Page 213 - An Introduction to Microelectromechanical Systems Engineering

192 MEM Structures and Systems in RF Applications

frequency range. Above the self-resonance frequency f SR =1 / (2π CL para ), the
inductance dominates and the capacitor looks to a circuit like an inductor (i.e., the
pair has an imaginary positive impedance).
Inductors are usually implemented as coils of a conductor, which have parasitic
capacitance between them. A circuit model can be made with each turn of the induc-
tor represented by an incremental inductor and its parasitic capacitance [see
Figure 7.1(d)]. A simplified model has an inductor L in parallel with a parasitic
capacitor C . At low frequencies, the capacitor has a large imaginary negative
para
impedance, and most current flows through the inductor. As the frequency rises,
however, the magnitude of the capacitor impedance falls, while the imaginary posi-
tive impedance of the inductor rises. Above the self-resonant frequency
f =1 / (2π LC ), the capacitance dominates (i.e., the pair has an imaginary
SR para
negative impedance), and the inductor ceases to function as one. In general, this
occurs at a lower frequency for inductors than for capacitors. As seen in the equa-
tion for Q, the quality factor for an inductor rises with frequency; however, because
the parallel capacitance reduces the effective inductance at higher frequencies, Q
eventually reaches a maximum before falling.

Surface-Micromachined Variable Capacitors
Capacitors with a constant capacitance are readily fabricated side by side with tran-
sistors in standard semiconductor integrated-circuit processes by sandwiching a
dielectric between two conductive layers. The primary reason for using on-chip
capacitors is the reduction in parts that must be used on a circuit board and the com-
mensurate reduction in cost. Other reasons include noise reduction and lowering
both parasitic capacitance and resistance. Because the capacitance per unit area in a
standard process is relatively small, large capacitances (more than a few picofarads)
occupy too great a chip area to be cost effective, and high-dielectric materials must
be integrated or off-chip components must be used.
Some analog circuits, such as voltage-controlled oscillators (VCOs) and tuning
circuits, require voltage-controlled variable capacitors (varactors). These are pres-
ently implemented on a separate semiconductor chip with a reverse-biased p-n diode
junction. Varying the dc voltage applied varies the depletion-region width and thus
the small-signal capacitance; capacitance tuning ranges from 2:1 to over 10:1 with
an applied voltage of 0–5V are available commercially. The greatest limitation of
semiconductor varactors is their Q, which is, at most, on the order of 50 in the giga-
hertz frequency range. High Q is required for oscillators with low phase noise [3]; an
example requirement is Q > 50 for a 2-pF capacitor in the range of 1 GHz [4].
Micromachining technology is expected to make an impact in the near future with
the commercial fabrication of variable capacitors with higher Q, the ability to be
fabricated on the same chip as semiconductor circuitry for a reduction in part count,
the ability to handle large ac input voltages that would forward bias diode varactors,
and potentially wider tuning range.
Micromachined variable capacitors can be divided into two broad categories,
surface-micromachined and bulk-micromachined. Surface-micromachined vari-
able capacitors tend to be simpler to fabricate, more readily integrated on the
same chip as existing circuitry, and use less expensive process steps than their