2018.06.21 Transfer Function
The last two sections were devoted to Part 1 and Part 2 of "Examples of Transfer Function Derivation for Step-Up/Step-Down Converters". This time, we will study the "Effect of the ON-Resistance of a Switch on the Transfer Functions".
In this study as well, we will take the same approach as used before. As before, the transfer functions to be derived are and , and once again, the transfer functions are derived in two steps.
Effect of the ON-Resistance of a Switch on the Transfer Functions
In transfer function derivations up till now, the effect of the ON-resistance of a switch (switching transistor) has not been considered. However, it is well known that in actuality a switch has an ON-resistance, and that the ON-resistance affects the actual operation. Here, we consider the effect of this parameter of the switch ON-resistance.
We start with the step-up/step-down converter for which ton≠ton’ in " Example of Transfer Function Derivation for a Step-Up/Step-Down Converter - 2 ", and use a similar procedure.
The circuit on the right is the simplified circuit for the step-up/step-down converter described the last time, with the ON-resistance for the MOSFET that is the switch indicated by RONp and RONn.
●Step 1: Consider the stable states of the system
① The coil current does not change over
② The capacitor charge amount does
not change over one period
Terms (in red) relating to the ON-resistance are added to the equation.
●Step 2: Determine change amounts for an external disturbance, and describe the transfer functions
A calculation example from equations 5-27 and 5-28 above is shown below.
Upon substituting , , in equations 5-27 and 5-28, the following is obtained.
Taking equations 5-31 and 5-32 as a system of simultaneous equations and determining and , we obtain the following.
As can be seen from the results, the first-order imaginary terms differ considerably. This is as was explained in the chapter "What are Transfer Functions"; here, we present only the characteristic results in the graphs that follow.
Finally, the total transfer functions with and without the ON-resistance added are summarized below.