27 February, 2007

Fundamental Parameters of RLC Circuit

There are two fundamental parameters that describe the behavior of RLC circuits: the resonant frequency and the damping factor. In addition, other parameters derived from these first two are discussed below.

Resonant frequency:
The undamped resonance or natural frequency of an RLC circuit (in radians per second) is:

In the more familiar unit hertz, the natural frequency becomes

Damping factor :
The damping factor of a series RLC circuit (in radians per second) is:
for a parallel RLC circuit is

Derived Parameters

The RLC circuit may be used as a bandpass or band-stop filter by replacing R with a receiving device with the same input resistance, and the bandwidth (in radians per second) is

Alternatively, the bandwidth in hertz is
The bandwidth is a measure of the width of the frequency response at the two half-power frequencies. As a result, this measure of bandwidth is sometimes called the full-width at half-power. Since electrical power is proportional to the square of the circuit voltage (or current), the
frequency response will drop to at the half-power frequencies.

Quality or Q factor :
The Quality of the series tuned circuit, or Q factor, is calculated as the ratio of the resonance frequency ωo to the bandwidth Δω (in radians per second):

Or in hertz:
For the parallel tuned circuit:

Q is a dimensionless quantity.

For derivations and circuit analysis view following site :

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