Datasheet

'i
L
=
(in Amps)
V
IN
D
2Lfs
V
IN
R
DSON
0.144 fs
L >
( )
D
D'
2
-1
( )
D
D'
+1
(in H)
Hz
1
2S(R
C
+ R
O
)C
C
f
PC
=
Hz
1
f
ZC
=
2SR
C
C
C
LM5000
SNVS176D –MAY 2004–REVISED MARCH 2007 www.ti.com
To keep a current programmed control converter stable above duty cycles of 50%, the inductor must meet
certain criteria. The inductor, along with input and output voltage, will determine the slope of the current through
the inductor (see Figure 22 (a)). If the slope of the inductor current is too great, the circuit will be unstable above
duty cycles of 50%.
The LM5000 provides a compensation pin (COMP) to customize the voltage loop feedback. It is recommended
that a series combination of R
C
and C
C
be used for the compensation network, as shown in Figure 19. The
series combination of R
C
and C
C
introduces pole-zero pair according to the following equations:
(3)
where
• R
O
is the output impedance of the error amplifier, 850kΩ (4)
For most applications, performance can be optimized by choosing values within the range 5kΩ ≤ R
C
≤ 20kΩ and
680pF ≤ C
C
≤ 4.7nF.
COMPENSATION
This section will present a general design procedure to help insure a stable and operational circuit. The designs
in this datasheet are optimized for particular requirements. If different conversions are required, some of the
components may need to be changed to ensure stability. Below is a set of general guidelines in designing a
stable circuit for continuous conduction operation (loads greater than 100mA), in most all cases this will provide
for stability during discontinuous operation as well. The power components and their effects will be determined
first, then the compensation components will be chosen to produce stability.
INDUCTOR SELECTION
To ensure stability at duty cycles above 50%, the inductor must have some minimum value determined by the
minimum input voltage and the maximum output voltage. This equation is:
where
• fs is the switching frequency
• D is the duty cycle
• R
DSON
is the ON resistance of the internal switch (5)
This equation is only good for duty cycles greater than 50% (D>0.5).
(6)
The inductor ripple current is important for a few reasons. One reason is because the peak switch current will be
the average inductor current (input current) plus Δi
L
. Care must be taken to make sure that the switch will not
reach its current limit during normal operation. The inductor must also be sized accordingly. It should have a
saturation current rating higher than the peak inductor current expected. The output voltage ripple is also affected
by the total ripple current.
DC GAIN AND OPEN-LOOP GAIN
Since the control stage of the converter forms a complete feedback loop with the power components, it forms a
closed-loop system that must be stabilized to avoid positive feedback and instability. A value for open-loop DC
gain will be required, from which you can calculate, or place, poles and zeros to determine the crossover
frequency and the phase margin. A high phase margin (greater than 45°) is desired for the best stability and
transient response. For the purpose of stabilizing the LM5000, choosing a crossover point well below where the
right half plane zero is located will ensure sufficient phase margin. A discussion of the right half plane zero and
checking the crossover using the DC gain will follow.
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