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ST1S40IPUR Datasheet(PDF) 9 Page - STMicroelectronics |
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ST1S40IPUR Datasheet(HTML) 9 Page - STMicroelectronics |
9 / 30 page ST1S40 Functional description Doc ID 17928 Rev 4 9/30 Three main terms can be identified to obtain the loop transfer function: 1. from control (output of E/A) to output, GCO(s) 2. from output (Vout) to the FB pin, GDIV(s) 3. from the FB pin to control (output of E/A), GEA(s). The transfer function from control to output GCO(s) results: Equation 1 where RLOAD represents the load resistance, Ri (0.3 Ω) the equivalent sensing resistor of the current sense circuitry, ωp the single pole introduced by the LC filter and ωz the zero given by the ESR of the output capacitor. FH(s) accounts for the sampling effect performed by the PWM comparator on the output of the error amplifier that introduces a double pole at one half of the switching frequency. Equation 2 Equation 3 where: Equation 4 Sn represents the ON time slope of the sensed inductor current, Se the slope of the external ramp (VPP peak-to-peak amplitude 1.25 V) that implements the slope compensation to avoid sub-harmonic oscillations at duty cycle over 50%. The sampling effect contribution FH(s) is: Equation 5 where: G CO s () R LOAD R i ------------------ 1 1 R out T SW ⋅ L ---------------------------- m C 1D – () 0,5 – ⋅ [] ⋅ + --------------------------------------------------------------------------------------------- 1 s ω z ------ + 1 s ω p ------ + ---------------------- F H s () ⋅⋅ ⋅ = ω Z 1 ESR C OUT ⋅ ------------------------------- = ω p 1 R LOAD C OUT ⋅ -------------------------------------- m C 1D – () 0,5 – ⋅ LC OUT f SW ⋅⋅ --------------------------------------------- + = m C 1 S e S n ------ + = S e V pp f SW ⋅ = S n V IN V OUT – L ------------------------------ R i ⋅ = F H s () 1 1 s ω n Q P ⋅ ------------------- s 2 ω n 2 ------ ++ ------------------------------------------- = |
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