137
Figure 6-8:
Q
T
as a function of mass for sample D5 for four different proof mass distributions.
Figure 6-9: Coupling factor as a function of mass attached to a cantilever with length 18 mm.
6.5 Electrical Characterisation
The same series of samples was used to investigate the electrical output performance from the piezoelectric cantilever structures. A modest electrical power output a few
nano-watts was produced when the composite unimorph structure was operated in its bending mode. The output power is affected by the distance from the centroid of the
piezoelectric material layer to the neutral axis of the composite cantilever,
d
. The samples used in the experiment have a
d
value of 6 µm, which was calculated from equation 3-22 by using the parameters in Table 6-1 and with the assumption that the
138 elastic moduli for the AgPd electrode and PZT layer are 116 GPa and 60 GPa
respectively.
The electrical output power from the devices was measured by connecting the lower and upper electrodes to a programmable load resistance and then converting the voltage into
a digital signal to be measured with a National Instruments Sequence Test programme. A series of different experiments was carried out to investigate the output power as a
function of cantilever length, electrical load resistance, proof mass and input acceleration level.
The mechanical damping factor is a property of the system which is difficult to control. However, the electrical damping factor can simply be varied by using different resistive
load. As can be seen from equation 2-16, once the resistive load is matched with the mechanical damping, maximum energy is transferred from the mechanical to the
electrical domain.
6.5.1 Excitation without Proof Mass
By careful selection of resistive loads, the electrically induced damping can be adjusted so that it is equal to the mechanical damping. Once the optimal resistive load is
obtained, maximum output power is produced. Figure 6-10 shows the experimental and theoretically calculated results for samples D6 and D5 when excited to their resonant
frequencies at an acceleration level of 100 milli ‘g’ ≈ 1 ms
2
. Optimum output power for samples D6 and D5
is obtained by driving into resistive loads of 60 kΩ and 39 kΩ respectively.
The required value for the resistive load was found to be a function of the length of the cantilever, as shown in Figure 6-11. This shows that as cantilever length increases the
mechanical damping also increases which is reflected by the matched electrical resistive load. At optimum resistive load, the output power increases with cantilever length as
shown in Figure 6-12, which is in good agreement with theoretical calculations.
