concept kit:pwm buck converter average model (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/Vp

-

+

U?PWM_CTRL

VP = 2.5VREF = 1.23

D

U?BUCK_SW

L1 2

C

Rload

Vo

ESR

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


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)


NJM2309 Datasheet

NJM2309 Typical Application Circuit


Filter & Load

PWM Controller

Power Switches

Schematic is captured from NJM2309 datasheet page 4.


1

2?

3?

4?

5?

TASK: Design and Evaluation of the Circuit

NJM2309 Typical Application Circuit

Buck Regulator Design Workflow


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

Rload

0

Comp

C2

R2 C1

FB

Type 2 Compensator

Rupper

Rlower

0

d

Vin

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

Vo

ESR

Buck Regulator Design Workflow


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


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 = 1k

then: Rupper = 5.346k

Setting Output Voltage: Rupper, Rlower


lower

upperREFOUT

R

RVV 1

2

Inductor Selection: L


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

Rload

Vo

ESR

max,

min,max,

2 Iosc

LOUTICCM

Vf

RVVL

3

Capacitor Selection: C, ESR (NJM2309)


Capacitor Value

From

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

Rload

Vo

ESR

RIPPLEL

RIPPLEO

I

VESR

,

,

4

F)H(

785,7max,

LV

VC

OUT

I

R20.842k

Type 2 Compensator

C21f

C11k

L100uH

1 2

C1000uF

Rload3.3

0

0

COL1kF

LOL

1kH

FB

Rupper

5.346k

Rlower

1k

0

d

V31Vac

0Vdc

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 0.52

Vo

ESR132m

Stabilizing the Converter (NJM2309)


Specification:

VOUT = 3.3V

VIN = 6 ~ 32V

ILOAD = 0.2 ~ 1A

PWM Controller:

VREF = 0.52V

VP = 2.5V

fOSC = 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

R20.842k

Type 2 Compensator

C21f

C11k

L100uH

1 2

C1000uF

Rload3.3

0

0

COL1kF

LOL

1kH

FB

Rupper

5.346k

Rlower

1k

0

d

V31Vac

0Vdc

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 0.52

Vo

ESR132m


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


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 1.0MHz

P(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


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 3 -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)



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.

R254.655k

Type 2 Compensator

C297.07p

C10.874n

L100uH

1 2

C1000uF

Rload3.3

0

0

COL1kF

LOL

1kH

FB

Rupper

5.346k

Rlower

1k

0

d

V31Vac

0Vdc

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 0.52

Vo

ESR132m



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 1.0MHz

P(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.



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

Load

Vo

I1

TD = 10mTF = 25u

PW = 0.43mPER = 1

I1 = 0I2 = 0.8

TR = 20u

Rload16.5

0

FB

Rupper

5.346k

Rlower

1k

0

d

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 0.52

L100uH

1 2

C1000uF

ESR132m

R254.655k

Type 2 Compensator

C297.07p

C10.874n



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


.TRAN 0 20ms 0 1u

3

4

5

2

1


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 10.8ms

1 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

R254.655k

Type 2 Compensator

C297.07p

C10.874n

Rupper

5.346k

Rlower

1k

I1

TD = 10mTF = 25u

PW = 0.43mPER = 1

I1 = 0I2 = 0.8

TR = 20u

Rload16.5

0

pwm

pwm

0

Vin

12Vdc

FB

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 105K

VP = 2.5VREF = 0.52

Comp

L100uH

1 2

C1000uFIC = 3.3

ESR132m

+ -

+ - S1S

RON = 100m

D1DIODE

load

Vo

Reference: Load Transient Response Simulation

with PWM IC Transient Model


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


.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 10.8ms

1 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.


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 from the table)K 3 Input the chosen value (start from k=2)

-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)



B. Feedback Loop Compensators

Type 1 Compensator

C1

VOUT

FB

Rupper

Rlower

0

d

REF

PWM

1/Vp

-

+

PWM_CTRL

Type1 Compensator Type2 Compensator Type2a Compensator

Type2b Compensator Type3 Compensator

Type2b Compensator

C1

VOUT

FB

Rupper

Rlower

0

d

REF

PWM

1/Vp

-

+

PWM_CTRL

R2

Type2a Compensator

C1

VOUT

FB

Rupper

Rlower

0

d

REF

PWM

1/Vp

-

+

PWM_CTRL

R2

Type3 Compensator

C1

FB

Rupper

Rlower

0

d

REF

PWM

1/Vp

-

+

PWM_CTRL

C2

R2

C3

R3

VOUT

Type2 Compensator

C1

FB

Rupper

Rlower

0

d

REF

PWM

1/Vp

-

+

PWM_CTRL

C2

R2

VOUT


Simulations Folder name

1. Stabilizing the Converter....................................................

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

ac

stepload

Libraries :

1. ..¥bucksw.lib

2. ..¥pwm_ctr.lib

Tool :

• Type 2 Compensator Calculator (Excel sheet)

C. Simulation Index

concept kit:pwm buck converter average model (njm2309)

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