SC2440 Datasheet, PDF (20/26 Pages) Semtech Corporation – 2.5 MHz Dual Switching Regulator with Integrated 2A Switches

SC2440
POWER MANAGEMENT
Applications Information
In addition C₅ and R₅ form a zero with angular frequency:
ω_Z1
=
−
1
R₅C
5
=
−
15.4
1
KΩ ⋅
470pF
= −140 Krads^−1 = −22KHz
The output-to-control transfer function
v_COMP
v_OUT
=
v_COMP
v_FB
⋅
v_FB
v_OUT
is
also
shown
in
Figure
13.
Its
mid-
band
gain
(between
z₁
and
p₃)
is
G_MAR₅

R₂
R₁ + R₂

.
The
overall loop gain T(s) is the product of the control-to-
output and the output-to-control transfer functions. To
simplify T( jω) Bode plot, the feedback network is
assumed to be resistive. If the overall loop gain is to
cross 0dB at one tenth of the switching frequency
( ^ω_C
=
ω_S
10
=
πf
5
)
at
–20dB/decade,
then
its
mid-band
gain
(between z₁ and p₂) will be
ω_c
ω_p2
=
ω_S
10
n
C₁R_OUT
=
ω_SC₁R_OUT
10n
.
This is also equal to
G_MPR_OUTG_MAR₅

R₂
R₁ + R₂

.
Therefore
the crossover frequency. However it reduces the phase
m(1a1r)gainn.dA(1n2e)swtiimthant=e1o.fThRe_{5 caonmdpCe5ncsaantiobneisotbhteanincehdecfrkoemd}
by measuring the loop gain and the phase or by observing
the inductor current and the output voltage during load
transient. Choose
give at least 45°
othf ^{ephlaarsgeesmt Rar5}gainn.dTthhee
csomrraellsepsotnCd⁵intog
load transient should not show any ringing or excessive
oisvaerssmhoaolltc(esreaemFiicgucarepsac1i4to(cr)(,1104-4(d7)p, _{F1)7t(ob)roalnl odff1t7h(ec)l)o. oCp6}
gain at
phase
high frequency.
margin over a
FliemeidtefodrwfraerqduceanpcaycirtoarnCge₁₁
boosts
and is
sometimes used to improve loop response. C₁₁ will be
more effective if R₁ >> R₁R₂ .
Example: Determine the compensation components for
the 1.3MHz 12V to 5V and 3.3V converter in Figure 1.
For both channels, ω_S = 8.2Mrads^−1 , I_OUT(MAX) = 2A and
C₁ = 10µF . n is assumed to be 1 in (11) and (12).
For the 3.3V output:
R₅
=
¹
+
23.3K
10K

10
8.2×10⁶ ⋅10^−5
⋅ (1) ⋅ (5.7) ⋅ (2.8 ×10^−4 )
= 16.9KΩ
C₅
=
10^−5 ⋅ 3.3V
(1) ⋅16.9K ⋅ (2A)
= 1nF
For the 5V channel:
G_MPR_OUT
G_MAR₅

R₂
R₁ + R₂

=
ωC₁R_OUT
10n
.
Re-arranging,
R₇
=
¹
+
40.2K
10K

10
8.2 ×10⁶ ⋅10^−5
⋅ (1) ⋅ (5.7) ⋅ (2.8 ×10^−4
)
= 25.5KΩ
R₅
=
¹
+
R₁
R₂

ω_SC₁
10nG_MPG_MA
(11)
ω_z1 is shown to be less than ω_p2 in Figure 13. Making
ω_z1 = ω_p2 gives a first-order estimate of C₅:
C₅
=
C₁R_{OUT (MIN)}
nR₅
(12)
Ncoontivceerttehra. _{ItnRc5redaestienrgmRin5}einsctrheeasmeisdt-hbaenmdidlo-boapngdaginaionf
the
and
C₈
=
(1)
10^−5 ⋅ 5V
⋅25.5K ⋅(2A)
=
1nF
Cm_{6aargnidn.CL9o(abdotthra1n0sipeFn)t}
are then added to
responses of both
increase gain
channels are
observed using these values. There is very little inductor
current overshoot even
and 220pF respectively
(wFiitghurCe⁵
and
14).
TCh⁸eremdeuacseudretod
470pF
overall
loop gain and phase plots of the converter are also
shown.
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20
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