Page 111 - MEMS Mechanical Sensors

100 Mechanical Transduction Techniques

a max

3dB

Amplitude

f 1 f 2 Frequency
f 0
Figure 5.10 A typical characteristic of a resonant system.

mechanism will be greater than that of a low-Q system. A high Q means little energy
is required to maintain the resonance at constant amplitude, thereby broadening the
range of possible drive mechanisms to include weaker techniques. A high Q-factor
also implies the resonant structure is well isolated from its surroundings, and there-
fore, the influence of external factors (e.g., vibrations) will be minimized.
The Q-factor can also be calculated from Figure 5.10 using

f
Q = 0 (5.21)
∆ f

where resonant frequency f corresponds with a , the maximum amplitude, and ∆f
max
0
is the difference between frequencies f and f . Frequencies f and f correspond to
2
1
2
1
amplitudes of vibration 3 dB lower than a .
max
The Q-factor is limited by the various mechanisms by which energy is lost from
the resonator. These damping mechanisms arise from three sources:
1. The energy lost to a surrounding fluid (1/Q );
a
2. The energy coupled through the resonator’s supports to a surrounding solid
(1/Q );
s
3. The energy dissipated internally within the resonator’s material (1/Q).
i
Minimizing these effects will maximize the Q-factor as shown here:

1 1 1 1
= + + (5.22)
Q Q Q Q
a s i
Energy losses associated with 1/Q are potentially the largest, and therefore the
a
most important, of the loss mechanisms. These losses occur due to the interactions