# Tuned Circuit Filter Quality Factor

### - the Q factor or quality factor can be applied to many elements of filter design and has an important impact on LC tuned circuits..

Q, Quality Factor Tutorial Includes:
Q, quality factor basics     Inductor Q     RLC network Q

Quality factor or Q factor affects LC filter circuits in the same way that it does for inductors and capacitors.

It is generally very important to ensure that the Q is maintained at a sufficiently high levels for the circuit to provide adequate filtering.

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

There are some simple formulas or equations that can be used to determine the LC filter quality factor or Q 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. The introduction of any resistance into the circuit will introduce losses and reduce the filter Q factor.
• 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.

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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:

$Q=\frac{1}{R}\sqrt{\frac{L}{C}}$

The LC Q factor for a parallel tuned circuit is:

$Q=R\sqrt{\frac{C}{L}}$

Where series or parallel tuned the resistance has a marked affect on the filter Q factor.

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