Focus in chaos
In open space, waves can be focused, for example by a parabola. The
2D numerical simulation below shows an omnidirectional emitter on
the right and a wire-frame parabola on the left. The parabola
focuses the neat wave emitted by the emitter. This produces the
bright magenta spot in front of it. (The four colors green, magenta,
yellow and cyan code the wave phase, the brightness codes the wave
The purpose is to put a receiving antenna at that focus point (the
bright magenta spot). That way, being located in a zone where the
wave is strong, the receiving antenna will have a strong signal. In
the picture below, the antenna in the magenta spot gets a much
stronger signal than the other one, despite the fact that they are
located at the same distance from the emitter:
Below is a calculation of the wave echoing in a virtual room with
metallic pillars. In-between he pillars, there is no more neat
wavefront that can be focused by a parabolic reflector:
This is a problem, for example for devices like WiFi receivers or
cell phones, that are typically used inside buildings or amongst
dense city structures. They cannot focus the radio waves using a
But there is a solution, using "phased elements" like in high-tech
In order to increase the number of persons that will be able to
follow, here is an analogy, to make the phase thing more palpable:
It is being told that in 212 BC,
Archimedes helped Syracuse defeat the Roman navy. He made the
soldiers that defended Syracuse use polished bronze shields to
focus the Sun towards the Roman ships. The shields acted like a
solar furnace and put the ships on fire one by one. Many
historians now rather the believe that the bronze mirrors were
only used to blind the sailors and that the ships were put on fire
by conventional means, like incendiary bombs thrown by catapults.
But let's stick to the idea that the ships were indeed put on fire
by the focused sunlight and that each soldier along the shore
turned his mirror accurately to direct the sun rays towards the
same spot on a ship (a magenta spot...)
Now suppose that the Romans had arrived on a cloudy day and there
was no visible sun... Archimedes still could have disturbed them
using soldiers and their shields placed along the shore. He could
have asked each soldier to push his shield violently into the
water to emit a shockwave on the surface of the sea. One
shockwave, sent by one soldier, would have been inoffensive when
it reached a ship a hundred meters away. But what if a hundred
soldiers pushed their shields in the water... All the small
shockwaves arriving altogether on one ship would sum up and form a
little tsunami. That would have made a real strong splash on the
side of the ship and if at that same time the general leading the
invasion was dining aboard the ship and a few droplets fell on his
table, that would have ruined his fighting spirit, lead him to
nervous breakdown and make the conquest of Syracuse abort.
But... in order for this psychological warfare to operate
properly, the shockwaves need to arrive on the target at the same
time; in order to unite. There is a problem here, because the
soldiers along the shore are not all at the same distance from the
ship. If they all plunge their shields in the water at the same
time, say when a drum is hit, the shockwaves will start at the
same time but they will arrive on the ship at different times,
hence there will be no effect.
Each soldier must be told to wait a given time after the drum hit,
before plunging his shield in the water. The closer a soldier is
to the ship, the longer he has to wait. Let's call this delay a
To target a different enemy ship, situated at a different
position, the time shifts will be different.
Now let's suppose that Archimedes asked the soldiers to do
something different. Rather than plunge their shields in the water
one sudden time, they have to oscillate the shields back and forth
in the water at a steady frequency. Push the shield, then pull it
back, then push it again, then pull it back again, push, pull,
push-pull... This creates a continuous wave on the water surface.
Each push and pull (a "period") has to span one second. A drummer
is asked to hit his drum once a second, so that the soldiers can
That won't do... because the waves generated by the soldiers do no
arrive on the target ship "in phase". When the wave generated by
one soldier pushes water towards the flank of the ship, the wave
generated by another soldier pulls the water away from the ship.
The two waves cancel each other out... On the average most waves
will cancel each other out and the enemy ship will be only
For this to work, each soldier needs to adapt his "phase", in such
a way that when all the waves arrive on the target, they are "in
phase" (all pulling or all pushing). To achieve this, Archimedes
can give one of these two instructions to each soldier:
- "When you hear the drum hit, you must be pushing your shield,
you must be pulling, you must in-between pulling and pushing..."
- "You step a little further into the sea, you step a little
So, each soldier will have the
appropriate "phase shift" to have the waves arrive "in phase" on
This is what radars that use phased elements do, in order to have
their radar beam directed towards a given target.
