High-Efficiency, 2A, Current-Mode

Synchronous, Step-Down Switching Regulator

______________________________________________________________________________________ 17

The effect of the inner current loop at higher frequen-

cies is modeled as a double-pole (complex conjugate)

( )

(

)

SAMPLING

2

2

SW

C

SW

1

G

s

s

s

1

f

Q

f

=

+

+

π ×

×

π ×

(

)

C

S

1

Q

K

1 D

0.5

=





π ×

× −

−





And the resonant frequency is:

or:

SW

SAMPLING

f

f

2

=

Having defined the power modulator’s transfer function,

the total system transfer can be written as follows (see

Figure 3):

where:

( )

(

)

(

)

FF

FF

FF

sC R1 1

R2

G

s

R1 R2

sC

R1|| R2

1

+

=

×

+





+





( )

FF

R2

G

s

R1 R2

=

+

Also:

( )

(

)

VEA

VEA

A

(dB)/20

C C

EA

A

(dB)/20

C

C

MV

sC R

1

G

s

10

10

sC R

1

g

+

=

×

















+

+

















which simplifies to:

( )

(

)

VEA

VEA

A

(dB)/20

C C

EA

A

(dB)/20

C

MV

sC R

1

G

s

10

10

sC

1

g

+

=

×















 +

















VEA

A

(dB)/20

C

MV

10

when R

g

<<

( )

(

)

(

)

OUT

FILTER

LOAD

1

S

OUT

LOAD

SW

sC

ESR 1

G

s

R

K

1 D

0.5

1

sC

1

R

f

L

−

+

=

×













× −

−













+

+









×

















The dominant poles and zeros of the transfer loop gain

are shown below:

(

)

(

)

VEA

MV

P1

A

(dB)/20

C

P2

S

1

OUT

LOAD

SW

P3

SW

Z1

C C

Z2

OUT

g

f

2

10

C

1

f

K

1 D 0.5

1

2

C

R

f

L

1

f

f

2

1

f

2

C R

1

f

2

C

ESR

−

=

π ×

×

=









× − −









π ×

+





×









=

=

π ×

=

π ×

The order of pole-zero occurrence is:

P1

P2

Z1

CO

P3

Z2

f

f

f

f

f

f

<

≤

<

≤

<

a graphical representation of the asymptotic system

closed-loop response, including dominant pole and zero

locations.

The loop response’s fourth asymptote (in bold, Figure 3)

is the one of interest in establishing the desired cross-

over frequency (and determining the compensation

component values). A lower crossover frequency pro-

vides for stable closed-loop operation at the expense of

a slower load- and line-transient response. Increasing

the crossover frequency improves the transient response

at the (potential) cost of system instability. A standard

rule of thumb sets the crossover frequency between

1/10 and 1/5 of the switching frequency. First, select

the passive power and decoupling components that

meet the application’s requirements. Then, choose the

small-signal compensation components to achieve the

desired closed-loop frequency response and phase

margin as outlined in the Closing the Loop: Designing

the Compensation Circuitry section.

Closing the Loop: Designing the

Compensation Circuitry

approximately 1/10 to 1/5 of the switching frequency