MAX1530_09 Datasheet, PDF (25/33 Pages) Maxim Integrated Products – Multiple-Output Power-Supply Controllers for LCD Monitors

Multiple-Output Power-Supply Controllers for
LCD Monitors
amplifier g_m, the compensation resistor R_COMP, the FB
regulation V_FB, and the output voltage set point V_OUT:
V_OUT
V_{UNDER_ AC} =
×
⎛ A_VCS × R_DS(ON) × ΔI_LOAD⎞
⎝⎜ ^+ΔSC_UNDER
⎠⎟
V_FB × R_COMP × g_m
Use the following to calculate the slope compensation
change during the sag:
ΔSC_UNDER =
437.5mV ×
⎛
⎝⎜^{DUNDER -}
V_OUT
V_IN
⎞
⎠⎟
where D_UNDER is the duty cycle at the valley of the sag,
which is usually 50%.
The actual undershoot is always equal to or bigger than
the worst of V_{ESR_STEP}, V_{SAG_LC}, and V_{UNDER_AC}.
The amplitude of the soar due to the finite output
capacitance and inductor slew rate is a function of the
load step, the output capacitor value, the inductor
value, and the output voltage:
V_{SOAR _ LC}
=
2
L
×
× (ΔI_LOAD)²
C_OUT × V_OUT
The amplitude of the overshoot due to the AC load reg-
ulation is:
V_OUT
V_{OVER_ AC} =
×
⎛ A_VCS × R_DS(ON) × ΔI_LOAD⎞
⎝⎜ ^+ΔSC_OVER
⎠⎟
V_FB × R_COMP × g_m
where ΔSC_OVER is the change of the slope compensa-
tion during the overshoot, given by:
ΔSC_OVER =
437.5mV
×
⎛
⎝⎜
V_OUT
V_IN
-
⎞
D_{OVER⎠⎟}
where D_OVER is the duty cycle at the peak of the over-
shoot, which is typically 0%.
Similarly, the actual overshoot is always equal to or big-
ger than the worst of V_{ESR_STEP}, V_{SOAR_LC}, and
V_{OVER_AC}.
Given the component values in the circuit of Figure 1,
during a 1.5A step load transient, the voltage step due to
capacitor ESR is negligible. The voltage sag due to finite
capacitance and inductor slew rate is 81mV, and the
voltage undershoot due to the AC load regulation is
170mV. The total undershoot seen in the Typical
Operating Characteristics is 170mV. The voltage soar
due to finite capacitance and inductor slew rate is
155mV, and the voltage overshoot due to the AC load
regulation is 167mV. The total overshoot seen the in the
Typical Operating Characteristics is 200mV.
Compensation Design
The step-down controller of the MAX1530/MAX1531
uses a peak current-mode control scheme that regu-
lates the output voltage by forcing the required current
through the inductor. The MAX1530/MAX1531 use the
voltage across the high-side MOSFET’s R_DS(ON) to
sense the inductor current. Using the current-sense
amplifier’s output signal and the amplified feedback
voltage sensed at FB, the control loop sets the peak
inductor current by:
I_PEAK
=
(V_OUT - V_OUT(SET)) × V_FB
V_OUT(SET) × R_DS(ON) ×
× A_VEA
A_VCS
where V_FB = 1.238V is the FB regulation voltage, A_VCS
is the gain of the current-sense amplifier (3.5 typical),
A_VEA is the DC gain of the error amplifier (2000 typ),
V_OUT(SET) is the output voltage set point, and R_DS(ON)
is the on-resistance of the high-side MOSFET.
The total DC loop gain (A_DC) is approximately:
A_DC
=
V_FB ×
V_OUT(SET)
R_LE × A_VEA
× R_DS(ON) × A_VCS
R_LE is the equivalent load resistance, given by:
R_LE =
⎛
⎜
⎝
V_OUT
I_LOAD(MAX)
⎞
⎟
⎠
||
⎛
⎝⎜
L
n
×
×
f_SW
D'- D
⎞
⎠⎟
In the above equation, D’ = 1 - D, n is a factor deter-
mined by the slope compensation m_c and the inductor
current ramp m₁, as shown below:
n = 1 + ^mC
m₁
The slope compensation of the MAX1530/MAX1531 is
219mV/µs. The inductor current ramp is a function of
the input voltage, output voltage, inductance, high-side
MOSFET on-resistance R_DS(ON), and the gain of the
current-sense amplifier A_VCS, and is:
m₁ =
V_IN - V_OUT
L
×
R_DS(ON) × A_VCS
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