Passive Components:Air Core Inductors

Air Core Inductors

Air core inductors do not use a magnetic core to concentrate the lines of magnetic flux. Instead the flux lines exist in the immediate neighborhood of the coils without tight confinement. As a result, the inductance of an air core coil is considerably lower than one with a magnetic core. In fact, at low frequencies, the quality factor is reduced by a factor of mr when the loss factor is small. At high frequencies however, the loss factor may be so high that the addition of a magnetic core and increased inductance actually ends up degrading the quality factor below the air core value. Discrete air core inductors have been used in RF applications and have been wound using discrete magnet or Litz wire onto forming cylinders.

For ICs, especially RF and microwave circuits, spiral metallization deposited on a substrate is a common means to obtain small amounts of inductance with relatively high-quality factors. Inductance values that can be obtained by these techniques are usually in the low nH range (1–20 nH). Estimating inductance values using air cores is much more complicated than in the case of highly permeable cores due to the lack of flux concentration. Formulas have been derived for different spiral air coil shapes (assuming perfectly insulating substrates) and are tabulated in several handbooks for inductance calculations [6–9]. An example of a useful inductance formula [9] is

The formula is an approximation that loses accuracy as the device size becomes large (i.e., large rout with respect to rin).

The loss factors of such devices are strongly influenced by the nonidealities of the substrates and insulators on which they are deposited. For example, aluminum spiral inductors fabricated on silicon with highly doped substrates and epitaxial layers can have significant reduction in quality factor due to the conductivity of the underlying layers. These layers act as ground planes producing the effect of an image of the spiral underneath. This in turn causes a loss in inductance. This can be as much as 30–60% when compared with a spiral over a perfect insulator. In addition, an increase in the loss factor occurs due to circulating eddy currents in the conductive under layers. Increases in the effective resistance of 5–10 times the perfect insulator case is possible, increasing with increased frequency. All these effects can be seen to degrade the performance of these inductors thus requiring design optimization [10–12].

These substrate effects appear in the form of coupling capacitances from the spiral metal to the substrates as well as spreading resistances in the substrate itself. The spreading resistance is frequency- dependent, increasing with higher frequency. The amount of coupling to the substrate depends on the coupling capacitances and hence the separation of the spiral from the substrate. This distance is the dielectric thickness used in the IC process. Only with very large dielectric thicknesses are the substrate effects negligible. In practical cases where it is relatively thin and limited to a few microns, the effects are very large giving an overall quality factor, Q, which is significantly lower than the Q of the spiral without the substrate. Figure 6.7 shows a typical degradation curve of Q on a resistive substrate for “thick” and “thin” separations or dielectric thicknesses. The trends of this curve are also similar if the dielectric thickness variable is replaced by the substrate resistivity as a variable. The exact amount of degradation depends on the separation involved, the dielectric constant, and the resistivity of the substrate. With these quantities known it is possible to construct a circuit model to include these effects and hence solve for the overall quality factor including the substrate effects.

To improve the inductor quality factor on a resistive substrate, some design solutions are possible. One solution to this problem is to increase the substrate resistivity. Another is to design a spiral with

small footprint to reduce coupling to the substrate. In order to offset the increased resistance (which also reduces Q) thicker metallization would be necessary and clearly a trade-off situation arises requiring some design optimization by circuit modeling or more accurately by electromagnetic finite-element analysis.