Correct formula for primary inductance

In just about every design guide I saw, the formula for primary inductance of flyback is: However in "SMPS Design" by Pressman/Billings the equation for CCM is: To bring second equation to the first form Kr should be = Vin/(Vin-Vds), which is always > 1. Does not look right.

Question: Which equation should I use?

UPDATE: I'm accepting @andy-aka answer because it prompted me to verify the derivations in Pressman's book. Turns out that at some point they use DCM formula dI = 2 x Iedc (instead of CCM dI = 2 x Iedc x Kr) to substitute dI in Lp equation.

So, the answer is: First formula is correct, second is wrong. Although I suspect one of the two Vin(min) in it can be substituted for Vin(min) + Vds to account for voltage drop in a switch, like it is done in the book.

• Set Kr=1 for DCM, and it gives you the DCM equation. The CCM equation is modified by a factor of (Vinmin-Vds)/Vinmin. Is that related to the lower value of Kr by any chance? – Neil_UK Jun 6 '18 at 8:22
• Oops, yeah, I kinda had a brain fart with DCM. Let me edit that out of the question. I don't know about any relationship like that one, though. – Maple Jun 6 '18 at 8:27
• If I use that factor it would mean Kr = Vin/(Vin-Vds), which is > 1. Doesn't look right. – Maple Jun 6 '18 at 8:37

$K_R$ is the ratio of the peak to peak current to the peak current: - So, for the flyback transformer above with 1:1 turns ratio and ignoring the fact that primary currents and secondary currents always fall to zero when the control voltage changes, the peak to peak current is 1.062 amps - 0.531 amps = 0.531 amps. Therefore $K_R$ is clearly 50%.

For DCM peak to peak current is the same as peak current hence $K_R$ is 1 across the range of loads it is used for: - Picture source

• In your first example Kr < 1. In your second example Kr = 1. In the equation from Pressman Kr > 1. I've edited the question to bare minimum to make it clear what I am asking about – Maple Jun 6 '18 at 9:56
• It's reasonably easy to derive for DCM but, for CCM, instead of using Imax for the energy equation, you develop an energy equation that uses Imax and Imin. For DCM Imin is clearly zero of course. Have you thought about deriving it? I have neither of those books so I can't really do an A vs B thing. However I do have suspicions about the 2nd formula because it looks like the DCM formula. – Andy aka Jun 6 '18 at 10:05
• OK, I worked backwards through the derivations in Pressman and found the place where Kr went missing. They have correct formula for Lp = (Vin * D)/(dI * Fsw), then they replace dI = Ieds*2, which should be dI = Ieds*2*Kr. Ieds*2 is indeed DCM case. Wow! I found an error in Pressman/Billings 8O. And I did not know what flyback is a week ago :D – Maple Jun 6 '18 at 10:51
• @Maple well done on that - it's not that hard to solve and once done it's never forgotten! Pressman/Billings take note! – Andy aka Jun 6 '18 at 12:10