Basic Wireless Communication for Microcontrollers

Chapter 1 - Electricity and Magnetism

Wave Propagation

     Now that you have seen a brief introduction to the postulates of E&M, we can show how they allow propagating EM waves to exist, which is our primary reason for discussing E&M in the first place. Some phenomena mentioned here (such as reflection, diffraction and attenuation) will be explained further in the section "Boundary Conditions".

What's a Wave?

     In everyday life, a wave is a disturbance in some material or medium, like ripples in a pond which travel across the surface. The postulates allow certain disturbances to occur in the E and B fields. If you consider E and B fields to be a medium, then it makes sense to call propagating disturbances in it waves.
     The disturbances or waves are caused by the symmetrical interaction of the E field with B. It is symmetrical in the sense that an oscillating E field gives rise to an oscillating B field and vice versa. This interaction is expressed by the last two postulates. Since there are no free electric charges in air or in space, the current term in the curl B postulate (number 6) is zero, so the equations become: curl B=Uo*Epsilon_o*dE/dt and curl E=-dB/dt. The curl of one field depends solely on the time derivative of the other.
     Another, simpler, way of stating this is that the spatial distribution of the B field depends on the time rate of change of the E field, and the spatial distribution of the E field depends on the time rate of change of the B field.
     This means that if you have an oscillating E field in one location, it gives rise to an oscillating B field in the surrounding area. This oscillating B field then, in turn, gives rise to an oscillating E field in an even greater surrounding area and the exchange of energy from E field to B field moves outward in space as time progresses. A diagram of a typical EM wave far away from the trasmitting antenna is shown in figure 1. Note how the E and B fields change in both time and space in a similar way.

Figure 1 - Part A shows the electric (E) and magnetic (B) field vectors, at one instant in time, in a section of space where a linearly-polarized plane EM wave is traveling. The arrow along the main axis shows the direction of travel. Part B shows the same section of space a quarter of a cycle later, and you can see that the wave has shifted forward by 1/4 cycle. These "snapshot" views of instants in time show a sinusoidal variation of the vector magnitudes over distance. Since the wave is also traveling in space as time progresses, a stationary observer would also note a sinusoidal oscillation in time at any given point.


     Because of their interdependence, the E field and B field are simply proportional to each other in free space (such as an air-filled open area). Therefore, the EM wave amplitude can be specified by either the E field or B field strength, it is not necessary to know both. The strength of the B field is simply the strength of the E field divided by the impedance of free space (Eta_o).
     The wave moves out from the transmitting antenna at the speed of light (300 million meters per second or 186,000 miles per second). Therefore, after a very short delay time proportional to the distance between you and the transmitter, the wave arrives at your location. At this point, as well as throughout all the space in which it travels, it consists of weak electric and magnetic fields.
     Because the propagating wave is, mathematically, a solution to the differential equations of postulates 6 and 7, the postulates totally determine the behavior of the wave. The propagation speed of phase velocity, Vphi, is dependent only on the constants Uo and Epsilon_o and is given by 1/sqrt(Epsilon_o*Uo) in meters per second (go ahead, try calculating it from the values for Epsilon_o and Uo given earlier!).
     Far away from the source of the wave, an in the absence of any obstructions, the E and B fields will be roughly uniform over the plane which is perpendicular to the direction of propagation. In other words, if you are standing at a certain position and you are receiving an EM wave of a given strength, and then you move in any direction which is perpendicular to the direction of wave travel, you will still see the same wave with the same amplitude. A wave with this property is called a plane wave. Plane waves are a convenient mathematical tool since they

Energy in EM Waves

     Back in the section on DC Circuits, we discussed how E and B fields have energy associated with them. Because EM waves transport E and B fields from one location to another, they also transport energy. The energy is proportional to the magnitude of E or the magnitude of B squared, similar to how electrical energy in a circuit is proportional to V or I squared.

Polarization

     When an EM wave is propagating in free space, the E and B field vectors are perpendicular to each other, and both are perpendicular to the direction of propagation. Polarization referrs to the direction of the E field vectors in the wave. Depending on the type of transmitting antenna, the wave can have linear polarization, circular polarization, or in the most general case, elliptical polarization (which is a combination of linear and circular).
     In linear polarization, the E field always points along the same line. If this line is parallel to the earth's surface, the wave is said to have horizontal polarization. If it is perpendicular, then vertical polarization. It can also be anywhere inbetween, but antennas are usually oriented to produce one or the other.
     For circular polarization, the E field direction roatates around in a circle, once per cycle, as the wave propagates forward. If we could see the "tip" of the E field vector, it would trace out a corkscrew pattern as the wave moves forward.

