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Boost Operation (Continued)
The LM2716 has a current mode PWM boost converter. The
signal flow of this control scheme has two feedback loops,
one that senses switch current and one that senses output
voltage.
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 2 (a)). If the slope of the inductor current is too
great, the circuit will be unstable above duty cycles of 50%.
If the duty cycle is approaching near 85% up to the maximum
of 95%, it may be necessary to increase the inductance by
as much as 2X. See Inductor and Diode Selection for more
detailed inductor sizing.
The LM2716 provides a compensation pin (V
C2
) to custom-
ize the voltage loop feedback. It is recommended that a
series combination of R
C2
and C
C2
be used for the compen-
sation network, as shown in Figure 3. For any given appli-
cation, there exists a unique combination of R
C2
and C
C2
that will optimize the performance of the LM2716 circuit in
terms of its transient response. The series combination of
R
C2
and C
C2
introduces a pole-zero pair according to the
following equations:
where R
O
is the output impedance of the error amplifier,
approximately 850kΩ. For most applications, performance
can be optimized by choosing values within the range 5kΩ≤
R
C2
≤20kΩ(R
C2
can be up to 200kΩif C
C4
is used, see
High Output Capacitor ESR Compensation) and 680pF ≤
C
C2
≤4.7nF. Refer to the Applications Information section for
recommended values for specific circuits and conditions.
Refer to the Compensation section for other design require-
ment.
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 differ-
ent 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 continu-
ous conduction operation (loads greater than approximately
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 AND DIODE SELECTION
Although the inductor sizes mentioned earlier are fine for
most applications, a more exact value can be calculated. 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 equa-
tion is:
where F
SW
is the switching frequency, D is the duty cycle,
and R
DSON
is the ON resistance of the internal switch taken
from the graph "Boost Switch R
DSON
vs. Input Voltage" in the
Typical Performance Characteristics section. This equation
is only good for duty cycles greater than 50% (D>0.5), for
duty cycles less than 50% the recommended values may be
used. The corresponding inductor current ripple as shown in
Figure 2 (a) is given by:
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 or I
LOAD
/D’) plus ∆i
L
.
As a side note, discontinuous operation occurs when the
inductor current falls to zero during a switching cycle, or ∆i
L
is greater than the average inductor current. Therefore, con-
tinuous conduction mode occurs when ∆i
L
is less than the
average inductor current. 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.
The output diode for a boost regulator must be chosen
correctly depending on the output voltage and the output
current. The typical current waveform for the diode in con-
tinuous conduction mode is shown in Figure 2 (b). The diode
must be rated for a reverse voltage equal to or greater than
the output voltage used. The average current rating must be
greater than the maximum load current expected, and the
peak current rating must be greater than the peak inductor
current. During short circuit testing, or if short circuit condi-
tions are possible in the application, the diode current rating
must exceed the switch current limit. Using Schottky diodes
with lower forward voltage drop will decrease power dissipa-
tion and increase efficiency.
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 feed-
back 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 LM2716, choosing a crossover point well be-
low 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.
OUTPUT CAPACITOR SELECTION
The choice of output capacitors is somewhat arbitrary and
depends on the design requirements for output voltage
ripple. It is recommended that low ESR (Equivalent Series
LM2716
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