Aula conversores cccc basicos

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					CONVERSORES CC/CC


    Introdução



                    1
 DC-DC Converter (Chopper)
 DEFINITION:
    Converting the unregulated DC input to a controlled DC
     output with a desired voltage level.

      General block diagram:

             DC supply
          (from rectifier-
                                         DC output   LOAD
           filter, battery,
           fuel cell etc.)


                                      Vcontrol
                                  (derived from
                                feedback circuit)

 APPLICATIONS:
      Switched-mode power supply (SMPS), DC motor control,
       battery chargers                                       2
  Linear regulator
 Transistor is operated in linear (active)            + VCEce    IL

   mode.                                                                +
                                                                   RL   Vo
                                              Vin
 Output voltage                                                        


           Vo  Vin  Vce

 The transistor can be conveniently                LINEAR REGULATOR
   modelled by an equivalent variable
   resistor, as shown.
                                                        + Vce 
                                                                   IL
 Power loss is high at high current due                 RT             +
   to:                                                             RL   Vo
                                              Vin
                                                                        
           Po  I L 2  RT
           or
           Po  Vce  I L                             EQUIVALENT             3

                                                        CIRCUIT
  Switching Regulator
                                                                   + Vce    IL
 Transistor is operated in switched-mode:
                                                                                   +
       Switch closed: Fully on (saturated)                                  RL
       Switch opened: Fully off (cut-off)      Vin                                Vo
       When switch is open, no current flow                                       
        in it
       When switch is closed no voltage drop         SWITCHING REGULATOR
        across it.
                                                                              IL

 Since P=V.I, no losses occurs in the                             SWITCH
                                                                                   +
   switch.                                       Vin
                                                                             RL    Vo
     Power is 100% transferred from                                               
       source to load.
     Power loss is zero (for ideal switch):
                                                           EQUIVALENT CIRCUIT
                                                      Vo
 Switching regulator is the basis of all DC-
   DC converters                                       Vin

                                                       (ON) (OFF) (ON)
                                                       closed open closed
                                                                                        4
                                                              DT    T
CONVERSORES CC/CC


  CONVERSÃO BUCK



                    5
Buck (step-down) converter
             S                         L

                                                           +
      Vd                       D            C    RL
                                                        Vo

                                                       

                     CIRCUIT OF BUCK CONVERTER
                          iL
             S                     + vL 
                                                       +
      Vd                  D                      RL    Vo

                                                       


             CIRCUIT WHEN SWITCH IS CLOSED

                 S         iL

                                   +   vL 
                                                               +
       Vd                                         RL           Vo
                           D

                                                               
                                                                    6
            CIRCUIT WHEN SWITCH IS OPENED
Switch is turned on (closed)
                                                                             + vL -
                                                                         + vL -
 Diode is reversed biased.                                   S              iL                        +
                                                         S              i+
                                            Vd
                                                                         L
                                                                                      C         +
                                                                                               RL      Vo
                                                                   + VD
                                       Vd                                         C       RL   Vo
                                                                   VD                                 
 Switch conducts inductor                                                                    
   current
                                                    vL
                                             vL

                                        V Vo
 This results in positive inductor   VdVo
                                          d

                                                                       opened             opened
   voltage, i.e:                                        closed
                                                    closed
                                                                  opened              opened
                                                                                 closed
                                                                             closed

                                                                                               t       t
     v L  Vd  Vo

 It causes linear increase in the     Vo Vo
                                         
   inductor current                       iL i
                                               L



           di                         iLmax
                                          iLmax
     vL  L L                           IL
                                            I
            dt                        iLmin L
                                            iLmin
            1
      iL   v L dt
            L                                                DT         T
                                                                                                   t
                                                                                                           t
                                                                                                               7
                                                                  DT         T
Switch turned off (opened)
                                                                          + vL -
                                                                       + vL -
                                                             S            iL                        +
 Because of inductive energy                            S             iL
                                                                                 C                + V
                                            Vd                         D                       RL     o
    storage, iL continues to flow.    Vd                           D
                                                                              C             RL    Vo
                                                                                                    
                                                                                                  

