Concept Kit:PWM Buck Converter Average Model
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Transcript of 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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 2
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 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:
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 4
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 5
D
U2BUCK_SW
vin
+
-
vout
+
-
D
iin iout
Buck Regulator Design Workflow
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 6
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 7
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 8
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 9
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 10
lower
upperREFOUT
R
RVV 1
2
Inductor Selection: L
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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)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 12
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 13
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)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 14
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.
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 15
PWMGsGsHsT )()()(GPWM
G(s)
H(s)
Stabilizing the Converter5
Stabilizing the Converter (Example)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 16
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 17
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).
Stabilizing the Converter (Example)
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 18
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 19
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.
Stabilizing the Converter (Example)
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)
Stabilizing the Converter (Example)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 20
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
Stabilizing the Converter (Example)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 21
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.
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 22
Stabilizing the Converter (Example)
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)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 23
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 24
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)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 25
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 26
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
All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 27
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