Concept Kit:PWM Buck Converter Transients Model

Concept Kit:PWM Buck Converter

Transients Model

All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 1

Power Switches(Semiconductor)

Filter & LoadPWM IC (Voltage Mode)

VREF

+-

VOUTL1 2

C

Rload

Vo

ESROSC

REF

E / A

Comp

+

-

-

+

U?PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

pwm

+ -

+ - S1S

RON = 100m

D1DIODE

Contents

1. Concept of Simulation

2. Buck Converter Circuit

3. Power Switches (Semiconductor)

4. Buck Converter Design Workflow

Setting PWM Controller’s Parameters.

Programming Output Voltage: Rupper, Rlower

Inductor Selection: L

Capacitor Selection: C, ESR

Stabilizing the Converter

5. Buck Converter Simulation (Example)

5.1 Switching Waveforms

5.2 Power State Switches Voltage and Current

6. Load Transient Response Simulation (Example)

7. Buck Converter Optimization (Example)

8. Converter Efficiency

8.1 Converter Efficiency vs. MOSFET, Rds(on)

8.2 Converter Efficiency vs. DIODE, VF

9. Simulation Using Real Device Models

9.1 Switching Waveforms (Real Device Models)

9.2 Converter Efficiency (Real Device Models)

Simulation Index


1

2

3

4

5


Power Switches(Semiconductor)

• MOSFET

• Diode

Filter & Load

Parameter:

• L

• C

• ESR

• Rload

PWM IC (Voltage Mode)

Parameter:

• VOSC

• VREF

• VP

Models:

Block Diagram:

1.Concept of Simulation

VREF

+-

VOUT

L1 2

C

Rload

Vo

ESROSC

REF

E / A

Comp

+

-

-

+

U?PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

pwm

+ -

+ - S1S

RON = 100m

D1DIODE

Rload

0

FB

Rupper

Rlower

0

pwmVin

Vo

R2

Type 2 Compensator

C2

C1

L1 2

C

ESR

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

+ -

+ - S1S

RON = 100m

D1DIODE

2.Buck Converter Circuit


Filter & Load

PWM Controller

Power Switches

3.Power Switches (Semiconductor)

• A Near-Ideal DIODE can be modeled by using SPICE primitive model (D), which

parameters are : N=0.01 RS=0.

• A near-ideal MOSFET can be modeled by using PSpice VSWITCH that is voltage

controlled switch.


pwm

+ -

+ - S1S

RON = 100m

D1DIODE

MOSFET

The parameter RON represents Rds(on) characteristics of MOSFET, that are usually provide by the manufacturer datasheet. The value could be about 10m to 10 ohm.

4.Buck Regulator Design Workflow

The Purpose of the Circuit Simulation

• To Evaluate and Verify the Design of the PWM Buck Converter.

• To Optimize the Parameters of the PWM Buck Converter.


Setting PWM Controller’s Parameters: FOSC , VREF, VP1

Setting Output Voltage: Rupper, Rlower2

Inductor Selection: L3

Capacitor Selection: C, ESR4

Setting the Compensator Parameters: R2, C1, C25

Continue next slide



Evaluations:

• Switching Waveforms,

• Power State Switches Voltage and Current,

• Load Step Transient Response,

• and so on

Optimization: L (example)

Evaluations:

• Converter Efficiency vs. MOSFET, Rds(on)

• Converter Efficiency vs. Diode, VF

Evaluations Using Real Device Models

Rload

0

FB

Rupper

Rlower

0

pwmVin

Vo

R2

Type 2 Compensator

C2

C1

L1 2

C

ESR

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

+ -

+ - S1S

RON = 100m

D1DIODE



1

2

3

4

5

OSCREF

E / A

Comp

+

-

-

+

U?PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

Setting PWM Controller’s Parameters


comp

PWM

FB

1

• FOSC, Oscillation frequency (frequency of the

sawtooth signal).

