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Transfer Function

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

Example of Deviation for a Step-up Converter

In succession to the previous discussion of step-down converters, this time we present a derivation example for step-up converters. Please refer to the previous section as necessary.

Example of Transfer Function Derivation for Step-up Converters

This time, we shall derive the transfer functions for a step-up converter. But as with a step-down converter, the transfer functions to be derived are and . When deriving the transfer functions for step-down converters, the following two steps were taken; and when addressing step-up converters as well, we resort to the same steps for our derivation of the transfer functions.

t20_graf01

●Step 1: Consider the stable states of the system

The procedure is similar to that for the step-down converter. Figure 6 is the basic circuit of a diode-rectified step-up converter. The stable states of the system are the following two states; each is represented by an equation and a graph.

① The coil current does not change over one period
② The capacitor charge amount does not change over one period

t20_graf02

t20_graf03

●Step 2: Determine change amounts for an external disturbance, and describe the transfer functions

Calculation examples are shown below.

t20_graf04

Upon substituting in equations 5-7 and 5-8, the following are obtained.

t20_graf05

Then, taking equations 5-11 and 5-12 to be simultaneous equations and determining dentatsu_170314_01 and dentatsu_170314_02 , we obtain the following.

t20_graf06

For the sake of comparison, the transfer functions have been provided along with those for step-down converters. Of course, the derivation results are different, but what should be noted here is that the same approach as with the step-down mode is used for the step-up mode as well to derive dentatsu_170314_01 and dentatsu_170314_02.

Key Points:

・For both types of converter, what are derived are Δvout/ΔD and ΔiL/ΔD.

・Transfer functions are derived in two steps--by considering the stable states of the system, and then by determine the amount of change given for an external disturbance.

・In this section, we derived the transfer functions for a step-up converter, but the approach was entirely the same as the derivation for a step-down converter.


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