Page 41 - PEN eBook July 2023

Power Supply

Merging Equations 3 and 5, we get Equations 6 and 7:

Z , Z , V , M, ω, Φ , Φ and Φ are all known. From Equation 5, V and Φ are functions of α, β and
1 2 1 Z1 Z2 I2 2 V2
V . Given V , V , α and β, the only two functions I and Φ are determined by solving the nonlinear
out s out 2 V1
equation system of Equations 6 and 7 by using the Newton-Raphson algorithm to avoid simplified
approximations.

Neglecting rectifier switching losses, the authors calculated the average output current (I ) of the
out
rectifier as:

Considering that a part of I is lost because of the MOSFET switching losses:
out

The switching current (I ) can be considered as sought by an equivalent dissipative current
sw,rec
source connected in parallel to the rectifier output. Such current effectively allows analysis of the
impact of rectifier switching losses on the output power and efficiency of the WPTS. Accordingly,
the equivalent current I is given by:
sw,rec

From Equations 8, 9 and 10, the net output current (I ), accounting for the effect of the rectifier
out,net
MOSFET losses, is determined. I results correlate to the current I through a nonlinear equation,
out,net 2
which is also dependent on the sign of fire angles α and β. Given α and β, the rectifier I versus V
out out
curve, which also represents the output characteristic of the WPTS, can be determined for different

rectifier MOSFETs to identify the device, ensuring the best power and efficiency performance.

The Tx current I can be determined by:
1

JULY 2023 | www.powerelectronicsnews.com 41