What is the Significance of Q factor in AC circuits?

Quality factor Q is a measure of ‘goodness’ of a coil, inductor or capacitor, or a resonant circuit in terms of performance, losses and bandwidth. Higher the value, the lower are the losses in relation to reactive power. By this yardstick, an ideal inductor would have infinitely large Q factor.

Quality factor is defined as ratio of energy stored in resonator to the energy lost in one cycle of oscillation of AC current waveform. In a resonant circuit, it is the ratio of power stored in circuit reactance elements to power dissipated in the circuit. Q of a resonator is also equal to the ratio of its center frequency to its bandwidth when driven by an AC source. These two definitions give more or less same results.

Quality factor Q = Power stored / power dissipated. For a series circuit consisting of reactance X and resistance R, the quality factor is given by

Q factor of Inductor or capacitor

The formula applies to a series resonance circuit, and will also apply to parallel resonance circuit if resistance is in series with an inductor. It may be noted that Q factor depends on frequency, since reactance X is a function of frequency. It goes up with frequency for inductance, while it goes down with frequency for capacitors. Further, lower is the series resistance R, higher is the quality factor. This means, for an ideal inductor or capacitor, Q is infinity. A good capacitor may have a Q factor of 5,000 at 1MHz, while it may be as low as 100 or lower at 1 KHz.

An ideal inductor has zero resistance, and current in such inductor lags the voltage by 90°. A practical inductor, made from a coil of wire, will always have some resistance due to resistance of the conductor. It also has a core of some magnetic material, which also consumes some energy, and offers some equivalent of resistance. These resistive components cause the inductor to deviate from ideal conductor, and it behaves as an inductor in series with a resistance. This deviation is expressed in terms of ‘Quality Factor (Q) of inductor. It is the ratio of inductive impedance to the resistance of an inductor.

Another way of understanding Q factor is by considering series resonant circuit. Current in series RLC circuit is maximum at resonance frequency, where it is governed by resistance alone. The increase in current causes rise in voltage across L and C. This magnification of voltages at series resonance is be termed as Q factor. Physically this means voltage across inductor or capacitor is Q time greater than source voltage. This means it is possible to get a voltage as high as 10 KV across capacitor or inductor in series LC circuit with a source voltage of just 100 V, if the equivalent or total series resistance in circuit is sufficiently low.

Q is defined as ratio of voltage across L or C to the applied voltage.

For an inductor

Another way of looking at this could be in terms of ratio of reactive power to active power of inductor. It is also equal to energy stored in inductor divided by the energy consumed per cycle of supply voltage.

An ideal inductor will thus have a quality factor of infinity. A practical inductor will have a finite value of quality factor. The higher the quality factor, the closer is the inductor to an ideal one. Actual Q will lie anywhere between 10 to a few thousands.

Capacitor losses are miniscule in comparison, and quality factor Q is extremely high. Therefore, its inverse, called Dielectric Loss factor, or Tan delta is used. A capacitor with Tan delta of 0.0002 (for PP capacitor) will have a Q factor of 5000. If a capacitor is designed for high frequency operations, manufacturers often provide data sheet giving Q values at different frequencies, or may even provide graphs of Q Vs. frequency.

Q factor of a series circuit

Quality factor is a very useful tool for circuit analysis and design. It is possible to get much higher voltage in a circuit than source voltage by making use of this phenomenon. In the RLC resonant circuit above, voltages across L and C cancel each other, and full source voltage appears across R. If source voltage is 100 V, current I will be 10 Amp. Therefore, Voltages V_L and V_C will both be (10 A *200 =) 2000 Volts each, twenty times the source current. Quality factor of this circuit is (2000/10=) 20, the is ratio of reactance of C or L to series resistance R. This is also the amplification factor of voltage for this circuit. By varying the series resistance R, it is possible to increase or decrease the high voltage thus obtained.