Electronics

Making AC More Efficient

Complex numbers are useful for AC circuit analysis because they provide a suitable method of symbolically denoting phase shift between AC quantities like voltage and current. However, for most people the equivalence between abstract vectors and real circuit quantities is not an easy one to grasp. Earlier in this chapter we saw how AC voltage [...]

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Complex number arithmetic

In view of the fact that complex numbers are legitimate mathematical entities, just like scalar numbers, they can be added, subtracted, multiplied, divided, squared, inverted, and such, just like any other kind of number. Some scientific calculators are programmed to directly perform these operations on two or more complex numbers, but these operations can also [...]

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Polar To Rectangular Conversion

In order to work with these complex numbers without drawing vectors, we first need some kind of standard mathematical notation. There are two basic forms of complex number notation: polar and rectangular.Polar form is where a complex number is denoted by the length (otherwise known as the magnitude, absolute value, or modulus) and the angle [...]

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Complex of Vectors

If vectors with uncommon angles are added, their magnitudes (lengths) add up quite differently than that of scalar magnitudes: (Figure 6.1) Figure 6.1: Vector magnitudes do not directly add for unequal angles If two AC voltages – 90o out of phase – are added together by being connected in series, their voltage magnitude does not [...]

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Addition of vectors

Vectors are mathematical objects just like numbers on a number line: they can be added, subtracted, multiplied, and divided. Addition is perhaps the easiest vector operations to visualize, so we’ll begin with that. If vectors with common angles are added, their magnitudes (lengths) add up just like regular scalar and vector quantities: (Figure 5.1) Figure [...]

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Signal Processing Systems

How exactly can we represent AC quantities of voltage or current in the form of a vector? The length of the vector represents the magnitude (or amplitude) of the waveform, like this: (Figure 4.1) The greater the amplitude of the waveform, the greater the length of its corresponding vector. The angle of the vector, however, [...]

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Waveform Generator

  Waveform Generator When two or more AC voltages or currents those are out of step with each other, that mean’s two waveforms are not synchronized: that their peaks and zero points do not match up at the same points in time. The graph in figure 3.1 illustrates an example of this. Figure 3.1: Out [...]

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Triangular and Square Wave Generator

AC (alternating current) voltage alternates in polarity and AC current alternates in direction. We also know that AC can alternate in a variety of different ways, and by tracing the alternation over time we can plot it as a “waveform.” We can measure the rate of alternation by measuring the time it takes for a [...]

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Electronic circuit calculations

Alternating Current (AC) refers to voltage or current that changes polarity or direction, respectively, over time. AC electromechanical generators, known as alternators, are of simpler construction than DC electromechanical generators.When an alternator produces AC voltage, the voltage switches polarity over time, but does so in a very particular manner. When graphed over time, the “wave” [...]

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