Lower bands not only exhibit less radiation power, but require bigger horn antennas that complicate the optical and mechanical parts of the unit. On the other hand, microwave components for the D band could make the unit pricy and uncompetitive. So that’s why the choice for the BIS_WDS is around the E and W bands.

The system:

The system is simple; the devil is in the details. Radiation comes into the hole in the left, is reflected by a mirror into a PVC lens that focus it into the radiometer. The mirror angle oscillates driven by a coil, allowing the radiometer to scan the scene in front of the system up to 15 times a second. The radiometer consists in 32 small horn antennas with LNA (Low Noise Amplifiers), these are misnamed as Pixels. A video signal is built by sequencing the reading of the 32 Pixels at 34 positions of the mirror, which allows creating a 34 by 32 pixel image.

My client company, ATG (Advanced Technical Group) was in charge of the Radiometer.  Given the Pixels, the radiometer subsystem had the task of polarizing them, keeping their temperature low and constant, do the analog to digital conversion, apply a digital filter, create the video signal and deliver it through a TCP/IP network… Lots of physics here! Let’s see some of it.

The Pixel

The Pixel consists in a W band horn antenna, a five stage low noise amplifier (LNA) and a detector. The LNA uses a device called InP HEMT’s, this meaning Indium Phosphide High Electron Mobility Transistor. The physics of this device is similar to that of a field effect transistor (FET) only that instead of a silicon PN junction, there is a Schottky junction over a 3-5 semiconductor that shows very high electron mobility. Also, there’s this thing about the channel being kind of small… 2000 Armstrong!

The channel being so small makes a lot of difference.  Power is dissipated in such a small volume that the smallest change in the quiescent point may bring a huge change in local temperature. The static I-V curves of an HEMT device show negative slopes in the saturation region, this happens because electron mobility decreases with temperature, as the drain voltage increases and channel temperatures goes up, the electron mobility comes down.  (More on this http://includesoft.com/DSP/discussion_on_bias_voltages_accu.htm )

There’s another negative thing about temperature, it increases the amplifier noise figure, so there’s a compromise between gain and noise, the operating current has to be the one that renders the best signal to noise ratio. This requires some lab work beyond C++ and circuit design.

A change in gain will produce the same change in the output level as a change in temperature of the target, so the gain must be kept constant. Since the gain depends on the quiescent point, then this should be kept constant, right? The question is how constant it needs to be, how much technology you need to put into this problem? This is a nice physics problem too.

The Pixel has another interesting element besides the HEMT’s, the detector.  The whole point of amplifying is bringing the microwave to a “detectable” level. A detector is a nonlinear network that renders a “DC” component in response to microwave input power. At low frequencies, anything can be nonlinear, but at microwave frequencies, most nonlinear behaviors disappear. For instance, a PN junction, which is an almost a perfect rectifier at low frequencies, at high frequencies is just a resistor; the injected carriers have no time to recombine and come right back when polarity reverses too soon.  The kind of diode used for detecting microwaves is called a “reverse diode”. This name is because it conducts with the reverse polarity thanks to the tunnel effect. When polarized directly, tunnel effect disappears. Tunneling is a quantum effect; electrons bound in momentum by the semiconductor energy bands show a Heisenberg uncertainty in their position.  When a PN junction becomes too narrow, electrons near the junction, have a substantial probability of being on the other side of the junctions energy barrier; this explains the tunneling current. This quantum effect don’t even have a known response time, limits to its frequency bandwidth comes down to how fast can the junction be driven.

Cooling the Pixels

 Even when having a perfectly constant quiescent point, if the external temperature changes the channel temperature will follow, so some means of temperature control has to be implemented. A quiescent temperature must be chosen and then it must be kept constant for the specified range of ambient temperatures that the BIS_WDS will be required to operate.

The simplest and cheapest way of accomplishing temperature stabilization is by heating.  If ambient temperature cools, the current to the heater is increased, if it warms, then current to the heater is reduced keeping the temperature of the controlled space constant. But noise power grows with temperature; heating the Pixels is not an acceptable solution here, so then it must be cooling.

Heating devices can easily be made small, but common coolers… Fortunately there are these devices called TEC’s (ThermoElectric Coolers) that use Peltier effect for pumping heat. These TEC’s are reversible heat engines; if you drive current through them, they will pump heat, but if you heat the hot side keeping the other cool, then it will generate electric power.

