Tag: Free Book on AC
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7.3 Other Waveshapes
As strange as it may seem, any repeating, non-sinusoidal waveform is actually equivalent to a series of sinusoidal waveforms of different amplitudes and frequencies added together. Square waves are a very common and well-understood case, but not the only one. Electronic power control devices such as transistors and silicon-controlled rectifiers (SCRs) often produce voltage and…
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7.2 Square Wave Signals
It has been found that any repeating, non-sinusoidal waveform can be equated to a combination of DC voltage, sine waves, and/or cosine waves (sine waves with a 90 degree phase shift) at various amplitudes and frequencies. This is true no matter how strange or convoluted the waveform in question may be. So long as it…
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7.1 Introduction to Mixed-Frequency AC Signals
In our study of AC circuits thus far, we’ve explored circuits powered by a single-frequency sine voltage waveform. In many applications of electronics, though, single-frequency signals are the exception rather than the rule. Quite often we may encounter circuits where multiple frequencies of voltage coexist simultaneously. Also, circuit waveforms may be something other than sine-wave…
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6.6 Q Factor and Bandwidth of a Resonant Circuit
The Q, or quality, factor of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit corresponds to a more narrow bandwidth, which is desirable in many applications. More formally, Q is the ratio of power stored to power dissipated in the…
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6.5 Resonance in Series-Parallel Circuits
In simple reactive circuits with little or no resistance, the effects of radically altered impedance will manifest at the resonance frequency predicted by the equation given earlier. In a parallel (tank) LC circuit, this means infinite impedance at resonance. In a series LC circuit, it means zero impedance at resonance: However, as soon as significant…
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6.4 Applications of Resonance
So far, the phenomenon of resonance appears to be a useless curiosity, or at most a nuisance to be avoided (especially if series resonance makes for a short-circuit across our AC voltage source!). However, this is not the case. Resonance is a very valuable property of reactive AC circuits, employed in a variety of applications.…
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6.3 Simple Series Resonance
A similar effect happens in series inductive/capacitive circuits. When a state of resonance is reached (capacitive and inductive reactances equal), the two impedances cancel each other out and the total impedance drops to zero! Example: Simple series resonant circuit. With the total series impedance equal to 0 Ω at the resonant frequency of 159.155 Hz,…
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6.2 Simple Parallel (Tank Circuit) Resonance
Resonance in a Tank Circuit A condition of resonance will be experienced in a tank circuit when the reactance of the capacitor and inductor are equal to each other. Because inductive reactance increases with increasing frequency and capacitive reactance decreases with increasing frequency, there will only be one frequency where these two reactances will be…
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6.1 An Electric Pendulum
Capacitors store energy in the form of an electric field, and electrically manifest that stored energy as a potential: static voltage. Inductors store energy in the form of a magnetic field, and electrically manifest that stored energy as a kinetic motion of electrons: current. Capacitors and inductors are flip-sides of the same reactive coin, storing…
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5.6 R, L and C Summary
With the notable exception of calculations for power (P), all AC circuit calculations are based on the same general principles as calculations for DC circuits. The only significant difference is that fact that AC calculations use complex quantities while DC calculations use scalar quantities. Ohm’s Law, Kirchhoff’s Laws, and even the network theorems learned in…
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5.5 Susceptance and Admittance
What is Conductance? In the study of DC circuits, the student of electricity comes across a term meaning the opposite of resistance: conductance. It is a useful term when exploring the mathematical formula for parallel resistances: Rparallel = 1 / (1/R1 + 1/R2 + . . . 1/Rn). Unlike resistance, which diminishes as more parallel…
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5.4 Series-parallel R, L, and C
Now that we’ve seen how series and parallel AC circuit analysis is not fundamentally different than DC circuit analysis, it should come as no surprise that series-parallel analysis would be the same as well, just using complex numbers instead of a scalar to represent voltage, current, and impedance. Take this series-parallel circuit for example: Example…
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5.3 Parallel R, L, and C
We can take the same components from the series circuit and rearrange them into a parallel configuration for an easy example circuit: Example R, L, and C parallel circuit. Impedance in Parallel Components The fact that these components are connected in parallel instead of series now has absolutely no effect on their individual impedances. So…
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5.2 Series R, L, and C
Let’s take the following example circuit and analyze it: Example series R, L, and C circuit. Solving for Reactance The first step is to determine the reactance (in ohms) for the inductor and the capacitor. The next step is to express all resistances and reactances in a mathematically common form: impedance. (Figure below) Remember that…
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5.1 Review of R, X, and Z
Before we begin to explore the effects of resistors, inductors, and capacitors connected together in the same AC circuits, let’s briefly review some basic terms and facts. Resistance This is essentially friction against the flow of current. It is present in all conductors to some extent (except superconductors!), most notably in resistors. When the alternating…