9.9 : Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

The power dissipation in the resistor is proportional to the square of the current. This shows that the power dissipation is also maximum when the current is maximum in a resonance condition. This maximum power is given by:

where I_max is the maximum current at resonance.

The bandwidth of a circuit is defined as the frequency range over which the power dissipated decreases to half its maximum value. This occurs at the half-power frequencies, where the current reduces to about 70.7% of its maximum level. Bandwidth is calculated as the difference between the higher and lower half-power frequencies.

At resonance, reactive power does not dissipate but instead oscillates between the inductor and the capacitor, while resistive power is dissipated in the resistor. The quality factor relates to the maximum energy stored in the circuit versus the energy dissipated per cycle. In application, a radio transmitter with a higher Q factor for its RLC filter can better isolate a desired signal from nearby frequency noise. The trade-off is bandwidth: a higher Q reduces bandwidth, which could limit the filter's applicability in systems requiring a more comprehensive frequency range.

An RLC series resonance circuit exemplifies precision engineering in radio transmission by functioning as an effective band-pass filter. This circuit is precisely engineered to allow a peak in current magnitude at the resonance frequency, enabling selective frequency transmission and reception.