A6211 Buck Regulator: How to Calculate Output Voltage for 200mA LED String?

Good day to all,
Please I need your support on how to calculate the output voltage of this Buck Regulator Led Driver(A6211).I want to use the chip to drive strings of Leds that require a constant current of 200mA and minimum voltage of 38.4V and maximum of 43.2V.The calculation of the Led Current is okay,it is calculated with this formula:

iLED = Vcsreg /Rsense,

however i wasn unable to figure out how to calculate the Output voltage.According to the datasheet,the Minimum Output voltage depends on Minimum (T-on) and the switching frequency.The formula for the T-on and Switching frequency are as:

1----T-on = k x(R-on + Rint) x(Vout/Vin)

2--- Fsw = 1/ [k x (R-on + Rint)] where k=0.0139 and Rint(internal resistance)=5kOhms.
However on page 8 there is another formula for the calculation of the Output Voltage:
Vout = (Vin - Iav x Rds-on) xD - Vd x(1 - D) - RL x Iav
where Iav = average ripple current
D = Duty cycle
RL = Resistance of the inductor
Rds-on = On-Resistance
The duty cycle is giving as:
D= Ton / Ton + Toff where Ton & Toff Minimum is 110ns and Maximum is 150ns
according to the datasheet.
The problem i am having is that i do not know how to determine the Ton and Toff which i can use to calculate the duty cycle.
I was also unable to figure out how to calculate the R-on and Rds-on.
I would be glad if somebody could put me through on how to do These calculations.thank you all for the Support.
Best regards.
NOTE:I attached the datasheet of the chip to this message.

A6211-Datasheet

To actually answer your questions :

*RDS(on)* can be found in the datasheet at *Electrical Characteristics* [*pg 4*] and is *0.25Ω Typical* and *0.4Ω Max* -- (I would use the _Max_ value).

*R-on* is, apparently, the same as *R-ton* [judging by the *Functional Block Diagram* on *pg 3*]

But, as Colin pointed out, the actual Vout is determined by the sum of the forward voltages of all of the LEDs in the series string. And, because this is a *Buck Converter*, the *Input Voltage* must be higher than the voltage across the LEDs [plus _overhead_]. *Page 9 -- Minimum and Maximum Output Voltages* is where you'll find information on what the minimum input voltage must be. This is probably a bit confusing, but what you are looking for, in terms of selecting the proper input voltage, is the *Minimum Input Voltage for the Maximum Output Voltage*. And then select an input voltage that's at or higher than that Minimum Input Voltage [but not higher than the Maximum Input Voltage as stated in the data sheet. That would be: 48V.] The closer you can get to the Minimum Input Voltage, though, the better the efficiency.

The A6211 is a _Current Regulator_. Basically, what a current regulator does is, raise the output voltage until the proper amount of current is flowing in the load [in this case, the _load_ is the LEDs]. It knows when the proper amount of current is flowing through the load by monitoring the voltage across the sense resistor. In the case of the A6211, it raises the voltage across the LEDs until there is 0.2V across the sense resistor. And then, it keeps adjusting the output voltage to keep 0.2V across the sense resistor. And, actually, in the case of the A6211, it maintains an _average_ voltage of 0.2V across the sense resistor. What makes this a current regulator is the fact that it's the _current_ flowing through the sense resistor that changes the voltage across the sense resistor. Thus, it's the _current_ that is being set by that voltage. It's simple *Ohms Law* -- *Ileds = 0.2V/Rsense*.

To determine the voltage across the string of LEDs, get the forward voltage for each LED from the LED's datasheet, and add them up. So, if you have 5 LEDs and each has a forward voltage of 3.6V, then the voltage across the LEDs will be 5*3.6 = 18V.

If this is for production [i.e. will be manufactured in quantity], then I would use the *Maximum* forward voltage indicated in the LEDs datasheet. But, if this is a "one off" [i.e. just making it for yourself or a friend, etc] then that might not be so critical -- the point being, you don't what this thing to be in production and then suddenly you start getting units that fail at quality control because the manufacturer shifted their process, causing the Forward Voltage to increase beyond your design point -- it happens! So always design at the extremes!

For a better understanding of the nature of LEDs and how to drive them properly, check out my Blog at: http://www.sinistercircuits.com/Blog/LEDs_LightemWithoutSmokinem/index.php