LM3551 Datasheet, PDF (12/15 Pages) National Semiconductor (TI) – 1A White LED Driver with Flash Timeout Protection

Application Information (Continued)
tance loss due to capacitor voltage coefficient. See the
capacitor manufacturer’s datasheet for DC bias perfor-
mance.
COMPENSATION
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 LM3551/2, choosing a crossover point well
below where the right half plane zero is located will ensure
sufficient phase margin.
To ensure a bandwidth of ¹â„2 or less of the frequency of the
RHP zero, calculate the open-loop DC gain, A_DC. After this
value is known, you can calculate the crossover visually by
placing a −20dB/decade slope at each pole, and a +20dB/
decade slope for each zero. The point at which the gain plot
crosses unity gain, or 0dB, is the crossover frequency. If the
crossover frequency is less than ¹â„2 the RHP zero, the phase
margin should be high enough for stability. The equation for
A_DC is given below with additional equations required for the
calculation:
loop should be designed to have a bandwidth of less than ¹â„2
the frequency of the RHP zero. This zero occurs at a fre-
quency of:
where I_LOAD is the maximum load current.
Compensation Components
The LM3551 and LM3552 provide a compensation pin (V_C)
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 the typical application
circuit. For any given application, there exists a unique com-
bination of R_C and C_C that will optimize the performance of
the LM3551/2 circuit in terms of its transient response. The
series combination of R_C and C_C introduces a pole-zero pair.
The frequency of the pole created is determined by the
equation:
where R_O is the output impedance of the error amplifier,
approximately 900kΩ. Since R_C is generally much less than
R_O, it has little 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 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:
mc ) 0.072 x fs (in V/s)
where R_L is the minimum load resistance, fs is the switching
frequency, V_IN is the minimum input voltage, g_m is the error
amplifier transconductance and R_DSON-S is the power switch
on-resistance. The value for g_m and R_DSON-S are found in
the Electrical Characteristics table.
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
Now R_C can be chosen with the selected value for C_C.
Check to make sure that the pole f_PC is still in the 10Hz to
500Hz range, and change each value slightly if needed to
ensure both component values are in the recommended
range. For both typical applications circuits shown on the
front page, the Recommended value for C_C is 4.7nF and
R_C = 10kΩ for Lumiled applications. 10nF and 27kΩ are
recommended for Sharp applications.
RECOMMENDED MINIMUM COMPONENT
SPECIFICATIONS
Component
L1
C_IN
C_OUT
C_FTO
Value
4.7µH
4.7µF (Sharp)
10µF (Lumiled)
4.7µF (Sharp)
10uF (Lumiled)
User
Determined
Ratings
2.0A 30% I_SAT
Rating
10V X5R or
X7R
16V X5R or
X7R
6.3V X5R or
X7R
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