Datasheet

f
ZC
=
1
2SC
C
R
C
(in Hz)
f
PC
=
1
2S(R
C
+ R
O
)C
C
(in Hz)
(in Hz)
RHPzero =
V
OUT
(D')
2
2S,
LOAD
L
f
Z1
=
1
2SR
ESR
C
OUT
(in Hz)
f
P1
=
1
2S(R
ESR
+ R
L
)C
OUT
(in Hz)
LM5000
www.ti.com SNVS176D –MAY 2004–REVISED MARCH 2007
OUTPUT CAPACITOR SELECTION
The choice of output capacitors is somewhat more arbitrary. It is recommended that low ESR (Equivalent Series
Resistance, denoted R
ESR
) capacitors be used such as ceramic, polymer electrolytic, or low ESR tantalum.
Higher ESR capacitors may be used but will require more compensation which will be explained later on in the
section. The ESR is also important because it determines the output voltage ripple according to the approximate
equation:
ΔV
OUT
≊ 2Δi
L
R
ESR
(in Volts) (7)
After choosing the output capacitor you can determine a pole-zero pair introduced into the control loop by the
following equations:
(8)
where
• R
L
is the minimum load resistance corresponding to the maximum load current (9)
The zero created by the ESR of the output capacitor is generally very high frequency if the ESR is small. If low
ESR capacitors are used it can be neglected. If higher ESR capacitors are used see the HIGH OUTPUT
CAPACITOR ESR COMPENSATION section.
RIGHT HALF PLANE ZERO
A current mode control boost regulator has an inherent right half plane zero (RHP zero). This zero has the effect
of a zero in the gain plot, causing an imposed +20dB/decade on the rolloff, but has the effect of a pole in the
phase, subtracting another 90° in the phase plot. This can cause undesirable effects if the control loop is
influenced by this zero. To ensure the RHP zero does not cause instability issues, the control loop should be
designed to have a bandwidth of ½ the frequency of the RHP zero or less. This zero occurs at a frequency of:
where
• I
LOAD
is the maximum load current (10)
SELECTING THE COMPENSATION COMPONENTS
The first step in selecting the compensation components R
C
and C
C
is to set a dominant low frequency pole in
the control loop. Simply choose values for R
C
and C
C
within the ranges given in the INTRODUCTION TO
COMPENSATION section to set this pole in the area of 10Hz to 100Hz. The frequency of the pole created is
determined by the equation:
where
• R
O
is the output impedance of the error amplifier, 850kΩ (11)
Since R
C
is generally much less than R
O
, it does not have much effect on the above equation and can be
neglected until a value is chosen to set the zero f
ZC
. f
ZC
is created to cancel out the pole created by the output
capacitor, f
P1
. The output capacitor pole will shift with different load currents as shown by the equation, so setting
the zero is not exact. Determine the range of f
P1
over the expected loads and then set the zero f
ZC
to a point
approximately in the middle. The frequency of this zero is determined by:
(12)
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