A simple scheme to generate the inverter voltage from 1.5V to 3V can be made on the basis of slightly modified the well-known multivibrator. Under these denominations in the scheme of the frequency converter is approximately 130 kHz. Inductance value can be calculated or chosen experimentally. But you can simply adjust the frequency of the converter to produce maximum output voltage. Schottky diode VD1 can be replaced by any other similar characteristics.
Parts list : R1,R3 : 1K R2 : 2K2 C1 : 470pF C2 : 100uF/3,3V C3 : 1000uF L1 : 470uH VD1 : 15MQ040 VT1, VT2 : BC547