MAX1584 Datasheet, PDF (20/29 Pages) Maxim Integrated Products – 5-Channel Slim DSC Power Supplies

5-Channel Slim DSC Power Supplies
I_IND(PK) = 1.25 x I_OUT / (1 - D)
Inductance values smaller than L_IDEAL can be used to
reduce inductor size; however, if much smaller values are
used, inductor current rises and a larger output capaci-
tance might be required to suppress output ripple.
Step-Up Compensation
The inductor and output capacitor are usually chosen
first in consideration of performance, size, and cost.
The compensation resistor and capacitor are then cho-
sen to optimize control-loop stability. In some cases, it
helps to readjust the inductor or output capacitor value
to get optimum results. For typical designs, the compo-
nent values in the circuit of Figure 1 yield good results.
The step-up converter employs current-mode control,
thereby simplifying the control-loop compensation.
When the converter operates with continuous inductor
current (typically the case), a right-half-plane zero
appears in the loop-gain frequency response. 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 right-half-plane zero.
The relevant characteristics for step-up channel com-
pensation are as follows:
• Transconductance (from FBSU to CCSU), g_MEA
(135µS)
• Current-sense amplifier transresistance, R_CS
(0.3V/A)
• Feedback regulation voltage, V_FB (1.25V)
• Step-up output voltage, V_SU, in V
• Output load equivalent resistance, R_LOAD, in
Ω = V_SUOUT / I_LOAD
The key steps for step-up compensation are as follows:
1) Place f_C sufficiently below the right-half-plane zero
(RHPZ) and calculate C_C.
2) Select R_C based on the allowed load-step transient.
R_C sets a voltage delta on the C_C pin that corre-
sponds to load-current step.
3) Calculate the output-filter capacitor (C_OUT) required
to allow the R_C and C_C selected.
4) Determine if C_P is required (if calculated to be >10pF).
For continuous conduction, the right-half-plane zero fre-
quency (f_RHPZ) is given by the following:
f_RHPZ = V_SUOUT (1 - D)² / (2π x L x I_LOAD)
where D = the duty cycle = 1 - (V_IN / V_OUT), L is the
inductor value, and I_LOAD is the maximum output cur-
rent. Typically, target crossover (f_C) for 1/6 of the
RHPZ. For example, if we assume f_OSC = 500kHz, V_IN
= 2.5V, V_OUT = 5V, and I_OUT = 0.5A, then R_LOAD =
10Ω. If we select L = 4.7µH, then:
f_RHPZ = 5 (2.5 / 5)² / (2π x 4.7 x 10^-6 x 0.5) = 84.65kHz
Choose f_C = 14kHz. Calculate C_C:
C_C = (V_FB / V_OUT)(R_LOAD / R_CS)(g_M / 2π x f_C)(1 - D)
= (1.25 / 5)(10 / 0.3) x (135µS / (6.28 x 14kHz) (2/5)
= 6.4nF
Choose 6.8nF.
Now select R_C so transient-droop requirements are
met. As an example, if 4% transient droop is allowed,
the input to the error amplifier moves 0.04 x 1.25V, or
50mV. The error-amp output drives 50mV x 135µS, or
6.75µA across R_C to provide transient gain. Since the
current-sense transresistance is 0.3V/A, the value of R_C
that allows the required load step swing is as follows:
R_C = 0.3 I_IND(PK) / 6.75µA
In a step-up DC-DC converter, if L_IDEAL is used, output
current relates to inductor current by:
I_IND(PK) = 1.25 x I_OUT / (1 - D) = 1.25 x I_OUT x V_OUT /
V_IN
So for a 500mA output load step with V_IN = 2.5V and
V_OUT = 5V:
R_C = [1.25(0.3 x 0.5 x 5) / 2)] / 6.75µA = 69.4kΩ
Note that the inductor does not limit the response in this
case since it can ramp at 2.5V / 4.7µH, or 530mA/µs.
The output filter capacitor is then chosen so the C_OUT
R_LOAD pole cancels the R_C C_C zero:
C_OUT x R_LOAD = R_C x C_C
For the example:
C_OUT = 68kΩ x 6.8nF / 10Ω = 46µF
Choose 47µF for C_OUT. If the available C_OUT is sub-
stantially different from the calculated value, insert the
available C_OUT value into the above equation and
recalculate R_C. Higher substituted C_OUT values allow a
higher R_C, which provides higher transient gain and
consequently less transient droop.
If the output filter capacitor has significant ESR, a zero
occurs at the following:
Z_ESR = 1 / (2π x C_OUT x R_ESR)
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