Abstract
In this chapter, a four-phase model for high-V in multi-MHz converters is described, which allows a separation of loss causes and loss locations. Non-linear parasitic capacitance, transition losses, dead time, and high-side supply generation have a major impact on the model accuracy. An improved model for both an asynchronous and a synchronous buck converter is proposed, which matches efficiency measurements by less than 3%. A preference for an asynchronous or a synchronous buck converter can be hardly distinguished as the achieved efficiency depends on the operating point, on the available switch technologies, and on the implementation of the high-side supply generation. A synchronous converter is superior in efficiency only if the dead time is precisely regulated to fully eliminate dead time related losses across varying operating points. A design indicator is proposed, which allows to benchmark an efficiency performance of converters independently of the operating point, which enables a comparison of state-of-the-art converters published at different operating points.
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Appendix
Appendix
5.1.1 I Switch Conduction Losses
The total switch conduction losses P cond in buck converter are the sum of the conduction losses P cond,hs of the high-side switch and P cond,ls of the low-side switch.
Average losses over a power switch (conduction losses) in on-state during the on-time t on with an on-state resistance R on,hs of the high-side switch are calculated as
During the on-time of, e.g., the high-side switch, the inductor current is linearly rising from 
to 
(current ramp). In this time, the inductor current is
Inserting (5.20) into (5.19) and solving the integral results in
Expressing (5.21) by the output current by substituting 
leads to
As t on is vanishing in (5.21), the average power for a ramp current is independent of the ramp time. Consequently, the calculation of P cond,ls is accordingly for the falling current ramp from I Lmax to I Lmin during the on-time of the low-side switch, which is t off of the buck converter, with the on-state switch resistance R on,ls.
Thus, the total conduction losses are
Writing the equation in dependence of V
in and V
out by substituting the duty cycle 
results in
The first term of (5.24) shows that the losses of the high-side switches contribute with a factor of 
, while the losses of the low-side switch contribute with a factor of 
.
5.1.2 I Calculation of the DC Losses in the Inductor
The inductor DC losses P L,DC are calculated the same way as the switch conduction losses, as the inductor current ramps are also causing losses at the inductor DC resistance R dcr, instead of the switch on-state resistance. The average power loss P L,DC are thus calculated by modifying (5.23) (substitution of R on,hs and R on,ls) to
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Wittmann, J. (2020). Efficiency and Loss Modeling of High-Vin Multi-MHz Converters. In: Integrated High-Vin Multi-MHz Converters. Springer, Cham. https://doi.org/10.1007/978-3-030-25257-1_5
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DOI: https://doi.org/10.1007/978-3-030-25257-1_5
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