Concept Kit:PWM Buck Converter Transients Model

PWM IC Power Switches Filter & Load
(Voltage Mode)
U?
(Semiconductor)
PWM_IC RON = 100m
1
L
2 Vo
VOUT
-
-

+ E/A S1 D1 C

-
+

+
+
Comp S DIODE

+
-
- Rload
OSC pwm
REF ESR

FOSC = 52K
VREF VREF = 1.23
VP = 2.5

Concept Kit:
PWM Buck Converter
Transients Model
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 1

Contents
1. Concept of Simulation
2. Buck Converter Circuit
3. Power Switches (Semiconductor)
4. Buck Converter 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

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.Concept of Simulation
Block Diagram:

PWM IC Power Switches Filter & Load
(Voltage Mode) (Semiconductor)
Parameter: VOUT
Parameter: • MOSFET •L
-
+

• VOSC • Diode •C
• VREF • ESR
VREF • VP • Rload

Models:
U? RON = 100m L
PWM_IC 1 2 Vo

S1 D1
-
C
+

-
S DIODE
+
-

+ E/A + pwm Rload
Comp
- ESR
OSC
REF

FOSC = 52K
VREF = 1.23
VP = 2.5


2.Buck Converter Circuit
Power Switches Filter & Load
RON = 100m L
1 2 Vo

S1 D1 C

-
+
S DIODE

+
-
Vin pwm Rload

ESR

0
PWM Controller
Type 2 Compensator
C2

R2 C1

Rupper

U3
PWM_IC

- FB
+ E/A +
Comp
-
Rlower
OSC
REF

FOSC = 52K
VREF = 1.23 0
VP = 2.5


3.Power Switches (Semiconductor)

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.

RON = 100m

S1 D1
• A Near-Ideal DIODE can be modeled by
-
+

S DIODE
+
-

pwm using SPICE primitive model (D), which
MOSFET
parameters are : N=0.01 RS=0.
• A near-ideal MOSFET can be modeled by
using PSpice VSWITCH that is voltage
controlled switch.


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.

1 Setting PWM Controller’s Parameters: FOSC , VREF, VP

2 Setting Output Voltage: Rupper, Rlower



5 Setting the Compensator Parameters: R2, C1, C2

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



RON = 100m 3 L
1 2 Vo

S1 D1 C

-
+
S DIODE

+
-
Vin pwm Rload

ESR

4
0

5 Type 2 Compensator
C2

R2 C1 2
Rupper

U3
PWM_IC

- FB
+ E/A +
Comp
-
Rlower
OSC
REF

FOSC = 52K
1 VREF = 1.23 0
VP = 2.5


1 Setting PWM Controller’s Parameters
U? comp
PWM_IC • FOSC, Oscillation frequency (frequency of the
- FB
sawtooth signal).

PWM + E/A
Comp
+
• VREF, feedback reference voltage, value is
- OSC given by the datasheet
REF

FOSC = 52K • VP = (Error Amp. Gain  vFB ) / d
VREF = 1.23
VP = 2.5 • vFB = vFBH – vFBL
The Comparator compares the error voltage
(between FB and REF) with a sawtooth signal • d = dMAX – dMIN
(frequency = FOSC, peak saw voltage =
VP) to generate PWM signal, as shown in the
• Error Amp. Gain is 100 (approximated)
figure below.
where
f = FOSC
3.0V VP is the sawtooth peak voltage.
2.0V

SEL>>
VP vFBH is maximum FB voltage where d = 0
0V
V(osc) V(comp)
vFBL is minimum FB voltage where d =1(100%)
dMAX is maximum duty cycle, e.g. d = 0(0%)

V(PWM) Duty cycle (d) is a value from 0 to 1
dMIN is minimum duty cycle, e.g. d =1(100%)
Time


1 Setting PWM Controller’s Parameters (Example)
 If the VP ( sawtooth signal amplitude ) does not informed by the datasheet,
It can be approximated from the characteristics below.

from
vFBH
VP = (Error Amp. Gain  vFB )/d

vFB = •Error Amp. Gain = 100 (approximated)
25mV
•from the graph on the left, vFB = 25mV
(15m - (-10m))
vFBL
d = 1 (100%) • d = 1 – 0 = 1

VP ≈ ( 100  25mV )/1
dMIN dMAX
≈ 2.5V
LM2575: Feedback Voltage vs. Duty Cycle

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

2 Setting Output Voltage: Rupper, Rlower

• Use the following formula to select the resistor values.

