LP2975 Datasheet, PDF (22/37 Pages) National Semiconductor (TI) – MOSFET LDO Driver/Controller

LP2975
SNVS006F – SEPTEMBER 1997 – REVISED APRIL 2013
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Figure 24. Phase Shift Due to f_pg
Because of this, there is no exact number for f_pg/f_c that can be given as a fixed limit for stable operation.
However, as a general guideline, it is recommended that f_pg ≥ 3 f_c.
If this is not found to be true after inital calculations, the ratio of f_pg/f_c can be increased by either reducing C_EFF
(selecting a different FET) or using a larger value of C_OUT.
Along with these two methods, another technique for improving loop stability is the use of a feed-forward
capacitor (see next section, Feed-Forward Compensation). This can improve phase margin by cancelling some
of the excess phase shift.
Feed-Forward Compensation
Phase shift in the loop gain of the regulator results from f_p (the pole from the output capacitor and load
resistance), f_pg (the pole from the FET gate capacitance), as well as the IC's internal controller pole (see typical
curve). If the total phase shift becomes excessive, instability can result.
The total phase shift can be reduced using feed-forward compensation, which places a zero in the loop to reduce
the effects of the poles.
The feed-forward capacitor C_F can accomplish this, provided it is selected to set the zero at the correct
frequency. It is important to point out that the feed-forward capacitor produces both a zero and a pole. The
frequency where the zero occurs will be defined as f_zf, and the frequency of the pole will be defined as f_pf. The
equations to calculate the frequencies are:
f_zf = 6.6 × 10^-6/ [C_F × (V_OUT/1.24 − 1) ]
f_pf = 6.6 × 10^-6/ [C_F × (1 − 1.24/V_OUT)]
In general, the feed-forward capacitor gives the greatest improvement in phase margin (provides the maximum
reduction in phase shift) when the zero occurs at a frequency where the loop gain is >1 (before the crossover
frequency). The pole must occur at a higher frequency (the higher the better) where most of the phase shift
added by the new pole occurs beyond the crossover frequency. For this reason, the pole-zero pair created by C_F
become more effective at improving loop stability as they get farther apart in frequency.
In reviewing the equations for f_zf and f_pf, it can be seen that they get closer together in frequency as V_OUT
decreases. For this reason, the use of C_F gives greatest benefit at higher output voltages, declining as V_OUT
approaches 1.24V (where C_F has no effect at all).
In selecting a value of feed-forward capacitor, the crossover frequency f_c must first be calculated. In general, the
frequency of the zero (f_zf) set by this capacitor should be in the range:
0.2 f_c ≤ f_zf ≤ 1.0 f_c
The equation to determine the value of the feed-forward capacitor in fixed-voltage applications is:
C_F = 6.6 × 10^-6/ [f_zf × (V_OUT/1.24 − 1) ]
In adjustable applications (using an external resistive divider) the capacitor is found using:
C_C = 1/(2 π × R1 × f_zf)
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