concept kit:pwm buck converter average model

Concept Kit:PWM Buck Converter

Average Model

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

• Concept of Simulation

• Buck Converter 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 (Example)

• Load Transient Response Simulation (Example)

Appendix

A. Type 2 Compensation Calculation using Excel

B. Feedback Loop Compensators

C. Simulation Index



Power Switches

Averaged Buck

Switch Model

Filter & Load

Parameter:

• L

• C

• ESR

• Rload

PWM Controller (Voltage Mode

Control)

Parameter:

• VP

• VREF

Models:

Block Diagram:

Concept of Simulation

VREF

+-

VOUT

D

U?BUCK_SW

REF

PWM

1/Vp

-

+

U?PWM_CTRL

VP = 2.5VREF = 1.23

L1 2

C

Rload

Vo

ESR

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 Converter Circuit


Filter & Load

PWM Controller

Power Switches

Averaged Buck Switch Model

• 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


D

U2BUCK_SW

vin

+

-

vout

+

-

D

iin iout

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

Buck Regulator Design Workflow


1

2

3

4

5

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

• VREF, feedback reference voltage, value

is given by the datasheet

• VP = (Error Amp. Gain vFB ) / d

• vFB = vFBH – vFBL

• d = dMAX – dMIN

• Error Amp. Gain is 100 (approximated)

where

VP is the sawtooth peak voltage.

vFBH is maximum FB voltage where d = 0

vFBL is minimum FB voltage where d =1(100%)

dMAX is maximum duty cycle, e.g. d = 0(0%)

dMIN is minimum duty cycle, e.g. d =1(100%)

Setting PWM Controller’s Parameters


REF

PWM

1/Vp

-

+

U?PWM_CTRL

VP = 2.5VREF = 1.23

vcomp

d

Error Amp.

FB

The PWM block is used to transfer the error voltage

(between FB and REF) to be the duty cycle.

If vFBH and vFBL are not provided, the default value, VP=2.5 could be used.

1

Time

V(PWM)

V(osc) V(comp)

0V

2.0V

3.0V

SEL>> VP

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

from

VP = (Error Amp. Gain vFB )/d

•Error Amp. Gain = 100 (approximated)

• from the graph on the left, vFB = 25mV

(15m - (-10m))

•d = 1 – 0 = 1

VP ≈ ( 100 25mV )/1

≈ 2.5V


If the VP ( sawtooth signal amplitude ) does not informed by the datasheet,

It can be approximated from the characteristics below.

LM2575: Feedback Voltage vs. Duty Cycle

Setting PWM Controller’s Parameters (Example)

vFB =

25mV

d = 1 (100%)

dMIN dMAX

vFBH

vFBL

1

If vFBH and vFBL are not provided, the default value, VP=2.5 could be used.

• Use the following formula to select the resistor values.

• Rlower can be between 1k and 5k.

Example

Given: VOUT = 5V

VREF = 1.23

Rlower = 1k

then: Rupper = 3.065k

Comp

C2

R2 C1

Type 2 Compensator

FB

Rupper

Rlower

0

d

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

Error Amp.

Vo

Setting Output Voltage: Rupper, Rlower


lower

upperREFOUT

R

RVV 1

2

Inductor Selection: L


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,min is load resistance at the minimum output current ( IOUT,min )

• fosc is switching frequency

L1 2

C

Rload

Vo

ESR

max,

min,max,

2 Iosc

LOUTICCM

Vf

RVVL

3

Inductor Selection: L (Example)


Inductor Value

from

Given:

• VI,max = 40V, VOUT = 5V

• IOUT,min = 0.2A

• RL,min = (VOUT / IOUT,min ) = 25

• fosc = 52kHz

Then:

• LCCM 210(uH),

• L = 330(uH) is selected

L1 2

C

Rload

Vo

ESR

max,

min,max,

2 Iosc

LOUTICCM

Vf

RVVL

3

Capacitor Selection: C, ESR


Capacitor Value

• The minimum allowable output capacitor value should

be determined by

Where

• VI, max is the maximum input voltage.

• L (H) is the inductance calculated from previous step ( ).

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

the following equation.

L1 2

C

Rload

Vo

ESR

F)H(

785,7max,

LV

VC

OUT

I

RIPPLEL

RIPPLEO

I

VESR

,

,

4

3

Capacitor Selection: C, ESR (Example)


Capacitor Value

From

and

Given:

• VI, max = 40 V

• VOUT = 5 V

• L (H) = 330

Then:

• C 188 (F)

In addition:

• ESR 100m

L1 2

C

Rload

Vo

ESR

RIPPLEL

RIPPLEO

I

VESR

,

,

4

F)H(

785,7max,

LV

VC

OUT

I

• Loop gain for this configuration is

L1 2

Rload

C

0

Comp

C2

R2 C1

Type 2 Compensator

FB

Rupper

3.066k

Rlower

1.0k

0

d

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

Vo

ESR

• 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.


PWMGsGsHsT )()()(GPWM

G(s)

H(s)

Stabilizing the Converter5

Stabilizing the Converter (Example)


Specification:

VOUT = 5V

VIN = 7 ~ 40V

ILOAD = 0.2 ~ 1A

PWM Controller:

VREF = 1.23V

VP = 2.5V

fOSC = 52kHz

Rlower = 1k,

Rupper = 3.1k,

L = 330uH,

C = 330uF (ESR = 100m)

Task:

• to find out the element of the

Type 2 compensator ( R2, C1,

and C2 )

L330uH

1 2

C330uF

Rload5

0

0

COL1kF

LOL

1kH

C2

R2 C1

FB

Rupper

3.1k

Type 2 Compensator

Rlower

1.0k

0

d

V31Vac

0Vdc

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

Vo

ESR100m

G(s)

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

5

1

3

4

2

L330uH

1 2

C330uF

Rload5

0

0

COL1kF

LOL

1kH

R20.756k

FB

Rupper

3.1k

Type 2 Compensator

Rlower

1k

0

d

V31Vac

0Vdc

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

Vo

ESR100m

C21f

C11k


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 (Example)5

C1=1kF is AC shorted, and C2 1fF is AC opened (or

Error-Amp without compensator).


Type 2 Compensator Calculator

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


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

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


Frequency

100Hz 1.0KHz 10KHz 100KHz

P(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

5

K-factor (Choose K and from the table)K 6 -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)



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=6 is chosen for Phase margin = 46.

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.

R2122.780k

Type 2 Compensator

C221.6p

C10.778n

L330uH

1 2

C330uF

Rload5

0

0

COL1kF

LOL

1kH

FB

Rupper

3.1k

Rlower

1k

0

d

V31Vac

0Vdc

Vin

12Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

Vo

ESR100m



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=122.780k, C1=0.778nF, and C2=21.6pF.

*Analysis directives:

.AC DEC 100 0.1 10MEG

5

Frequency

100Hz 1.0KHz 10KHz 100KHz

P(v(d))

0d

90d

180d

(9.778K,45.930)

DB(v(d))

-40

0

40

80

-100

SEL>>

(9.778K,0.000)

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



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 Transient Response Simulation (Example)


R2122.780k

C221.6p

Type 2 Compensator

C10.778n

Load

Vo

I1

TD = 10mTF = 25u

PW = 0.43mPER = 1

I1 = 0I2 = 0.8

TR = 20u

Rload25

0

FB

Rupper

3.1k

Rlower

1k

0

d

Vin

20Vdc

D

U2BUCK_SW

REF

PWM

1/Vp

-

+

U3PWM_CTRL

VP = 2.5VREF = 1.23

L330uH

1 2

C330uF

ESR100m

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


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 10.9ms

1 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

>>

Load Transient Response Simulation (Example)

A. Type 2 Compensation Calculation using Excel

Switching frequency, fosc : 52.00 kHz Given spec, datasheetCross-over frequency, fc (<fosc/4) : 10.00 kHz Input the chosen value ( about 10kHz or < fosc/4 )Rupper : 3.1 kOhm Given spec, datasheet, or calculated Rlower : 1 kOhm Given spec, datasheet, or value: 1k-10k OhmR2 (Rupper//Rlower) : 0.756 kOhm (automatically calculated)

PWMVref : 1.230 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 + ): -44.211 dB Read from simulation resultPhase (PWM) at foc : 65.068 Read from simulation result

K-factor (Choos K and from the table)K 6 Input the chosen value (start from k=2)

-199 (automatically calculated)

Phase margin : 46 (automatically calculated) Target value > 45

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

Technology

ctrl fb d pwm

ctrl fb d pwm

datasheetd pwm vp

vfbl d

vp esrref vp

ctrl buck

duty cycle d value

d iout