• 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%)

The Comparator compares the error voltage

(between FB and REF) with a sawtooth signal

(frequency = FOSC, peak saw voltage =

VP) to generate PWM signal, as shown in the

figure below.

Time

V(PWM)

V(osc) V(comp)

0V

2.0V

3.0V

SEL>>VP

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

f = FOSC

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.

FB

Rupper

Rlower

0

R2

Type 2 Compensator

C2

C1

Comp

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

• 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

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

Rload

0

FB

Rupper

Rlower

PWM

0

pwm

Vin

Vo

R2

Type 2 Compensator

C2

C1

L1 2

C

ESR

Comp

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

+ -

+ - S1S

RON = 100m

D1DIODE

• Loop gain for this configuration is

• 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.

• The element of the Type 2 compensator ( R2, C1, and C2 ) can be extracted by using

Type 2 Compensator Calculator (Excel sheet) and open-loop simulation with the

Average Models (ac models).


PWMGsGsHsT )()()(

GPWM

G(s)

H(s)

Stabilizing the Converter5

Remark: The Average Models are not included with this package.

Rload5

0

Rupper

3.1k

Rlower

1k

pwm

0

pwm

Vin

12Vdc

FB

Vo

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

R2122.780k

C221.60p

Type 2 Compensator

C10.778n

Comp

L330uH

1 2

C330uFIC = 5

ESR100m

+ -

+ - S1S

RON = 100m

D1DIODE

5.Buck Converter Simulation (Example)


Specification:

VOUT = 5V

VIN = 7 ~ 40V

ILOAD = 0.2 ~ 1A

L = 330uH,

C = 330uF (ESR = 100m),

Rupper = 3.1k,

Rlower = 1k,

PWM Controller:

fOSC = 52kHz

VP1 = 2.5V

VREF = 1.23V

Task:

•Voltage and Current Waveforms Evaluation.

1. Please see topic: 6.1 Calculate the VP, for detail.

2. Please check the Average Model manual for the Type2 Compensator’s elements (R2, C1, and C2) calculation.

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

2

*Analysis directives:

.TRAN 0 10ms 0 200n SKIPBP

Time

9.925ms 9.935ms 9.945ms 9.955ms 9.965ms

V(Vo)

5.02V

5.04V

5.06V

SEL>>

(9.942m,5.0345)

(9.931m,5.0511)

I(L)

1.0A

I(S1:3)

0A

1.0A

2.0A

V(PWM)

0V

5.0V

Simulation Measurement


A: Control Voltage V(PWM)

D: Output Ripple Voltage, 20 mV/div,

• The simulation results are compared with the measurement data (National

Semiconductor Corp. IC LM2575 datasheet).

• Output ripple voltage (Simulation) is 16.6mVP-P.

5.1 Switching Waveforms

C: Inductor Current I(L), 0.5A/div

B: Switch Current ID(S1), 1A/div

VOUT = 5V

A: Output Pin Voltage, 10V/div

B: Output Pin Current, 1A/div

C: Inductor Current, 0.5A/div


Time

9.925ms 9.930ms 9.935ms 9.940ms 9.945ms 9.950ms 9.955ms 9.960ms 9.965ms 9.970ms

1 V(D1:A,D1:C) 2 I(D1)

-16V

0V

16V1

-1.6A

-0.8A

0A

0.8A

1.6A2

SEL>>SEL>>

(9.942m,-11.908)

(9.951m,1.0950)

1 V(S1:3,S1:4) 2 I(S1:3)

0V

4V

8V

12V

16V1

0A

0.4A

0.8A

1.2A

1.6A2

>>

(9.933m,12.008)

(9.951m,1.0946)


5.2 Power State Switches Voltage and Current

• Switch (MOSFET) has the steady state voltage: VDS, PEAK = 12.008V and

current: ID, PEAK = 1.0946A

• Diode has the steady state voltage: VAK, PEAK = -11.908V and current: IF, PEAK

= 1.095A

SW (MOSFET) Voltage VDS

SW (MOSFET) Current ID

Diode Voltage VAK

Diode Forward Current IF

I1

TD = 10mTF = 25u

PW = 0.43mPER = 1

I1 = 0I2 = 0.8

TR = 20u

Rload25

0

Rupper

3.1k

Rlower

1k

pwm

pwm

0

Vin

12Vdc

FB

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

R2122.780k

Type 2 Compensator

C221.60p

Comp

C10.778n

L330uH

1 2

C330uFIC = 5

ESR100m

+ -

+ - S1S

RON = 100m

D1DIODE

load

Vo

6.Load Transient Response Simulation (Example)


The converter are connected with step-load to perform load transient response simulation.



