fS

2

<

fESR

3.16

2SfCRC

d

d

CC1

1

2Sfp1RC

RC =

fC x RGM

ADC x GM x RGM x H x fP1 - fC

:

Q =

1

S mc x D' - 0.5)

fESR =

2SCOUTRESR

1

(Hz)

1

COUTR

fp1 =

+

(mc x D' - 0.5)

1

fsLCOUT

1

2S

(Hz)

VIND' x 1.8RSN

L

Sn =

mc = 1+

Se

Sn

R

1.8RSN

R

fSL

mc x D' - 0.5

ADC =

1

1+

LM3477

SNVS141K – OCTOBER 2000 – REVISED MARCH 2013

www.ti.com

(37)

(38)

Se = fS(VSL + 50x10

−6 R

SL)

(39)

(40)

(41)

(42)

(43)

With the power stage known, a compensator can be designed to achieve improved performance and stability.

The LM3477/A will typically require only a single resistor and capacitor for compensation, but depending on the

power stage it could require three or four external components.

It is a good idea to check that Q is between 0.15 and 2, if it was not already done when selecting the inductor. If

Q is less than 0.15 or greater than 2, skip to SAMPLING POLE QUALITY FACTOR before continuing with the

compensator design.

First, a target crossover frequency (fc) for the loop gain must be selected. The crossover frequency is the

bandwidth of the converter. A higher bandwidth generally corresponds to faster response times and lower

overshoots to load transients. However, the bandwidth should not be much higher than 1/10 the switching

frequency. The LM3477/A operates with a 500kHz switching frequency, so it is recommended to choose a

crossover frequency between 10kHz - 50kHz.

The schematic of the LM3477/A compensator is shown in Figure 32. The default design uses Rc and CC1 to form

a lag (type 2) compensator. The CC2 capacitor can be added to form an additional pole that is typically used to

cancel out the esr zero of the output capacitor. Finally, if extra phase margin is needed, the Cff capacitor can be

added (this does not help at low output voltages, see below).

The strategy taken here for choosing Rc and CC1 is to set the crossover frequency with Rc, and set the

compensator zero with CC1. Using the selected target crossover frequency, fC, set RC to:

(44)

fC = Crossover frequency in Hertz (20kHz - 50kHz is recommended)

RGM = 50x10

3Ω

GM = 1000x10−6 A/V

The compensator zero, fZ1, is set with CC1. When fast transient responses are desired, fZ1 should be placed as

high as possible, however it should not be higher than the selected crossover frequency fC. The guideline

proposed here is to choose CC1 such that fZ1 falls somewhere between the power pole fP1 and ½ decade before

the selected crossover frequency fc:

(45)

In this compensation scheme, the pole created by CC2 is used to cancel out the zero created by the ESR of the

output capacitor. In other schemes such as the methods discussed in SAMPLING POLE QUALITY FACTOR, the

ESR zero is used. For the typical case, use CC2 if:

(46)

24

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