Fig. 2 (a) A case study of gain with frequency variation for excitation inductance Lt=∞. (b) The gain curve as a function of frequency for different inductances Lr for LCLLC circuit. (c) The output gain as a function of frequency for different inductance Lt for LCLLC circuit. (d) The fitting results on the first resonant frequency F as a function of the different inductance. The R2 is 0.986 of the LCLLC structure and 0.995 of the LCLC structure, respectively. (e) The resonant gain of LCLC&LCLLC circuits at the frequency of 200kHz. (f) The gain relationship between the different transformer inductances Lt corresponding to the different capacitive loads at the target frequency of 200 kHz.
Based on Eq. (6), the target frequency (200 kHz) could be shifted to first resonant frequency when Lt is 10.5 μH. Fig. 2d indicates a compared study between the fitted curve between Eq. (5) (adjusting Lr , named LCLC) and Eq. (6) (adjusting Lt , named LCLLC). The descending rate near 200 kHz by LCLLC is lower than that by LCLC. The attenuation rate (0.90) is similar with the result by adjustment of Lr (0.928). However, coefficient of attenuation term by adjustment of Lt (74.31) is lower than that by adjustment of Lr (200). Moreover, the curve by LCLLC with adjusting excitation inductance of transformer shows a slow change near the targeted frequency (200 kHz), while a relatively large change for LCLLC with adjusting inductance of first resonant frequency. Fig. 2d demonstrates that with a large range of excitation inductances, the resonant frequency changes in a relatively narrow change, which indicates that fine turning of excitation inductance of transformer is a proper way to shift targeted frequency to resonant frequency.
Fig. 2e shows the voltage gain for LCLC and LCLLC resonant step-up tanks when the same targeted frequency (200 kHz) is first resonant frequency. The Lr is 4.1 μH for LCLC circuit, whileLt is 10.5 μH for LCLLC circuit. Fig. 2e shows that the voltage gain of the LCLLC circuit structure is 72.91 dB, compared to 52.24 dB for the LCLC circuit. Furthermore, the voltage gain of third harmonic (600 kHz) is only -32 dB, which is also lower than that by LCLC (-27dB).
The above theoretical analysis showed a simple way to select parameters of resonant step-up tank. First, the tentative parameters of step-up tank based on the targeted resonant frequency and voltage gain. Then, the parameter sweeps of Lt (excitation inductance of transformer) was employed on the condition without high-order harmonics. The least-square fitting is also used to process the simulated data between first resonant frequency and values ofLt . Finally, an adaptive commercial excitation inductance of transformer is selected to shift targeted frequency to resonant frequency, then boost the output voltage.
Due to the individual difference, the capacitive bio-load by TTFields also changes in a certain range, which could interference the resonant step-up converter, then affect output voltage. Since the bio-load is a capacitive impedance for TTField treatment, which could involves the resonant step-up tank. Fig. 2f shows the voltage gain with capacitive impedance change. With proper selction of excitation inductance, the maximum voltage gain at resonant frequency can be also achieved with proper excitation inductance for bio-loads with 60-90 Ω.