MAX15053_1107 Datasheet, PDF (17/21 Pages) Maxim Integrated Products – High-Efficiency, 2A, Current-Mode Synchronous, Step-Down Switching Regulator

High-Efficiency, 2A, Current-Mode
Synchronous, Step-Down Switching Regulator
The effect of the inner current loop at higher frequen-
cies is modeled as a double-pole (complex conjugate)
frequency term, GSAMPLING(s), as shown:
G_SAMPLING(s)
=
s²
(π × f_SW )²
+
1
s
π × f_SW
× Q_C
+1
where the sampling effect quality factor, QC, is:
Q_C
=
π
×
K _S
1
× (1−
D)
−
0.5
And the resonant frequency is:
ωSAMPLING(s) = π × fSW
or:
f_SAMPLING
=
f_SW
2
Having defined the power modulator’s transfer function,
the total system transfer can be written as follows (see
Figure 3):
Gain(s) = GFF(s) × GEA(s) × GMOD(DC) × GFILTER(s) ×
GSAMPLING(s)
where:
G_FF
(s)
=
R2
R1+ R2
×
(sC_FFR1+ 1)
sC_FF (R1|| R2) +
1
Leaving CFF empty, GFF(s) becomes:
Also:
G_FF
(s)
=
R2
R1+ R2
G_EA (s)
=
10 ^A
VEA ^(dB)/20
×

sC

C^{R}
C
(sC_CR_C + 1)
+ ^{10 A VEA (dB)/20}
g_MV



+

1

which simplifies to:
G_EA (s)
=
10
A
VEA ^(dB)/20
×
(sC_CR_C + 1)

sC

C_{}¹⁰
A
VEA ^(dB)/20
g_MV



+

1

when
R_C
<<
10 ^{A VEA (dB)/20}
g_MV
G_FILTER
(s)
=
R_LOAD
×

_sC
OUT
(sC_OUTESR +
 1
_RLOAD
+
K _S
× (1−
f_SW
1)
D) −
×L
0.5



−1
+

1^{}
The dominant poles and zeros of the transfer loop gain
are shown below:
f_P1
=
2π
g_MV
× 10 ^{A VEA (dB)/20}
×
C_C
f_P2
=
2π
×
C_OUT
 1
_RLOAD
1
+ ^{K}
S
×(1−D) −0.5_
f_SW × L



−1
f_P3 = ₂₁(f_SW)
f_Z1
=
2π
×
1
C _CR _C
f_Z2
=
2π ×
1
C_OUTESR
The order of pole-zero occurrence is:
f_P1 < f_P2 ≤ f_Z1 < f_CO ≤ f_P3 < f_Z2
Under heavy load, fP2, approaches fZ1. Figure 3 shows
a graphical representation of the asymptotic system
closed-loop response, including dominant pole and zero
locations.
The loop response’s fourth asymptote (in bold, Figure 3)
is the one of interest in establishing the desired cross-
over frequency (and determining the compensation
component values). A lower crossover frequency pro-
vides for stable closed-loop operation at the expense of
a slower load- and line-transient response. Increasing
the crossover frequency improves the transient response
at the (potential) cost of system instability. A standard
rule of thumb sets the crossover frequency between
1/10 and 1/5 of the switching frequency. First, select
the passive power and decoupling components that
meet the application’s requirements. Then, choose the
small-signal compensation components to achieve the
desired closed-loop frequency response and phase
margin as outlined in the Closing the Loop: Designing
the Compensation Circuitry section.
Closing the Loop: Designing the
Compensation Circuitry
1) Select the desired crossover frequency. Choose fCO
approximately 1/10 to 1/5 of the switching frequency
(fSW).
2) Determine RC by setting the system transfer’s fourth
asymptote gain equal to unity (assuming fCO > fZ1,
fP2, and fP1) where:
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