Abstract
In the most familiar form of mechanical oscillations, the pendulum, the total system energy constantly bounces back and forth between the kinetic and potential forms. In the absence of friction (i.e., energy dissipation), a pendulum would oscillate forever. Similarly, after two ideal electrical elements capable of storing energy (a capacitor (which is initially charged) and an inductor) are connected in parallel then the total initial energy of the system bounces back and forth between the electric and magnetic energy forms. This process is perceived by the observer as “electrical oscillations and the parallel LC circuit is said to be “in resonance”. The phenomenon of electrical resonance is essential to wireless radio communications technology because without it, simply put, there would be no modern communications. In this chapter, we study behaviour and derive the main parameters of electrical resonant circuits.
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Notes
- 1.
This is the second-order differential equation with a standard form of the solution.
- 2.
Remember, this is a relative comparison, thus it is agreed convention that the negative reactance is associated with a capacitance because \({X}_{\mathrm{C}} = \frac{1} {\mathrm{j}\omega C} = -j \frac{1} {\omega C}\).
- 3.
That is, \(\vert Z\vert = \sqrt{\mathfrak{R}{(Z) }^{2 } + \mathfrak{I}{(Z) }^{2}}\).
- 4.
\(\cos [\arctan x] = 1/\sqrt{1 + {x}^{2}}\).
- 5.
\(\sin [\arctan x] = x/\sqrt{1 + {x}^{2}}\).
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© 2012 Springer Science+Business Media, LLC
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Sobot, R. (2012). Electrical Resonance. In: Wireless Communication Electronics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1117-8_5
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DOI: https://doi.org/10.1007/978-1-4614-1117-8_5
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Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-1116-1
Online ISBN: 978-1-4614-1117-8
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