28 SUPERCAPACITORS www.we-online.com Issue 1 2024 Power Electronics Europe www.power-mag.com supercapacitor is therefore 100F at a rated voltage of 2.7V. As the minimum required capacitance is 76F, the unit will provide sufficient energy capacity. A step-down converter was selected as the current source for charging, which converts a DC input voltage of 12V to a DC output voltage of 2.7V. The step-up converter used requires an input voltage of at least 1V. For this reason, the calculation must also be based on 1V for the lower supercapacitor voltage (Figure 3). Figure 3 (top) shows the measured and calculated voltage charging characteristic for the supercapacitor as it is charged with a constant current of 3A from 0.95 to 2.7V. During the charging process, the load was switched off. The following parameters were selected for calculating the theoretical curves: RESR + Rp = 0.08Ω, C = 100F and V1 = 2.7V. The voltage increases linearly from the residual voltage of 0.95V to almost 2.7V. During this period, which lasts around 32 to 86 seconds, the current is constantly regulated to 3A. The loading time for this process given by This constant current charging process is followed by a phase of constant voltage charging, as can be seen from the exponential fall in charging current in Figure 3 (bottom). The discharging process The measured data for the discharging process is also compared with the theoretical model. The step-up converter discharges the supercapacitor from = 2.7V to its cut-off voltage of 1V. It supplies a WPT system with a small array of LEDs at a voltage of 5V and a power consumption of approx. 0.75W. The efficiency of the systems is generally not constant, but changes with the input voltage, the ambient temperature, and various design factors. In this example, the efficiency changes from 90% at 2.7V to around 70% as soon as the converter approaches its cut-off voltage of 1V. For simplicity, an average output power of Pc = 0.75W is used, calculated as: The function P(t) was determined experimentally on the basis of the total current and voltage curves of the converter and the LED array. As the calculation was carried out on the basis of an average output power, only the current curve in Figure 4 deviates increasingly from the theoretical curve. The time required for this discharge process is given by: This corresponds to the time after which the measured voltage has dropped from 2.7V to the cut-off voltage of 1V. The voltage curve is shown in Figure 4. A #X++#$# c#( \*Vf#g#l#+Vib#g]#h#bc#9V Figure 2: Example application using a supercapacitor in a wireless power module. !# """#`# X #n7# #!$7%H7&# X++#$ #*#!#+Vfb#.# #\\*Vf#g]"#W# \X#g]"]#h#,*+#9V# Figure 3: Voltage (top) and current (bottom) characteristics for charging the supercapacitor with constant current.
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