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PWM Controller                           Power Switches                        Filter & Load
       (Voltage Mode Control)                       U?
         U?
         PWM_CTRL                                   BUCK_SW
                                                                                             L
                                                                                                                   VOUT
                                                                                       1         2         Vo
-




                           -
 +




            PWM                                                                                      C
                           +
                                                    D
             1/Vp
                                                                                                           Rload
                               REF                                                                   ESR


VREF     VP = 2.5
         VREF = 1.23




Case Study:
NJM2309 Application Circuit Design
(PWM Step-down Converter)
                       All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                1
Contents
 •   Design Specification
 •   NJM2309 Typical Application 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
 • Load Transient Response Simulation
       Reference: Load Transient Response Simulation with PWM IC Transient Model
 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
Design Specification
                                                                           NJM2309 Datasheet
Step-Down (Buck) Converter :
    • VIN, MAX = 32 (V)
    • VIN, MIN = 6 (V)
    • VOUT = 3.3 (V)
    • VOUT, Ripple = 1% ( 33mVP-P )
    • IOUT, MAX = 1.0 (A)
    • IOUT, MIN = 0.2 (A)



Control IC :
   • NJM2309 (Switching Regulator Control IC for Step-Down)
   • Switching Frequency – fosc = 105 (kHz)


                  All Rights Reserved Copyright (C) Bee Technologies Corporation 2011          3
NJM2309 Typical Application Circuit
                                                                         Power Switches     Filter & Load

                           PWM Controller




 Schematic is captured from NJM2309 datasheet page 4.



                                All Rights Reserved Copyright (C) Bee Technologies Corporation 2011         4
NJM2309 Typical Application Circuit
TASK: Design and Evaluation of the Circuit
                                                                                3?




                                                                                                    2?




                1                                                                              4?




                    5?




                         All Rights Reserved Copyright (C) Bee Technologies Corporation 2011             5
Buck Regulator Design Workflow
                                1 Setting PWM Controller’s Parameters: VREF, VP


                                      2 Setting Output Voltage: Rupper, Rlower


                                                   3 Inductor Selection: L


                                             4 Capacitor Selection: C, ESR


                                       5 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.

                                        6 Load Transient Response Simulation


                                 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                6
Buck Regulator Design Workflow
                       U2
                       BUCK_SW                              3        L
                                                                 1              2              Vo

                       D                                                            C
       Vin
                                                                                           Rload
                                                                                    ESR


                                                                                    4
   0
                                                  5      Type 2 Compensator
                                                                     C2


                                                                R2        C1
                                                                                                          2
                                              U3       Comp                                             Rupper
                                              PWM_CTRL

                                                                     -                    FB
                       d
                                                 PWM                 +
                                                  1/Vp                                                  Rlower
                                                                          REF

                                        1     VP = 2.5
                                                                                                    0
                                              VREF = 1.23



             All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                 7
1   Setting PWM Controller’s Parameters




     Table is captured from NJM2309 datasheet page 2.



     VREF = VB = 0.52 (V)

     VP=2.5 (vFBH and vFBL are not provided, the default value is used).




                           All Rights Reserved Copyright (C) Bee Technologies Corporation 2011   8
2   Setting Output Voltage: Rupper, Rlower

• Use the following formula to select the resistor values.

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


        Given:    VOUT = 3.3V
                  VREF = 0.52V
                   Rlower = 1k
        then:      Rupper = 5.346k




                     All Rights Reserved Copyright (C) Bee Technologies Corporation 2011   9
3   Inductor Selection: L

    L
1         2           Vo       Inductor Value
                               from
              C

                     Rload                          LCCM 
                                                           VI , max VOUT  RL, min
              ESR
                                                                                2 foscVI , max
                        Given:
                            • VI,max = 40(V), VOUT = 3.3(V)
                            • IOUT,min = 0.2(A)
                            • RL,min = (VOUT / IOUT,min ) = 16.5()
                            • fosc = 105(kHz)

                        Then:
                               • LCCM  72.1(uH),
                                L = 100(uH) is selected


                    All Rights Reserved Copyright (C) Bee Technologies Corporation 2011          10
4   Capacitor Selection: C, ESR (NJM2309)

