The quality factor (Q) of a resonant circuit characterizes its quality. The higher value of this indicator corresponds to a narrower bandwidth (which is ideal for many circuits). Simply put, the quality factor is the ratio of the energy accumulated in the circuit reactance to the energy consumed by the active resistance of the circuit:

If the resistor is connected in series with the inductor, this formula applies to bothseries resonantcircuits and parallel resonant circuits. In fact, in practical circuits, we often worry about the resistance of inductors, which can limit the quality factor. Note: Some textbooks on parallel resonant circuits in the "Q" formula interchange X and R. This is correct for large R values connected in parallel with C and L, and our formula is correct for small R values connected in series with L.

The practical application of Q factor (Q) is that the voltage across L or C in a series resonant circuit is Q times the total applied voltage, and in a parallel resonant circuit, the current flowing through L or C is Q times the total applied current.

Series resonantcircuit.

The resonance of a series LC circuit is represented by the minimum total impedance of the circuit, which is equal to the active resistance (with a relatively small value), while the current becomes maximum. The condition for resonance is equal inductive and capacitive reactance X=X Ç. When the frequency of the generator is greater than the frequency of the circuit, inductive resistance outweighs capacitive resistance, and the circuit represents the inductive resistance of the generator. If the frequency of the generator is lower than the frequency of the circuit, the capacitive resistance is greater than the inductive resistance, and the circuit of the generator is a capacitive resistance.

The current at resonance is at its maximum value, while the impedance is at its minimum value. The magnitude of the current depends on the size of the resistance. Impedance increases at frequencies higher or lower than resonance.

The peak value of resonant current can be changed by selecting the value of the series resistance, thereby altering the quality factor. All of these values will affect bandwidth. Circuits with low resistance and high Q-factor have a narrower passband than circuits with high resistance and low Q-factor. The dependence of circuit bandwidth on its resonant frequency and quality factor is determined by the following simple formula: