pwm buck converter using average model

Concept Kit:PWM Buck Converter Average Model

All Rights Reserved Copyright (C) Bee Technologies Corporation 2010

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

Pre Version

Contents

1. Concept of Simulation

2. Buck Converter Circuit

3. Switches

4. Filter & Load

4.1 Inductor

4.2 Capacitor

5. PWM Controller

5.1 Error Amp.

5.2 PWM

6. Stabilizing the Converter (Example)

7. Load Transient Response Simulation (Example)

Type 2 Compensator Calculator

Simulation Index


2


3

Power Switches

Averaged Buck Switch Model

Filter & Load

Parameter:• L• C• ESR• Rload

PWM Controller (Voltage Mode Control)

Parameter:• VP

• VREF

Models:

Block Diagram:

1.Concept of Simulation

VREF

VOUT

D

U ?B U C K _ S W

REF

PWM

1 / V p

-

+

U ?P W M _ C TR L

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

L1 2

C

R lo a d

V o

E S R

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

2.Buck Converter Circuit


4

Filter & Load

PWM Controller

Power Switches

3.Switches

• The Averaged Buck Switch Model represents relation between input and output of the switch that is controlled by duty cycle – d (value between 0 and 1).

• Transfer function of the model is

vout = d vin

• The current flow into the switch is

iin = d iout


5

D

U 2B U C K _ S W

vin

+

-

vout

+

-D

iin iout

4.1 Filter & Load: Inductor


6

Inductor Value• The output inductor value is selected to set the

converter to work in CCM (Continuous Current Mode) or DCM (Discontinuous Current Mode).

• Calculated by

Where

• LCCM is the inductor that make the converter to work in CCM.

• VI,max is input maximum voltage

• RL(max) is load resistance at the minimum output current (IOUT)

• fosc is switching frequency

L1 2

C

R lo a d

V o

E S R

max,

(max)max,

2 Iosc

LOICCM

Vf

RVVL

(1)

4.2 Filter & Load: Capacitor


7

Capacitor Value• The minimum allowable output capacitor value should

be determined by

Where

• IL, RIPPLE is an inductor ripple current, chosen to be 25% of IOUT.

• VO,RIPPLE is an output ripple voltage.

• fosc is switching frequency

• In addition, the output ripple voltage due to the capacitor ESR must be considered as the following equation.

L1 2

C

R lo a d

V o

E S R

RIPPLEOosc

RIPPLEL

Vf

IC

,

,

8(min)

RIPPLEL

RIPPLEO

I

VESR

,

,

(2)

(3)

• The Error Amp. compares the feedback voltage ( FB ) to the reference voltage ( Parameter: VREF ), the output signal will be fed back to the controller to regulate the converter output voltage as the above equation.

5.1 PWM Controller: Error Amp.


8

C o m p

C 2

R 2 C 1

Type 2 Compensator

F B

R u p p e r

R lo we r

0

d

REF

PWM

1 / V p

-

+

U 3P W M _ C TR L

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

Error Amp.

Vo

lower

upperREFOUT

R

RVV 1 (4)

TimeV(PWM)

V(osc) V(comp)0V

2.0V

3.0V

SEL>>

5.2 PWM Controller: PWM


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• The PWM block is used to transfer the error voltage (between FB and REF) to be the duty cycle.

• The error voltage (vcomp) will be compared with

sawtooth signal ( amplitude = VP ) to create the

pulse that the duty cycle depends on the vcomp

• Transfer function of the PWM block is

VP

Duty cycle (d) is a value from 0 to 1

d = vcomp / VP

GPWM = 1/VP

REF

PWM

1 / V p

-

+

U ?P W M _ C TR L

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

vcomp

d

Error Amp.

FB

• Loop gain for this configuration is

L1 2

R lo a d

C

0

C o m p

C 2

R 2 C 1

Type 2 Compensator

F B

R u p p e r3 . 0 6 6 k

R lo we r1 . 0 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 = 1 . 2 3

V o

E S R

• The purpose of the compensator G(s) is to tailor the converter loop gain (frequency response) to make it stable when operated in closed-loop conditions.

5.3 PWM Controller: Compensator


10

PWMGsGsHsT )()()( GPWM

G(s)

H(s)

6.Stablilizing the Converter (Example)


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Specification:VOUT = 5VVIN = 7 ~ 40VILOAD = 0.2 ~ 1A

L = 330uH, C = 330uF (ESR = 100m),Rupper = 3.1k,Rlower = 1k,

PWM Controller:fOSC = 52kHzVP = 2.5VVREF = 1.23V

Task: to find out the element of the Type 2 compensator ( R2, C1, and C2 )

L3 3 0 u H

1 2

C3 3 0 u F

R lo a d5

0

0

C O L1 k F

L O L

1 k H

C 2

R 2 C 1

F B

R u p p e r3 . 1 k

Type 2 Compensator

R lo we r1 . 0 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 = 1 . 2 3

V o

E S R1 0 0 m

G(s)

e.g. Characteristics from National Semiconductor Corp. IC: LM2575

L3 3 0 u H

1 2

C3 3 0 u F

R lo a d5

0

0

C O L1 k F

L O L

1 k H

R 20 . 7 5 6 k

F B

R u p p e r3 . 1 k

Type 2 Compensator

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 = 1 . 2 3

V o

E S R1 0 0 m

C 21 f

C 11 k



12

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 the 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 models (ac models).