    L
1        2           Vo       Capacitor Value
                              From                              C  7,785 
                                                                                     VI , max
                                                                                                F
             C
                                                                                  VOUT  L( H)
                    Rload
                              and                                          VO , RIPPLE
             ESR
                                                                ESR 
                                                                           IL , RIPPLE
                              Given:
                                  •       VI, max = 40 V
                                  •       VOUT = 3.3 V, VOUT, Ripple = 1% ( 33mVP-P )
                                  •       L (H) = 100
                                  •       IOUT, MAX = 1(A), IL, Ripple = 0.25(A)
                              Then:
                                       C  944 (F), C = 1000(F) is selected

                              In addition:
                                       ESR  132m


                   All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                 11
5   Stabilizing the Converter (NJM2309)

                                                     U2                                          L
Specification:                                       BUCK_SW
                                                                                         1
                                                                                                 100uH
                                                                                                         2             Vo
VOUT = 3.3V                                           D                                                      C
                                                                                                             1000uF
VIN = 6 ~ 32V                 Vin                                                                                     Rload
                              12Vdc                                                                          ESR      3.3
ILOAD = 0.2 ~ 1A                                                                                             132m




PWM Controller:           0
                                                                    G(s)          Type 2 Compensator
VREF = 0.52V 1                                                                           C2
                                                                                          1f
VP = 2.5V          e.g. Given values
                   from National                                                      R2            C1
fOSC = 105kHz                                                                         0.842k        1k
                   Semiconductor Corp.
                   IC: LM2575                                                                                                     Rupper

Rlower = 1k, 2                                                      U3
                                                                                                                                  5.346k
                                                                      PWM_CTRL
Rupper = 5.346k,                                         LOL                                -                   FB
L = 100uH,     3                                         1kH
                                                                d
                                                                           PWM               +

C = 1000uF (ESR = 132m)          4          COL
                                                                           1/Vp                                                   Rlower
                                                                                                                                  1k
                                              1kF                                                 REF

                                                                      VP = 2.5
                                                                                                                              0
Task:                                         1Vac
                                                     V3               VREF = 0.52

                                              0Vdc
• to find out the element of the
  Type 2 compensator ( R2, C1,                       0

  and C2 )

                   All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                                     12
5   Stabilizing the Converter (NJM2309)
 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).
                                               U2                                       L
                                               BUCK_SW                                  100uH
                                                                                1               2             Vo

                                                D                                                   C
                                                                                                    1000uF
                      Vin                                                                                    Rload
                      12Vdc                                                                         ESR      3.3
                                                                                                    132m



                                                                                                             Step2 Set C1=1kF, C2=1fF,
                  0                                                      Type 2 Compensator
                                                                                                             and R2=calculated value
Step1 Open the loop with                                                         C2
                                                                                 1f                          (Rupper//Rlower) as the
LoL=1kH and CoL=1kF then inject                                                                              initial values.
                                                                             R2            C1
an AC signal to generate Bode                                                0.842k        1k

plot.                                                                                                                    Rupper
                                                                                                                         5.346k
                                                              U3
                                                              PWM_CTRL

                                                    LOL                             -                   FB
                                                          d
                                                                 PWM
                                                    1kH                             +
                                                                  1/Vp                                                   Rlower
                                        COL                                                                              1k
                                        1kF                                              REF

                                                              VP = 2.5
                                               V3             VREF = 0.52                                            0
                                        1Vac
                                        0Vdc
                                                                C1=1kF is AC shorted, and C2 1fF is AC opened (or
                                                               Error-Amp without compensator).
                                               0

                              All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                  13
5   Stabilizing the Converter (NJM2309)

Type 2 Compensator Calculator                                         Step3 Select a crossover frequency
                                                                      (about 10kHz or fc < fosc/4 ), for
Switching frequency, fosc :               105.00 kHz                  this example, 10kHz is selected.
Cross-over frequency, fc                                              Then complete the table.
(<fosc/4) :                                 10.00       kHz
Rupper :                                    5.346       kOhm
                                                                           values from 2
Rlower :                                        1       kOhm
R2 (Rupper//Rlower) :                       0.842       kOhm             (automatically calculated)
                                                                   Calculated value of
PWM                                                                the Rupper//Rlower
Vref :                                      0.520 V
                                                                 values from 1
Vp (Approximate) :                            2.5 V




                    All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                    14
5        Stabilizing the Converter (NJM2309)
    40