 Rupper 
VOUT  VREF1  
 Rlower  Type 2 Compensator
C2
• Rlower can be between 1k and 5k.

R2 C1
Example
Given: VOUT = 5V U3 Comp Rupper
PWM_IC
VREF = 1.23
- FB
Rlower = 1k
+ E/A
then: Rupper = 3.065k
+
Comp
- Rlower
OSC
REF

FOSC = 52K
VREF = 1.23 0
VP = 2.5



L
1 2 Vo Inductor Value
C
• The output inductor value is selected to set the
converter to work in CCM (Continuous Current
Rload
ESR
Mode) or DCM (Discontinuous Current Mode).
• Calculated by

LCCM 
VI , max VOUT  RL, min
2 fosc VI , max
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


3 Inductor Selection: L (Example)

L
1 2 Vo Inductor Value
C
from

ESR
Rload
LCCM 
VI , max VOUT  RL, min
2 foscVI , max
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



L
1 2 Vo Capacitor Value
• The minimum allowable output capacitor value should
C
be determined by
Rload
ESR

C  7,785 
VI , max
F
VOUT  L( H)
Where
• VI, max is the maximum input voltage.
• L (H) is the inductance calculated from previous step ( 3 ).

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

VO , RIPPLE
ESR 
IL , RIPPLE

4 Capacitor Selection: C, ESR (Example)

L
1 2 Vo Capacitor Value
From
C
C  7,785 
VI , max
F
ESR
Rload
VOUT  L( H)
and
VO , RIPPLE
ESR 
IL , RIPPLE
Given:
• VI, max = 40 V
• VOUT = 5 V
• L (H) = 330
Then:
• C  188 (F)

In addition:
• ESR  100m


5 Stabilizing the Converter
• Loop gain for this configuration is H(s)
RON = 100m L
1 2 Vo

S1 D1 C

-
+
S DIODE

+
-
Vin Rload
pwm
ESR

T ( s)  H ( s)  G( s)  GPWM 0
G(s)
Type 2 Compensator
C2

R2 C1

• The purpose of the compensator G(s)
GPWM U3 Comp Rupper
is to tailor the converter loop gain PWM_IC

FB
(frequency response) to make it stable PWM
+ E/A +
-

Comp
when operated in closed-loop - OSC
Rlower
REF
conditions. FOSC = 52K
VREF = 1.23 0
VP = 2.5

• 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).

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


5.Buck Converter Simulation (Example)
Specification: RON = 100m
L
330uH
1 2 Vo
VOUT = 5V
S1 D1 C

-
+
VIN = 7 ~ 40V S DIODE 330uF

+
-
Vin IC = 5 Rload
ILOAD = 0.2 ~ 1A 12Vdc pwm
ESR
5

100m

L = 330uH, 0 Type 2 Compensator 2
C = 330uF (ESR = 100m), C2
21.60p
Rupper = 3.1k,
Rlower = 1k, e.g. Characteristics
R2
122.780k
C1
0.778n

from National
PWM Controller: Semiconductor Corp. U3 Comp Rupper
fOSC = 52kHz IC: LM2575 PWM_IC 3.1k
FB
VP1 = 2.5V
-
+ E/A
pwm +
Comp
VREF = 1.23V - OSC
Rlower
1k
REF

Task: FOSC = 52K
VREF = 1.23 0
VP = 2.5

•Voltage and Current Waveforms Evaluation. *Analysis directives:
.TRAN 0 10ms 0 200n SKIPBP

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.


5.1 Switching Waveforms
Simulation Measurement
5.0V

0V
A: Control Voltage V(PWM)
V(PWM)
2.0A
B: Switch Current ID(S1), 1A/div
1.0A

0A
I(S1:3)

1.0A

C: Inductor Current I(L), 0.5A/div
I(L)
5.06V
(9.942m,5.0345)
5.04V
(9.931m,5.0511)
SEL>> D: Output Ripple Voltage, 20 mV/div,
5.02V VOUT = 5V
9.925ms 9.935ms 9.945ms 9.955ms 9.965ms
V(Vo)
A: Output Pin Voltage, 10V/div
Time B: Output Pin Current, 1A/div
C: Inductor Current, 0.5A/div
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.


