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Half-Wave Rectifier Theory

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					 Half-Wave Rectifier

                                                             Ideal diode model
                                                                             T
                                                            Vout
     Vin                           Vout
                                                                                      Vdc



    Diode conducts only for positive input
                                                                    Vin
    voltages. An AC input with zero average
    yields a non-sinusoidal output with a
    non-zero DC component. The
    conversion of AC to DC is called
    rectification.                                      Constant voltage drop model
                                                Vout
    The “conduction angle” θc is that part of                 vd
    the cycle during which the diode is
    conducting.
                                                                                      Vdc
    The average DC component is given by


                        
                            T
                   1                                   θc
             Vdc               V (t ) dt                     Vin
                   T    0




© Bob York, 2006-2009                                                                 Back to TOC
 Half-Wave Rectifier

 Assume constant voltage drop model                                                                       T

   Vin (t )  Vm sin t
                                                                               Vout          vd
               V (t )  vd        Vin  vd                                                                               Vdc
   Vout (t )   in
                   0             otherwise

  Conduction Angle
                                                                                        θc    Vin

                        vd                                   vd 
     ton  sin 1                toff    sin 1            
                        Vm                                   Vm 
                                                      vd                     2vd
      c   (toff  ton )    2sin 1                          c             for vd  Vm
                                                                                                    Ideal rectifier:
                                                      Vm                     Vm
                                                                                                     vd  0

   Average DC Value
                                                                                                     c  
                                                                                                             Vm
                                                                                                   Vdc          0.318Vm
                  T                          toff
          1                          1
    Vdc              Vout (t ) dt                 Vm sin t  vd  dt                                      
          T    0                     T   ton


          Vm    vd  c vd 
                  2
                                                                         Vm   vd   vd 
                                                                                      2
             1 2                                              Vdc     1         for vd  Vm
              Vm   2 Vm 
                                                                          2 Vm 2Vm2 

© Bob York, 2006-2009                                                                                               Back to TOC
 Half-Wave Rectifier

                                               Ideal diode model


   Suppose we reverse the diode: now
   only the negative portion of the input     Vin
   signal passes through

                                                                          Vdc

                                                         Vout


       Vin                     Vout



                                                    θc
                                                                            Vdc
     Other than the poarity reversal, all
     math on conduction angle and DC
     magnitude is identical
                                                                vd
                                            Constant voltage drop model

© Bob York, 2006-2009                                                           Back to TOC
 Peak Detector




 Vin                    Vout




© Bob York, 2006-2009          Back to TOC
 Peak-Detector with Load

    Any load or leakage path will discharge the
    capacitor. In this case, the output will
    depend on how the RC time constant
    compares with the period of the input signal.
                                                            C = 10 nF    τ = 0.1 T


     Vin                      Vout    10 kΩ
                     C




     The plots at right consider the various               C = 100 nF    τ=T
     cases for the simple circuit above with
     a 1kHz, 5V sinusoidal input


           τ = RC             T = 1 mS

   For   τ « T, circuit acts like an ideal rectifier
   For   τ » T, circuit acts like an ideal peak detector   C = 1000 nF   τ = 10 T




© Bob York, 2006-2009                                                                Back to TOC
 Peak-Detector as an AM Demodulator




                                  Output of detector


                  Amplitude-modulated signal




© Bob York, 2006-2009                                  Back to TOC

				
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Description: Half-Wave Rectifier Theory