SNVA994 Application note

5.1 Flyback Regulator Modulator Modeling

These equations model the plant of a peak current mode flyback regulator in continuous conduction mode.

Table 5-1 Control Loop Equations

	Simplified Formula	Comprehensive Formula
Modulator Equations
Modulator Transfer Function	Equation 26. $\frac{{\hat{V}}_{L O A D} (s)}{{\hat{V}}_{C O M P} (s)} = A_{M} \frac{(1 + \frac{s}{ω_{Z_E S R}}) (1 - \frac{s}{ω_{Z_R H P}})}{(1 + \frac{s}{ω_{P_L F}})}$	Equation 27. $\frac{{\hat{V}}_{L O A D} (s)}{{\hat{V}}_{C O M P} (s)} = A_{M} \frac{(1 + \frac{s}{ω_{Z_E S R}}) (1 - \frac{s}{ω_{Z_R H P}})}{(1 + \frac{s}{ω_{P_L F}}) (1 + \frac{s}{{Q \times ω}_{n}} + \frac{s^{2}}{{ω_{n}}^{2}})}$
Modulator DC Gain	Equation 28. $A_{M} = G_{C O M P} \times \frac{N_{P}}{N_{S}} \frac{{V_{L O A D}}^{2}}{P_{O U T}} \frac{(1 - D)}{(1 + D) \times A_{C S} \times R_{S}}$
RHP Zero	Equation 29. $ω_{Z_R H P} = \frac{\frac{{N_{P}}^{2}}{{N_{S}}^{2}} \times \frac{{V_{L O A D}}^{2}}{P_{O U T}} \times {(1 - D)}^{2}}{L_{M} \times D}$
ESR Zero	Equation 30. $ω_{Z_E S R} = \frac{1}{C_{L O A D} \times R_{E S R}}$
Low Frequency Pole	Equation 31. $ω_{P_L F} = \frac{1 + D}{C_{L O A D} \times \frac{{V_{L O A D}}^{2}}{P_{O U T}}}$
Sub-Harmonic Double Pole	Not Considered	Equation 32. $ω_{n} = π \times f_{S W}$
Quality Factor	Not Considered	Equation 33. $Q = \frac{1}{π [D^{'} \times (1 + \frac{s_{e}}{s_{n}}) - \frac{1}{2}]}$
Slope Compensation	Not Considered	Equation 34. $s_{e} = (V_{S L O P E} + I_{S L O P E} \times R_{S L}) \times f_{S W}$
Sensed Rising Inductor Slope	Not Considered	Equation 35. $s_{n} = \frac{V_{S U P P L Y} \times (1 - D) \times R_{S} \times A_{C S}}{L_{M}}$