Constructive and Destructive Interference Beam Forming and Beam
Steering
Slide 2
If vector A and vector B are pointing in the same direction the
magnitude of vector A and the magnitude of vector B sum to create a
greater magnitude vector C travelling in the same direction. Vector
Math If vector A and vector B are pointing in the opposite
direction the magnitude of vector A and the magnitude of vector B
cancel to create no vector C.
Slide 3
In the real world vectors do not always point in the same
direction. To find the magnitude in a certain direction vectors can
be broken down into x and y components and then summed as in the
previous example. Vector Math
Slide 4
Electromagnetic Waves
Slide 5
Electromagnetic waves are transverse waves The magnetic (H)
field vector is perpendicular to the direction of motion. The
electric (E) field vector is perpendicular to the direction of
motion The magnetic field, electric field and direction of motion
vectors are all 90 degrees apart. A cancelling signal would be
identical to the target electromagnetic wave (type), be 180 degrees
out of phase (both H and E), and be of equal or greater intensity
(ie magnitude, amplitude). The longitudinal motion of the wave is
not important in cancelling the target wave.
Slide 6
Acoustic Waves Acoustic waves are pressure waves, which
consists of a compression phase and a rarefaction phase. A
noise-cancellation speaker emits a sound wave with the same
amplitude but with inverted phase (also known as anti-phase) to the
original sound. The waves combine to cancel each other out. A
noise-cancellation speaker may be co-located with the sound source
to be attenuated. In this case it must have the same audio power
level as the source of the unwanted sound. Alternatively, the
transducer emitting the cancellation signal may be located at the
location where sound attenuation is wanted (e.g. the user's ear).
This requires a much lower power level for cancellation but is
effective only for a single user.
Slide 7
Acoustic Waves
Slide 8
What is a Pressure Wave? Since a sound wave consists of a
repeating pattern of high-pressure and low-pressure regions moving
through a medium, it is sometimes referred to as a pressure wave.
If a detector, whether it is the human ear or a man-made
instrument, were used to detect a sound wave, it would detect
fluctuations in pressure as the sound wave impinges upon the
detecting device. At one instant in time, the detector would detect
a high pressure; this would correspond to the arrival of a
compression at the detector site. At the next instant in time, the
detector might detect normal pressure. And then finally a low
pressure would be detected, corresponding to the arrival of a
rarefaction at the detector site. The fluctuations in pressure as
detected by the detector occur at periodic and regular time
intervals. In fact, a plot of pressure versus time would appear as
a sine curve. The peak points of the sine curve correspond to
compressions; the low points correspond to rarefactions; and the
"zero points" correspond to the pressure that the air would have if
there were no disturbance moving through it. The diagram below
depicts the correspondence between the longitudinal nature of a
sound wave in air and the pressure-time fluctuations that it
creates at a fixed detector location.
Slide 9
Acoustic Waves
Slide 10
Sound Waves and the Eardrum When a pressure wave reaches the
ear, a series of high and low pressure regions impinge upon the
eardrum. The arrival of a compression or high pressure region
pushes the eardrum inward; the arrival of a low pressure regions
serves to pull the eardrum outward. The continuous arrival of high
and low pressure regions sets the eardrum into vibrational
motion.
Slide 11
Electromagnetic Wave Constructive Interference Waves add in
intensity (ie amplitude or magnitude) when their peaks & trough
sync (ie of the same type, frequency and phase)
Slide 12
Example Video of Constructive Interference
Slide 13
Acoustic and electromagnetic waves contain the most energy when
first emitted from the source. While in transit the energy of the
wave decays exponentially as the wave travels. In the figure, the
direction of motion m is North. m=4 m=3 m=2 m=1 Wave Energy
MinMax
Slide 14
The waves from these routers have already travelled a distance
from the source and presently each have magnitude 2. Wave Energy
Example AB
Slide 15
The waves meet at a point in space (a), are of the same type,
frequency and are in phase, therefore where the waves meet, the
energies of the two waves will sum. Wave Energy Example a AB
Slide 16
The resultant wave is a combination of the two waves A and B.
Note the resultant is greater in magnitude than either A or B and
moves along a new Northerly path. Wave Energy Example A C B
Slide 17
A B D F G C=A+B E=C+D 1) The red and green vectors A & B
sum to create the resultant vector C. 2) The burgundy and blue
vectors C & D sum to create the resultant vector E. This is an
example of wave superposition or constructive interference. Each
resultant vector carries more energy than its constituents. 3) The
purple and orange vectors (not shown) F & G sum to create an
equal and opposite vector to E. This is an example of destructive
interference. The two vectors of equal magnitude and in opposite
directions cancel.
Slide 18
Wave Energy Example Beam Forming & Beam Steering When
displayed graphically the energy in transit can be visualized as a
beam of energy steering through free space.
Slide 19
Appendix A - Advantages of Directional Antennas Over
Omnidirectional
Slide 20
Acoustic (sound) and electromagnetic (wireless) waves can be
sent from one location to another using air as a medium. In many
applications its desirable for the emitter to direct the waves.
When waves are directed a gain is realized because the same amount
of energy is routed into a smaller square area intensifying the
emission. An example of this phenomenon would be a laser beam,
ordinary light compressed into a pencil beam. Acoustic and
electromagnetic waves contain the most energy when first emitted
from the source. While in transit the energy of the wave decays
exponentially (for more on this see far field). Waves are
represented as vectors because they have an intensity and a
direction. When illustrating a vector an arrow shows the intensity
(length of the arrow) and the direction. Advantages of Directional
Antennas Over Omnidirectional
Slide 21
Appendix B Other Integrated Wave Energy Technologies
Slide 22
Vehicular Ad-hoc Networking Beam Forming & Beam Steering
When displayed graphically the energy in transit can be visualized
as a beam of energy steering through free space.