Q Quality Factor Tutorial

- tutorial and information about Q, quality factor used with resonant circuits and components to indicate resistive losses, resonant sharpness, etc..

The Q, quality factor of an inductor or tuned circuit is often used to give an indication of its performance in an RF or other circuit.

Values for Q or quality factor are often seen quoted and can be used in defining the performance of an inductor or tuned circuit.

Accordingly the Q or quality factor is an important factor in the definition of various RF components and circuits.

Q, quality factor basics

The concept of Q factor or quality factor is one that is applicable in many areas of physics and engineering. The Q, quality factor is a dimensionless parameter that indicates the energy losses within a resonant element which could be anything from a mechanical pendulum, and element within a mechanical structure, or within electronics within a resonant circuit, and in particular an inductor.

While the Q of an element relates the losses this links directly in to the bandwidth of the resonator with respect to its centre frequency. As such the Q or quality factor is particularly important within RF tuned circuits, filters, etc..

The Q indicates energy loss relative to the amount of energy stored within the system. Thus the higher the Q the lower the rate of energy loss and hence oscillations will reduce more slowly, i.e. they will have a low level of damping and they will ring for longer.

For electronic circuits, energy losses within the circuit are caused by resistance. Although this can occur anywhere within the circuit, the main cause of resistance occurs within the inductor. Accordingly inductor Q is a major factor within resonant circuits.

Effects of Q

When dealing with RF tuned circuits, there are many reasons why Q or Q factor is important. Usually a high level of Q, quality factor is beneficial, but in some applications a defined level of Q may be what is required.

Some of the considerations associated with Q in RF tuned circuits are summarised below:

  • Bandwidth:   With increasing Q or quality factor, so the bandwidth of the tuned circuit filter is reduced. As losses decrease so the tuned circuit becomes sharper as energy is stored better in the circuit.

    Q quality factor

    It can be seen that as the Q increases, so the 3 dB bandwidth decreases and the overall response of the tuned circuit increases.
  • Ringing:   As the Q of a resonant circuit increases so the losses decrease. This means that any oscillation set up within the circuit will take longer to die away. In other words the circuit will tend to "ring" more. This is actually ideal for use within an oscillator circuit because it is easier to set up and maintain an oscillation as less energy is lost in the tuned circuit.
  • Oscillator phase noise:   Any oscillator generates what is known as phase noise. This comprises random shifts in the phase of the signal. This manifests itself as noise that spreads out from the main carrier. As might be expected, this noise is not wanted and therefore needs to be minimised. The oscillator design can be tailored to reduce this in a number of ways, the chief one being by increasing the Q, quality factor of the oscillator tuned circuit.
  • General spurious signals:   Tuned circuits and filters are often used to remove spurious signals. The sharper the filter and the higher the level of Q, the better the circuit will be able to remove the spurious signals.
  • Wide bandwidth:   In many RF applications there is a requirement for wide bandwidth operation. Some forms of modulation require a wide bandwidth, and other applications require fixed filters to provide wide band coverage. While high rejection of unwanted signals may be required, there is a competing requirement for wide bandwidths. Accordingly in many applications the level of Q required needs to be determined to provide the overall performance that is needed meeting requirements for wide bandwidth and adequate rejection of unwanted signals.

Q quality factor equations

The basic Q quality factor equation is based upon the energy losses within the inductor, circuit or other form of component.

The definition of Q quality factor is the energy stored divided by the energy lost per cycle. This means that we can mathematically express Q, quality factor as:

Q quality factor equation

When looking at the bandwidth of an RF resonant circuit this translates to:

Q quality factor equation

Inductor Q and bandwidth
Q of a tuned circuit with respect to its bandwidth

Within any RF or other circuit, each individual component can contribute to the Q or quality factor of the circuit network as a whole. The Q of the components such as inductors and capacitors are often quoted as having a certain Q or quality factor.

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