General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters

This paper presents a general model and its experimental validation for electrically tunable electromagnetic energy harvesters. Electrical tuning relies on the adjustment of the electrical load so that the maximum output power of the energy harvester occurs at a frequency which is different from the mechanical resonant frequency of the energy harvester. Theoretical analysis shows that for this approach to be feasible the electromagnetic vibration energy harvester’s coupling factor must be maximized so that its resonant frequency can be tuned with the minimum decrease of output power. Two different-sized electromagnetic energy harvesters were built and tested to validate the model. Experimentally, the micro-scale energy harvester has a coupling factor of 0.0035 and an untuned resonant frequency of 70.05 Hz. When excited at 30 mg, it was tuned by 0.23 Hz by changing its capacitive load from 0 to 4000 nF; its effective tuning range is 0.15 Hz for a capacitive load variation from 0 to 1500 nF. The macro-scale energy harvester has a coupling factor of 552.25 and an untuned resonant frequency of 95.1 Hz and 95.5 Hz when excited at 10 mg and 25 mg, respectively. When excited at 10 mg, it was tuned by 3.8 Hz by changing its capacitive load from 0 to 1400 nF; it has an effective tuning range of 3.5 Hz for a capacitive load variation from 0 to 1200 nF. When excited at 25 mg, its resonant frequency was tuned by 4.2 Hz by changing its capacitive load from 0 to 1400 nF; it has an effective tuning range of about 5 Hz. Experimental results were found to agree with the theoretical analysis to within 10%