Lecture01 TRƯỜNG ĐIỆN TỪ

ELECTROMAGNETICS AND APPLICATIONS


Handouts:
Prerequisites:
Administration sheet
6.002, 6.003, 8.02, 18.02

Subject outline, lecture notes

Homework set 1, text errata

6.013(New) Content:
Wireless communications (3.2 weeks)

Media and boundaries (1.5 weeks)

Circuits (1 week)

Motors, generators, MEMS, power transmission (1.2 weeks)

Limits to computation speed (1 week)

Microwave communications and radar (2 weeks)

Acoustics (1 week)

Optical communications (1 week)

L1-1

WIRELESS COMMUNICATION IS UBIQUITOUS

Local Telecommunications Network:
Cell phones (who has one?)
Wireless phones, data
Wires, coaxial cables
Optical fibers

Link to
national net
Local
cell
Homes

Base station

Other Communications Links:
Central office
Microwave and optical fiber links

Urban network
International satellite links

Transoceanic links, ionosphere
Satellite

Radio hams (any here? DX record?)
Interplanetary links
National Network

NATION A

Ionospheric link
OCEAN


NATION B
L1-2


WIRELESS COMMUNICATION IS UBIQUITOUS

Other Forms of Wireless Communications:
Broadcast:

Data links:

Passive:

Terrestrial radio, television, data
Satellite TV, radio, data
(~40,000 km - ~0.3 seconds roundtrip)
WWV Time signals (clocks, watches)
Computers to/from peripherals
Hearing aids (from CPU)
Remote controllers (optical and radio)
Wired home, office, factory
Pills with sensors (TV, chemical)
(what frequencies penetrate body?)

IR, microwave (satellites, factories,
faucets, doors, thermometers, cameras)
L1-3


COMMUNICATION REQUIRES ENERGY AND POWER
Power Requirements
Typical receivers need:
Eb > ~4 × 10-20 Joules/bit
Power received [W]:
P = MbpsEb (Mbps is data rate, bits/sec)
e.g. 10-9 Watts permits Mbps = ~10-9/4 × 10-20 = 2.5 × 1010 bps
This can send 2.5 × 1010/(8 × 7 × 108 bits/CD) = 4.5 CD’s/second!)

Transmitted Intensity is Pr(θ
θ,φ
φ,r) [W/m2]
2
2
For isotropic radiation: Pr ( θ, φ,r ) = PR 4 πr  W m 



PR = total power radiated (W)
2
PR [W ] = ∫ Pr ( θ, φ,r ) r sin θdθdφ

where:

In general:

%
(&(
'

4π

isotropic
Pr(θ,φ,r) z θ

area =
r2(dθ)(sin θ dφ)

=

dΩ

∫ PrΩ ( θ, φ )[W

steradian] dΩ

4π

r
x

φ

backlobes

main beam

[Steradian is a unit of solid angle; [dθ] [sin θ dφ] is in steradians if
dθ and dφ are in units of radians. A sphere spans 4π steradians]

L1-4


ANTENNA GAIN G(θ,φ)
θφ
Gain over Isotropic G(θ,φ):
θφ
G ( θ, φ ) =

Pr ( θ, φ,r )
PR 4 πr

2

(By definition, PR is at
antenna input; we assume
lossless antennas here)

At receiver: Pr(θ,φ,r)[Wm-2] = G(θ,φ) PR/4πr2

Example – Cellular Phone:
If PR = 1 Watt, then Pr at 10 km = 1/4πr2
= 8 × 10-10 [W/m2] for isotropic antenna (G = 1)

How to Increase Gain?

Focus the energy: lenses, mirrors, phasing

L1-5


2]
ANTENNA EFFECTIVE AREA Ae(θ,φ)[m
θφ

Power Received Prec from a particular direction
2
2
Prec = A e m  Pr  W m 





by definition of A e )
 (



Say Go = 10

Antenna Effective Area and Gain
A e ( θ, φ ) = G ( θ, φ ) λ

2

4π

Antenna Tower

Go

(to be proved later)

Cellular Phone Base-Station – Received Power

cellular-phone
base station

Given:
PR = 1 Watt, G = 1 for an isotropic antenna (is it isotropic?)

Pr = 1/4πr2 = 8 × 10-14 [W/m2] at r = 1000 km (or 40-dB margin for r = 10 km)

Prec = AePr (Ae depends on the base-station Gbs and λ)

λ = c/f = 3 × 108 [m/s]/900 MHz = 33.3 cm
Ae(base station) = Gbsλ2/4π = 10 × 0.332/(4 × 3.14) = 0.088 m2
Prec = AePr = 0.088 × 8 × 10-14 = 7.1 × 10-15 [W]
Data Rate [bps] = Prec[J/s]/Eb[J/b] = 7.1 × 10-15/(4 × 10-20) = 176 kbps
Wishful thinking! Data rate per line limited by bandwidth and frequency reuse
L1-6


CIRCUIT PROPERTIES OF ANTENNAS

Equivalent circuit of antenna

Radiation Resistance Rr
PR = i Rr
Rr = PR

Reactance

i(t)

2

jX

+

Rr

v(t)

i2

-

- VTh +

Open-Circuit Voltage (Thevenin voltage)
Induced by incoming waves
Maximum power extractable
from the antenna:

Prec = ( VTh (t) 2 )

2

Reactive elements are tuned out
Rr

Rr

Rr

- VTh +

L1-7


WHAT DO WE NOT YET KNOW?

° What is an electromagnetic wave?
° How does it propagate through air and space,
around buildings, around the earth?
° How do we launch and receive them?
° How do we engineer wireless communications
systems using waves? Examples.

L1-8