pwm step-down converter(njm2309)

Case Study:NJM2309 Application Circuit Design (PWM Step-down Converter)

All Rights Reserved Copyright (C) Bee Technologies Corporation 2011

1

Power Switches Filter & LoadPWM Controller (Voltage Mode Control)

VREF

VOUT

REF

PWM

1 / V p

-

+

U ?P W M _ C TR L

V P = 2 . 5V R E F = 1 . 2 3

D

U ?B U C K _ S W

L1 2

C

R lo a d

V o

E S R

Contents

• Design Specification• NJM2309 Typical Application Circuit• Averaged Buck Switch Model• Buck Regulator Design Workflow

1. Setting PWM Controller’s Parameters.

2. Programming Output Voltage: Rupper, Rlower

3. Inductor Selection: L

4. Capacitor Selection: C, ESR

5. Stabilizing the Converter

• Load Transient Response Simulation Reference: Load Transient Response Simulation with PWM IC Transient Model

Appendix

A. Type 2 Compensation Calculation using Excel

B. Feedback Loop Compensators

C. Simulation Index


2

Design Specification

Step-Down (Buck) Converter :

• VIN, MAX = 32 (V)

• VIN, MIN = 6 (V)

• VOUT = 3.3 (V)

• VOUT, Ripple = 1% ( 33mVP-P )

• IOUT, MAX = 1.0 (A)

• IOUT, MIN = 0.2 (A)

Control IC :• NJM2309 (Switching Regulator Control IC for Step-Down)• Switching Frequency – fosc = 105 (kHz)


3

NJM2309 Datasheet

NJM2309 Typical Application Circuit


4

Filter & Load

PWM Controller

Power Switches

Schematic is captured from NJM2309 datasheet page 4.


5

1

2?

3?

4?

5?

TASK: Design and Evaluation of the Circuit

NJM2309 Typical Application Circuit

Buck Regulator Design Workflow


6

Setting PWM Controller’s Parameters: VREF, VP1

Setting Output Voltage: Rupper, Rlower2

Inductor Selection: L3

Capacitor Selection: C, ESR4

Stabilizing the Converter: R2, C1, C2

• Step1: Open the loop with LoL=1kH and CoL=1kF then inject an AC signal to generate Bode plot. (always default)

• Step2: Set C1=1kF, C2=1fF, (always keep the default value) and R2= calculated value (Rupper//Rlower) as the initial values.

• Step3: Select a crossover frequency (about 10kHz or fc < fosc/4). Then complete the table.

• Step4: Read the Gain and Phase value at the crossover frequency (10kHz) from the Bode plot, Then put the values to the table

• Step5: Select the phase margin at the fc ( > 45 ). Then change the K value until it gives the satisfied phase margin, for this example K=6 is chosen for Phase margin = 46.

• Remark: If K-factor fail to gives the satisfied phase margin, Increase the output capacitor C then try Step1 to Step5 again.

Load Transient Response Simulation

5

6

L1 2

C

R lo a d

0

C o m p

C 2

R 2 C 1

F B

Type 2 Compensator

R u p p e r

R lo we r

0

d

V inD

U 2B U C K _ S W

REF

PWM

1 / V p

-

+

U 3P W M _ C TR L

V P = 2 . 5V R E F = 1 . 2 3

V o

E S R

Buck Regulator Design Workflow


7

1

2

3

4

5

VREF = VB = 0.52 (V)

VP=2.5 (vFBH and vFBL are not provided, the default value is used).

Setting PWM Controller’s Parameters


8

Table is captured from NJM2309 datasheet page 2.

1

• Use the following formula to select the resistor values.

• Rlower can be between 1k and 5k.

