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LT1946A

2.7MHz Boost DC/DC Converter with 1.5A Switch and Soft-Start

Linear Technology 

LT1946A

APPLICATIO S I FOR ATIO

As with any feedback loop, identifying the gain and phase

contribution of the various elements in the loop is critical.

Figure 4 shows the key equivalent elements of a boost

converter. Because of the fast current control loop, the

power stage of the IC, inductor, and diode have been

replaced by the equivalent transconductance amplifier

GMP. GMP acts as a current source where the output

current is proportional to the VC voltage. Note that the

maximum output current of GMP is finite due to the current

limit in the IC.

From Figure 4, the DC gain, poles and zeroes can be

calculated as follows:

Output

Pole:

P1

=

2•

π

2

• RL

• COUT

Error

Amp

Pole:

P2

=

2•π

1

• RO

•CC

Error

Amp

Zero:

Z1 =

1

2 • π •RC

•CC

DC

Gain:

A

=

1.25

VOUT

• G MA

• RO

• G MP

• RL

–

GMP

+

VC

GMA

RC

RO

CC

1.250V

REFERENCE

VOUT

ESR

RL

COUT

R1

R2

ESR

Zero:

Z2

=

1

2 • π • ESR • COUT

RHP Zero: Z3 =

VIN2 •RL

2

2 • π • VOUT • L

High

Frequency

Pole:

P3

>

FS

3

Using the circuit of Figure 1 as an example, Table 3 shows

the parameters used to generate the bode plot shown in

Figure 5.

Table 3. Bode Plot Parameters

Parameter

Value

Units

RL

28

Ω

COUT

2.2

µF

RO

10

MΩ

CC

270

pF

RC

27.4

kΩ

VOUT

12

V

VIN

5

V

GMA

40

µmho

GMP

5

mho

L

2.2

µH

FS

2.7

MHz

ESR

10

mΩ

Comment

Application Specific

Application Specific

Not Adjustable

Adjustable

Adjustable

Application Specific

Application Specific

Not Adjustable

Not Adjustable

Application Specific

Not Adjustable

Not Adjustable

From Figure 5, the phase when the gain reaches 0dB is

122° giving a phase margin of 58°. This is more than

adequate. The cross-over frequency is 90kHz, which is

about 30 times lower than the frequency of the right half

plane zero Z2. It is important that the cross-over frequency

be at least 3 times lower than the frequency of the RHP zero

to achieve adequate phase margin.

GMA: TRANSCONDUCTANCE AMPLIFIER INSIDE IC

GMP: POWER STAGE TRANSCONDUCTANCE AMPLIFIER

COUT: OUTPUT CAPACITOR

RL: OUTPUT RESISTANCE DEFINED AS VOUT DIVIDED BY ILOAD (MAX)

R1, R2: FEEDBACK RESISTOR DIVIDER NETWORK

RO: OUTPUT RESISTANCE OF GMA

RC: COMPENSATION RESISTOR

CC: COMPENSATION CAPACITOR

Figure 4. Boost Converter Equivalent Model

8

sn1946a 1946afs

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