Stuff we learned:
max duty cycle should be between 0.4 - 0.6 (we’ll spec it to be 0.5)
operating switching frequency should be between 50 to 140 kHz
For CCM flyback primary inductance:
Innoswitch Example:
Nominal Primary Inductance of 430 microH
0.312 duty cycle
Vin max-410v
Vin min- 310v
100 kHz\
32 inductor turns
Po- 189 W
0.6 Z factor
Primary Side Inductance Calculation:
DCM formula: https://www.infineon.com/dgdl/an-1024.pdf?fileId=5546d462533600a401535591115e0f6d
If Cres doesn’t exist (which doesnt exist in the InnoSwitch design), then the following formula comes out (found on a different DCM source, https://www.monolithicpower.com/how-to-design-a-flyback-converter-in-seven-steps )
To check whether that formula is correct, let’s take the 180W innoswitch example and then plug in their design parameters and see if the inductance we get is close to what they used:
We don’t know how FACTOR_Z impacts the primary inductor calcs, so we’ll just ignore that.
What is z-factor btw
https://piexpertonline.power.com/help/piexpert/en/topics/z_factor_definition.htm
Plugging in the values yields 414.1 uH, which is very close to the 430uH they used!
So now we can calculate with our parameters:
efficiency = 95% (the 180W example used 97% in calculation, but only achieved 95% irl)
Vin_min = 90V (min voltage of battery pack)
Pout_max = 70W (a little more than the 60W expected max power draw in requirements page)
K = 1 (because DCM)
f = 55 kHz (datasheet recommends 50-140kHz, but since lower freq is more efficient (less switching loss), we will also pick a low value. 55 is between 50 ('recommded min) and 57, which is the 180W example amount)
So the L we get from the above equation is the maximum primary side inductance we can use such that the converter is always in DCM, even in worst-case scenarios (which were the inputs to the above).
We will also spec the inductor to be slightly less than 250uH, just to be safe, so L = 240uH.
Using that inductance value, we can then reverse-calculate the duty cycle we expect to see at certain operating parameters (pack voltage and power consumption):
Nominal duty cycle of 0.23 is reasonable, so L = 240uH is reasonable!
Turns Ratio Calculation
Output voltage is a function of turns ratio, input voltage and duty cycle, in the following formula:
In our applications, since the input voltage is significantly higher than the output voltage, we expect N2 to be less than N1. Also, since it’s a ratio, we can define the ratio as ‘n:1’, where n is the number of coils on the primary side for a given number of coils on the secondary side (simplified to 1 for math’s purposes)
So then, the formula becomes:
Then, clearly, if n is very large, then D has to be larger to compensate in order to keep Vout the same. Likewise, is n is smaller, then D has to be smaller to compensate.
We will define the ‘worst case scenario’ as when D is as large as possible (0.5), and ask ‘at this point, what is the MAXIMUM value of n before the output voltage can no longer be the desired amount (12V). We will actually round 12V up to 12.5 just to be safe. In this worst-case scenario, we also will define the Vin to be the minimum (90V), since lower Vin means larger D.
So then, we define our worst-case parameters as follows:
Therefore, for an N:1 turns-ratio transformer, N must be less than 7.2. Conveniently, we will pick N=7, so our transformer should have a 7:1 primary to secondary turns ratio