2018.01.11

Points of this article

・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.

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.

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.

●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

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

Calculation examples are shown below.

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

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

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 and .

Downloadable materials, including lecture materials from ROHM-sponsored seminars and a selection guide for DC-DC converters, are now available.

- Transfer function of each converter
- Switching Transfer Functions: Derivation of Step-down Mode Transfer Functions Serving as a Foundation
- Example of Derivation for a Step-Down Converter
- Example of Derivation for a Step-Up/Step-Down Converter – 1
- Example of Derivation for a Step-Up/Step-Down Converter – 2

- What are transfer functions?
- What is the Transfer Function of an Amplifier?
- What is the Transfer Function of a Slope?
- What is the switching transfer function?
- Transfer function of each converter
- Example of Derivation for a Step-Down Converter
- Example of Derivation for a Step-Up/Step-Down Converter – 1
- Example of Derivation for a Step-Up/Step-Down Converter – 2
- Switching Transfer Functions: Derivation of Step-down Mode Transfer Functions Serving as a Foundation