The application of these TEC’s to cooling poses two very interesting physics problems. One is the heat flow in a thermal system involving heat pipes for conveying the heat out of the box. These heat pipes are kind of “air conditioner machines” with no moving parts. The working fluid evaporates at the hot end and diffuses to the cold where vapors disappear as they condense; capillarity of a wick then brings this liquid back to the hot end again.

This whole heat transfer problem is also a nice example of a physics analogy, since it can be tackled using a lumped heat circuit approach.

The other part of the problem is how to stabilize the temperature. The technique here is the PID (Proportional, Integral Differential) control. Its Implementation involves some C++; it is one of the tasks of the DSP (Digital Signal Processor) in the system. A temperature sensor is attached to the Pixels; temperature is sampled every second; the difference of the temperature reading to the temperature wanted is called error signal. A proportional control would be one in which the TEC current is made Proportional to the error signal in such a way that the TEC current is increased when warm or decreased if overcooled. The problem with a Proportional control is that you need an error to sustain a current. To avoid this you can add to the current a contribution that is proportional to the sum of the error signal, this way as long as there’s an error signal the total current will increase until there’s no error signal. That would be a Proportional Integral control. But there’s a problem with this one too… it is not stable; it will oscillate around the target temperature. To damp these oscillations, you need a contribution to the TEC current that is proportional to the change of the error signal; that would be the Derivative part of the PID control. Even with these three contributions, you may still get oscillations; you may also be over damping, making it a lazy control to external changes; or under damped, which would make it slow to settle into the right temperature. The contributions must be balanced as near as possible to the critical damping, but for this you need to have a good initial estimate and then plan your experiments well or you may be guessing for months. (The whole story on this http://includesoft.com/DSP/a_pid_to_control_temperature.htm )

And there’s more…

The detected signal must be amplified, converted and digitally filtered. For amplification, an operational amplifier must be chosen among the hundreds that are available in the market, what specs are more important?  The low noise or low offset drift with temperature? For answering that, the spectrum of the signal must be figured out. How fast the signal must be sampled? What kind of digital filter would be the best?  Should we use a Finite Impulse Response (FIR) digital filter or an Infinite Impulse Response (IIR)? That means, plenty opportunities for using a physics background.

Some articles on the above :

http://includesoft.com/DSP/pink_spectrum.htm

http://includesoft.com/DSP/a_test_signal_discussion.htm

http://includesoft.com/DSP/delay_and_the_averaging.htm

http://includesoft.com/DSP/video_amplifier_for_the_radiomet.htm

The TCAS or Traffic Collision Avoidance System

A traffic collision avoidance system is a piece of equipment that you can find today in every commercial aircraft designed to reduce the chances of mid-air collisions. It was the Aeroméxico Flight 498 in 1986 collision that finally spurred the US Congress and other regulatory bodies into action and led to mandatory collision avoidance equipment.

The idea is simple enough; TCAS detects any nearing aircraft and issues a warning to the pilot. When two nearing aircraft are TCAS equipped, both TCAS talk to each other for coordinating theirs maneuvers. This is, one pilot is advised to descend while the other to climb.  The actual solution is not that simple as its principle.

I bet that when I first mentioned aircraft detection you immediately thought RADAR… I did. Yet RADAR is not it. Radar  is based on sending a strong RF beam and detecting the faint signal that bounces back from an intruder plane. For the kind of range a TCAS requires, Radar’s are bulky, pricy and require lots of power, totally unsuitable for an aircraft. Even for ground stations, most of the air traffic surveillance since the 50’s is based on much simple and smaller beacon radars that rely on all aircraft having a transponder.

The transponder has a sensitive receiver to detect even faint interrogation signals from beacon radars and transmits back a strong reply with the added bonus of altitude and identity information allowing full location and ranging. This scheme reduces the required power, bulkiness and price in orders of magnitude.

TCAS will be interrogating transponders, so it doesn’t need parabolic rotating antennas to pick up their replies; stronger signals allow for compact solutions with no moving parts. To the right, an entire TCAS from Honeywell showing the top and bottom antennas, the control unit and the panel display.

Ready for some physics? ...The TCAS Antenna

A rotating parabolic antenna being directional is straight forward, but one with no moving parts is not. Interrogations may be radiated in an omnidirectional manner as long as the direction from which a reply is coming from can be determined, that would be the intruder aircraft’s bearing angle. Quad parallel ¼ l rod antennas systems are the type used for this job (Figure 1). The carrier frequency used for the reply signals is of 1090MHz, so ¼ l is only 2.7”. Being the rod spacing about the size of the rods, the whole antenna array is about the size of a fist. Bearing detection comes in two flavors: amplitude and phase.