Switching frequency, fosc : 52.00 kHzCross-over frequency, fc (<fosc/4) : 10.00 kHzRupper : 3.1 kOhmRlower : 1 kOhmR2 (Rupper//Rlower) : 0.756 kOhm (automatically calculated)

PWMVref : 1.230 VVp (Approximate) : 2.5 V


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

Calcuted value of the Rupper//Rlower

from

d = vcomp / VP

Suppose that the error amp. gain is 100.

vcomp = gain (-vFB) then

d = (100 (-vFB) ) / VP

From the graph on the left, vFB = -25mV

VP = (100 (-vFB) ) / dVP ≈ (100 (-(-25mV)) ) / 1

≈ 2.5V


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If the VP ( sawtooth signal amplitude ) does not informed by the datasheet, It can be approximate from the characteristics below.

LM2575: Feedback Voltage vs. Duty Cycle


vFB = -25mV

d = 1 (100%)

Parameter extracted from simulationSet: R2=R1, C1=1k, C2=1fGain (PWM) at foc ( - or + ) : -44.211Phase (PWM) at foc : 65.068


15

Frequency

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

0d

90d

180d

SEL>>

(10.000K,65.068)

DB(v(d))

-80

-40

0

40

80

(10.000K,-44.211)

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

K-factor (Choose K and from the table)K 6q -199 ° (automatically calculated)

Phase margin : 46 (automatically calculated)

R2 : 122.780 kOhm (automatically calculated)C1 : 0.778 nF (automatically calculated)C2 : 21.600 pF (automatically calculated)



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Step5 Select the desired amount of phase margin you need at fc ( > 45 ). Then change the K value until it gives the satisfied phase margin, for this example K=25 is chosen for Phase margin = 46.

R2, C1, and C2 are calculated

K Factor, introduce by Dean Venable, 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 from a few straight-forward algebraic equations.

R 21 2 2 . 7 8 0 k

Type 2 Compensator

C 22 1 . 6 p

C 10 . 7 7 8 n

L3 3 0 u H

1 2

C3 3 0 u F

R lo a d5

0

0

C O L1 k F

L O L

1 k H

F B

R u p p e r3 . 1 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 = 1 . 2 3

V o

E S R1 0 0 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, C1=0.778nF, C2=21.6pF, and R2=122.780k.

*Analysis directives: .AC DEC 100 0.1 10MEG

Frequency

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

0d

90d

180d

(9.778K,45.930)

DB(v(d))

-40

0

40

80

-100SEL>>

(9.778K,0.000)

• Phase margin = 45.930 at the cross-over frequency - fc = 9.778kHz.


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

Cursor Search

Phase at fc

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



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R 21 2 2 . 7 8 0 k

C 22 1 . 6 p

Type 2 Compensator

C 10 . 7 7 8 n

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 d2 5

0

F B

R u p p e r3 . 1 k

R lo we r1 k

0

d

V in2 0 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 = 1 . 2 3

L3 3 0 u H

1 2

C3 3 0 u F

E S R1 0 0 m

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

5V/2.5 = 0.2A step to 0.2+0.8=1.0A load

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

Simulation Measurement


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Output Voltage Change

Load Current

• The simulation results are compared with the measurement data (National Semiconductor Corp. IC LM2575 datasheet).

Time

9.9ms 10.1ms 10.3ms 10.5ms 10.7ms 10.9ms1 V(vo) 2 I(load)

4.4V

4.5V

4.6V

4.7V

4.8V

4.9V

5.0V

5.1V

5.2V1

0A

0.5A

1.0A

1.5A

2.0A

2.5A

3.0A

3.5A

4.0A2

>>



Switching frequency, fosc : 52.00 kHz Spec, datasheetCross-over frequency, fc (<fosc/4) : 10.00 kHz Input the chosen valueRupper : 3.1 kOhm Spec, datasheetRlower : 1 kOhm Spec, datasheetR2 (Rupper//Rlower) : 0.756 kOhm (automatically calculated)

PWMVref : 1.230 V Spec, datasheetVp (Approximate) : 2.5 V Spec, datasheet + calculating, (or leave default 2.5V)

Parameter extracted from simulationSet: R2=R2, C1=1k, C2=1fGain (PWM) at foc ( - or + ) : -44.211 dB Read from simulation resultPhase (PWM) at foc : 65.068 ° Read from simulation result

K-factor (Choos K and q from the table)K 6 Input the chosen valueq -199 ° (automatically calculated)

Phase margin : 46 (automatically calculated)

R2 : 122.780 kOhm (automatically calculated)C1 : 0.778 nF (automatically calculated)C2 : 21.60 pF (automatically calculated)


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Simulation Index


22

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)

pwm buck converter using average model

Technology

converter loop

converter output voltage

converter exampletype

converter exampletip

compensator r2

output ripple voltage

output signal

error voltage vcomp