            Gain: T(s) = H(s)GPWM
     0
                                                                            Step4 Read the Gain and Phase value
                              (10.000K,-36.242)
                                                                            at the crossover frequency (10kHz)
                                                                            from the Bode plot, Then put the values
 -40
                                                                            to the table.
 -80
          DB(v(d))
180d


                                            Phase  at fc
                              (10.000K,84.551)

                                                                       Parameter extracted from simulation
                                                                       Set: R2=R1, C1=1k, C2=1f
    0d                                                                 Gain (PWM) at foc ( - or + ) : -36.242
SEL>>
                                                                       Phase (PWM) at foc :            84.551
    100Hz            1.0KHz       10KHz           100KHz    1.0MHz
        P(v(d))
                                Frequency



         Tip: To bring cursor to the fc = 10kHz type “ sfxv(10k) ” in Search Command.


                                     Cursor Search


                                   All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                15
5     Stabilizing the Converter (NJM2309)

                                                     Step5 Select the phase margin at fc
K-factor (Choose K and from the table)              (> 45 ). Then change the K value
K                         3                          (start from K=2) until it gives the
                     -217        (automatically calculated)phase margin, for this
                                                     satisfied
                                                     example K=3 is chosen for Phase
Phase margin :          48         (automatically calculated) 48.
                                                     margin =


R2 :                 54.655 kOhm (automatically calculated)
                                                                                          As the result; R2,
C1 :                  0.847 nF   (automatically calculated)
                                                                                          C1, and C2 are
C2 :                  97.07 pF   (automatically calculated)                               calculated.

Remark: If K-factor fail to gives the satisfied phase margin, Increase the output
capacitor C then try Step1 to Step5 again.

   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).

                        All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                    16
5   Stabilizing the Converter (NJM2309)
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.                     U2                       L
                                   BUCK_SW                                   100uH
                                                                     1               2             Vo

                                    D                                                    C
                                                                                         1000uF
                 Vin                                                                              Rload
                 12Vdc                                                                   ESR      3.3
                                                                                         132m
                                                                                                     The calculated values of
             0
                                                                                                     the type 2 elements are:
                                                              Type 2 Compensator
                                                                      C2
                                                                                                     R2=54.655k,
                                                                      97.07p
                                                                                                     C1=0.874nF ,
                                                                  R2
                                                                  54.655k
                                                                                C1
                                                                                0.874n
                                                                                                     C2=97.07pF.
                                                                                                              Rupper
                                                                                                              5.346k
                                                   U3
                                                   PWM_CTRL

                                        LOL                              -                   FB
                                              d
                                                      PWM
                                        1kH                              +
                                                       1/Vp                                                   Rlower
                            COL                                                                               1k
                            1kF                                               REF

                                                   VP = 2.5
                                   V3              VREF = 0.52                                            0
                            1Vac
                            0Vdc
                                                                                         *Analysis directives:
                                   0                                                     .AC DEC 100 0.1 10MEG

                         All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                    17
5    Stabilizing the Converter (NJM2309)
                       Gain and Phase responses after stabilizing
                  80


                  40
                                                                (9.2368K,0.000)

                   0


                 -40


                 -80   Gain: T(s) = H(s) G(s)GPWM
                       DB(v(d))
                180d


                135d                                                                     Phase  at fc
                 90d
                                                                (9.2368K,48.801)

                 45d


                  0d
               SEL>>
                -45d
                  100Hz                    1.0KHz                 10KHz                  100KHz       1.0MHz
                      P(v(d))
                                                                Frequency



    • Phase margin = 48.801 at the cross-over frequency - fc = 9.237kHz.
      Tip: To bring cursor to the cross-over point (gain = 0dB) type “ sfle(0) ” in Search Command.


                                  Cursor Search

                                All Rights Reserved Copyright (C) Bee Technologies Corporation 2011            18
Load Transient Response Simulation
The converter, that have been stabilized, are connected with step-load to perform load transient
response simulation.

