# Tuned Circuit Filter Quality Factor

### In this section

Resonant circuits consist of inductors and capacitors. It is therefore often necessary to look at the quality factor of an LC, i.e. inductor capacitor system.

It is necessary to be able determine the LC filter Q factor to assess the performance of these circuits.

Fortunately there are some simple formulae or equations that can be used to determine the LC filter quality factor.

## Q factor and LCR tuned circuits

One of the key features of an LC tuned circuit is that at resonance the inductive and capacitive reactances become equal. However dependent upon the type of tuned circuit, the effect is slightly different.

There are two basic types of tuned circuit:

• Parallel tuned circuit:   At resonance the impedance of a parallel tuned circuit peaks, decreasing either side of resonance. Below resonance the inductive reactance dominates and above resonance it becomes capacitive. As a result of its action any alternating or RF signal voltage placed across the circuit will peak at resonance.
• Series tuned circuit:   The series tuned circuit is very much the inverse of the parallel tuned circuit in that rather than showing a peak in impedance at resonance there is a minimum.

The equivalent circuit for a series tuned network is given below. In this, the resistance "R" is the equivalent series resistance for the inductor and capacitor:

A parallel tuned circuit is also affected by the resistance in the circuit.

.

In the case of the parallel tuned LC circuit, the Q factor is still an issue. Again there is resistance within both the inductor and capacitor. However as the inductor resistance dominates normally, it has been included in this leg for convenience.

## LC Q factor equations

When determining the Q of an LC tuned circuit it is necessary to determine whether the circuit is series or parallel tuned. The LC Q factor for a series tuned circuit is:

The LC Q factor for a parallel tuned circuit is:

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