Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

Resonance in a parallel RLC circuit occurs when the net reactance is zero, meaning the capacitive and inductive effects cancel each other out. This condition is achieved when:

Solving for the resonant frequency gives:

This resonant frequency is where the circuit will exhibit purely resistive behavior, and the current through the resistor will be at its maximum. The power dissipated in the circuit is maximum at resonance due to the maximum current flow. At the half-power point frequencies, the current is approximately 0.707 of the maximum current, leading to half the maximum power dissipation. The bandwidth of the parallel RLC circuit is the difference between these half-power frequencies and is found using:

The quality factor (Q) is a dimensionless parameter that compares the resonant frequency to the bandwidth, indicating the selectivity or sharpness of the resonance peak. In high-quality circuits where Q≥10, the half-power frequencies can be approximated using:

 A higher Q factor signifies that the circuit is highly selective, resonating strongly at a narrow range of frequencies around the resonance frequency. This property is particularly beneficial in radio communications, allowing for filtering unwanted frequencies and minimizing interference. Parallel resonance circuits are particularly useful in filtering applications acting as band-stop or notch filters, blocking a specific frequency range while allowing others to pass. This makes them valuable in signal processing for eliminating unwanted frequencies or noise.