather satellites
Cosmic
Radio & optical interplanetary
communications, radar, lidar
Radio & optical
astronomy
L17-1
COMMUNICATION REQUIRES ENERGY AND POWER
Typical receivers need:
Eb > ~10-20 Joules/bit
Received power required:
Prec = MbpsEb [Watts]
(Mbps is data rate, bits/sec)
L17-2
RADIATED POWER
Transmitted Intensity:
I(θ,φ,r) [W/m2]
For isotropic radiation: I(θ,φ,r) = PR/4πr2 [Wm-2]
Total power radiated [W]
PR =
2π π
∫0 ∫0
I(θ,φ,r) r2 sinθ dθ dφ
dΩ (steradians)
Antenna pattern:
Isotropic:
z
area =
(r dθ)(r sin θ dφ)
θ
I(θ,φ,r)
dΩ steradians
r
x
φ
Steradian: unit of solid angle
dθ, dφ:
units of radians.
Spheres: span 4π steradians
main beam
I(θ,φ,r)
sidelobes
backlobes
L17-3
ANTENNA GAIN G(θ,φ)
Gain over Isotropic, G(θ,φ):
G(θ,φ) =
I(θ,φ,r)_
(PR/4πr2)
Intensity actually radiated [Wm-2]
Intensity if PR were radiated isotropically
Intensity at receiver:
G(θ,φ)
I(θ,φ,r) = G(θ,φ) (PR/4πr2 ) [Wm-2]
sidelobes
backlobes
Isotropic gain
L17-4
HOW TO INCREASE ANTENNA GAIN G(θ,φ)?
Focus the energy
Lenses
Photographs illustrating lenses, mirrors, and
phasing removed due to copyright restrictions.
Mirrors
Phasing
L17-5
ANTENNA EFFECTIVE AREA Ae(θ,φ)[m2]
Intensity radiated in a particular direction
I(θ,φ,r) = Gt(θ,φ) (PR/4πr2 )
[ W/m2 ]
Power Received from a particular direction
Prec = I(θ,φ) A(θ,φ) [W]
Antenna Effective Area and Gain
A(θ,φ) = G(θ,φ) (λ2/4π) [m2]
Power Received from a particular direction
Prec = PtGtGr(λ/4πr)2 [W]
⇒
“reciprocity”
L17-6
CIRCUIT PROPERTIES OF ANTENNAS
Equivalent circuit of antenna
When transmitting:
Power radiated = PR
Radiation resistance Rr
i(t)
+
v(t)
-
PR = <i2(t)>Rr [W]
Reactance
-
VTh
jX
+
Thevenin voltage source
When receiving:
Thevenin voltage VTh is induced by incoming waves
Maximum power extractable
from the antenna:
Rr
Rr
- VTh +
Prec = <(VTh(t)/2)2>/Rr
Reactive elements are tuned out
L17-7
SUMMARY
Wireless communications are ubiquitous
G(θ,φ) = I(θ,φ,r) / (Pt/4πr2) = Antenna gain over isotropic
Boost antenna gain using lenses, mirrors, or phasing
Ar = Gr (λ2/4π) = Antenna effective area [m2]
M [bps] = Prec/Eb = IAe/Eb = PtGtGr(λ/4πr)2/Eb = data rate
Eb > ~10-20 [J] at the receiver
(see footnote 39 on p360)
Antennas have Thevenin equivalent circuits, radiation resistance
L17-8
EXAMPLE – INTERSTELLAR COMM.
PRad 2
r sin θ dθ dφ ⇒ ∫ G(θ, φ)dΩ = 4π
2
0 ∫0
4π
4πr
dΩ steradians
θB is “antenna
GoΩB = 4π ⇒ Go = 4π/ΩB
ΩB Go
beamwidth”
PRad = ∫
2π
π
G(θ, φ)
ΩB is the “beam solid angle”
Best microwave antennas: θB ≅ 1 arc min = (1/60)o(1/57) radians ≅ 2-12 rad
Go = 4π/ΩB ≅ 23/2-24 ≅ 227 ≅ 108 (or 80 dB)
Strongest transmitters ~ 106 Watts
Nearest stars ~1 light year = 3×107 sec × 3×108 m/s ≅ 1016 m
Pr ec
2
6
8
8
2
Pr ad
λ
10
10
10
0.03
=
≅
≅ 10 −15 [W] [J/s]
Gt Gr
2
32
4π
4πr
10 10 10
Data rate R ≅ Prec[J/s] / 10-20[J/bit] = 10-15/10-20 = 105 bits/sec
L17-9
MIT OpenCourseWare
http://ocw.mit.edu
6.013 Electromagnetics and Applications
Spring 2009
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.