Frequency Response of the Current Output

Подпись: i (t) —ш2 W0ej ш Frequency Response of the Current Output Frequency Response of the Current Output Подпись: (3.86)

If the voltage FRF given by Equation (3.85) is divided by the load resistance, the multi-mode current FRF is obtained as

Подпись: 0 1000 2000 3000 4000 5000 Frequency [Hz] Figure 3.8 Current FRFs of the bimorph for a broad range of load resistance (series connection of the piezoceramic layers)
The modulus of the current FRF is plotted versus the frequency in Figure 3.8. Unlike the voltage FRF shown in Figure 3.5, the amplitude of the current at every frequency decreases with increasing load resistance. Indeed this is the opposite of the voltage behavior shown in Figure 3.8, but the behavior at every frequency is still monotonic. For every excitation frequency, the maximum value of the current is obtained when the system is close to short- circuit conditions. The enlarged views of the current FRFs around the first two resonance frequencies are plotted in Figure 3.9, showing the change in the resonance frequency with increasing load resistance. Moreover, being analogous to the behavior of voltage output close to open-circuit conditions, the current FRFs become indistinguishable close to short-circuit conditions. That is, if one plotted the current FRF of the 10 ^ case, the resulting curve would not look any different than that of the 100 ^ case.

Frequency Response of the Current Output
Подпись: -100 Q 1 kQ 10 kQ  100 kQ Д-— — і 1 MQ  , ^ 10 MQ Ri increases — 1100 1150 1200 1250 Frequency [Hz]

Frequency Response of the Current OutputFigure 3.9 Current FRFs of the bimorph with a focus on the first two vibration modes: (a) mode 1; and (b) mode 2 (series connection)

Figure 3.10 shows the current output as a function of load resistance for excitations at the fundamental short-circuit and open-circuit resonance frequencies. It is clear from Figure 3.10 that the current output is very insensitive to the variations of the region of low load resistance (i. e., the slope is almost zero for Rl ^ 0). In this region of relatively low load resistance, the current output is larger at the short-circuit resonance frequency, as in the case of the voltage output (in Figure 3.7), since the system is close to short-circuit conditions. Then, the current output starts decreasing with increasing load resistance and the curves intersect at a certain value of load resistance (around 120 Ш). For the values of load resistance larger than the value at this intersection point, the current output at the open-circuit resonance frequency becomes larger since the system approaches the open-circuit conditions. As in the voltage versus load resistance graph, the asymptotic trends for Rl ^ 0 and Ri appear to

Frequency Response of the Current Output

be linear.

Updated: September 27, 2015 — 7:20 am