                                       U2                                          L       3    Load
                                       BUCK_SW                                     100uH
                                                                           1               2             Vo

                                        D                                                       C
                                                                                                1000uF                       I1
                   Vin                                                                                        Rload        I1 = 0
                   12Vdc                                                                        ESR           16.5         I2 = 0.8
                                                                                                132m                       TD = 10m
                                                                                                                           TF = 25u
                                                                                                    4                     TR = 20u
                                                                                                                           PW = 0.43m
                                                                                                                           PER = 1
               0                                                  Type 2 Compensator
                                                                            C2
                                                                   5       97.07p
                                                                                                                        3.3V/16.5 = 0.2A
                                                                        R2            C1                                step to 0.2+0.8=1.0A
                                                                        54.655k       0.874n
                                                                                                                        load
                                                                                                                      Rupper
                                                                                                                      5.346k
                                                       U3
                                                       PWM_CTRL

                                                                               -                    FB                     2
                                                  d
                                                          PWM                  +
                                                           1/Vp                                                       Rlower
                                                                                    REF
                                                                                                                      1k


*Analysis directives:                                  VP = 2.5
                                                       VREF = 0.52                                               0
.TRAN 0 20ms 0 1u                                                    1




                           All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                                 19
Load Transient Response Simulation
Simulation
                   3.5V       4.0A
               1          2


                              3.5A
                   3.4V

                                           Output Voltage Change
                              3.0A
                   3.3V


                              2.5A
                   3.2V

                              2.0A

                   3.1V
                              1.5A


                   3.0V                    Load Current
                              1.0A


                   2.9V
                              0.5A


                     >>
                   2.8V         0A
                                9.9ms   10.0ms 10.1ms          10.3ms 10.4ms 10.5ms 10.6ms   10.8ms
                                   1     V(vo) 2     I(load)
                                                                       Time



• The simulation results illustrates the transient response of the converter with
  the stepping load .2A to 1A.


                          All Rights Reserved Copyright (C) Bee Technologies Corporation 2011         20
Reference: Load Transient Response Simulation
with PWM IC Transient Model
 After the converter have been designed, the PWM IC Transient Model could be applied for more
 realistic simulation.

                                                                                              L       3    load
                                          RON = 100m                                          100uH
                                                                                      1               2              Vo

                                                   S1     D1                                              C




                                               -
                                           +
                                                   S      DIODE                                           1000uF                             I1




                                           +
                                           -
                        Vin                                                                               IC = 3.3        Rload            I1 = 0
                        12Vdc       pwm                                                                                   16.5             I2 = 0.8
                                                                                                          ESR                              TD = 10m
                                                                                                          132m                             TF = 25u
                                                                                                                 4                        TR = 20u
                                                                                                                                           PW = 0.43m
                                                                                                                                           PER = 1
                    0                                                       Type 2 Compensator
                                                                                      C2
                                                                             5       97.07p
                                                                                                                                       3.3V/16.5 = 0.2A
                                                                                 R2              C1                                    step to 0.2+0.8=1.0A
                                                                                 54.655k         0.874n
                                                                                                                                       load
                                                                                                                                      Rupper
                                                                                                                                      5.346k
                                                                  U3         Comp
                                                                  PWM_IC

                                                                                          -                    FB                         2
                                                                        +         E/A
                                                        pwm                           +
                                                                    Comp
                                                                        -
                                                                                                                                      Rlower
                                                                                OSC                                                   1k
                                                                                               REF

 *Analysis directives:                                            FOSC = 105K
                                                                                                                                  0
                                                                  VREF = 0.52
 .TRAN 0 12ms 0 200n SKIPBP                                       VP = 2.5       1



 Remark: PWM IC Transient Model and Simulations are not included with this package.

                                  All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                                         21
Reference: Load Transient Response Simulation
with PWM IC Transient Model
 Simulation
                         3.5V       4.0A
                     1          2


                                    3.5A
                         3.4V
                                                  Output Voltage Change
                                    3.0A
                         3.3V

                                    2.5A
                         3.2V

                                    2.0A

                         3.1V
                                    1.5A

                         3.0V
                                                  Load Current
                                    1.0A


                         2.9V
                                    0.5A

                                      >>
                         2.8V         0A
                                               10.0ms        10.2ms        10.4ms        10.6ms           10.8ms
                                           1     V(Vo)   2    I(load)
                                                                            Time


  The PWM IC Transient Model enables The VOUT, RIPPLE and others switching
   characteristics to be included in the simulation.
 Remark: PWM IC Transient Model and Simulations are not included with this package.