 Diode is forward biased                          vL
                                            vL
                                           VdVo
 Current now flows                  VdVo                          opened                 opened
                                                        closed                  closed
                                                                 opened                  opened
    (freewheeling) through the                   closed                      closed                   t
    diode.                                                                                        t



   The inductor voltage can be             Vo
                                                   iL
    derived as:                       Vo
                                            iL
                                          iLmax
                                             I
                                     iLmax L
             vL  Vo                  IL
                                           iLmin

                                     iLmin                          (1-D)T
                                                                                                          t   8
                                                                 (1-D)T
                                                                 DT     T
                                                                                                      t
    Analysis
                                                               vL
 When the switch is closed (on):
                           diL    di V  Vo            Vd Vo
      vL  Vd  Vo  L          L  d                                    closed
                           dt      dt      L
                                                                                            t
                           V 
        iL opened     o   (1  D)T
                           L 

 Derivative of iL is positive constant.
  Therefore iL must increase linearly.                         iL

 From figure:
                                                                       iL max
             diL iL iL Vd  Vo
                               
             dt     t DT             L
                                V  Vo 
                                                          IL                                iL
               iL closed   d        DT
                                L 
                                                                       iL min
 For the switch opened:
                                                                                                t
             di     di    V 
 vL  Vo  L L  L  o                                                           DT   T
              dt     dt    L                      Vo 
    diL iL      iL             iL opened  
                          Vo                            (1  D)T
                                                L                                             9
    dt    t (1  D)T      L 
Steady-state operation
   iL
                                                                        Increasing current

                                                                t

   iL                                                                    Decaying current


                                                                    t

   iL                                                                   Steady-state current


                                                                t
 Steady state operation requires that iL at the end of switching cycle is the
   same at the begining of the next cycle. That is the change of iL over one
   period is zero, i.e.:
               iL closed   iL opened  0
              Vd  Vo           V                    Vo  DVd                            10
                        DTs   o   (1  D)Ts  0
              L                 L 
  Average, Maximum and Minimum
  Inductor Current     iL


                    Imax
                IL                                            iL

                    Imin

                                                               t
 Average inductor current = average current in RL:
             Vo
        IL  IR 
             R
 Maximum current:                            iL Vo 1  Vo            1 (1  D) 
                              I max  I L          (1  D)T   Vo           
                                               2  R 2 L              R    2Lf 


                                              iL       1 (1  D) 
 Minimum current:            I min  I L         Vo           
                                               2       R    2Lf 


 Inductor current ripple            iL  I max  I min                        11
Average, Maximum and Minimum
Inductor Current
 Inductor current ripple

                     Vo (1  D )
             iL 
                         Lf

 Considering input voltage Vd constant:     iL
                     Vd D(1  D)
             iL 
                         Lf
                                                                 D
 So, the maximum current ripple occurs for D=0.5
                      Vd
               iL max 
                      4 Lf
 Then, the inductance value for a given current ripple can be
  obtained
                                                                     12
  Continuous Current Mode (CCM)
             iL

      Imax




       Imin                                                       t
              0
 From the previous analysis:

                                      iL       1 (1  D) 
                      I min  I L         Vo           
                                       2        R   2Lf 
 For continuous operation:

                      1 (1  D)                   (1  D)
                  Vo             0  L  Lmin          R
                     R    2Lf                       2f
 This is the minimum inductor current to ensure continuous mode of
                                                                      13
   operation.
  Output voltage ripple
 Capacitor current:
            ic  iL  iR                              L   iL       iR

                                                                        +
 The charge can be written as:                            iC
                                                                        Vo
                                   Q
    Q  CVo  Q  C V o Vo                                         
                                   C
 Using the triangle area formula:
           1  T   i  i                iL                              imax
     Q    L   L
           2  2  2  8                                                   iL=IR
                                                                Vo/R          imin
 Ripple voltage (pp)
                 i                     0
           Vo  L                              iC
                 8 fC
 The ripple can be reduced by:         0

       Increasing switching frequency;
       Increasing the inductor size;
       Increasing the capacitor size.                                  14
Basic design procedures
                           SWITCH                       L

                                               Lmin= ?
                                                                       RL
                                               L = 10Lmin
               Vd                                                      Po = ?
                          f=?             D
            (input                                             C       Io = ?
                          D=?                               ripple ?
            spec.)
                          TYPE ?



