In this example, the main equations governing the weight and the losses in the different elements of a converter are simplified and assembled to show
how the switching frequency impacts the weight and efficiency of a converter.
Semiconductor : 0 weight, constant conduction losses plus switching losses proportionnal with switching frequency
Filter : LC product chosen to respect V@150kHz<73dBuV, L/C ratio chosen to limit voltage dip/overshoot to 10%
Inductor : Weight assumed to be as k.(L.Ipk.Irms)^(3/4) and losses to be as k'.weight, with k and k' identified on a 2kg, 1mH, 100A (pk & rms) inductor with 60W losses
Capacitor : Weight assumed to be as k".C.Vē and no losses with k" identified on a 1mF, 600V, 330g capacitor
Heatsink : 0 losses, weight inversely proportional to Rth, Rth calculated to extract semiconductor and filter losses while respecting deltaTetha
Specs : User defined values for input voltage, output current and difference of temperature between ambiant and heatsink, and values of switching frequency to be scanned.
With such very simple equations the general behaviour of the power desnity/efficiency tradeoff is shown; very low switching frequency requires bulky passive
components with a lot of losses in the inductor, at high switching frequency the increase of switching losses makes the heatsink very big, and in between
there is a switching frequency that optimizes efficiency and another one that maximizes power density.
Of course, more accurate results would require more sophisticated models of the different components, and the present sheet should only be used for understanding the
different tradeoffs. However, quite good results can be obtained if the different coefficient used in the formulas are tuned for a given application
(which is basically the equivalent of small-signal variation around a given design).