NCV887001D1R2G Datasheet NCV887001D1R2G, NCV887000D1R2G | P13-P15

NCV8870

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13

Table 1. BOOST CCM AND DCM TRANSFER FUNCTION EXPRESSIONS (continued)

Sampling Double

Pole (w

n

)

p

T

s

−

Sampling Quality

Coefficient (Q

p

)

1

p

(

m

c

(

1 * D

)

* 0.5

)

−

F

m

1

2M )

R

OUT

T

s

LM

2

ǒ

1

2

)

S

a

S

n

Ǔ

1

S

n

m

c

T

s

H

d

hR

OUT

R

i

2V

OUT

D

@

M * 1

2M * 1

Control-Output

Transfer Function

(H

ctrl_output

(f))

F

m

H

d

ǒ

1 ) j

2pf

w

z1

Ǔǒ

1 * j

2pf

w

z2

Ǔ

ǒ

1 ) j

2pf

w

p1

Ǔǒ

1 ) j

2pf

w

n

Q

p

)

ǒ

j

2pf

w

n

Ǔ

2

Ǔ

F

m

H

d

ǒ

1 ) j

2pf

w

z1

Ǔǒ

1 * j

2pf

w

z2

Ǔ

ǒ

1 ) j

2pf

w

p1

Ǔǒ

1 ) j

2pf

w

p2

Ǔ

Table 2. FLYBACK CCM AND DCM TRANSFER FUNCTION EXPRESSIONS

CCM DCM

Duty ratio (D)

V

OUT

V

OUT

) NV

IN

Where:

V

OUT

NV

IN

2t

L

Ǹ

t

L

+

N

2

L

p

T

s

R

OUT

V

OUT

/V

IN

DC Conversion Ra-

tio (M)

N @ D

1 * D

N @ D

2 @ t

L

Ǹ

Inductor On-slope (S

n

), V/s

V

IN

L

p

R

i

V

IN

L

p

R

i

Compensation Ramp (m

c

)

1 )

S

a

S

n

1 )

S

a

S

n

C

out

ESR Zero (w

z1

)

1

r

CF

C

OUT

1

r

CF

C

OUT

Right-Half-Plane Zero (w

z2

)

(

1 * D

)

2

R

OUT

DL

p

N

2

R

OUT

N

2

L

p

@

1

M(M ) 1)

Modulator Pole (w

p1

)

DȀ

3

t

L



ǒ

1 ) 2

S

a

S

n

Ǔ

) 1 ) D

R

OUT

C

OUT

2

R

OUT

C

OUT

w

p2

−

2F

SW



ǒ

1

D

1 )

1

M

Ǔ

2

F

m

1

DȀ

2

t

L



ǒ

1 ) 2

S

a

S

n

Ǔ

) 2M ) 1

1

S

n

m

c

T

s

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Table 2. FLYBACK CCM AND DCM TRANSFER FUNCTION EXPRESSIONS

DCMCCM

H

d

R

OUT

R

i

N

V

IN



1

2t

L

Ǹ

Control-output Transfer Func-

tion (H

ctrl_output

(f))

F

m

H

d

ǒ

1 ) j

2pf

w

z1

Ǔǒ

1 * j

2pf

w

z2

Ǔ

ǒ

1 ) j

2pf

w

p1

Ǔ

F

m

H

d

ǒ

1 ) j

2pf

w

z1

Ǔǒ

1 * j

2pf

w

z2

Ǔ

ǒ

1 ) j

2pf

w

p1

Ǔǒ

1 ) j

2pf

w

p2

Ǔ

Once the desired cross-over frequency (f

c

) gain

adjustment and necessary phase boost are determined from

the H

ctrl_output

(f) gain and phase plots, the Table 3 equations

may be used. It should be noted that minor compensation

component value adjustments may become necessary when

R

2

≤ ~10·R

esd

as a result of approximations for determining

components R

2

, C

1

, C

2

.

