Buck circuit inductance calculation 2

I was talking about calculating critical mode of buck converter inductance, given that when input voltage is constant, if my input voltage is AC voltage, for example, input source is a battery, at this time we need to read maximum voltage and maximum voltage of inductance. At minimum voltage running at full load, what voltage is maximum peak inductor current in discontinuous mode?

First, determine input maximum DC voltage Uin_max, minimum DC voltage Uin_min, output voltage Uo and output current Io.

Depending on input voltage, maximum and minimum duty cycle can be calculated,

Maximum Duty Cycle ······················································································· ····················Formula 1

Minimum duty cycle ······················································································· ·························································································· ·····································

The average current in Buck inductor is Io. If designed to be critical below lowest input voltage, it will be intermittent over the entire input range.

According to above figure, if output voltage and current are constant, current of inductor varies with input voltage,

Switch on time in critical mode ··············Formula 3

Handset off time ······················································································· ················​​

And because ······················································································· ··· ···Formula 5

According to duty cycle formula, when input voltage becomes higher, D becomes smaller, so Ton becomes smaller, and average current Io of inductor per cycle remains unchanged. Assuming that peak current of inductor remains unchanged, then inductor flows through current section of triangle formed over time =Io×T, period of T is fixed and Ton becomes smaller. If peak current remains same, that is, △I does not change, and output voltage does not change, if Tm is fixed and T does not change, This will cause Io will become smaller, which is same as previous Required Io does not break phase, To keep Io unchanged, only peak value becomes larger. Let's prove it below.

according to The change in inductance current can be calculated

········Formula 6

According to formula 1 and formula 5, formula 6 can be converted to following formula

Formula 7

From meaning of formula 7, when Uin becomes larger, △I becomes larger.

According to above conclusions, it can be concluded that maximum peak current of step-down inductor occurs at lowest input voltage.

Knowing maximum peak current of inductor, we can calculate number of turns of inductor,

Choose Ae carefully, and △B in intermittent mode is in range of 0.2-0.25T

Number of turns of inductor

Example: Input voltage 18V-26V, required output voltage 12V, output current 2A, calculate inductance and number of turns, select EE16 magnetic circuit, work in critical and intermittent modes, switching frequency 60kHz, diode Voltage drop Vd=0, 7V, if necessary, it can be installed at a critical point below maximum voltage, because output current 2A.

Peak current at critical point

Maximum load at lowest voltage

Inductance inductance

The actual value is 15 µH, cross-sectional area of ​​the conductor is EE16

According to above conclusions

Here △I is generated at maximum voltage

Number of turns of inductor = 24 turns