Tag: Resonance
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14.8 Waveguides
A waveguide is a special form of transmission line consisting of a hollow, metal tube. The tube wall provides distributed inductance, while the empty space between the tube walls provide distributed capacitance. Wave guides conduct microwave energy at lower loss than coaxial cables. Waveguides are practical only for signals of extremely high frequency, where the…
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14.7 Impedance Transformation
Standing waves at the resonant frequency points of an open- or short-circuited transmission line produce unusual effects. When the signal frequency is such that exactly 1/2 wave or some multiple thereof matches the line’s length, the source “sees” the load impedance as it is. The following pair of illustrations shows an open-circuited line operating at…
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14.5 Long and Short Transmission Lines
In DC and low-frequency AC circuits, the characteristic impedance of parallel wires is usually ignored. This includes the use of coaxial cables in instrument circuits, often employed to protect weak voltage signals from being corrupted by induced “noise” caused by stray electric and magnetic fields. This is due to the relatively short timespans in which…
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14.4 Finite-length Transmission Lines
A transmission line of infinite length is an interesting abstraction, but physically impossible. All transmission lines have some finite length, and as such do not behave precisely the same as an infinite line. If that piece of 50 Ω “RG-58/U” cable I measured with an ohmmeter years ago had been infinitely long, I actually would…
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14.3 Characteristic Impedance in Transmission lines
The Parallel Wires of Infinite Length Suppose, though, that we had a set of parallel wires of infinite length, with no lamp at the end. What would happen when we close the switch? Being that there is no longer a load at the end of the wires, this circuit is open. Would there be no…
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14.2 Circuits and the Speed of Light
Suppose we had a simple one-battery, one-lamp circuit controlled by a switch. When the switch is closed, the lamp immediately lights. When the switch is opened, the lamp immediately darkens: (Figure below) Lamp appears to immediately respond to switch. Actually, an incandescent lamp takes a short time for its filament to warm up and emit…
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14.1 A 50-Ohm Cable?
Early in my explorations of electricity, I came across a length of coaxial cable with a label of “50 ohms” printed along its outer sheath (Figure below). Coaxial cable is a two-conductor cable made of a single conductor surrounded by a braided wire jacket, with a plastic insulating material separating the two. As such, the…
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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…