Given: VOUT = 3.3V

VREF = 0.52V

Rlower = 1kthen: Rupper = 5.346k

Setting Output Voltage: Rupper, Rlower


9

lower

upperREFOUT

R

RVV 1

2

Inductor Selection: L


10

Inductor Value

from

Given:

• VI,max = 40(V), VOUT = 3.3(V)

• IOUT,min = 0.2(A)

• RL,min = (VOUT / IOUT,min ) = 16.5()

• fosc = 105(kHz)

Then:

• LCCM 72.1(uH),

L = 100(uH) is selected

L1 2

C

R lo a d

V o

E S R

max,

min,max,

2 Iosc

LOUTICCM

Vf

RVVL

3

Capacitor Selection: C, ESR (NJM2309)


11

Capacitor ValueFrom

and

Given:

• VI, max = 40 V

• VOUT = 3.3 V, VOUT, Ripple = 1% ( 33mVP-P )

• L (H) = 100

• IOUT, MAX = 1(A), IL, Ripple = 0.25(A)

Then:

C 944 (F), C = 1000(F) is selected

In addition:

ESR 132m

L1 2

C

R lo a d

V o

E S R

RIPPLEL

RIPPLEO

I

VESR

,

,

4

F)H(

785,7max,

LV

VC

OUT

I

R 20 . 8 4 2 k

Type 2 Compensator

C 21 f

C 11 k

L1 0 0 u H

1 2

C1 0 0 0 u F

R lo a d3 . 3

0

0

C O L1 k F

L O L

1 k H

F B

R u p p e r5 . 3 4 6 k

R lo we r1 k

0

d

V 31 V a c0 V d c

V in1 2 V d c

D

U 2B U C K _ S W

REF

PWM

1 / V p

-

+

U 3P W M _ C TR L

V P = 2 . 5V R E F = 0 . 5 2

V o

E S R1 3 2 m

Stabilizing the Converter (NJM2309)


12

Specification:VOUT = 3.3VVIN = 6 ~ 32VILOAD = 0.2 ~ 1A

PWM Controller:VREF = 0.52VVP = 2.5VfOSC = 105kHz

Rlower = 1k,Rupper = 5.346k,L = 100uH, C = 1000uF (ESR = 132m)

Task: • to find out the element of the

Type 2 compensator ( R2, C1, and C2 )

G(s)

e.g. Given values from National Semiconductor Corp. IC: LM2575

5

1

3

4

2

R 20 . 8 4 2 k

Type 2 Compensator

C 21 f

C 11 k

L1 0 0 u H

1 2

C1 0 0 0 u F

R lo a d3 . 3

0

0

C O L1 k F

L O L

1 k H

F B

R u p p e r5 . 3 4 6 k

R lo we r1 k

0

d

V 31 V a c0 V d c

V in1 2 V d c

D

U 2B U C K _ S W

REF

PWM

1 / V p

-

+

U 3P W M _ C TR L

V P = 2 . 5V R E F = 0 . 5 2

V o

E S R1 3 2 m


13

Step2 Set C1=1kF, C2=1fF, and R2=calculated value (Rupper//Rlower) as the initial values.

Step1 Open the loop with LoL=1kH and CoL=1kF then inject an AC signal to generate Bode plot.

The element of the Type 2 compensator ( R2, C1, and C2 ), that stabilize the converter, can be extracted by using Type 2 Compensator Calculator (Excel sheet) and open-loop simulation with the Average Switch Models (ac models).

Stabilizing the Converter (NJM2309)5

C1=1kF is AC shorted, and C2 1fF is AC opened (or Error-Amp without compensator).


Type 2 Compensator Calculator

Switching frequency, fosc : 105.00 kHzCross-over frequency, fc (<fosc/4) : 10.00 kHzRupper : 5.346 kOhmRlower : 1 kOhmR2 (Rupper//Rlower) : 0.842 kOhm (automatically calculated)

PWMVref : 0.520 VVp (Approximate) : 2.5 V


14

Step3 Select a crossover frequency (about 10kHz or fc < fosc/4 ), for this example, 10kHz is selected. Then complete the table.

Calculated value of the Rupper//Rlower

values from 2

values from 1

5

Frequency

100Hz 1.0KHz 10KHz 100KHz 1.0MHzP(v(d))

0d

180d

SEL>>

(10.000K,84.551)

DB(v(d))-80

-40

0

40

(10.000K,-36.242)

Parameter extracted from simulationSet: R2=R1, C1=1k, C2=1fGain (PWM) at foc ( - or + ) : -36.242Phase (PWM) at foc : 84.551


15

Step4 Read the Gain and Phase value at the crossover frequency (10kHz) from the Bode plot, Then put the values to the table.


Tip: To bring cursor to the fc = 10kHz type “ sfxv(10k) ” in Search Command.