5V/25 = 0.2A step to 0.2+0.8=1.0A load

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

>>



Output Voltage Change

Load Current

• The simulation results are compared with the measurement data (National

Semiconductor Corp. IC LM2575 datasheet).

6.Load Transient Response Simulation (Example)

Rload25

0

Rupper

3.1k

Rlower

1k

pwm

0

pwm

Vin

12Vdc

FB

Vo

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

R2122.780k

C221.60p

Type 2 Compensator

C10.778n

Comp

L{L}

1 2

C330uIC = 5

ESR100m

PARAMETERS:

L = 330u

+ -

+ - S1S

RON = 100m

D1DIODE

Specification:

VOUT = 5V

VIN = 7 ~ 40V

ILOAD = 0.2 ~ 1A

L = Optimization Parameter

C = 330uF (ESR = 100m),

Rupper = 3.1k,

Rlower = 1k,

PWM Controller:

fOSC = 52kHz

VP = 2.5V

VREF = 1.23V

Task:

•Optimize the Inductor value.

7.Buck Converter Optimization (Example)




.STEP PARAM L LIST 330u, 220u, 100u

Time

9.925ms 9.930ms 9.935ms 9.940ms 9.945ms 9.950ms 9.955ms 9.960ms 9.965ms 9.970ms

V(Vo)

5.02V

5.06V

5.08V

SEL>>

(9.942m,5.0300)

(9.931m,5.0555)

I(L)

0A

200mA

400mA

600mA

I(S1:3)

0A

500mA

V(PWM)

0V

5.0V


7.Buck Converter Optimization (Example)

• As an equation (1), the converter works in DCM when the inductor: L is 100uH

at the minimum output current: ILOAD = 0.2A

• VOUT, RIPPLE = 25.5mVP-P when the inductor: L is 220uH (Increased from

16.6mVP-P of L=330uH). IF VOUT, RIPPLE = 25.5mVP-P is acceptable then L=220uH

can replace the 330uH.

A: V(PWM),

10V/div

D: VOUT, RIPPLE,

20 mV/div

C: I(L), 0.5A/div

B: ID(S1), 1A/div

VOUT, RIPPLE,

at L=220uH

L=330uH

L=220uH

L=100uH

L=100uH, converter work in DCM

Rload5

0

Rupper

3.1k

Rlower

1k

pwm

0

pwm

Vin

12Vdc

FB

Vo

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

R2122.780k

C221.60p

Type 2 Compensator

C10.778n

Comp

L330uH

1 2

C330uFIC = 5

ESR100m

PARAMETERS:

Rdson = 100m

+ -

+ - S1S

RON = {Rdson}

D1DIODE

8.Converter Efficiency


Perform transient simulation to measure the converter efficiency at Rds(on) = 100m and 1 .



.STEP PARAM Rdson LIST 100m, 1

Time

9.0ms 9.2ms 9.4ms 9.6ms 9.8ms 10.0ms

100*AVG(W(Rload))/-AVG(W(Vin))

70

80

90

100

(9.500m,98.492)

(9.500m,90.917)


8.1 Converter Efficiency vs. MOSFET Rds(on)

• The converter efficiency is decreased from 98.5% to 90.9% when

Rds(on) increase from 100m to 1.