                                    All Rights Reserved Copyright (C) Bee Technologies Corporation 2011            22
A. Type 2 Compensation Calculation using Excel
      Switching frequency, fosc :         105.00 kHz        Given spec, datasheet
      Cross-over frequency, fc
      (<fosc/4) :                          10.00   kHz      Input the chosen value ( about 10kHz or < fosc/4 )
      Rupper :                             5.346   kOhm     Given spec, datasheet, or calculated
      Rlower :                                 1   kOhm     Given spec, datasheet, or value: 1k-10k Ohm
      R2 (Rupper//Rlower) :                0.842   kOhm     (automatically calculated)

      PWM
      Vref :                               0.520 V          Given spec, datasheet
      Vp (Approximate) :                      2.5 V         Given spec, or calculated, (or leave default 2.5V)

      Parameter extracted from simulation
      Set: R2=R2, C1=1k, C2=1f
      Gain (PWM) at foc ( - or + )
      :                              -36.242 dB             Read from simulation result
      Phase (PWM) at foc :            84.551               Read from simulation result

      K-factor (Choos K and  from the table)
      K                                       3             Input the chosen value (start from k=2)
                                           -217           (automatically calculated)

      Phase margin :                          48            (automatically calculated) Target value > 45

      R2 :                                54.655 kOhm       (automatically calculated)
      C1 :                                 0.874 nF         (automatically calculated)
      C2 :                                 97.07 pF         (automatically calculated)


                           All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                   23
B. Feedback Loop Compensators
                                                                            Type2 Compensator

                                                                                            C2
              Type 1 Compensator                                                                                                                          Type2a Compensator
                                        VOUT                                                                             VOUT                                                          VOUT
                         C1                                                       R2                  C1                                                      R2             C1


                                            Rupper                                                                            Rupper                                                       Rupper


    PWM_CTRL                                                   PWM_CTRL                                                                         PWM_CTRL

                     -             FB                                                   -                       FB                                                 -              FB
d                                                        d                                                                                  d
      PWM                                                         PWM                                                                             PWM
                     +                                                                  +                                                                          +
       1/Vp                                 Rlower                   1/Vp                                                     Rlower               1/Vp                                    Rlower
                          REF                                                                 REF                                                                      REF


                                        0                                                                                 0                                                            0

       Type1 Compensator                                                Type2 Compensator                                                               Type2a Compensator


              Type2b Compensator                                       Type3 Compensator

                         R2                                                            C2


                                        VOUT                                                                         VOUT
                         C1                                                  R2                  C1

                                                                                                                                       C3
                                            Rupper
                                                                                                                         Rupper

    PWM_CTRL                                                 PWM_CTRL                                                                  R3

                     -             FB                                              -                       FB
d                                                    d
      PWM                                                      PWM
                     +                                                             +
                                            Rlower              1/Vp                                                     Rlower
       1/Vp
                          REF                                                           REF



                                        0                                                                            0

       Type2b Compensator                                               Type3 Compensator



                                        All Rights Reserved Copyright (C) Bee Technologies Corporation 2011                                                                                24
C. Simulation Index

Simulations                                                                                   Folder name
1. Stabilizing the Converter.................................................... ac
2. Load Transient Response.................................................. stepload


Libraries :
1. ..¥bucksw.lib
2. ..¥pwm_ctr.lib

Tool :
• Type 2 Compensator Calculator (Excel sheet)




                        All Rights Reserved Copyright (C) Bee Technologies Corporation 2011             25

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Concept Kit:PWM Buck Converter Average Model (NJM2309)