   Calculate D to obtain required output voltage.
   Select a particular switching frequency (f) and device
      preferably f>20KHz for negligible acoustic noise
      higher fs results in smaller L and C. But results in higher losses. Reduced efficiency, larger
        heat sink.
      Possible devices: MOSFET, IGBT. Low power MOSFET can reach MHz range.
   Calculate Lmin. Choose L>10 Lmin
   Calculate C for ripple factor requirement.
      Capacitor ratings:
             must withstand peak output voltage
             must carry required RMS current. Note RMS current for triangular w/f is Ip/3, where Ip
              is the peak capacitor current given by iL/2.
             ECAPs can be used
      Wire size consideration:
      Normally rated in RMS. But iL is known as peak. RMS value for iL is given as:
                                                    2
                                     2    i 2 
                        I L, RMS  I L   L                                                15
                                          3 
    Examples
   A buck converter is supplied from a 50V battery source. Given L=400uH,
    C=100uF, R=20 Ohm, f=20KHz and D=0.4. Calculate: (a) output voltage (b)
    maximum and minimum inductor current, (c) output voltage ripple.

   A buck converter has an input voltage of 50V and output of 25V. The switching
    frequency is 10KHz. The power output is 125W. (a) Determine the duty cycle,
    (b) value of L to limit the peak inductor current to 6.25A, (c) value of capacitance
    to limit the output voltage ripple to 0.5%.

   Design a buck converter such that the output voltage is 28V when the input is
    48V. The load is 8ohm. Design the converter such that it will be in continuous
    current mode (IL<10%I0max). The output voltage ripple must not be more than
    0.5%. Considering the switching frequency equal to 20kHz, specify the values of
    L and C. Suggest the power switch also.



                                                                                           16
CONVERSORES CC/CC


  CONVERSÃO BOOST



                    17
Boost (step-up) Converter
                      L              D




        Vd                                   C          +
                             S
                                                   RL   Vo

                                                        
                     CIRCUIT OF BOOST CONVERTER
             iL       L                  D
                    + vL 

        Vd                                              +
                                 S           C
                                                   RL   Vo
                                                        


                   CIRCUIT WHEN SWITCH IS CLOSED
                      L
                                     D
                    + vL -
                                                        +
       Vd                                    C     RL
                             S                          Vo

                                                        
                                                             18
                  CIRCUIT WHEN SWITCH IS OPENED
     Boost Analysis: Switch Closed
                                                Vd



         diL  di   V
vL  Vd  L   L  d
                                           vL   CLOSED

         dt    dt   L                                                              t

diL iL iL                    V DT
              iL closed  d                             V d V o

dt   t DT                        L
                                           iL                                iL




      iL
             L          D
                                                         DT              T   t
           + vL 
                                      +
Vd                          C         vo
                    S
                                      


                                                                                   19
     Switch Opened
                iL
                                 D
            + vL -
                                               +
Vd                                   C         vo
                     S
                                               -
                                                              Vd


                                                         vL
                                                                    OPENED

                  diL   di   V  Vo                                                           t
     vL  Vd  Vo  L  L  d
                  dt    dt     L                                        V d V o

     diL iL    iL     V  Vo
                      d
     dt   t (1  D)T      L                                                           iL

                         Vd  Vo  (1  D)T
                                                    iL

       iL opened 
                                 L                                  ( 1-D )T

                                                                   DT              T   t


                                                                                             20
 Steady-State Operation

                iL closed   iL opened  0
               Vd DT Vd  Vo  (1  D)T                         Vd
                                                   0  Vo 
                  L                 L                           1 D

 Boost converter produces output voltage that is greater or
  equal to the input voltage.
 Alternative explanation:
    when switch is closed, diode is reversed. Thus output is
      isolated. The input supplies energy to inductor.
    When switch is opened, the output stage receives energy
      from the input as well as from the inductor. Hence output is
      large.
    Output voltage is maintained constant by virtue of large C.
                                                                       21
 Average, Maximum, Minimum
 Inductor Current
 Input Power = Output Power
                                                2
                                     Vd 
                                     (1  D) 
                    Vo 2                       Vd
                                                        2
           Vd I d        Vd I L 
                     R                    R       (1  D) 2 R