Efficiency (%)

Rds(on) = 100m, Efficiency = 98.5 %

Rds(on) = 1, Efficiency = 90.9 %

Rds(on)=100mRds(on)=1

Rload5

0

Rupper

3.1k

Rlower

1k

pwm

0

pwm

Vin

12Vdc

FB

Vo

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

R2122.780k

C221.60p

Type 2 Compensator

C10.778n

Comp

L330uH

1 2

C330uFIC = 5

ESR100m

PARAMETERS:

Rdson = 100m

+ -

+ - S1S

RON = {Rdson}

D1DIODE

8.2 Converter Efficiency vs. Diode, VF


Perform transient simulation to measure the converter efficiency at DIODE (N) = 0.01 and 1.



.STEP D DIODE(N) LIST 0.01, 1

V_V1

0V 0.12V 0.24V 0.36V 0.48V 0.60V 0.72V 0.84V 0.96V 1.08V

I(D1)

0A

0.1A

0.2A

0.3A

0.4A

0.5A

0.6A

0.7A

0.8A

0.9A

1.0A

VF increases when DIODE (N) increases.

VF

Diode Forward I – V Characteristics

Diode Forward Voltage vs. Diode model parameter: N

Time

9.0ms 9.2ms 9.4ms 9.6ms 9.8ms 10.0ms


70

80

90

100

(9.500m,90.564)

(9.500m,98.492)


8.2 Converter Efficiency vs. Diode, VF

Efficiency (%)

DIODE (N) = 0.01, Efficiency = 98.5 %

DIODE (N) = 1, Efficiency = 90.6 %

N=0.01

N=1

• The converter efficiency is decreased from 98.5% to 90.6% when

DIODE’s parameter N increase from 0.01 to 1.

Rload5

D1

0

Rupper

3.1k

Rlower

1k

pwm

0

Vin

12Vdc

FB

Vo

U1

OSCREF

E / A

Comp

+

-

-

+

U3PWM_IC

FOSC = 52K

VP = 2.5VREF = 1.23

-++ -

E1

E

0

R2122.780k

C221.60p

Type 2 Compensator

C10.778n

Comp

L330uH

1 2

C330uFIC = 5

ESR100m

9.Simulation Using Real Device Models


As we can see in the efficiency simulation (topic #9) that’s how the switching devices

characteristics effect the simulation result. For the accurate simulation result, the accurate

models, that relate to the real devices characteristics, are needed.

The Real Device Models of MOSFET and Schottky Barrier Diode

Time

9.925ms 9.935ms 9.945ms 9.955ms 9.965ms

V(Vo)

5.02V

5.04V

5.06V

I(L)

1.0A

I(U1:D)

0A

1.0A

SEL>>

V(PWM)

0V

5.0V



A: Control Voltage V(PWM), 10V/div


• The real device model enable designers to include the spike signal in the

switching waveforms simulation.

9.1 Switching Waveforms (Real Device Models)

C: Inductor Current I(L), 0.5A/div

B: MOSFET Drain Current ID, 1A/div

VOUT = 5V

A: Output Pin Voltage, 10V/div

B: Output Pin Current, 1A/div

C: Inductor Current, 0.5A/div


Spike current Spike current

Time

9.0ms 9.2ms 9.4ms 9.6ms 9.8ms 10.0ms


70

80

90

100

(9.500m,92.877)


9.2 Converter Efficiency (Real Device Models)

• The converter efficiency is decreased from 98.5% to 92.9% when the

device models are changed from the near-Ideal to the real model.

Efficiency (%)

Efficiency = 92.9 %

Simulation Index


Simulations Folder name

1. Switching Waveforms......................................................

2. Power Stage Switches Voltage and Current....................

3. Load Transient Response................................................

4. Buck Converter Optimization............................................

5. Converter Efficiency vs. MOSFET Rds(on) ....................

6. Converter Efficiency vs. MOSFET Diode, VF..................

waveforms

powersw

stepload

optimize

efficiency-diode

efficiency-rdson

Libraries :

1. ..¥pwmic.lib

2. ..¥diode.lib

Concept Kit:PWM Buck Converter Transients Model

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