ISL6566_06 Datasheet, PDF (24/29 Pages) Intersil Corporation – Three-Phase Buck PWM Controller with Integrated MOSFET Drivers for VRM9, VRM10, and AMD Hammer Applications

ISL6566
Fortunately, there is a simple approximation that comes very
close to an optimal solution. Treating the system as though it
were a voltage-mode regulator, by compensating the L-C poles
and the ESR zero of the voltage mode approximation, yields a
solution that is always stable with very close to ideal transient
performance.
Select a target bandwidth for the compensated system, f₀. The
target bandwidth must be large enough to assure adequate
transient performance, but smaller than 1/3 of the per-channel
switching frequency. The values of the compensation
components depend on the relationships of f₀ to the L-C pole
frequency and the ESR zero frequency. For each of the
following three, there is a separate set of equations for the
compensation components.
Case 1:
---------1----------
2π LC
>
f₀
R_C
=
R_FB
2----π_{----f--0---V-----p---p--------L---C---}
0.66 V_{I N}
C_C
=
--------0---.--6---6----V----^I--^N----------
2πV_PPR_FBf₀
Case 2:
---------1----------
2π LC
≤
f₀
<
2----π^----C-----(^{-1-E-----S----R-----})
R_C
=
R_FB
V-----_P----P----(_--2----π_----)_--²_----f--0--²_{----L----C---}
0.66 V_IN
C_C
=
--------------------0----.-6----6---V-----^I--^N---------------------
(2π)² f₀₂ V_PPR_FB LC
(EQ. 29)
Case 3:
f₀ > _2----π----C-----₍-1-E-----S----R-----₎
R_C
=
R_FB
--------2----^π----f--⁰---V-----^p---^p---L---------
0.66 V_IN (ESR)
C_C
=
-0---.--6---6----V----^I--^N----⁽--E-----S----R-----⁾-------C---
2πV_PPR_FBf₀ L
In Equations 29, 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_PP is the peak-to-peak
sawtooth signal amplitude as described in the Electrical
Specifications.
Once selected, the compensation values in Equations 29
assure a stable converter with reasonable transient
performance. In most cases, transient performance can be
improved by making adjustments to R_C. Slowly increase the
value of R_C while observing the transient performance on an
oscilloscope until no further improvement is noted. Normally,
C_C will not need adjustment. Keep the value of C_C from
Equations 29 unless some performance issue is noted.
The optional capacitor C₂, is sometimes needed to bypass
noise away from the PWM comparator (see Figure 20). Keep a
position available for C₂, and be prepared to install a high-
frequency capacitor of between 22pF and 150pF in case any
leading edge jitter problem is noted.
Output Filter Design
The output inductors and the output capacitor bank together to
form a low-pass filter responsible for smoothing the pulsating
voltage at the phase nodes. The output filter also must provide
the transient energy until the regulator can respond. Because it
has a low bandwidth compared to the switching frequency, the
output filter limits the system transient response. The output
capacitors must supply or sink load current while the current in
the output inductors increases or decreases to meet the
demand.
In high-speed converters, the output capacitor bank is usually
the most costly (and often the largest) part of the circuit. Output
filter design begins with minimizing the cost of this part of the
circuit. The critical load parameters in choosing the output
capacitors are the maximum size of the load step, ∆I, the load-
current slew rate, di/dt, and the maximum allowable output-
voltage deviation under transient loading, ∆V_MAX. Capacitors
are characterized according to their capacitance, ESR, and
ESL (equivalent series inductance).
At the beginning of the load transient, the output capacitors
supply all of the transient current. The output voltage will initially
deviate by an amount approximated by the voltage drop across
the ESL. As the load current increases, the voltage drop across
the ESR increases linearly until the load current reaches its final
value. The capacitors selected must have sufficiently low ESL
and ESR so that the total output-voltage deviation is less than
the allowable maximum. Neglecting the contribution of inductor
current and regulator response, the output voltage initially
deviates by an amount
∆V ≈ (ESL) -d---i + (ESR) ∆I
dt
(EQ. 30)
The filter capacitor must have sufficiently low ESL and ESR so
that ∆V < ∆V_MAX.
Most capacitor solutions rely on a mixture of high frequency
capacitors with relatively low capacitance in combination with
bulk capacitors having high capacitance but limited high-
frequency performance. Minimizing the ESL of the high-
frequency capacitors allows them to support the output voltage
as the current increases. Minimizing the ESR of the bulk
capacitors allows them to supply the increased current with less
output voltage deviation.
The ESR of the bulk capacitors also creates the majority of the
output-voltage ripple. As the bulk capacitors sink and source
the inductor ac ripple current (see Interleaving and Equation 2),
a voltage develops across the bulk capacitor ESR equal to
I_C,PP(ESR). Thus, once the output capacitors are selected, the
maximum allowable ripple voltage, V_PP(MAX), determines the
lower limit on the inductance.
L ≥ (ESR) -^--V-----^I-^N------^–----N------V----^O----^U----^T---^-----V----^O----^U----^T--
f_S V_{I N} V_{P P( M A X )}
(EQ. 31)
24
FN9178.4
March 9, 2006