Cursor Search

Gain: T(s) = H(s)GPWM

Phase at fc

5

K-factor (Choose K and from the table)K 3q -217 ° (automatically calculated)

Phase margin : 48 (automatically calculated)

R2 : 54.655 kOhm (automatically calculated)C1 : 0.847 nF (automatically calculated)C2 : 97.07 pF (automatically calculated)



16

Step5 Select the phase margin at fc (> 45 ). Then change the K value (start from K=2) until it gives the satisfied phase margin, for this example K=3 is chosen for Phase margin = 48.

As the result; R2, C1, and C2 are calculated.

K Factor enable the circuit designer to choose a loop cross-over frequency and phase margin, and then determine the necessary component values to achieve these results. A very big K value (e.g. K > 100) acts like no compensator (C1 is shorted and C2 is opened).

5

Remark: If K-factor fail to gives the satisfied phase margin, Increase the output capacitor C then try Step1 to Step5 again.

R 25 4 . 6 5 5 k

Type 2 Compensator

C 29 7 . 0 7 p

C 10 . 8 7 4 n

L1 0 0 u H

1 2

C1 0 0 0 u F

R lo a d3 . 3

0

0

C O L1 k F

L O L

1 k H

F B

R u p p e r5 . 3 4 6 k

R lo we r1 k

0

d

V 31 V a c0 V d c

V in1 2 V d c

D

U 2B U C K _ S W

REF

PWM

1 / V p

-

+

U 3P W M _ C TR L

V P = 2 . 5V R E F = 0 . 5 2

V o

E S R1 3 2 m



17

The element of the Type 2 compensator ( R2, C1, and C2 ) extraction can be completed by Type 2 Compensator Calculator (Excel sheet) with the converter average models (ac models) and open-loop simulation.

The calculated values of the type 2 elements are: R2=54.655k, C1=0.874nF , C2=97.07pF.

*Analysis directives: .AC DEC 100 0.1 10MEG

5

Frequency

100Hz 1.0KHz 10KHz 100KHz 1.0MHzP(v(d))

-45d

0d

45d

90d

135d

180d

SEL>>

(9.2368K,48.801)

DB(v(d))

-80

-40

0

40

80

(9.2368K,0.000)

• Phase margin = 48.801 at the cross-over frequency - fc = 9.237kHz.


18


Tip: To bring cursor to the cross-over point (gain = 0dB) type “ sfle(0) ” in Search Command.

Cursor Search

Gain: T(s) = H(s) G(s)GPWM

Phase at fc

5

Gain and Phase responses after stabilizing

L o a d

V o

I 1

TD = 1 0 mTF = 2 5 u

P W = 0 . 4 3 mP E R = 1

I 1 = 0I 2 = 0 . 8

TR = 2 0 u

R lo a d1 6 . 5

0

F B

R u p p e r5 . 3 4 6 k

R lo we r1 k

0

d

V in1 2 V d c

D

U 2B U C K _ S W

REF

PWM

1 / V p

-

+

U 3P W M _ C TR L

V P = 2 . 5V R E F = 0 . 5 2

L1 0 0 u H

1 2

C1 0 0 0 u F

E S R1 3 2 m

R 25 4 . 6 5 5 k

Type 2 Compensator

C 29 7 . 0 7 p

C 10 . 8 7 4 n



19

The converter, that have been stabilized, are connected with step-load to perform load transient response simulation.

3.3V/16.5 = 0.2A step to 0.2+0.8=1.0A load

*Analysis directives: .TRAN 0 20ms 0 1u

3

4

5

2

1


20

Output Voltage Change

Load Current

• The simulation results illustrates the transient response of the converter with the stepping load .2A to 1A.


Time

9.9ms 10.0ms 10.1ms 10.3ms 10.4ms 10.5ms 10.6ms 10.8ms1 V(vo) 2 I(load)

