3. Discontinuous conduction mode in a flyback converter including diode forward voltage drop The nonideal flyback converter illustrated in Fig. 1 employs a diode having forward voltagedrop Vo. For this

problem, you should assume all other elements are ideal. Lm is themagnetizing inductance referred to the transformer secondary side as indicated. Thetransformer turns ratio is n1:n2. Express your results in terms of the transistor duty cycle D, the input voltage Vg, the diode forward voltage drop VD, the transformer turns n1 and n2, and the dimensionless parameter K = 2 LM/RT; where Ts is the switching period. (a) (15 points) Derive an expression for the conditions under which this converter operates in the discontinuous conduction mode. Express your result in the form K< Kcrit, and give an expression for Kcrit- (b) (15 points) Derive an equation for the steady-state output voltage V. Manipulate your equation into the form V = f(D, K, Vg, VD, n1, n2)

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7