 Average inductor current:
                                            Vd
                             IL 
                                        (1  D) 2 R

 Maximum inductor current:
                                      iL       Vd       V DT
                     I max  I L                      d
                                       2    (1  D) 2 R   2L

 Minimum inductor current:
                                      iL       Vd       V DT
                    I min  I L                       d     22

                                       2    (1  D) 2 R   2L
 L and C Values
                                                     Vd
                                                vL
 For CCM:
                        Vd     V DT
      I min  0               d   0
                    (1  D) R
                           2
                                2L
               D 1  D  TR                                     VdVo
                        2

      Lmin                                                                Imax
                      2                         iL
                                                                           Imin
 Considering Vin=cte:
       Vd DT V0 1  D  DT D 0.5      VT
 iL                        iL max = 0      iD                        Imax
          L         L                    4L
                                                                          Imin
 Output voltage ripple
                                                     Io=Vo / R
                  V        
             Q   o        DT  C Vo
                  R                           ic


      Vo DT Vo D   Vin 1  D  D D 0.5 Vin
Vo                             
       RC    RCf        RCf             4 RCf         Q                          23

                                                                 DT   T
  Examples
 The boost converter has the following parameters: Vd=20V,
  D=0.6, R=12.5ohm, L=65uH, C=200uF, fs=40KHz. Determine
  (a) output voltage, (b) average, maximum and minimum inductor
  current, (c) output voltage ripple.

 Design a boost converter to provide an output voltage of 36V
  from a 24V source. The load is 50W. The voltage ripple must be
  less than 0.5%. Specify the duty cycle ratio, inductor and
  capacitor size, and power device, considering a switching
  frequency equal to 50kHz.




                                                                   24
Buck-Boost Converter
                  S
                                    D
                                                   +

         Vd                             C
                           L                  RL   Vo
                                                   
    RL


              CIRCUIT OF BUCK-BOOST CONVERTER


               S                D
                           +                        +

         Vd           iL   vL                      Vo
                                                   



              CIRCUIT WHEN SWITCH IS CLOSED

              S                 D
                           +                       +
         Vd           iL   vL
                                                   Vo
                           
                                                    

              CIRCUIT WHEN SWITCH IS OPENED             25
  Buck-boost Analysis
                                                   Vd
                                              vL
 Switch turned on:

                 diL      di V i  V
   vL  Vd  L         L  d  L  d                   VdVo
                  dt      dt L DT L                                     Imax

                     Vd DT                    iL
    (iL )closed                                                      Imin
                        L
                                                                        Imax
 Switch turned off:                          iD
                                                                        Imin


               diL    di     V    iL    V         Io=Vo / R
  vL  Vo  L       L  o              o
                dt     dt    L (1  D )T L
                   V (1  D )T                ic
   (iL )opened  o
                        L
                                                    Q
                                                                               26

                                                               DT   T
  Output Voltage
 Steady state:
                   iL ( closed )   iL ( opened )  0
                       Vd DT Vo (1  D)T                 D 
                                        0  Vo  Vs       
                          L        L                     1 D 
 NOTE: Output of a buck-boost converter either be higher or lower than
   input.
       If D>0.5, output is higher than input
       If D<0.5, output is lower input

 Output voltage is always negative.


 Note that output is never directly connected to load.


 Energy is stored in inductor when switch is closed and transferred to
                                                                          27
   load when switch is opened.
  Average Inductor Current
 Considering no power losses in the converter:

                              Vo2
                    Po  Ps       Vd I s
                               R
 The average input current can be related to average inductor
   current as:
                         Is  IL D
                           Vo2
                               Vd I L D
                            R
 Substituting for V0:

                        Vo2   P     Vd D
                  IL        o 
                       Vd RD Vd D R(1  D)2
                                                                 28
 L and C Values
 Maximum and minimum inductor current:
                               iL     Vd D      V DT
                I max  I L                   d
                                2    R(1  D) 2    2L
                               i      Vd D      V DT
                I min    IL  L               d
                                2    R(1  D) 2   2L
 For CCM:
                 Vd D       Vd DT              (1  D) 2 R
                                  0  Lmin 
              R (1  D) 2
                             2L                    2f