 Bearing Determination by Phase

The physics behind bearing detection by phase is depicted in the figure bellow. B being the intruder’s bearing and F_nm , the phases between elements E_n and E_m.

A little more physics… The phases in the above equations would be the ones that would be measured in opened elements, or in other words, in the unrealistic absence of currents. Yet, some energy needs to be absorbed from the incident wave to feed the receiver input circuits, so there will definitely be current in every element. These currents will induce voltages in the neighboring elements affecting the phases to be measured. Fortunately, symmetry forces any reactive phase shift in F₄₃ to be the same as in F₁₂ and also forces shifts in F₂₃ to be the same as in F₁₄, So, as for canceling out the mentioned reactive effects of a real antenna, the sum of these phase shifts is introduced in the above expression for the bearing.

B = 45 – atan2(F₁₂ + F₄₃ , F₁₄  + F₂₃)

It may be shocking that the expression for the bearing B is not dependent on the actual size of the antenna, yet it is not that just any size would the same; small antennas render smaller phase shifts for the same bearings. In other words, smaller antennas are less sensitive to intruder bearings changes than bigger ones.

Bearing Determination by Amplitude

A perfectly loaded dipole absorbs power from an incident electro-magnetic wave, leaving a shadow behind it.  Though this shadowing effect practically disappears due to diffraction after a few wave lengths, a dipole within a shadow will be absorbing less power from the wave. The amplitudes of the received signals in quad dipole antenna will then depend on the wave angle of incidence, since the dipoles in the back will be shadowed more or less depending on how behind they are to the front ones. TCAS amplitude systems take advantage of this effect allowing their bearing determinations to challenge in accuracy those of phase systems. (More at http://includesoft.com/DSP/The_quad_antenna.htm )

There’s a lot more physics to the TCAS: signal spectrum; information compression; global positioning; noise; thermal gradient; among other many. Yet, I was not involved with TCAS design or its development in any way, then… what’s my relation to TCAS? The main product line of ATG (Advance Technical Group), my client company since 2005, is equipment for testing that TCAS and transponders comply with the standard specifications.

TCAS Testing

Many of the tests consist in standard electronic measurements like RF pulse power, shape, carrier frequency etc., yet, the really tough ones are the behavioral tests or is how is the TCAS responding in air traffic scenarios. This requires that the test equipment be connected to the TCAS antenna and generate the same replies signals as real aircraft intruders would be doing. This is not just generating four sets of reply RF pulses (one for each antenna element), but also that their time positions be consistent with the simulated intruders distance down to +/- 25ft in 180 miles and that the relative phases (or amplitudes) be consistent with its bearing angle down to +/- 2°. For this kind of accuracy in 180 miles, not only the roundness of the Earth must be considered, but also that it is not a perfect sphere but an ellipsoid, so soon enough I was dealing with coordinate transformations from geodetic to ECEF (Earth Centered Earth Fixed). These calculation where to be performed, not by an “Intel Inside” computer, but by a way less powerful Texas Instrument DSP (Digital Signal Processor) chip, where floating point operations were limited to single precision. For those interested in more detail, I wrote a couple of internal reports on these issues: http://includesoft.com/DSP/ecef_calculation_for_range_and_b.htm and  http://includesoft.com/DSP/ErrorAnalysis.htm .

The task further complicates with that is not just one intruder, but up to 432 are required and of those, the last 32 are dynamic intruders, meaning that they must move according to a flight plan, which must include realistic turns. That brings some plane dynamics into the game as well as 2D kinematics.  (You may read all about is at http://includesoft.com/DSP/realistic_trajectories.htm )

But the fun is not over, the system must also simulate the motion of the own aircraft; meaning the one the TCAS under test is supposed to be on. So the scenario to simulate is the one that the TCAS under test should be “seeing”. If the own aircraft is flying, say North and an intruder at 2 o’clock is flying West, then TCAS must see this intruder as moving SW. Also, if the “own” is turning, then the bearing angle of all intruders must change accordingly. When all above is accomplished, then the “own” coordinates could be fed from a flight simulator, so you could have now a flight simulator with a TCAS!

