Parallel RLC Circuit
Figure 5. RLC parallel circuit |
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The properties of the parallel RLC circuit can be obtained from the duality relationship of electrical circuits and considering that the parallel RLC is the dual impedance of a series RLC. Considering this it becomes clear that the differential equations describing this circuit are identical to the general form of those describing a series RLC.
For the parallel circuit, the attenuation α is given by
and the damping factor is consequently
This is the inverse of the expression for ζ in the series circuit. Likewise, the other scaled parameters, fractional bandwidth and Q are also the inverse of each other. This means that a wide band, low Q circuit in one topology will become a narrow band, high Q circuit in the other topology when constructed from components with identical values. The Q and fractional bandwidth of the parallel circuit are given by
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