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AC Electrical Theory.
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Forward: The articles collected under the heading "From Transmitter to Antenna" make extensive use of a set of techniques known loosely as "AC Theory", "Lumped Component Circuit Analysis" or "Complex Numbers". Anyone interested in matters related to analog electrical engineering, either in an amateur or professional capacity, needs to be familiar with this subject; but realistically, many will never have been taught it, some will have forgotten it, and some (on account of how they were taught) will have developed a distinct aversion to it. A writer wishing to engage in discussions which require knowledge of this field will therefore find it prudent to provide the necessary background material. Rather than offering the usual terse list of standard formulae however; the decision was made to start with the basic laws of electricity and develop the subject in detail. The approach used is that of deriving and exploring results which are normally accepted without proof; and introducing the necessary mathematics as it comes to be required. All of the working is shown; so that anyone with a reasonable grasp of basic algebra should be able to follow the explanations given. The point in covering the subject in this way is that it is familiarity with the techniques used, rather than the ability to remember standard results, which constitutes the necessary skill. One matter which came to light during the drafting of this chapter is that different writers adopt different sign conventions for reactance, susceptance and admittance, and some simply ignore or dismiss errors of sign in their working. Most of the confusion arises because people fail to make clear distinctions between vectors, scalars and pseudo-scalars and so write expressions which are dimensionally inconsistent. Here, the emphasis is placed on starting with correctly defined vector equations; the point being to ensure that the method used always leads to the correct result, without the need to resolve sign ambiguities. Another matter which seems to have received little attention, is that of how and when a problem can be simplified by reducing it from a vector to a scalar form. A piece of working intended to define a magnitude, for example, does not require the use of complex numbers. The various possible simplifications are identified, proved, and collected as a set of theorems which, if memorised, enable solutions to be found in the minimum number of logical steps. In deciding whether or not to read this chapter; note that it establishes the notation and conventions used throughout the book. The previously mentioned attention to mathematical consistency, and the attempt to identify every possible short-cut, should also be of interest to advanced readers. Some, of course, will be of the opinion that the art of circuit analysis is now redundant due to the availability of circuit simulators. It must be emphasised therefore, that simulation and analysis do not serve the same purpose. Simulation shows what a circuit will do for a given choice of component values, and provides an easy method for exploring the effects of parasitic reactances and tolerances. Analysis, on the other hand, informs the process of inventing the circuit in the first place, and produces the equations used when calculating the component values. One thing which analysis provides outside the mathematics however, is a clear understanding of how electrical circuits work. In particular, it encourages the habit of thinking in impedance space, which gives direct insight into the workings of generally ill-understood circuits such as antenna matching networks. DWK. 29th December 2007  |
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© D W Knight 2007.
David Knight asserts the right to be recognised as the author of this work.