The above development project combines the physics background with the C/C++ skills, yet sometimes you may have the chance of even using the physics background by itself…

Squitter-Interrogation Collision Probability

When the use of TCAS started expanding, the 1030/1090 MHz spectrum rapidly became polluted around busy airports. Before, it was just ground stations interrogating, but after TCAS, every airplane was interrogating as well. Many techniques were developed to reduce the amount of replies. Side lobe suppression and whisper/shout use the principle of interrogating with two pulses at different power levels; a weak pulse (the whisper) and a stronger one (the shout). If the receiver picks up a second pulse after the first, the transponder won’t reply and of course, if it can’t receive any of them, it won’t respond either, so only those far enough not to hear the whisper and but near enough to still pick up the shout, will reply.

With the growing air traffic, these solutions became insufficient, so the squitter was invented. The idea is that a plane will fly broadcasting its unique identification (called Mode S address) every second; this unsolicited signal is called a “squitter”. When a TCAS or ground station picks up a squitter, it interrogates with this address and only the aircraft with that Mode S address will reply. But this technique has developed even more with the extended squitters, these will broadcast not only their Mode S address but also their GPS positions, so every TCAS out there may track this aircraft without even having to interrogate; that’s called passive tracking.

Finally we are ready for the story. This TCAS manufacturer that was using the tester from my client company, complained that the simulated intruders were not responding 100% to the interrogations of their TCAS under test. This particular test consisted in a long 12 hour simulated scenario where the TCAS unit was forced to interrogate 10 times a second; every 5 seconds a computer would be sampling the interrogation- reply pairs. If an interrogation was detected but not its replay, the test would fail. Roughly, 1 every 4 or 5 of those tests failed and the manufacturer claimed it was not their TCAS, but the test equipment that was not responding to all the interrogations. One possible explanation in which neither would be at fault was that the failure could be due to interrogation-squitter collisions. In other words, if a simulated intruder happened to be interrogated by the unit under test while it was transmitting a squitter, it will certainly miss it. But the complaining part was not buying this; no way can such an unlikely event cause so many failures!

Going for the physics background “bag of tricks”, I recalled from statistics, the Poison distribution.

The squitter, called DF-11, has a 60 ms duration and happens once a second. Since the interrogation, called UF-0, has 18.5 ms, the chance of any part of an interrogation happening while squittering is:

1)         p = (60+2x18.5ms) / 10⁶ ms = 0.000097

There is a 12 hour test that fails when a collision is detected.  For this test, 10 interrogations are made each second.  Events with such a low probability as Squitter-Interrogation collisions follow the Poison probability distribution .

2)         p(n/N) = (Np)ⁿ e^-Np/n!

Where N is the number of interrogations in 12 hours (432000) and n is the number of collisions. P(n/N) is the probability of  having precisely n collisions in N tries (interrogations).

Equation 2 is the limit of the binomial distribution for N -> ∞, while the product Np stays finite… or in practical terms Np << N or  p << 1 (rare events).  In our case this condition is very much true:

3)         Np = 432000*0.000097 = 41.904

So, our Poison distribution will be:

4)         p(n) = (51.84)ⁿ * 3.06x10^-23 /n!

Yet, not even all interrogations are observed, of the 432000 interrogations, only 2356 will be sampled by the computer (1 sample every 5 seconds), the probability of not observing a single collision in any of those samples, if n of them will happen is:

5)         Qo(n) = (1-n/432000)²³⁵⁶

Then the probability for observing one or more would be:

6)         Po(n) = 1 – Qo(n)

The probability for observing a collision when precisely n of them happen, will be the probability for observing at least one when precisely n collisions happen, that would be  Po, multiplied by the probability P(n) of having exactly that many collisions.  The probability of observing a collision, disregarding how many actually happened, would be the sum of the probabilities for each n form 1 to (in principle) 432000:

6)         P = S₁ Po(n) x p(n) = 0.2038

The chance of getting a collision failure is ~20% in the mentioned 12 hour test and that is 1 in 4, right? (That felt so good!)

There’s another nice example of a pure physics tasks. There was this project of an interrogator for testing transponders in actual flight. This involved power transmissions that raised safety concerns for those who would operate the instrument and even for unaware bystanders. So I got the task of calculating the radiation intensity in the vicinity of the interrogator and its compliance to radiation limits safety standards. You can read the resulting report at: http://includesoft.com/DSP/compliance_to_radiation_limits.htm .

A lot of the physics background use can also be found in the following reports:

http://includesoft.com/DSP/compensation_of_the_tcas_correct.htm

http://includesoft.com/DSP/ErrorAnalysis.htm

http://includesoft.com/DSP/ecef_calculation_for_range_and_b.htm