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2017.10.26 Transfer Function

Switching Transfer Functions: State-Space Averaging Method - From Another Viewpoint

DC/DC Converters: Sharing of Transfer Functions among Control Systems

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In the previous section, we used dynamic analysis to derive equations enabling the derivation of 161110_img01, for the purpose of state-space averaging. This time, we will use an approach based on a different viewpoint to derive the equations derived previously. This depends on an understanding of the basic principles used in equation derivations thus far. The equations and procedures of the previous section are necessary, and are used here again.

The following is the dynamic analysis described the last time. These are equations for the coil current and capacitor charge derived previously. Please review the analysis once again.    

20161020_graf_01

The final equations are written similarly to the last time, and as was explained the last time, if these equations are simultaneous, then 161110_img01 can be determined.

20161020_graf_03-1

From here we embark on this new approach. The following equations 4-28 and 4-29 represent the impedance using 161110_img05 for s.

tf_17_fom28-29

Here, setting 161110_img02 and rearranging, we obtain the following.

tf_17_fom30-31

These equations yield results similarly to the previously derived equations 4-26 and 4-27.

The basic conceptual procedure is:

① Consider the stable state of the system
  1) The coil current does not change in one period
  2) The capacitor charge amount does not change in one period
  ※At this time, express the impedance using161110_img03

② Set 161110_img03, and determine161110_img01

In this way, if the basic principles are understood,161110_img01can be determined comparatively simply.

This concludes our discussion of the state-space averaging method. Because the state-space averaging method is a method of approximation, it should always be kept in mind that the range of applicability and conditions for application of the method are important.

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