Line of Sight

     If no obstructions or other matter is encountered, EM waves travel in straight lines from the source. This type of radio wave propagation is called line of sight and is the only type of propagation in free space. Far away from the source of the waves, the waves always travel in divergent beams. An isotropic source (emitting equally in all directions) would create a beam whose front was like a spherical shell, with an area expanding with the square of the radius from the source. Anisotropic sources do not cover the entire spherical shell area, but the area of their wavefronts still expands with the square of the radius.
     Since EM waves carry energy, and energy must be conserved, this must mean that the energy per area must go down with the square of distance, at least when far away from the transmitting antenna, where the characteristcs of the wave are no longer dependent on the geometry of the antenna. So, when propagating in free space, no energy is lost in an EM wave, but the energy is getting more and more spread out as the wave travels farther from the antenna. It is also useful to note that the fact that the power per area is proportional to 1/r^2 means that the E or B field strength is proportional to simply 1/r.
     In line of sight propatation between points on the earth's surface, the primary limiting factor on distance, after mountains and buildings, is the horizon. Because the curvature of the earth is relatively gentle, it is possible to communicate much greater distances by placing the antenna at a higher altitude. This is why tall towers are often used for VHF, UHF, or microwave communications.

Attenunation in the Atmosphere

     Within earth's atmosphere, the approximation of line of sight propagation still holds fairly closely (variations in air pressure with altitude and temperature cause slight bending of the path of EM waves). However, the atmosphere does abosorb some energy from the EM wave. At frequencies below a few GHz this effect is negligible. However, at frequencies higer than 40GHz, oxygen in the air begins to significantly absorb RF energy. Even at lower microwave frequencies, the attenuation in rain or fog can be significant.

Reflection and Multipath

     As we will discuss in the section on boundary conditions, most objects will reflect EM waves to some degree. Mountains, the ground, aircraft, and buildings are but a few examples. This can play a major role in radio wave propagation near the earth's surface, either enabling communication when it wouldn't have otherwise been possible (such as reflecting a signal down into a valley) or preventing communication (such as when a mountain blocks the signal path).
     In certain cases, such as when in a city, a receiver will be exposed to a huge number of reflections of the signal. These reflections add together to create a signal either much stronger or much weaker than the original (it will be much weaker if many of the reflections are out of phase with each other, due to differing path lengths). This can cause signal strength to jump all over the place as a receiving antenna is moved down a street, such as when a person is talking on a cell phone. This effect is known as multipath and is one of the most serious problems facing wireless communications in cities, requiring many more transmitting sites than would otherwise be needed.

Skip and the Ionosphere

     At VHF and higher frequencies, line of sight propagation, along with reflection, usually dominates. At frequencies below 30 MHz (the HF region), a series of layers of charged particles,called the Ionosphere, from 60 to 120 miles above the earth, can reflect EM waves. During daylight hours, the lowest layer (D layer) of the ionosphere absorbs EM waves in the lower HF spectrum (below 10 MHz).
     If a wave is launched at HF frequencies toward the ionosphere, and it passes through the D layer and is reflected by the upper layers, it can come back down to earth far from where it originated. The ground can even reflect it back up and the process can happen several times in a row, even bringing the wave all the way around the earth with relatively little attenuation. This effect can be used for effective world-wide communications, but its usefulness is reduced somewhat because the ionosphere is affected by solar conditions and world-wide communications may be possible on some days and not on others.

Ground Wave

     We said earlier that, in line of sight propagation, the horizon is the primary limiting mechanism on range. When the wavelength of the EM wave becomes longer than a certain fraction of the earth's radius ( few hundredths of a percent of the radius) a modified form of line of sight can occur, in which a portion of the EM wave is bent around the horizon. This is due to diffraction, which we will discuss in a moment under the "Boundary Conditions" section.
     Because in this type of propagation the EM wave appears to "hug" the ground rather than just go off straight into space, it is called ground wave propagation. Generally, ground wave is more practical as you go lower in frequency, and it is only practical below 10MHz. It usually allows communication out to a few hundred miles.

Propagation Potpourri

     There are many other types of phenomena which allow communication farther than would be expected for line of sight. To list a few: sporadic E(also called meteor,in cases where meteors cause it), Auroral, transequatorial, knife-edge refraction, and tropospheric ducting. Only one of these is even of remote interest to microcontroller communication, and that's knife-edge refraction.
     Knife-edge refraction occurs when buildings or mountains get in the way of EM waves. In a way similar to ground wave, buildings or mountains can cause an EM wave to be bent as it passes over the top. The main difference is that, because a building or mountain is a much more abrupt feature than the earth's curvature, it can work at much shorter wavelengths (higher frequencies) than ground wave. In fact, knife-edge refraction can be significant even at VHF frequencies.

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