 Output voltage ripple:

                  V                        V DT Vo D
             Q   o     DT  C Vo  Vo  o  
                  R                         RC   RCf
                                                             29
    Converters in CCM: Summary
                                                Buck
     S                                          Vo
                      L                            D
V                                       +       Vd
                  D           C   RL            Vo 1  D
d
                                        Vo           
                                                 Vo    8 LCf 2
                                        
                                                       (1  D ) R
                                                Lmin 
          L                                               2f         Boost
                      D
                                                                     Vo    1
                                                                        
                                        +                            Vd 1  D
V
                              C         Vo                           Vo    D
d
              S                                                          
                                  RL                                 Vo    RCf
                                        
                                                                              D (1  D ) 2 R
                                                                     Lmin 
                                                                                   2f
                                                Buck  Boost
      S
                                                Vo      D
                                                   
                          D             +       Vd    1 D
V                             C         Vo      Vo    D
                  L                RL               
d
                                               Vo    RCf
                                                       (1  D) 2 R
                                                Lmin                                 30
                                                           2f
                 Exercício
 The buck-boost converter has the following
  parameters: Vd=12V, V0=-12V, R=12ohm,
  fs=40kHz, C=200uF. Determine (a) Duty
  cycle, (b) Average inductor current, (c)
  Inductance for IL=10%ILmax, (d) Output
  voltage ripple, (e) Minimum load for
  continuous conduction mode.




                                               31
Control of DC-DC Converter:
Pulse Width Modulation (PWM)

     Vo (desired)
                        +      Vcontrol                Switch control
                                                           signal
     Vo (actual)                          Comparator
                        -
                            Sawtooth
                            Waveform                       Sawtooth
                                                           Waveform


                                                               Vcontrol 1
                                                               Vcontrol 2




                                                              Switch
                                                              control
            ton 2                                              signal


            ton 1
                                                                            32
                    T
  CONVERSORES CC/CC


MODO DESCONTÍNUO DE CONDUÇÃO



                               33
                 CONVERSOR BUCK
      Desprezando-se as perdas:

             Pin  P0
      Substituindo a corrente
     média no indutor, tem-se:

    Vd  V0      DTs V0
                          2
Vd          DTs      
    L            2Ts   R

Vd
   2
        VdV0  D2Ts R  2LV02
                         
     V0      2           
                        
     Vd        8Lf s     
         1 1                   34
               RD 2      
         CONVERSOR BUCK
 Considerando a carga com uma fonte de corrente
  constante, tem-se:

            Vd  V0       DTs
        Vd          DTs        V0 I 0
            L             2Ts
        V0         Vd D 2
            
        Vd 2 LI 0  Vd D 2Ts

        V0    D2                      V0    D2
                                         2
        Vd D2  2 LI 0                Vd D  2I 
                VTs
                  i


                                                    35
               CONVERSOR BOOST

           I L
I Lmed          t1  t2 
           2Ts

V0        2 Vd Ts
    1 D
Vd          2 LI 0

V0      D2
    1
Vd      2I 




                                 36
 CONVERSOR BUCK-BOOST

           I L
I Smed          t1 
           2Ts

V0    2 Vd Ts
   D
Vd      2 LI 0

V0 D 2
  
Vd 2 I 




                          37
               Exercício
 Considere um conversor boost operando no
 MDC, com Vi=12-36V, V0=48V, fs=50kHz e
 P0=120W. Obtenha o máximo valor de L para
 garantir o modo descontínuo de condução.




                                             38
CONVERSORES CC/CC


CONVERSORES DERIVADOS



                        39
CONVERSOR CUK




                40
CONVERSOR SEPIC




                  41
CONVERSOR ZETA




                 42
Outros Conversores Não Isolados
 Buck / Boost multifásicos;
 Buck / Boost quadráticos;
 Boost-Half Bridge / Buck-Boost Half-Bridge




                                               43
CONVERSORES ISOLADOS
 Forward 1 chave / 2 chaves
 Push-Pull
 Half-Bridge
 Full-Bridge
 FlyBack
 Duplo Forward 1 ou 2 chaves
 Sepic / Cuk / Zeta isolados
 Conversores cc/cc trifásicos

                                 44

				
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