Page 40 - PEN eBook July 2023
P. 40
Power Supply
The relations among phase-lag (Φ), the angle between zero-crossing current (i t) and falling voltage
2
(v t) denoted by α, the angle between the rising voltage (v t) and (i t) denoted by β and D are given
2
2
2
by Equation 1, where D = 1 – (α ÷ β) ÷ π and Φ = (α – β) ÷ 2.
For unidirectional operations, values of practical interest for α and β are the ones ensuring 0 < D < 1
and –π ÷ 2 < Φ < π ÷ 2. Given V , α, β and the capacitances C and C , the WPTS output power and
s s1 s2
efficiency are influenced by the system’s total losses.
Considering the WPTS first harmonic solution:
The instant where i t crosses zero with the positive derivative is the reference for the phase angles.
2
The equations for the WPTS Tx-Rx coupled loops are:
Where
Applying Fourier formulas to the Tx and Rx voltages and currents provides:
40 JULY 2023 | www.powerelectronicsnews.com
