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.