2.8V

2.9V

3.0V

3.1V

3.2V

3.3V

3.4V

3.5V1

>>0A

0.5A

1.0A

1.5A

2.0A

2.5A

3.0A

3.5A

4.0A2

Simulation

R 25 4 . 6 5 5 k

Type 2 Compensator

C 29 7 . 0 7 p

C 10 . 8 7 4 n

R u p p e r5 . 3 4 6 k

R lo we r1 k

I 1

TD = 1 0 mTF = 2 5 u

P W = 0 . 4 3 mP E R = 1

I 1 = 0I 2 = 0 . 8

TR = 2 0 u

R lo a d1 6 . 5

0

p wm

p wm

0

V in1 2 V d c

F B

OSCREF

E / AComp

+

-

-

+

U 3P W M _ I C

F O S C = 1 0 5 K

V P = 2 . 5V R E F = 0 . 5 2

C o m p

L1 0 0 u H

1 2

C1 0 0 0 u FI C = 3 . 3

E S R1 3 2 m

+ -

+ - S 1S

R O N = 1 0 0 m

D 1D I O D E

lo a d

V o

Reference: Load Transient Response Simulation with PWM IC Transient Model


21

After the converter have been designed, the PWM IC Transient Model could be applied for more realistic simulation.

3.3V/16.5 = 0.2A step to 0.2+0.8=1.0A load

*Analysis directives: .TRAN 0 12ms 0 200n SKIPBP

3

4

5

2

1

Remark: PWM IC Transient Model and Simulations are not included with this package.

Time

10.0ms 10.2ms 10.4ms 10.6ms 10.8ms1 V(Vo) 2 I(load)

2.8V

2.9V

3.0V

3.1V

3.2V

3.3V

3.4V

3.5V1

0A

0.5A

1.0A

1.5A

2.0A

2.5A

3.0A

3.5A

4.0A2

>>

The PWM IC Transient Model enables The VOUT, RIPPLE and others switching characteristics to be included in the simulation.


22

Output Voltage Change

Load Current

Simulation

Remark: PWM IC Transient Model and Simulations are not included with this package.

Reference: Load Transient Response Simulation with PWM IC Transient Model

A. Type 2 Compensation Calculation using Excel

Switching frequency, fosc : 105.00 kHz Given spec, datasheetCross-over frequency, fc (<fosc/4) : 10.00 kHz Input the chosen value ( about 10kHz or < fosc/4 )Rupper : 5.346 kOhm Given spec, datasheet, or calculated Rlower : 1 kOhm Given spec, datasheet, or value: 1k-10k OhmR2 (Rupper//Rlower) : 0.842 kOhm (automatically calculated)

PWMVref : 0.520 V Given spec, datasheetVp (Approximate) : 2.5 V Given spec, or calculated, (or leave default 2.5V)

Parameter extracted from simulationSet: R2=R2, C1=1k, C2=1fGain (PWM) at foc ( - or + ) : -36.242 dB Read from simulation resultPhase (PWM) at foc : 84.551 ° Read from simulation result

K-factor (Choos K and q from the table)K 3 Input the chosen value (start from k=2)q -217 ° (automatically calculated)

Phase margin : 48 (automatically calculated) Target value > 45

R2 : 54.655 kOhm (automatically calculated)C1 : 0.874 nF (automatically calculated)C2 : 97.07 pF (automatically calculated)


23


24

B. Feedback Loop Compensators

Type 1 Compensator

C 1

V O U T

F B

R u p p e r

R lo we r

0

d

REF

PWM

1 / V p

-

+

P W M _ C TR L

Type1 Compensator Type2 Compensator Type2a Compensator

Type2b Compensator Type3 Compensator

Type2b Compensator

C 1

V O U T

F B

R u p p e r

R lo we r

0

d

REF

PWM

1 / V p

-

+

P W M _ C TR L

R 2

Type2a Compensator

C 1

V O U T

F B

R u p p e r

R lo we r

0

d

REF

PWM

1 / V p

-

+

P W M _ C TR L

R 2

Type3 Compensator

C 1

F B

R u p p e r

R lo we r

0

d

REF

PWM

1 / V p

-

+

P W M _ C TR L

C 2

R 2

C 3

R 3

V O U T

Type2 Compensator

C 1

F B

R u p p e r

R lo we r

0

d

REF

PWM

1 / V p

-

+

P W M _ C TR L

C 2

R 2

V O U T


25

Simulations Folder name

1. Stabilizing the

Converter....................................................

2. Load Transient Response..................................................

ac

stepload

Libraries :1. ..\bucksw.lib2. ..\pwm_ctr.lib

Tool :• Type 2 Compensator Calculator (Excel sheet)

C. Simulation Index

pwm step-down converter(njm2309)

Technology

output capacitor c

phase value

default value

vout iout

compensator r2

c2 step1

initial values

calculated value rupperrlower