Series polarised multimorph Evaluation of Electrical Output
163 The output power from the upper section of PZT was obtained by a configuration of 3;4
terminal connection of electrode 3 and 4 while the output power for the lower section of PZT was obtained by a configuration of 1;2 terminal connection of electrode 1 and
2. Figure 7-9 shows that the upper section of PZT produces a higher output power at about 32
µW compared to the lower section which produces about 24 µW. This is due to the fact that the distance from the PZT layer centroid to the neutral axis of a
multimorph structure
d
mm
for the upper PZT layer is greater than for the lower PZT section, as a result of a thicker electrode being printed on the bottom of the structure.
The additional layer of AgPd two prints with a thickness of 20 µm was printed as the
lower electrode also acts as a physical support to the free-standing structure.
The experiment results are consistent with the calculated results using equation 7-1, as shown in Figure 7-9. The maximum output power for both of the PZT sections were
measured when driven through an optimum resistive load of 18.5 k .
Figure 7-9: Output power as a function of resistive load for upper section and lower section of PZTs for a multimorph structure.
Figure 7-10 shows that the output power is scaled up when connecting the individual lower and upper sections of PZT to make a series configuration 1;4 short 2+3 and this
produced a maximum power of about 41 W, when driving a resistive load of 37.5 k.
The magnitude of the output power is significantly improved by a factor of about 400 compared to a unimorph structure with similar length which was reported in Chapter 5.
The plot also shows that a configuration of 2+4; 1+3 produces an optimum output
5 10
15 20
25 30
35
20 40
60 80
100 120
140
O u
tp u
t P
o w
e r
µ W
Resistive Load k Ω
Upper Experiment Upper Theoretica l
Lower Experiment Lower Theoretica l
164 power of 32
µ W when driving at a lower resistive load of 7.5 kΩ. Comparing the output
open circuit voltage, optimum resistive load and the measured capacitance of this configuration Table 7-2 to the configurations of 1;2 and 3;4 individual PZT section,
the 2+4; 1+3 configuration resembles a parallel connection of resistors, capacitors and DC voltage sources.
The central section of PZT with the configuration of 2;3 is electrically neutral and no net charge is produced when excited to its resonant frequency. However, a relatively
small output power of 9 nW was generated when driving a re sistive load of 20 kΩ,
which shows that there is a slight difference in the strength of the electrical potential across the electrodes which may be contributed by the upper and lower sections of the
PZT. The values of the measured capacitance, as shown in Table 7-2 and the optimum resistive load are similar to those of the individual PZT section, which verified that the
central section is electro-active and has the potential to produce an electrical output when the correct configuration of electrode terminals is in place.
Figure 7-10: Output power as a function of resistive load for a multimorph cantilever with a few different electrode configurations.
Figure 7-11 shows the output current-voltage relationship of the terminal connected configurations. Series configuration 1;4 short 2+3 produces the highest output voltage
at a lower output current, while a parallel configuration 2+4; 1+3 produces the highest output current at a lower output voltage. This shows that a series configuration function
165 is better for applications requiring a higher output voltage, whereas as will be shown in
the following section a parallel configuration is more suitable for applications that require a higher output current.
Figure 7-11: Output current-voltage for a series polarised sample.
In another experiment, the resultant voltage for sample BA2 was investigated by measuring the open-circuit voltage at a constant frequency of 403 Hz a resonant
frequency corresponding to an acceleration level of 0.5 g. The open-circuit voltage is increased consistently with acceleration level regardless of configuration with different
combination of PZT network, as shown in Figure 7-12. The open-circuit voltage of configuration 1;4 short 2+3 is equivalent to a series connection of two voltage sources
and produces a total output voltage that is equal to the sum of the individual lower configuration 1;2 and upper configuration 3;4 sections of the PZT.
Since the central PZT section is electrically neutral, the configuration of 1;4, which is equivalent to a series connection of three voltage sources produced the same voltage
output as the configuration where electrode 2 and 3 were shorted, as expected. This is consistent with the result of configuration 2;3, where no obvious increment of open
circuit voltage is noticed with increased acceleration level. Configuration 1+4; 2+3 is equivalent to two voltage sources connected in a parallel mode with different polarity
resulting in a voltage difference between two voltage sources.An open-circuit voltage of about 2.6 V was measured from a series connection of two voltage sources when
166 excited to an acceleration of 1.5 g, which is the sum of the voltages produced by the
upper 1.45 V and lower 1.15 V sections of the PZT.
Figure 7-12: Open circuit voltage as a function of acceleration level for a multimorph cantilever with a few different electrode configurations.
Table 7-3 summarises all the major configurations of terminal arrangement for a multimorph structure polarised in series mode. The table is divided into three columns,
where the first column is the notation for the configuration, while the second column shows the connection diagram of the multimorph structure and the equivalent circuit of
the configuration.
The equivalent circuit of the networks consist of individual components representing a resistor, a capacitor and a voltage source. The polarity of the component shown in the
table is the polarity of the charges produced as a result of stress applied on the PZT in bending mode at upward bending position as shown in Figure 7-7 a. The polarity,
however, is not static and is dependent on the bending position of the multimorph structure. In a downward bending position, the polarity will be opposite to that shown in
the table.
The third column of the table shows the equivalent circuit equations of capacitance, resistance and open-circuit voltage of the configuration. The equations were verified by
the experiment results discussed above.
167
Table 7-3: Summary of connection configurations for a series polarised sample.
Connection Configuration
Connection Diagram Equivalent circuits
1; 4 Short 2+3
4 ;
3 2
; 1
4 ;
3 2
, 1
4 ;
1
C C
C C
C
S
4 ;
3 2
; 1
4 ;
1
R R
R
S
4 ;
3 2
; 1
4 ;
1
V V
V
S
1; 4
3 ;
2 2
; 1
3 ;
2 2
; 1
4 ;
3 4
; 3
3 ;
2 2
; 1
4 ;
1
C C
C C
C C
C C
C
4 ;
1 3
; 1
2 ;
1 4
; 1
R R
R R
4 ;
3 3
; 2
2 ;
1 4
; 1
V V
V V
1+4; 2+3
4 ;
3 2
; 1
3 2
; 4
1
C C
C
4 ;
3 2
; 1
4 ;
3 2
; 1
3 2
; 4
1
R R
R R
R
4 ;
3 2
; 1
3 2
; 4
1
V V
V
2+4; 1+3
4 ;
3 3
; 2
2 ;
1 3
1 ;
4 2
C C
C C
4 ;
3 3
; 2
2 ;
1 4
; 3
3 ;
2 4
; 3
3 ;
2 2
; 1
3 1
; 4
2
R R
R R
R R
R R
R
3
4 ;
3 3
; 2
2 ;
1 3
1 ;
4 2
V V
V V
168