  • 1. PWM Controller Power Switches Filter & Load (Voltage Mode Control) U? U? PWM_CTRL BUCK_SW L VOUT 1 2 Vo - - + PWM C + D 1/Vp Rload REF ESR VREF VP = 2.5 VREF = 1.23 Case Study: NJM2309 Application Circuit Design (PWM Step-down Converter) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 1
  • 2. Contents • Design Specification • NJM2309 Typical Application 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 • Load Transient Response Simulation  Reference: Load Transient Response Simulation with PWM IC Transient Model 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
  • 3. Design Specification NJM2309 Datasheet Step-Down (Buck) Converter : • VIN, MAX = 32 (V) • VIN, MIN = 6 (V) • VOUT = 3.3 (V) • VOUT, Ripple = 1% ( 33mVP-P ) • IOUT, MAX = 1.0 (A) • IOUT, MIN = 0.2 (A) Control IC : • NJM2309 (Switching Regulator Control IC for Step-Down) • Switching Frequency – fosc = 105 (kHz) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 3
  • 4. NJM2309 Typical Application Circuit Power Switches Filter & Load PWM Controller  Schematic is captured from NJM2309 datasheet page 4. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 4
  • 5. NJM2309 Typical Application Circuit TASK: Design and Evaluation of the Circuit 3? 2? 1 4? 5? All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 5
  • 6. Buck Regulator Design Workflow 1 Setting PWM Controller’s Parameters: VREF, VP 2 Setting Output Voltage: Rupper, Rlower 3 Inductor Selection: L 4 Capacitor Selection: C, ESR 5 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. 6 Load Transient Response Simulation All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 6
  • 7. Buck Regulator Design Workflow U2 BUCK_SW 3 L 1 2 Vo D C Vin Rload ESR 4 0 5 Type 2 Compensator C2 R2 C1 2 U3 Comp Rupper PWM_CTRL - FB d PWM + 1/Vp Rlower REF 1 VP = 2.5 0 VREF = 1.23 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 7
  • 8. 1 Setting PWM Controller’s Parameters  Table is captured from NJM2309 datasheet page 2.  VREF = VB = 0.52 (V)  VP=2.5 (vFBH and vFBL are not provided, the default value is used). All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 8
  • 9. 2 Setting Output Voltage: Rupper, Rlower • Use the following formula to select the resistor values.  Rupper  VOUT  VREF1    Rlower  • Rlower can be between 1k and 5k. Given: VOUT = 3.3V VREF = 0.52V  Rlower = 1k then:  Rupper = 5.346k All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 9
  • 10. 3 Inductor Selection: L L 1 2 Vo Inductor Value from C Rload LCCM  VI , max VOUT  RL, min ESR 2 foscVI , max Given: • VI,max = 40(V), VOUT = 3.3(V) • IOUT,min = 0.2(A) • RL,min = (VOUT / IOUT,min ) = 16.5() • fosc = 105(kHz) Then: • LCCM  72.1(uH),  L = 100(uH) is selected All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 10
  • 11. 4 Capacitor Selection: C, ESR (NJM2309) L 1 2 Vo Capacitor Value From C  7,785  VI , max F C VOUT  L( H) Rload and VO , RIPPLE ESR ESR  IL , RIPPLE Given: • VI, max = 40 V • VOUT = 3.3 V, VOUT, Ripple = 1% ( 33mVP-P ) • L (H) = 100 • IOUT, MAX = 1(A), IL, Ripple = 0.25(A) Then:  C  944 (F), C = 1000(F) is selected In addition:  ESR  132m All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 11
  • 12. 5 Stabilizing the Converter (NJM2309) U2 L Specification: BUCK_SW 1 100uH 2 Vo VOUT = 3.3V D C 1000uF VIN = 6 ~ 32V Vin Rload 12Vdc ESR 3.3 ILOAD = 0.2 ~ 1A 132m PWM Controller: 0 G(s) Type 2 Compensator VREF = 0.52V 1 C2 1f VP = 2.5V e.g. Given values from National R2 C1 fOSC = 105kHz 0.842k 1k Semiconductor Corp. IC: LM2575 Rupper Rlower = 1k, 2 U3 5.346k PWM_CTRL Rupper = 5.346k, LOL - FB L = 100uH, 3 1kH d PWM + C = 1000uF (ESR = 132m) 4 COL 1/Vp Rlower 1k 1kF REF VP = 2.5 0 Task: 1Vac V3 VREF = 0.52 0Vdc • to find out the element of the Type 2 compensator ( R2, C1, 0 and C2 ) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 12
