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ADP3188 Datasheet(PDF) 21 Page - Analog Devices |
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ADP3188 Datasheet(HTML) 21 Page - Analog Devices |
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21 / 28 page  ADP3188 Rev. A | Page 21 of 28 A type-three compensator on the voltage feedback is adequate for proper compensation of the output filter. Equations 25 to 29 yield an optimal starting point for the design; some adjustments may be necessary to account for PCB and component parasitic effects (see the section). The first step is to compute the time constants for all of the poles and zeros in the system ( ) VID O X RT VID RT L DS D O E V R C n V D n L V V R R A R n R × × × × × − × × + × + × + × = 1 2 ( ) Ω m 24.2 V 1.3 Ω m 1 mF 4.45 4 V 0.49 0.432 1 nH 320 2 V 1.3 V 0.49 Ω m 1.4 Ω m 2.4 5 Ω m 1 4 = × × × × − × × + × + × + × = E R (25) () () µs 2.50 Ω m 10.63 Ω m 0.65 Ω m 1 Ω m 1 pH 350 Ω m 0.5 Ω m 1 mF 4.45 = − × + − × = ′ − × + ′ − × = X O O X O X A R R R R L R R C T (26) () ( ) ns 580 mF 4.45 Ω m 1 Ω m 0.5 Ω m 0.63 = × − + = × − ′ + = X O X B C R R R T (27) µs 4.7 Ω m 24.2 V 1.3 kHz 330 2 Ω m 2.4 5 nH 320 V 0.49 2 = × ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ × × − × = × ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ × × − × = E VID SW DS D RT C R V f R A L V T (28) () ( ) () ns 333 Ω m 1 µF 180 Ω m 0.5 Ω m 1 mF 4.45 Ω m 1 µF 180 mF 4.45 ' 2 2 = × + − × × × = × + − × × × = O Z O X O Z X D R C R R C R C C T (29) where, for the ADP3188, R' is the PCB resistance from the bulk capacitors to the ceramics and where RDS is the total low- side MOSFET on resistance per phase. In this example, AD is 5, VRT equals 0.49 V, R' is approximately 0.5 mΩ (assuming a 4-layer, 1 ounce motherboard), and LX is 350 pH for the eight Al-Poly capacitors. The compensation values can then be solved using the following: pF 342 Ω k 1.21 Ω m 24.2 µs 2.50 Ω m 1 4 = × × × = × × × = CA R R T R n C B E A O A (30) Ω k 13.7 pF 342 µs 4.7 = = = A C A C T R (31) nF 479 Ω k 1.21 ns 580 = = = B B B R T C (32) F p 24.3 Ω k 13.7 ns 333 = = = A D FB R T C (33) These are the starting values, prior to tuning the design, to account for layout and other parasitic effects (see the section). The final values selected after tuning are pF 22 pF 470 Ω k 1 . 12 pF 470 = = = = FB B A A C C R C |
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