Basic Wireless Communication for Microcontrollers

Chapter 1 - Electricity and Magnetism

AC E and B Fields

     In the static case, E and B fields are almost independent. The only link between them is that an E field causes charge to move, and that moving charge causes a B field. In the dynamic case E and B fields have the same effects as static fields (changing E fields cause charges to move and changing B fields alter the paths of moving charges),however, in addition, unlike static fields, changing E fields generate B fields and changing B fields give rise to E fields.
     Unfortunately, we cannot get into the reasons behind why E and B fields give rise to one another. Traditionally, this was just taken as an experimentally shown truth and stated as a pair of postulates, which we will give in the next section. During the last century, great strides were made in understanding the relationship between E and B fields (such as the B field being regarded as a consequence of relativity). What is presented here should be adequate for a practical understanding of the relationship, but references are given below for you to continue to explore this fascinating topic should you wish.

Inductance

     The E fields generated by changing B fields do not have the property of path invariance (this doesn't mean that they are a different kind of E field, it just means that the E field vectors from static sources always point toward or away from a source and those generated by changing B fields go around in circles and do not begin or end at a point or line). This means that the placement of wires matters in determining the voltage difference across the wire. In everyday electronics practice, this is just referred to as "stray inductance". In fact, all electromagnetic induction is caused by a varying B field. Wrapping wire around a core in a coil shape is just taking advantage of the voltage created by the E field generated by a changing B field. Electrons which are constrained to move along the circulating E field paths will continually gain or drop in voltage. Since inductance involves inducing voltage in a length of wire, it can be increased by having more turns of wire in the area where there is a strong, circulating E field.

Capacitance

     In the AC case, we can also have current in incomplete circuits. A capacitor, which is a pair of conductors separated by an insulator, allows charge to build up on the conductors when a voltage is applied. In the static case, the E field between the conductors (due to the voltage source) attracts charge to the ends of the conductors, until the E field from the charge just balances that of due to the voltage, and then the current stops. In the AC case, the E field keeps changing and, therefore, the charge on the conductors keeps changing. This results in current flow along the conductors just as if there were a complete circuit. In addition, the changing E field in the capacitor insulator generates a B field equivalent to that which would be produced if the circuit were complete. Because of this, it is often considered that a fake current is actually flowing between the capacitor plates, called a "displacement current".

Circuits, Again

     Although the pure DC circuit analogy breaks down when considering time-varying voltages and currents, as long as the frequency involved corresponds to a wavelength much longer than the lengths of wire involved, and stray capacitance and inductance are reduced by proper circuit construction, we can still draw meaningful schematic diagrams without having to specify the locations of all components.

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