  • 13. 5 Stabilizing the Converter (NJM2309) 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). U2 L BUCK_SW 100uH 1 2 Vo D C 1000uF Vin Rload 12Vdc ESR 3.3 132m Step2 Set C1=1kF, C2=1fF, 0 Type 2 Compensator and R2=calculated value Step1 Open the loop with C2 1f (Rupper//Rlower) as the LoL=1kH and CoL=1kF then inject initial values. R2 C1 an AC signal to generate Bode 0.842k 1k plot. Rupper 5.346k U3 PWM_CTRL LOL - FB d PWM 1kH + 1/Vp Rlower COL 1k 1kF REF VP = 2.5 V3 VREF = 0.52 0 1Vac 0Vdc  C1=1kF is AC shorted, and C2 1fF is AC opened (or Error-Amp without compensator). 0 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 13
  • 14. 5 Stabilizing the Converter (NJM2309) Type 2 Compensator Calculator Step3 Select a crossover frequency (about 10kHz or fc < fosc/4 ), for Switching frequency, fosc : 105.00 kHz this example, 10kHz is selected. Cross-over frequency, fc Then complete the table. (<fosc/4) : 10.00 kHz Rupper : 5.346 kOhm values from 2 Rlower : 1 kOhm R2 (Rupper//Rlower) : 0.842 kOhm (automatically calculated) Calculated value of PWM the Rupper//Rlower Vref : 0.520 V values from 1 Vp (Approximate) : 2.5 V All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 14
  • 15. 5 Stabilizing the Converter (NJM2309) 40 Gain: T(s) = H(s)GPWM 0 Step4 Read the Gain and Phase value (10.000K,-36.242) at the crossover frequency (10kHz) from the Bode plot, Then put the values -40 to the table. -80 DB(v(d)) 180d Phase  at fc (10.000K,84.551) Parameter extracted from simulation Set: R2=R1, C1=1k, C2=1f 0d Gain (PWM) at foc ( - or + ) : -36.242 SEL>> Phase (PWM) at foc : 84.551 100Hz 1.0KHz 10KHz 100KHz 1.0MHz P(v(d)) Frequency Tip: To bring cursor to the fc = 10kHz type “ sfxv(10k) ” in Search Command. Cursor Search All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 15
  • 16. 5 Stabilizing the Converter (NJM2309) Step5 Select the phase margin at fc K-factor (Choose K and from the table) (> 45 ). Then change the K value K 3 (start from K=2) until it gives the  -217  (automatically calculated)phase margin, for this satisfied example K=3 is chosen for Phase Phase margin : 48 (automatically calculated) 48. margin = R2 : 54.655 kOhm (automatically calculated) As the result; R2, C1 : 0.847 nF (automatically calculated) C1, and C2 are C2 : 97.07 pF (automatically calculated) calculated. Remark: If K-factor fail to gives the satisfied phase margin, Increase the output capacitor C then try Step1 to Step5 again.  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). All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 16
  • 17. 5 Stabilizing the Converter (NJM2309) 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. U2 L BUCK_SW 100uH 1 2 Vo D C 1000uF Vin Rload 12Vdc ESR 3.3 132m The calculated values of 0 the type 2 elements are: Type 2 Compensator C2 R2=54.655k, 97.07p C1=0.874nF , R2 54.655k C1 0.874n C2=97.07pF. Rupper 5.346k U3 PWM_CTRL LOL - FB d PWM 1kH + 1/Vp Rlower COL 1k 1kF REF VP = 2.5 V3 VREF = 0.52 0 1Vac 0Vdc *Analysis directives: 0 .AC DEC 100 0.1 10MEG All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 17
  • 18. 5 Stabilizing the Converter (NJM2309) Gain and Phase responses after stabilizing 80 40 (9.2368K,0.000) 0 -40 -80 Gain: T(s) = H(s) G(s)GPWM DB(v(d)) 180d 135d Phase  at fc 90d (9.2368K,48.801) 45d 0d SEL>> -45d 100Hz 1.0KHz 10KHz 100KHz 1.0MHz P(v(d)) Frequency • Phase margin = 48.801 at the cross-over frequency - fc = 9.237kHz. Tip: To bring cursor to the cross-over point (gain = 0dB) type “ sfle(0) ” in Search Command. Cursor Search All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 18
  • 19. Load Transient Response Simulation The converter, that have been stabilized, are connected with step-load to perform load transient response simulation. U2 L 3 Load BUCK_SW 100uH 1 2 Vo D C 1000uF I1 Vin Rload I1 = 0 12Vdc ESR 16.5 I2 = 0.8 132m TD = 10m TF = 25u 4 TR = 20u PW = 0.43m PER = 1 0 Type 2 Compensator C2 5 97.07p 3.3V/16.5 = 0.2A R2 C1 step to 0.2+0.8=1.0A 54.655k 0.874n load Rupper 5.346k U3 PWM_CTRL - FB 2 d PWM + 1/Vp Rlower REF 1k *Analysis directives: VP = 2.5 VREF = 0.52 0 .TRAN 0 20ms 0 1u 1 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 19
