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8.3 High-pass Filters
A high-pass filter’s task is just the opposite of a low-pass filter: to offer easy passage of a high-frequency signal and difficult passage to a low-frequency signal. As one might expect, the inductive (Figure below) and capacitive (Figure below) versions of the high-pass filter are just the opposite of their respective low-pass filter designs: Capacitive…
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8.2 Low-pass Filters
By definition, a low-pass filter is a circuit offering easy passage to low-frequency signals and difficult passage to high-frequency signals. There are two basic kinds of circuits capable of accomplishing this objective, and many variations of each one: The inductive low-pass filter in (Figure below) and the capacitive low-pass filter in (Figure also below). Inductive…
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8.1 What is a Filter?
It is sometimes desirable to have circuits capable of selectively filtering one frequency or range of frequencies out of a mix of different frequencies in a circuit. A circuit designed to perform this frequency selection is called a filter circuit, or simply a filter. A common need for filter circuits is in high-performance stereo systems,…
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7.5 Circuit Effects
The principle of non-sinusoidal, repeating waveforms being equivalent to a series of sine waves at different frequencies is a fundamental property of waves in general and it has great practical import in the study of AC circuits. It means that any time we have a waveform that isn’t perfectly sine-wave-shaped, the circuit in question will…
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7.4 More on Spectrum Analysis
Computerized Fourier analysis, particularly in the form of the FFT algorithm, is a powerful tool for furthering our understanding of waveforms and their related spectral components. This same mathematical routine programmed into the SPICE simulator as the .fourier option is also programmed into a variety of electronic test instruments to perform real-time Fourier analysis on…
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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…