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)
LM2700
www.ti.com SNVS152C –MAY 2001–REVISED MARCH 2013
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
C
≤ 20kΩ (R
C
can be up to 200kΩ if
C
C2
is used, see High Output Capacitor ESR Compensation) and 680pF ≤ C
C
≤ 4.7nF. Refer to the Application
Information section for recommended values for specific circuits and conditions. Refer to the COMPENSATION
section for other design requirement.
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 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 equation is:
(5)
where fs is the switching frequency, D is the duty cycle, and R
DSON
is the ON resistance of the internal switch
taken from the graph "R
DSON
vs. V
IN
" 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 18(a) is given by:
(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 or I
LOAD
/D') plus Δi
L
. As a side note, discontinuous operation occurs
when the inductor current falls to zero during a switching cycle, or Δi
L
is greater than the average inductor
current. Therefore, continuous conduction mode occurs when Δi
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 continuous conduction mode is shown in Figure 18(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 conditions 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 dissipation 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 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 LM2700, 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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