5.2 Power State Switches Voltage and Current
16V 1.6A
1 2
(9.933m,12.008)

12V 1.2A
SW (MOSFET) Voltage VDS

(9.951m,1.0946)
SW (MOSFET) Current ID
8V 0.8A

4V 0.4A

>>
0V 0A
1 V(S1:3,S1:4) 2 I(S1:3)
16V 1.6A
1 2 (9.951m,1.0950)
Diode Forward Current IF
0.8A

0V 0A

(9.942m,-11.908)
-0.8A

SEL>> Diode Voltage VAK
-16V -1.6A
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)
Time

• 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


6.Load Transient Response Simulation (Example)
The converter are connected with step-load to perform load transient response simulation.
L
load
RON = 100m 330uH
1 2 Vo

S1 D1 C

-
+
S DIODE 330uF I1

+
-
Vin IC = 5 Rload I1 = 0
12Vdc pwm 25 I2 = 0.8
ESR TD = 10m
100m TF = 25u
TR = 20u
PW = 0.43m
PER = 1
C2
21.60p 5V/25 = 0.2A step
to 0.2+0.8=1.0A load
R2 C1
122.780k 0.778n

U3 Comp Rupper
PWM_IC 3.1k
- FB
+ E/A
pwm +
Comp
-
Rlower
OSC 1k
REF

FOSC = 52K
*Analysis directives: VREF = 1.23
VP = 2.5
0



6.Load Transient Response Simulation (Example)

5.2V 4.0A
1 2

Output Voltage Change
5.1V 3.5A

5.0V 3.0A

4.9V 2.5A

4.8V 2.0A

4.7V 1.5A

Load Current
4.6V 1.0A

4.5V 0.5A

>>
4.4V 0A
9.9ms 10.1ms 10.3ms 10.5ms 10.7ms 10.9ms
1 V(Vo) 2 I(load)
Time

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


7.Buck Converter Optimization (Example)
PARAMETERS:
Specification: RON = 100m
L
{L}
L = 330u
Vo
VOUT = 5V 1 2

S1 D1 C

-
+
VIN = 7 ~ 40V S DIODE 330u

+
-
Vin IC = 5 Rload
ILOAD = 0.2 ~ 1A 12Vdc pwm
ESR
25

100m

L = Optimization Parameter 0 Type 2 Compensator
C = 330uF (ESR = 100m), C2
21.60p
Rupper = 3.1k,
Rlower = 1k, R2
122.780k
C1
0.778n

PWM Controller: U3 Comp Rupper
fOSC = 52kHz PWM_IC 3.1k
FB
VP = 2.5V + E/A
-

pwm +
VREF = 1.23V Comp
- OSC
Rlower
1k
REF

Task: FOSC = 52K
VREF = 1.23 0
VP = 2.5

•Optimize the Inductor value.
*Analysis directives:
.STEP PARAM L LIST 330u, 220u, 100u


7.Buck Converter Optimization (Example)

A: V(PWM), 5.0V
10V/div L=330uH
L=220uH
0V L=100uH
V(PWM)
500mA
B: ID(S1), 1A/div

0A
I(S1:3)
600mA
C: I(L), 0.5A/div L=100uH, converter work in DCM
400mA

200mA

0A
I(L)
5.08V
D: VOUT, RIPPLE, (9.931m,5.0555)
5.06V
20 mV/div
(9.942m,5.0300) VOUT, RIPPLE,
SEL>> at L=220uH
5.02V
9.925ms 9.930ms 9.935ms 9.940ms 9.945ms 9.950ms 9.955ms 9.960ms 9.965ms 9.970ms
V(Vo)
Time

• 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.

8.Converter Efficiency
Perform transient simulation to measure the converter efficiency at Rds(on) = 100m and 1 .
PARAMETERS:
Rdson = 100m
L
RON = {Rdson} 330uH
1 2 Vo

S1 D1 C

-
+
S DIODE 330uF

+
-
Vin IC = 5 Rload
12Vdc pwm 5
ESR
100m

C2
21.60p

R2 C1
122.780k 0.778n

U3 Comp Rupper
PWM_IC 3.1k
- FB
+ E/A
pwm +
Comp
-
Rlower
OSC 1k
REF

*Analysis directives: FOSC = 52K
0
.TRAN 0 10ms 0 200n SKIPBP VREF = 1.23
VP = 2.5

.STEP PARAM Rdson LIST 100m, 1


8.1 Converter Efficiency vs. MOSFET Rds(on)
Efficiency (%)
100

Rds(on) = 100m, Efficiency = 98.5 %
(9.500m,98.492)

90
Rds(on) = 1, Efficiency = 90.9 %
(9.500m,90.917)

80

Rds(on)=100m
Rds(on)=1

70
9.0ms 9.2ms 9.4ms 9.6ms 9.8ms 10.0ms
100*AVG(W(Rload))/-AVG(W(Vin))
Time

• The converter efficiency is decreased from 98.5% to 90.9% when
Rds(on) increase from 100m to 1.


