FAN5069_08 Datasheet, PDF (17/22 Pages) Fairchild Semiconductor – PWM and LDO Controller Combo

Poles and Zeros of Plant Transfer Function:
Plant zero frequency = f_z = ₂-----_×-----_π-----_×-----_C1----_o----_×-----_R-----_e---_s
Plant 1^st pole frequency = f_p1 = ₂-----_×-----_π-----_×-----_⎝⎛--_C-----_o-¹---_×-----_R-----_p----+-----_R-L--------_eL----_⎠⎞-
Plant 2^nd pole frequency =
f_p2
=
2^-----1×^-----π^--
×
⎛
⎝
C^-----_o^----1×^-----R^-----_L^-
+
R_{-L----ep-⎠⎞}
Plant 3^rd pole frequency = f_p3 = ₂----^ω-_×---ⁿ²--_π--^×---_×--^L---_R-^e---_p-
Plant gain (magnitude) response:
G_p (f) = 20 × logM₀ + 10 × log ---₁-----+-----_⎝⎛---_{f----p--f----1---⎠⎞}---₂-------_×--------₁-¹----+-+---_⎝⎛--^⎝⎛-_f-----^f_p---^ff_--^z---_2--^⎠⎞--_⎠⎞-²--₂-------_×-------₁-----+-----_⎝⎛---_{f----p--f----3---⎠⎞}---₂----
(EQ. 28)
(EQ. 29)
(EQ. 30)
(EQ. 31)
(EQ. 32)
Plant phase response:
∠G_P(f)
=
tan^–1 _⎝⎛ -_f-^f_z-_⎠⎞
– tan^–1_⎝⎛-_f-_p-^f--₁-_⎠⎞
– tan^–1_{⎝⎛f}--_p-^f--₂-_⎠⎞
–
–tan^–1
⎛
⎝
f^--_p^-f--₃^{-⎠⎞}
(EQ. 33)
Choose R1, R_BIAS to set the output voltage using EQ.6. Choose the zero crossover frequency F_cross of the overall
loop. Typically F_cross should be less than fifth of F_sw. Choose the desired phase margin; typically between 60° to 90°.
Calculate plant gain at F_cross using EQ.34 by substituting F_cross in place of f. The gain that the amplifier needs to pro-
vide to get the required crossover is given by:
G_AMP = --_G-----_p----₍---_F-¹---_c--_r--_o---_s---_s---₎
(EQ. 34)
The phase boost required is calculated as given in (EQ. 35)
Phase Boost = M – ∠G_P(F_cross ) – 90°
where M is the desired phase margin in degrees.
The feedback component values are calculated as given in equations below:
K
=
⎧
⎨^Tan
⎩
⎛
⎝
B_-----o_--4--o_---s_----t_⎠⎞
+ 45
⎫²
⎬
⎭
C2 = ₂-----_×-----_π-----_×-----_F----_c--_r--_o---_s---_s-¹---_×-----_G----_A----_M----_P-----_×-----_R----₁--
C1 = C2 × (K – 1)
C3 = -------------------------------¹--------------------------------
2 × π × F_cross × K × R3
R2 = ₂-----_×-----_π-----_×-----_F----_c--^K_r--_o---_s---_s----_×-----_C----₁--
R3 = ₍---_K---^R--–--¹---₁----₎
(EQ. 35)
(EQ. 36)
(EQ. 37)
(EQ. 38)
(EQ. 39)
(EQ. 40)
(EQ. 41)
© 2005 Fairchild Semiconductor Corporation
FAN5069 Rev. 1.1.5
17
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