  • 20. Load Transient Response Simulation Simulation 3.5V 4.0A 1 2 3.5A 3.4V Output Voltage Change 3.0A 3.3V 2.5A 3.2V 2.0A 3.1V 1.5A 3.0V Load Current 1.0A 2.9V 0.5A >> 2.8V 0A 9.9ms 10.0ms 10.1ms 10.3ms 10.4ms 10.5ms 10.6ms 10.8ms 1 V(vo) 2 I(load) Time • The simulation results illustrates the transient response of the converter with the stepping load .2A to 1A. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 20
  • 21. Reference: Load Transient Response Simulation with PWM IC Transient Model After the converter have been designed, the PWM IC Transient Model could be applied for more realistic simulation. L 3 load RON = 100m 100uH 1 2 Vo S1 D1 C - + S DIODE 1000uF I1 + - Vin IC = 3.3 Rload I1 = 0 12Vdc pwm 16.5 I2 = 0.8 ESR TD = 10m 132m TF = 25u 4 TR = 20u PW = 0.43m PER = 1 0 Type 2 Compensator C2 5 97.07p 3.3V/16.5 = 0.2A R2 C1 step to 0.2+0.8=1.0A 54.655k 0.874n load Rupper 5.346k U3 Comp PWM_IC - FB 2 + E/A pwm + Comp - Rlower OSC 1k REF *Analysis directives: FOSC = 105K 0 VREF = 0.52 .TRAN 0 12ms 0 200n SKIPBP VP = 2.5 1  Remark: PWM IC Transient Model and Simulations are not included with this package. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 21
  • 22. Reference: Load Transient Response Simulation with PWM IC Transient Model Simulation 3.5V 4.0A 1 2 3.5A 3.4V Output Voltage Change 3.0A 3.3V 2.5A 3.2V 2.0A 3.1V 1.5A 3.0V Load Current 1.0A 2.9V 0.5A >> 2.8V 0A 10.0ms 10.2ms 10.4ms 10.6ms 10.8ms 1 V(Vo) 2 I(load) Time  The PWM IC Transient Model enables The VOUT, RIPPLE and others switching characteristics to be included in the simulation.  Remark: PWM IC Transient Model and Simulations are not included with this package. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 22
  • 23. A. Type 2 Compensation Calculation using Excel Switching frequency, fosc : 105.00 kHz Given spec, datasheet Cross-over frequency, fc (<fosc/4) : 10.00 kHz Input the chosen value ( about 10kHz or < fosc/4 ) Rupper : 5.346 kOhm Given spec, datasheet, or calculated Rlower : 1 kOhm Given spec, datasheet, or value: 1k-10k Ohm R2 (Rupper//Rlower) : 0.842 kOhm (automatically calculated) PWM Vref : 0.520 V Given spec, datasheet Vp (Approximate) : 2.5 V Given spec, or calculated, (or leave default 2.5V) Parameter extracted from simulation Set: R2=R2, C1=1k, C2=1f Gain (PWM) at foc ( - or + ) : -36.242 dB Read from simulation result Phase (PWM) at foc : 84.551  Read from simulation result K-factor (Choos K and  from the table) K 3 Input the chosen value (start from k=2)  -217  (automatically calculated) Phase margin : 48 (automatically calculated) Target value > 45 R2 : 54.655 kOhm (automatically calculated) C1 : 0.874 nF (automatically calculated) C2 : 97.07 pF (automatically calculated) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 23
  • 24. B. Feedback Loop Compensators Type2 Compensator C2 Type 1 Compensator Type2a Compensator VOUT VOUT VOUT C1 R2 C1 R2 C1 Rupper Rupper Rupper PWM_CTRL PWM_CTRL PWM_CTRL - FB - FB - FB d d d PWM PWM PWM + + + 1/Vp Rlower 1/Vp Rlower 1/Vp Rlower REF REF REF 0 0 0 Type1 Compensator Type2 Compensator Type2a Compensator Type2b Compensator Type3 Compensator R2 C2 VOUT VOUT C1 R2 C1 C3 Rupper Rupper PWM_CTRL PWM_CTRL R3 - FB - FB d d PWM PWM + + Rlower 1/Vp Rlower 1/Vp REF REF 0 0 Type2b Compensator Type3 Compensator All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 24
  • 25. C. Simulation Index Simulations Folder name 1. Stabilizing the Converter.................................................... ac 2. Load Transient Response.................................................. stepload Libraries : 1. ..¥bucksw.lib 2. ..¥pwm_ctr.lib Tool : • Type 2 Compensator Calculator (Excel sheet) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 25