SNVA994A Application note

5.2 Compensation Modeling

These equations model a type II compensation network implemented using a transconductance error amplifier.

Table 5-2 Compensation Modeling Equations

	Simplified Formula	Comprehensive Formula
Feedback Equations
Feedback Transfer Function	Equation 36. $\frac{{\hat{V}}_{C O M P} (s)}{{\hat{V}}_{L O A D} (s)} = {- A}_{F B} \frac{(1 + \frac{s}{ω_{Z_E A}})}{s \times (1 + \frac{s}{ω_{P_E A}})}$
Feedback DC Gain	Equation 37. $A_{F B} = \frac{R_{F B B} \times g_{m}}{(R_{F B B} + R_{F B T}) \times C_{C O M P}}$	Equation 38. $A_{F B} = \frac{R_{F B B} \times g_{m}}{(R_{F B B} + R_{F B T}) \times (C_{C O M P} + C_{H F})}$
Low Frequency Zero	Equation 39. $ω_{Z_E A} = \frac{1}{R_{C O M P} \times C_{C O M P}}$	Equation 40. $ω_{Z_E A} = \frac{1}{R_{C O M P} \times C_{C O M P}}$
High Frequency Pole	Equation 41. $ω_{P_E A} = \frac{1}{R_{C O M P} \times C_{H F}}$	Equation 42. $ω_{P_E A} = \frac{C_{C O M P} + C_{H F}}{R_{C O M P} \times {C_{C O M P} \times C}_{H F}}$
Mid-band Gain	Equation 43. $G_{M I D} = \frac{R_{C O M P} \times R_{R F B B} \times g_{m}}{(R_{F B B} + R_{F B T})}$	Equation 44. $G_{M I D} = \frac{{C_{C O M P} \times R}_{C O M P} \times R_{R F B B} \times g_{m}}{(C_{C O M P} + C_{H F}) \times (R_{F B B} + R_{F B T})}$