1

(in Hz)

L

(in V/s)

n = 1+

2mc

m1

(no unit)

Leff =

L

(D')

2

Z

c

(in rad/s)

2fs

nD'

#

(

)

LM3310

www.ti.com

SNVS341E – AUGUST 2005 – REVISED MAY 2013

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 LM3310, choosing a crossover point well below where the

right half plane zero is located will ensure sufficient phase margin.

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 ½ the RHP zero, the phase margin should be high

where

•

•

(12)

(13)

(14)

(15)

mc

≊ 0.072fs (in V/s)

(16)

where

•

•

Characteristics section

(17)

INPUT AND OUTPUT CAPACITOR SELECTION

The switching action of a boost regulator causes a triangular voltage waveform at the input. A capacitor is

required to reduce the input ripple and noise for proper operation of the regulator. The size used is dependant on

the application and board layout. If the regulator will be loaded uniformly, with very little load changes, and at

lower current outputs, the input capacitor size can often be reduced. The size can also be reduced if the input of

the regulator is very close to the source output. The size will generally need to be larger for applications where

the regulator is supplying nearly the maximum rated output or if large load steps are expected. A minimum value

of 10µF should be used for the less stressful condtions while a 22µF to 47µF capacitor may be required for

higher power and dynamic loads. Larger values and/or lower ESR may be needed if the application requires very

low ripple on the input source voltage.

The choice of output capacitors is also somewhat arbitrary and depends on the design requirements for output

such as ceramic, polymer electrolytic, or low ESR tantalum. Higher ESR capacitors may be used but will require

more compensation which will be explained later on in the section. The ESR is also important because it

determines the peak to peak output voltage ripple according to the approximate equation:

(18)

A minimum value of 10µF is recommended and may be increased to a larger value. After choosing the output

capacitor you can determine a pole-zero pair introduced into the control loop by the following equations:

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