8.2 Converter Efficiency vs. Diode, VF
Perform transient simulation to measure the converter efficiency at DIODE (N) = 0.01 and 1.
PARAMETERS:
Rdson = 100m
L
RON = {Rdson} 330uH
1 2 Vo

S1 D1 C

-
+
S DIODE 330uF

+
-
Diode Forward Voltage vs. Vin IC = 5 Rload
12Vdc pwm 5
Diode model parameter: N ESR
100m

Diode Forward I – V Characteristics 0 Type 2 Compensator
1.0A C2
VF increases when DIODE (N) increases. 21.60p
0.9A

0.8A
R2 C1
0.7A
122.780k 0.778n

0.6A

0.5A
U3 Comp Rupper
0.4A PWM_IC 3.1k
0.3A - FB
+ E/A
0.2A pwm +
Comp
Rlower
0.1A VF - OSC 1k
REF
0A
0V 0.12V 0.24V 0.36V 0.48V 0.60V 0.72V 0.84V 0.96V 1.08V
I(D1) FOSC = 52K
V_V1
VREF = 1.23 0
*Analysis directives: VP = 2.5
.STEP D DIODE(N) LIST 0.01, 1


8.2 Converter Efficiency vs. Diode, VF
Efficiency (%)
100

DIODE (N) = 0.01, Efficiency = 98.5 %
(9.500m,98.492)

90
DIODE (N) = 1, Efficiency = 90.6 %
(9.500m,90.564)

80

N=0.01
N=1
70
9.0ms 9.2ms 9.4ms 9.6ms 9.8ms 10.0ms
Time

• The converter efficiency is decreased from 98.5% to 90.6% when
DIODE’s parameter N increase from 0.01 to 1.


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.
U1 L
330uH
1 2 Vo

C
D1 330uF
Vin IC = 5 Rload
12Vdc 5
ESR
100m

0 E1 Type 2 Compensator
+
-
+

E
-

C2
21.60p
The Real Device Models 0

of MOSFET and R2 C1
122.780k 0.778n
Schottky Barrier Diode

U3 Comp Rupper
PWM_IC 3.1k
- FB
+ E/A
pwm +
Comp
- Rlower
OSC 1k
REF

FOSC = 52K
VREF = 1.23 0
VP = 2.5


9.1 Switching Waveforms (Real Device Models)
5.0V

A: Control Voltage V(PWM), 10V/div
0V

V(PWM) Spike current Spike current
B: MOSFET Drain Current ID, 1A/div
1.0A

SEL>>
0A
I(U1:D)

1.0A

C: Inductor Current I(L), 0.5A/div
I(L)
5.06V

5.04V
5.02V VOUT = 5V
9.925ms 9.935ms 9.945ms 9.955ms 9.965ms A: Output Pin Voltage, 10V/div
V(Vo)
Time
B: Output Pin Current, 1A/div
C: Inductor Current, 0.5A/div

• The real device model enable designers to include the spike signal in the
switching waveforms simulation.


9.2 Converter Efficiency (Real Device Models)
Efficiency (%) 100

Efficiency = 92.9 % (9.500m,92.877)

90

80

70
9.0ms 9.2ms 9.4ms 9.6ms 9.8ms 10.0ms
Time

• 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.


Simulation Index

Simulations Folder name
1. Switching Waveforms...................................................... waveforms
2. Power Stage Switches Voltage and Current.................... powersw
3. Load Transient Response................................................ stepload
4. Buck Converter Optimization............................................ optimize
5. Converter Efficiency vs. MOSFET Rds(on) .................... efficiency-diode

6. Converter Efficiency vs. MOSFET Diode, VF.................. efficiency-rdson

Libraries :
1. ..¥pwmic.lib
2. ..¥diode.lib


Concept Kit:PWM Buck Converter Transients Model

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Concept Kit:PWM Buck Converter Transients Model