LTC4020 Inductor Calculation

Hello,

I am currently involved in the design of an universal and microcontroller based battery charger system.

The key requirements are:
- 10A charge current
- VIN ranging from 9V to 48V
- Battery Voltage Range from 3V to 53V
- Adjustable Charge current
- Adjustable Input current
- Adjustable Battery Voltage
- Adjustable Battery Chemistry

All adjustable parameters should be easily changeable by an embedded microcontroller.

First i tried to calculate the min. inductor value according to datasheet page 23.
The values i got seems to be a bit to small to me, so i searched the analog forums and found this two entries:

https://ez.analog.com/power/f/q-a/91126/ltc4020-no-load-stability/303105#303105

and https://ez.analog.com/power/f/q-a/100595/ltc4020-unstable-operation/303106#303106

Both are saying, that the formula specified on page 23 use an extra 'Imax' term in the denominator, which shouldn't be there.
Does this mean this is an errata in the datasheet?

I defined the worst cases and calculate it exactly according to the datasheet:

- Buck:
VinMax -> VinMax/2 (48V -> 24V)

Lmin = (Vout x (1- (Vout/VinMax)) / (fo x IRipple x IMAX) = (24V x (1- (24V/48V)) / (120kHz x 5A x 10A) = 2µH


- Boost:
VinMax -> VoutMax (48V -> 53V)

Lmin = (Vin x (1- (VinMax/VoutMax)) / (fo x IRipple + IMAX) = (48V x (1- (48V/53V)) / (120kHz x 3,23A x 11,042A) = ~ 1,06µH


If i remove the "Imax" denominator i get this values:
LminBuck  = ~ 20µH
LminBoost = ~11,7µH

This is quite a massive difference - so wich value is the correct one?
For me the second values seems to be more common in such power devices?

Another questions regarding the adjustable option:
1. ILIM and RNG/SS is adjusted by an DS4432 current sink DAC -> could this be suitable for this application?
2. Battery Voltage are adjusted using an 12bit voltage buffered DAC which makes an offset to the feedback node -> possible and accurate enough?

Kind Regards
Danie