Basic Wireless Communication for Microcontrollers

Chapter 1 - Electricity and Magnetism

DC Electric and Magnetic Circuits

Conduction, Current, and Circuits

     When a material such as copper is placed in an electric field, the electrons in the copper are pushed by the field and current flows. If there is a complete circuit so that the electrons don't just bunch up at the ends of the wire, and the E field is maintained, then we get a steady electric current or flow of charge. Because we are dealing with electrons in matter and not just a gas of electrons in a vacuum, they cannot accelerate forever. They accelerate until they bump into surrounding molecules. The net motion is one of a sort of vibration of electrons as they randomly bounce around, but still have a slight net velocity opposite the direction of the applied electric field.(figure 1) The force (and net movement) are opposite the field because electrons are negatively charged. This net speed is very low, often only a fraction of a millimeter per second. For this reason, it is referred to as drift velocity.

Figure 1 - Drift Velocity is the slight net movement of electrons in a conductor under the influence of an E field.

     An Ampere, the usual unit of electric current, represents one Coulomb of charge (6.25 million trillion electrons) passing a point per second. For most materials, the current is given by the equation: I=A*E* , where I is current in amperes, A is the material cross-sectional area in square meters, E is the field intensity in volts/meter, and (Greek letter sigma, "sig-mah") is the conductivity in Siemens/meter, which is the same as 1/(ohms*meters).
     If you take a block of material and provide a uniform electric field within it, you can determine the current flow from the above equation. Notice that the length of the block doesn't enter the equation. If you are used to thinking in terms of voltage rather than electric fields, this probably surprises you. Notice,too, however, that the units on E field strength are volts/meter, which implies that Voltage=E*d, where d is some distance in meters. If you re-express the equation in terms of voltage, you get I=A*(V/d)* , where d is the length of the block. This is probably more famliiar, because resistance is defined as R=d/(A*), and the equation can be written I=V/R, which is Ohm's Law.

Voltage

     Voltage is a measure of energy per coulomb of charge. As the charge(electrons) passes through the material, it keeps transfering energy to the block (warming it) because the electrons are bumping into the molecules. If you have a longer block, the electrons have to pass through a greater length of material, and they will transfer more energy than for a shorter block because there will be more collisions with molecules. This is why it makes sense to define a quantity involving the length, because it represents the energy transfered to the block, or equivalently, the potential energy difference, due to the electric field, between one end of the block and the other.
     This concept that fields are associated with energy (the ability to do work) is an important one. Since an electric or magnetic field can create a force of attraction or repulsion, it is possible to build up potential energy by moving an object which experiences the force against the force direction, similar to lifting a weight against gravity. In addition to this potential energy, it can be shown that all situations in which you create an E or B field involve storing up energy, so any E or B field can itself be considered to have energy associated with it.
     Static electric fields have the property of path invariance. This means that the voltage between any two points will be the same regardless of what path you travel to get from point A to point B. So, if you use a long, winding length of wire instead of a uniform block of material, and you attach the ends to a voltage source, the electric field will adjust itself throughout the surrounding area to produce whatever E field is necessary at each point to support a current equal to I=V/R. This is why you can measure the resistance of a wire without regard to what shape it is bent into, other than its cross-sectional area and length.
     Path invariance allows us to draw schematic diagrams. If the path taken between two points mattered, circuit problems would be much more difficult and the orientation and placement of all the wires in a circuit would have to be specified. This is fundamentally why antennas and high frequency circuits are much harder to work with than DC circuits: the "plumbing analogy" (voltage pushing charge through pipe-like wires which do not interact and whose position doesn't matter) breaks down.
     It is worth bearing in mind that voltage is relative (since it is the potential energy difference between two points) and that two points (or a point and an understood reference point) must always be specified when stating voltages.

