# 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: -