FN9309 Rev.3.00

Page 28 of 34

Jul 8, 2019

RAA212421

5. Application Guidelines

Compensator design goal:

•High DC gain

• Choose loop bandwidth fc to be about 1/10 of fSW

• Gain margin: >10dB

• Phase margin: >40°

The compensator design procedure is as follows:

The loop gain at crossover frequency of fc has a unity gain. Therefore, the compensator resistance R6 is determined

by Equation 14.

where:

GM is the transconductance, gm, of the voltage error amplifier in each phase.

Rcs is the current sense trans-resistance.

k is a constant to compensate for cross over frequency difference since the feed forward zero is placed at the

vicinity of fc.

Place the compensator zero in the vicinity of the power stage pole at full load. As an example, the compensator zero

is placed at 2.2 times the frequency of the power stage pole at full load. Compensator capacitor C6 is then given by

Equation 15.

There is an inherent integrator pole at DC by virtue of the compensation circuit which helps to achieve high DC

gain. Put another compensator pole at either ESR zero frequency or half switching frequency, whichever is lower,

in Equation 16. An optional zero can boost the phase margin.

ωCZ2 is a zero due to R1 and C4.

Put feedforward zero at fzff to boost the phase at cross-over. The fzff can be chosen in the vicinity of fc depending

on the amount of phase boost required.

Example: VIN1 = 24V, VO1 = 5V, IO1 = 1.1A, fSW = 500kHz, R2 = 90.9kΩ, Co1 = 32.1µF/5mΩ, L1 = 22µH,

fc = 50kHz, then compensator resistance R6:

Use 130kΩ as the closest standard value for R6.

Av S

()

vˆCOMP1

vˆFB1

-----------------------

GM R2

⋅

C6 C7

+

() R1 R2

+

()

⋅

--------------------------------------------------------

1

S

ωcz1

-------------

+



 1

S

ωcz2

-------------

+





S1

S

ωcp1

-------------

+



 1

S

ωcp2

-------------

+





---------------------------------------------------------------

=

=

(EQ. 13)

ωcz1

1

R6C6

---------------

ωcz2

1

R1C4

---------------

=

ωcp1

,

C6 C7

+

R6C6C7

----------------------- ωcp2

R1 R2

+

C4R1R2

-----------------------

=

,

=

,

=

R6

2

πfcVo1Co1Rcsk

GM VFB1

⋅

------------------------------------------------

16.1

3

×10 fcVo1Co1

⋅

==

(EQ. 14)

C6

Ro1Co1

2.2R6

----------------------

Vo1Co1

2.2Io1R6

------------------------

=

=

(EQ. 15)

C7 max

RcCo1

R6

------------------

1

πfSWR6

----------------------

(,

)

=

(EQ. 16)

C4

1

2

πfzffR1

-----------------------

=

(EQ. 17)

R6

16.1

3

×10 50kHz 5V 31.3μF

⋅

⋅

⋅

129.3k

Ω

==

(EQ. 18)