Current Flow Speed

     When people say that electricity travels at the speed of light, what they really mean is this: the influence (really an E field) which causes current to flow, travels from one end of the wire to the other at the speed of light. So, the time between when current begins to flow at one end of the wire until it also begins to flow at the other is the length of the wire divided by the speed of light. When a switch is closed at one end, an E field is generated at one end of the circuit and propagates, at the speed of light, toward the other end. As it goes, it starts the process of conduction at each point.
     This turn-on transient (such as when a switch is first closed) is really a complex subject. Not only does it involve the usual AC circuit theory and transmission line theory (which describes how long it takes the E field to propagate down the wire), but for a really complete understanding, one must take into account the amount of time it takes for the electrons to accelerate and settle into the steady bouncing and drifting. This is very fast (femtoseconds) and usually doesn't affect practical circuits because it would correspond to frequencies above visible light.

Variation in Conductivity

     Materials in general have a wide range of conductivity and the molecules in insulators have such a tight hold on their electrons that no current can flow, even in relatively strong E fields. In good and moderately good conductors, the current flow is very nearly linearly proportional to the applied E field. The reasons for the variation in conductivity among materials involves quantum mechanics and cannot be discussed here while keeping this tutorial concise. For more information, please see the bibliography.

Permanent Magnets

     In electromagnets, it is clear that the presence of the magnetic field depends on current flow. Permanent magnets, however, seem to be sources of constant magnetic fields without current flow. There are actually moving charges inside the magnet, though, which produce the magnetic field. Electrons are orbiting atomic nuclei, and electrons are also "spinning". I put spinning in quotes because, while this property of electrons is called "spin", and exhibits some of the properties you would expect from a spinning ball of charge, electrons are thought to be point particles (diameter=0), and the concept of a point spinning seems meaningless, so it is unclear what "spin" really is.
     In ferromagnetic materials such as iron, the cause of the strong magnetic effects we see is electron spin. Ferromagnetic atoms have several electrons which all spin the same way, without being paired with electrons spinning in the other direction to balance them, as they are in non-ferromagnetic materials. In a block of ferromagnetic material, groups of these atoms tend to line up their "unpaired" electron spins. When the groups interact with each other to form larger an larger groups with all the electron spins aligned, it can result in a significant fraction of all the electrons in the block being aligned in this way. The net result is a strong magnetic field which doesn't go away, even when no external field is applied.
     Because magnetic fields produce forces on moving charges, the B field produced by a magnet will interact with the moving charges in a piece of ferromagnetic metal or in another magnet (permanent or due to actual current in a wire) to produce the familiar force of attraction or repulsion.

Magnetic Circuits

     The concept of three linearly related quantities (voltage, current, and resistance) which describe a flowing entity is not unique to electric circuits. Water flow, heat flow, and static magnetic fields can also be described this way. When magnetic fields interact with magnetic materials (like iron or nickel), one can consider the magnetic field vectors to be like a flow of "magnetic current" through the material. An externally applied magnetic field (say, by a bar magnet) causes a magnetic field in the material which changes according to the permeability, cross-sectional area, and length of the material. If we refer to the applied magnetic field as H, and the field which results in the material as B, then they are linearly related by B=µ*H, where µ(Greek letter mu, "moo") is called the permeability. H is treated as if it were voltage, B like current, and µ like conductance or 1/resistance.
     This treatment results from an early theory of magnetism which considered magnetic force to be caused by a flowing "magnetic flux". In that language, magnetic field strength was called "flux density" (measured in webers/meter^2) and an externally applied field (like H above) was called a "magnetic coercive force" and had a separate unit, called the Oerstead. Permeabilty was called "Susceptance",and its reciprocal was "Reluctance", analgous to conductance and resistance. This language is still used today when dealing with situations where the magnetic circuit concept is useful, such as in designing transformers.
     We will touch on the interaction of magnetic fields with matter later in this chapter, but it is interesting to note, at this point, that Ohm's law has been generalized to situations not involving electric current.

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