Quality Factor of an Inductor
The Q of an on-chip inductor is affected by many things. At low frequencies, the Q tends to increase with frequency, because the losses are relatively constant (mostly due to metal resistance Rs ), while the imaginary part of the impedance is increasing linearly with frequency. However, as the frequency increases, currents start to flow in the substrate through capacitive and, to a lesser degree, magnetic coupling. This loss of energy into the substrate causes an effective increase in the resistance. In addition, the skin effect starts to raise the resistance of the metal traces at higher frequencies. Thus, most integrated inductors have Qs that rise at low frequencies and then have some peak beyond which the losses make the resistance rise faster than the imaginary part of the impedance, and the Q starts to fall off again. Thus, it is easy to see the need for proper optimization to ensure that the inductor has peak performance at the frequency of interest.
Re: Quality Factor of an Inductor
To add the Q factor of inductor, it is very essential to follow guidlines of the layout
1. Line spacing: At low frequencies (2 GHz or less), keep the line spacing as tight as possible. At higher frequencies, due to coupling between turns, larger spacing may be desirable.
2. Line width: Increasing metal width will reduce the inductance (fewer turns in a given area as well as less inductance per unit length) and will decrease the series resistance of the lines at low frequencies. Large inductance area means bigger capacitance, which means lower selfresonance, and more coupling of current into the substrate. Therefore, as W goes up, inductance comes down and the frequency of Qpeak gets lower (and vice versa). Line widths for typical 1- to 5-nH inductors in the 2- to 5-GHz range would be expected to be from 10 to 25 m m.
3. Area: Bigger area means that more current is present in the substrate, so high-frequency losses tend to be increased. Bigger area (for the same line width) means longer spirals, which means more inductance. Therefore, as the area goes up, inductance goes up, and the frequency of Qpeak gets lower (and vice versa).
4. Number of turns: This is typically a third degree of freedom. It is usually best to pick fewer rather than more turns, provided that the inductor does not get to be huge. Huge is, of course, a relative term, and it is ultimately up to the designers to decide how much space they are willing to devote to the inductor layout. Inner turns add less to the inductance but more resistance, so it is best to keep the inductor hollow. By changing the area and line width, the peak frequency and inductance can be fine-tuned.