NCV8870

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15

Table 3. OTA COMPENSATION TRANSFER FUNCTION AND COMPENSATION VALUES

Desired OTA Gain at Cross-over Frequency f

c

(G)

10

desired_G

fc_gain_db

20

Desired Phase Boost at Cross-over Frequency f

c

(boost)

ǒ

q

margin

* arg

ǒ

H

ctrl_output

(

fc

)

Ǔ

180°

p

* 90°

Ǔ

p

180°

Select OTA Compensation Zero to Coincide

with Modulator Pole at f

p1

(f

z

)

w

p1e

2p

Resulting OTA High Frequency Pole Placement (f

p

)

f

z

f

c

) f

c



2

tan(boost)

f

c

* f

z

tan(boost)

Compensation Resistor R

2

f

p

G

f

p

* f

z



V

OUT

1.2g

m



1 )

ǒ

f

c

f

p

Ǔ

2

Ǹ

1 )

ǒ

f

z

f

p

Ǔ

Ǹ

Compensation Capacitor C

1

2pf

z

R

2

Compensation Capacitor C

2

1

2pf

p

G

@

R

low

g

m

R

low

) R

1

OTA DC Gain (G

0_OTA

)

R

low

R

low

) R

1

@ g

m

@ R

0

Low Frequency Zero (w

z1e

)

1

2



ǒ

R

2

) R

esd

Ǔ

R

2

R

esd

C

2

ȧ

ȱ

Ȳ

1 * 1 * 4

R

2

R

esd

C

2

ǒ

R

2

) R

esd

Ǔ

2

C

1

Ǹ



ȧ

ȳ

ȴ

High Frequency Zero (w

z2e

)

1

2



ǒ

R

2

) R

esd

Ǔ

R

2

R

esd

C

2

ȧ

ȱ

Ȳ

1 ) 1 * 4

R

2

R

esd

C

2

ǒ

R

2

) R

esd

Ǔ

2

C

1

Ǹ



ȧ

ȳ

ȴ

Low Frequency Pole (w

p1e

)

1

2



ǒ

R

0

) R

2

) R

esd

Ǔ

R

2

ǒ

R

0

) R

esd

Ǔ

C

2

ȧ

ȱ

Ȳ

1 * 1 * 4

R

2

ǒ

R

0

) R

esd

Ǔ

C

2

ǒ

R

0

) R

2

) R

esd

Ǔ

2

C

1

Ǹ



ȧ

ȳ

ȴ

High Frequency Pole (w

p2e

)

1

2



ǒ

R

0

) R

2

) R

esd

Ǔ

R

2

ǒ

R

0

) R

esd

Ǔ

C

2

ȧ

ȱ

Ȳ

1 ) 1 * 4

R

2

ǒ

R

0

) R

esd

Ǔ

C

2

ǒ

R

0

) R

2

) R

esd

Ǔ

2

C

1

Ǹ



ȧ

ȳ

ȴ

OTA Transfer Function (G

OTA

(f))

-G

0_OTA

ǒ

1 ) j

2pf

w

z1e

Ǔ

ǒ

1 ) j

2pf

w

p1e

Ǔ



ǒ

1 ) j

2pf

w

z2e

Ǔ

ǒ

1 ) j

2pf

w

p2e

Ǔ

The open-loop-response in closed-loop form to verify the

gain/phase margins may be obtained from the following

expression.

T(f) + G

OTA

(f) H

ctrl_output

(f)

Low Voltage Operation

If the input voltage drops below the UVLO or MOSFET

threshold voltage, another voltage may be used to power the

device. Simply connect the voltage you would like to boost

to the inductor and connect the stable voltage to the VIN pin

of the device. In boost configuration, the output of the

converter can be used to power the device. In some cases it

may be desirable to connect 2 sources to VIN pin, which can

be accomplished simply by connecting each of the sources

through a diode to the VIN pin.

NCV887001D1R2G

NCV887001D1R2G

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