The number of turns of the primary is N= (Vin*Dmax)/(Ae*Fs*Bmax). For the secondary you just need to chose the conversion ratio. (Vin = input voltage, Ae = core effective area, Fs = switching frequency, Bmax = max magnetic flux density
Don't forget that flyback converter doesn't have a transformer, it's an inductor coupled, so it' better use a gap in it.
- Not very clear what you want to do. Lets assume that the current through the inductor is at all times greater than 0. (the delta-I is smaller than 2*Iavg).
- Lets assume the number of turns of the primary is N1, the number of turns of the secondary is N2.
- Lets assume the primary voltage is V1, the secondary voltage is V2.
- Lets assume there are no losses. If there are losses, you need to use V1', and V2', the primary and secondary voltages corrected for the losses.
- Lets assume the ON time of the primary transistor is T1, the on time of the secondary diode is T2.
- Now we calculate the flux difference during T1, which is equal to the flux difference during T2. (there is a steady-state in the circuit)
delta-flux = V1*T1/N1 = V2*T2/N2
- This gives you the equation for the turns ratio: