MAX1584 Datasheet, PDF (23/29 Pages) Maxim Integrated Products – 5-Channel Slim DSC Power Supplies

5-Channel Slim DSC Power Supplies
If Z_COUT is not less than Z_RHP / 10 (as is typical with
ceramic output capacitors) and continuous conduction
is required, then cross the loop over before Z_RHP and f₀:
f_C < f_0SC / 10, and f_C < Z_RHP / 10
In that case:
C_C = (V_IN / V_RAMP)(V_FB / V_OUT)(g_M / (2π x f_C))
Place:
1 / (2π x R_C x C_C) = 1 / (2π x R_LOAD x C_OUT), so that
R_C = R_LOAD x C_OUT / C_C
Or, reduce the inductor value for discontinuous operation.
AUX3 Step-Down Compensation
It is expected that most AUX3 step-down applications
employ continuous inductor current to optimize induc-
tor size and efficiency. To ensure stability, the control-
loop gain should cross over (drop below unity gain) at
a frequency (f_C) much less than that of the switching
frequency.
The relevant characteristics for voltage-mode step-
down compensation are as follows:
• Transconductance (from FB3 to CC3), g_MEA (135µS)
• Oscillator ramp voltage, V_RAMP (1.25V)
• Feedback regulation voltage, V_FB (1.25V)
• Output voltage, V_OUT3, in V
• Output load equivalent resistance, R_LOAD, in Ω =
V_OUT3 / I_LOAD
• Characteristic impedance of the LC output filter, R_O
= (L / C)^1/2
The key steps for AUX3 step-down compensation are
as follows:
1) Place f_C sufficiently below the switching frequency
(f_OSC / 10).
2) Calculate C_OUT.
3) Calculate the complex pole pair due to the output
LC filter.
4) Add two zeros to cancel the complex pole pair.
5) Add two high-frequency poles to optimize gain and
phase margin.
If we assume V_IN = 5V, V_OUT = 3.3V, and I_OUT =
300mA, then R_LOAD = 11Ω. If we select f_OSC = 500kHz
and L = 10µH, select the crossover frequency to be
1/10 the OSC frequency:
f_C = f_OSC / 10 = 50kHz
For 3.3V output, select R14 = 30.1kΩ and R15 =
18.2kΩ. See the Setting Output Voltages section.
Calculate the equivalent impedance, R_EQ:
R_EQ = R_SOURCE + R_L + ESR + R_DS(ON)
where R_SOURCE is the output impedance of the source
(this is the output impedance of the step-up converter
when the AUX3 step-down is powered from the step-
up), R_L is the inductor DC resistance, ESR is the filter-
capacitor equivalent resistance, and R_DS(ON) is the
on-resistance of the external MOSFET.
The output impedance of the step-up converter
(R_SOURCE) is approximately 1Ω at f₀. Since the sum of
R_L + ESR + R_DS(ON) is small compared to 1Ω, assume
R_EQ = 1Ω. Choose C_OUT so R_O is less than R_EQ / 2:
C_OUT > L / [(R_EQ / 2)²] = 10µH / 0.25 = 40µF
Choose C_OUT = 47µF:
C4 = (V_IN / V_RAMP)(1 / [2π x R14 x f_C])
= (5 / 1.25)(1/ [2π x 30.1k x 50kHz) = 423pF
Choose C4 = 470pF.
Cancel one pole of the complex pole pair by placing
the R4 C4 zero at 0.75 f₀. The complex pole pair is at
the following:
f₀ = 1 / [2π(L x C_OUT)^1/2]
= 1 / [2π(10µH x 47µF)^1/2] = 7.345kHz
Choose R4 = 1 / (2π x C4 x 0.75 x f₀)
= 1 / (2π x 470pF x 0.75 x 7.345kHz)
z
Choose R4 = 61.9kΩ (standard 1% value). Ensure that
R4 > 2 / g_MEA = 14.8kΩ. If it is not greater, reselect
R14 and R15.
Cancel the second pole of the complex pole pair by
placing the R14 C20 zero at 1.25 x f₀.
C20 = 1 / (2π x R14 x 1.25 x f₀)
= 1 / (2π x 30.1k x 1.25 x 7.345kHz) = 576pF
Choose C20 = 560pF.
Roll off the gain below the switching frequency by plac-
ing a pole at f_OSC / 2:
R22 = 1 / (2π x C20 [f_OSC / 2])
= 1 / (2π x 560pF x 250kHz) = 1.137kΩ
Choose R22 = 1.2kΩ.
If the output filter capacitor has significant ESR, a zero
occurs at the following:
Z_ESR = 1 / (2π x C_OUT x R_ESR)
Use the R4 C22 pole to cancel the ESR zero:
C22 = C_OUT x R_ESR / R4
If C22 is calculated to be <10pF, it can be omitted.
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