It works in the opposite direction too. Suppose that there is a
strong mist over the sea. The enemy fleet cannot be seen but
Archimeds wants to know where an enemy ship is situated anyway.
Suppose one persons aboard the ship falls into the water, which
triggers a shockwave that will ultimately reach the shore. When a
soldier along the shore sees the shockwave, he rises his hand.
Archimedes sees when each soldier rises his hand and immediately
feels where the shockwave was generated, hence where the enemy
ship is. And if no Roman falls into the water, Archimedes still
can generate a strong shockwave from the shore. A part of it will
bounce back on the ship and the soldiers can raise their hands
when the reflection arrives back. The time shift for each hand is
the clue to the position of the ship.
Radars rather use a continuous wave and rely on the phase shift...
And by the way, the wave that bounces back and arrives on the
shore, is ways to weak for a soldier to notice it, because the sea
is naturally undulating with waves. But modern electronics manage
to detect the weak signal anyway, "by summing up the observations
of all soldiers and over some timespan".
Now back to our pillars. A set of antennas can be placed somewhere
They are wired towards a central device that makes the sum of their
signals, in order to get one single and stronger signal:
The problem is that each antenna receives the wave with a different
phase. For example, the lowest antenna on the image and the
one left of it, are situated in a zone with the same wave phase
(cyan color...) Summing up their signals will yield a stronger
signal. But other antennas are in zones with different phases, hence
simply summing up all their signals will yield a poor result. A
phase shift element has to be inserted for each antenna, in order to
have the signals arrive with the same phase in the summing device:
Each phase shift element has to be tuned. This can be done by
software. One antenna can be chosen as reference, the other ones are
inhibited, then each one in turn is activated and its shift element
is tuned to get an optimal signal.
The antennas that yield a low signal can then be kept inhibited to
decrease the noise.
Practically, this would resemble those WiFi routers that have two
antennas at the back. But there would be much more than two
antennas. Maybe ten or even hundred. This will make the router have
some volume... It would not be practical on a cell phone... But it
will still be practical in many cases and the volume will decrease
over a few decades, when shorter wavelengths are being used.
Phased elements used in radars are top technology and can be very
expensive. But for the application discussed here, rudimentary phase
shifters are sufficient and their cost is negligible. It's like the
pistons of a trumpet, that change the pitch of the instrument by
changing the length of the resonating tube. Two "pistons" would be
enough to appropriately change the phase of a signal. Each "piston"
would be a few SMD components...
One advantage of parabolic antennas is that the same frequency can
be used by different pairs of communicating antennas in the same
array. Each antenna only "sees" the one it has to and will not
receive the signal from another emitter. Or to the least, the signal
from the intended correspondent will be much stronger. This can also
be achieved between the pillars. The animation below shows two wave
patterns. One is created by an emitter in a given place and the
other one by an emitter slightly aside of it. If the set of phase
shifters of a receiver is tuned for one antenna, it will not receive
the other antenna very well...
Reciprocally, any change in the surrounding, even a person moving,
can modify the wave pattern and make the phased elements need to
readjust. This implies that the choice for the positions of the
emitters and the receivers should take into account the probability
of being disturbed by movements.
The trick works both ways. An emitter too, can use a set of phased
elements, in order to create different wave patterns and privilege
one receiver or another between the pillars. Even if the receiver
has a single antenna, the emitter can tune its phased elements so
that the receiver is in a zone where the wave is strong.
If the elements of the emitter are close enough to each other, then
it can achieve some directivity, which in many cases allows to
increase the power on the receiver, even if the receiver is not
directly seen by the emitter.
If the array with the pillars was completely surrounded by a dense
mesh of elements, then it would be possible to create a single zone
where the wave is strong; where the receiver is situated. This would
be optimal... but if one is ready to place that much elements, then
it would probably be more useful to simply place one independent
element on each pillar... And if elements are situated everywhere
and are always in sight, then better use harmless infrared or
visible light modulated at high frequency, rather than radio
waves... (A shell of elements can have other applications anyway,
like in tomography, 3D manufacturing, memories...)
Overall, this should allow to create less electromagnetic pollution
for a same volume of data transfers.
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provided by Globe
Eric Brasseur - May 8 2012