ISL6323 Datasheet, PDF (29/34 Pages) Intersil Corporation – Hybrid SVI/PVI

ISL6323
Case 1:
---------------1----------------
2⋅π⋅ L⋅C
>
f₀
R_C
=
R_FB
⋅
2-----⋅_---π_-----⋅_---f--0-----⋅_{--V-----p---p----}⋅_{--------L-----}⋅_---C--
0.66 ⋅ V_IN
C_C
=
--------------0---.--6---6-----^â‹---V----^I--^N----------------
2 ⋅ π ⋅ V_PP ⋅ R_FB ⋅ f₀
Case 2:
---------------1----------------
2⋅π⋅ L⋅C
≤
f₀
<
------------------1-------------------
2 ⋅ π ⋅ C ⋅ ESR
R_C = R_FB ⋅ -V----^P----^P-----^â‹---⁽--20----.-^â‹_6---^π-6---⁾--_⋲----V^â‹----_I-f-_N0--²-----^â‹---L-----^â‹---C---
C_C
=
------------------------------0----.-6----6-----^â‹---V----^I--^N--------------------------------
(2 ⋅ π)² ⋅ f₀₂ ⋅ V_PP ⋅ R_FB ⋅ L ⋅ C
(EQ. 50)
Case 3:
f₀ > _2-----â‹---_π-----_â‹---C--1----_â‹---E----S-----R---
R_C = R_FB ⋅ _0-2---.--6^â‹---6^π-----_⋅â‹---f-V-⁰---_I--^â‹_N---V--_â‹--^p-E--^p---S--^â‹--R-L--
C_C
=
-----0---.--6---6-----^â‹---V----^I--^N-----^â‹---E-----S----R------^â‹-------C-------
2 ⋅ π ⋅ V_PP ⋅ R_FB ⋅ f₀ ⋅ L
Compensation Without Loadline Regulation
The non load-line regulated converter is accurately modeled
as a voltage-mode regulator with two poles at the LC
resonant frequency and a zero at the ESR frequency. A
type-III controller, as shown in Figure 23, provides the
necessary compensation.
C₂
R_C ^CC
COMP
C₁
R₁
R_FB
FB
ISL6323
VSEN
FIGURE 23. COMPENSATION CIRCUIT WITHOUT LOAD-LINE
REGULATION
The first step is to choose the desired bandwidth, f₀, of the
compensated system. Choose a frequency high enough to
assure adequate transient performance but not higher than 1/3
of the switching frequency. The type-III compensator has an
extra high-frequency pole, f_HF. This pole can be used for added
noise rejection or to assure adequate attenuation at the error
amplifier high-order pole and zero frequencies. A good general
rule is to choose f_HF = 10f₀, but it can be higher if desired.
Choosing f_HF to be lower than 10f₀ can cause problems with
too much phase shift below the system bandwidth as shown in
Equation 51.
R₁
=
R_FB
⋅ ------------C------^â‹---E----S-----R-------------
L ⋅ C – C ⋅ ESR
C₁
=
-----L-----^â‹---C-----^–-----C------^â‹---E----S-----R--
R_FB
C₂
=
----------------------------------------0---.--7---5-----^â‹---V-----^I-^N------------------------------------------
(2 ⋅ π)² ⋅ f₀ ⋅ f_HF ⋅ ( L ⋅ C) ⋅ R_FB ⋅ V_{P – P}
(EQ. 51)
R_C
=
-V----^P----^P-----^â‹---^⎝⎛---2----^π---^⎠⎞---²-----^â‹---f--⁰----^â‹---f--^H----^F-----^â‹---L-----^â‹---C-----^â‹---R-----^F----^B--
0.75 ^⋠V_IN ^{⋅ (2 ⋅ π ⋅ f}_HF ^{⋅ L ⋅ C–1)}
C_C
=
---------0---.--7---5-----^â‹---V----^I--^N------^â‹---⁽--2-----^â‹---^π-----^â‹---f--^H----^F----^â‹--------L-----^â‹---C----^–----1---⁾---------
(2 ⋅ π)² ⋅ f₀ ⋅ f_HF ⋅ ( L ⋅ C) ⋅ R_FB ⋅ V_{P – P}
In the solutions to the compensation equations, there is a
single degree of freedom. For the solutions presented in
Equation 52, R_FB is selected arbitrarily. The remaining
compensation components are then selected according to
Equation 52.
In Equation 52, L is the per-channel filter inductance divided
by the number of active channels; C is the sum total of all
output capacitors; ESR is the equivalent-series resistance of
the bulk output-filter capacitance; and V_P-P is the peak-to-
peak sawtooth signal amplitude as described in “Electrical
Specifications” on page 6.
Output Filter Design
Case 1:
---------------1----------------
2⋅π⋅ L⋅C
>
f₀
R_C = R_FB ⋅ ^2-----â‹---^π-----^â‹---0f--⁰-.--6-^â‹--6-V----_â‹-^p--V-^p---_I-^â‹-_N-------L----^â‹---C---
C_C
=
--------------0---.--6---6-----^â‹---V----^I--^N----------------
2 ⋅ π ⋅ V_PP ⋅ R_FB ⋅ f₀
Case 2:
---------------1----------------
2⋅π⋅ L⋅C
≤
f₀
<
2-----⋅^---π^-----⋅^---C--1----⋅^{---E----S-----R---}
R_C
=
R_F
B
⋅
-V----^P----^P-----^â‹---⁽--2-----^â‹---^π----⁾--²----^â‹-----f-⁰--²-----^â‹---L-----^â‹---C---
0.66 ⋅ V_IN
C_C
=
------------------------------0----.-6----6-----^â‹---V----^I--^N--------------------------------
(2 ⋅ π)² ⋅ f₀₂ ⋅ V_PP ⋅ R_FB ⋅ L ⋅ C
(EQ. 52)
Case 3:
f₀
>
------------------1-------------------
2 ⋅ π ⋅ C ⋅ ESR
R_C
=
R_FB
⋅
-2-----^â‹---^π-----^â‹---f--⁰-----^â‹---V----^p---^p-----^â‹---L--
0.66 ⋅ V_IN ⋅ ESR
C_C
=
----0----.--6---6-----^â‹---V----^I--^N-----^â‹---E----S-----R------^â‹-------C-------
2 ⋅ π ⋅ V_PP ⋅ R_FB ⋅ f₀ ⋅ L
29
FN9278.2
April 7, 2008