Vin for calculation of number of turns in transformer pirmary

Subject: Input voltage for calculation of transformer pirmary number of turns

Colleagues,

I'm making calculations for a push-pull transformer and following equations in Microchip application note AN1207 (pp.51ff).

\({\Delta} B = \frac{V_P T_{ON}}{N_P A_{core}}\) eq.175

\(N_P=\frac{V_{DC,min}-V_{Q,on}}{A_{core}f_{PWM} {\Delta} B}D_{max}\) eq.176

where
\(V_{DC}\) is the input voltage
\(D_{max}\) is the max PWM duty cycle (between 0 and 0.5 for push-pull topology)

Why do they use \(V_{DC,min}\) and not \(V_{DC,max}\) in this calculation?
I though that higher voltage across the primary will cause higher magnetic flux. Higher magnetic flux can saturate the core.

Any suggestion, insight or reference is really appreciated!

Cheers,
- Nick

I agree that it should be \(V_{DC,max}\). Don't know why they used \(V_{DC,min}\).