FAN5069_08 Datasheet, PDF (16/22 Pages) Fairchild Semiconductor – PWM and LDO Controller Combo

FAN5069 has a high gain error amplifier around which
the loop is closed. Figure 24 shows a Type-3 compensa-
tion network. For Type-2 compensation, R3 and C3 are
not used. Since the FAN5069 architecture employs sum-
ming current mode, Type-2 compensation can be used
for most applications.
For further information about Type-2 compensation
networks, refer to:
■ Venable, H. Dean, "The K factor: A new mathematical
tool for stability analysis and synthesis,” Proceedings
of Powercon, March 1983.
Note: For critical applications requiring wide loop
bandwidth using very low ESR output capacitors,
use Type-3 compensation.
Type 3 Feedback Component Calculations
Use the following steps to calculate feedback components:
Notation:
C₀ = Net Output Filter capacitance
G_p(s) = Net Gain of Plant = control-to-output transfer function
L = Inductor Value
R_DSON = ON-state Drain-to Source Resistance of Low-side MOSFET
R_es = Net ESR of the Output Filter Capacitors
R_L = Load Resistance
T_s = Switching Period
V_IN = Input Voltage
F_SW = Switching Frequency
Equations:
Effective current sense resistance = R_i = 7 × R_DSON
Current modulator DC gain = M_i = ^R-_R----^L-_i
Effective ramp amplitude = _{Vm = 3.33 × 10}¹⁰ _× ⁽_---^V_----^I_--^N_{----R-–---r-}¹_-a---^._m-⁸_----p⁾_---^×_-----^T_----^s_-
Voltage modulator DC gain = M_v = ^V-_V----^Im-^N--
Plant DC gain = M_o = M_v || M_i = -_MM-----_vv----+^×----^MM-----ⁱⁱ
Sampling gain natural frequency = ω_n = _T--^π--_s-
Sampling gain quality factor (damping) = Q_z = ^–--_π--²-
Effective inductance
=
L_e
=
M_-M-----Ov--
×
⎛
⎝
L
+
-_ω^M----_n-^v---_×-^×----_Q-^R----_{zi ⎠⎞}
R_p = -_MM-----_vv----_××----_RR-----_ii--+^×-----^RR-----^LL- = (M_v × R_i) || R_L
(EQ. 19)
(EQ. 20)
(EQ. 21)
(EQ. 22)
(EQ. 23)
(EQ. 24)
(EQ. 25)
(EQ. 26)
(EQ. 27)
© 2005 Fairchild Semiconductor Corporation
FAN5069 Rev. 1.1.5
16
www.fairchildsemi.com