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MAX15053 Scheda tecnica(PDF) 17 Page - Maxim Integrated Products |
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MAX15053 Scheda tecnica(HTML) 17 Page - Maxim Integrated Products |
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17 / 21 page  The effect of the inner current loop at higher frequencies is modeled as a double-pole (complex conjugate) fre- quency term, GSAMPLING(s), as shown: ( ) ( ) SAMPLING 2 2 SW C SW 1 Gs ss 1 fQ f = + + π× × π× where the sampling effect quality factor, QC, is: ( ) C S 1 Q K 1 D 0.5 = π× × − − And the resonant frequency is: ωSAMPLING(s) = π × fSW or: SW SAMPLING f f 2 = Having defined the power modulator’s transfer function, the total system transfer can be written as follows (see Figure3): Gain(s) = GFF(s) × GEA(s) × GMOD(DC) × GFILTER(s) × GSAMPLING(s) where: ( ) ( ) ( ) FF FF FF sC R1 1 R2 G s R1 R2 sC R1|| R2 1 + = × + + Leaving CFF empty, GFF(s) becomes: ( ) FF R2 G s R1 R2 = + Also: ( ) ( ) VEA VEA A (dB)/20 CC EA A (dB)/20 C C MV sC R 1 G s 10 10 sC R 1 g + = × + + which simplifies to: ( ) ( ) VEA VEA A (dB)/20 CC EA A (dB)/20 C MV sC R 1 G s 10 10 sC 1 g + = × + VEA A (dB)/20 C MV 10 when R g << ( ) ( ) ( ) OUT FILTER LOAD 1 S OUT LOAD SW sC ESR 1 G sR K 1 D 0.5 1 sC 1 R f L − + = × ×− − ++ × The dominant poles and zeros of the transfer loop gain are shown below: ( ) ( ) VEA MV P1 A (dB)/20 C P2 S 1 OUT LOAD SW P3 SW Z1 CC Z2 OUT g f 2 10 C 1 f K 1 D 0.5 1 2C R fL 1 f f 2 1 f 2 CR 1 f 2 C ESR − = π× × = ×− − π× + × = = π× = π× The order of pole-zero occurrence is: P1 P2 Z1 CO P3 Z2 ff f f f f < ≤< ≤ < Under heavy load, fP2, approaches fZ1.Figure3shows a graphical representation of the asymptotic system closed-loop response, including dominant pole and zero locations. Theloopresponse’sfourthasymptote(inbold,Figure3) is the one of interest in establishing the desired crossover frequency (and determining the compensation component values). A lower crossover frequency provides for stable closed-loop operation at the expense of a slower load- and line-transient response. Increasing the crossover frequency improves the transient response at the (poten- tial) cost of system instability. A standard rule of thumb sets the crossover frequency between 1/10 and 1/5 of the switching frequency. First, select the passive power and decoupling components that meet the application’s requirements. Then, choose the small-signal compen- sation components to achieve the desired closed-loop frequency response and phase margin as outlined in the Closing the Loop: Designing the Compensation Circuitry section. Closing the Loop: Designing the Compensation Circuitry 1) Select the desired crossover frequency. Choose fCO approximately 1/10 to 1/5 of the switching frequency (fSW). 2) Determine RC by setting the system transfer’s fourth asymptote gain equal to unity (assuming fCO > fZ1, fP2, and fP1) where: MAX15053 High-Efficiency, 2A, Current-Mode Synchronous, Step-Down Switching Regulator www.maximintegrated.com Maxim Integrated │ 17 |
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