What is Quality Factor or Q Factor?
Q factor is the dimensionless parameter that describes the efficiency and sharpness of a reactive component, mainly inductor and capacitor in an AC circuit. It is the ratio of reactive power to real power of the component. For an inductor, the Q factor is nothing but the ratio of 2πfL to R, which means the inductive reactance is divided by the resistance of the component. \[ Q = \frac{X_L}{R} = \frac{2\pi f L }{ R}\]
The Q factor will be more if resistance is less compared to the inductance of the circuit. This means the more inductive the component is, the higher its inductive quality. In the case of a capacitor, the same thing happens. The capacitive reactance divided by the resistance inherent in the capacitor gives the Q factor. This represents how effectively the capacitor stores energy relative to how much energy it loses as heat. \[ Q = \frac{X_C}{R} = \frac{1}{2\pi f C R}\] The Q factor of a capacitor is high, means the component exhibits stronger capacitive behavior relative to its resistive property. This implies better quality of the capacitor in respect of its capacitive behavior.
A high Q factor indicates lower energy loss, as the resistance of the capacitor component or inductor component is much smaller compared to its reactance (either capacitive or inductive). Therefore, the ohmic power loss or energy dissipation during operation is minimal, making the component more efficient.
A high Q factor results in a narrower bandwidth and sharper resonance, which is desirable in applications like filters and tuned circuits. Conversely, a lower Q factor leads to higher energy losses and a poorer quality of response in filtering or resonance-based applications.
What is Dissipation Factor or D Factor?
Dissipation factor or simply D – factor of a component is also a dimensionless quantity. This factor indicates the energy loss in the capacitor or inductor when it is connected with an AC source. In other words, it represents how much energy is dissipated as heat relative to the energy stored in a capacitor or an inductor. Actually, how much energy will be stored as electromagnetic or electrostatic energy in an inductor or a capacitor, respectively is determined from the inductive reactance or capacitive reactance of the component respectively. The real energy lost from that component during operation is determined by its pure resistance value. The ratio of the energy lost to the energy stored in the form of electromagnetic energy or electrostatic energy is determined by the dissipation factor or D factor. From that it can be established that the dissipation factor is the ratio of resistance to the reactance of the component.
Now, the dissipation factor \( D \) is the ratio of resistance \( R \) to reactance \( X \), where \( X \) is either \( \frac{1}{2\pi fC} \) for a capacitor or \( 2\pi fL \) for an inductor. So, the dissipation factor becomes: \[ D = \begin{cases} 2\pi f C R & \text{(for a capacitor)} \\ \frac{R}{2\pi f L} & \text{(for an inductor)} \end{cases} \] Now, if we multiply both the numerator and the denominator by \( I^2 \), we get: \[ D = \frac{I^2 R}{I^2 X} \] Here, \( I^2 R \) represents the ohmic (real) power loss, and \( I^2 X \) represents the reactive power of the inductor or capacitor. From the power triangle, we know that the angle \( \delta \) is the angle between the real power and apparent power. The tangent of this angle, \( \tan \delta \), is the ratio of real power i.e. resistive (ohmic) power loss to reactive power. Hence, the dissipation factor can also be written as: \[ D = \tan \delta \] A higher \( D \)-factor implies greater losses and poorer quality, while a lower \( D \)-factor indicates lower losses and better quality. The relationship between the quality factor \( Q \) and the dissipation factor \( D \) is: \[ Q = \frac{1}{D} \]