HALF WAVE RECTIFIER

Generally, the term rectifier is used in many places but as in electrical the rectifiers are used to convert the input a.c signal into pulsating d.c signal. The rectifier is classified into three basis on the type of rectification and by the type of transformer. They are
                                                          i)Half wave Rectifier
                                                          ii)full wave rectifier (center tapped)
                                                          iii)bridge rectifier
lets get into the types in detail:

HALF WAVE RECTIFIER:
                   Half wave rectifier is a device which rectifies the half wave of the ac signal to the dc. The half wave rectifier consist of a a.c supply, a transformer, a pn junction diode (which acts as a switch), a capacitor(for regulating output),a load.

WORKING:
                  The a.c signal input (normally 220-240v) is straightly fed into a step down transformer. Since the working condition of the diode is limited upto few volts, we have to step down the high voltage input.  then the voltage is fed into the pn diode. there are two types of modes on the pn junction diode
CASE 1:
when the positive half of the a.c input is flows through the diode, the positive terminal flows through the p side of the diode hence it is in forward bias hence the diode conducts and a pulsating half cycle output is obtained.
CASE 2:
when the negative half of the a.c input is flows through the diode, the negative terminal flows though the n side of the diode hence it is in reverse bias condition, hence the diode acts as a off switch and hence no output is obtained.

     Then the current flows through the capacitor connected in series. The capacitor generally turns the pulsating output into a constant dc output in other words it acts as a filter. thus the output is obtained as dc.

OUTPUT AND INPUT WAVEFORM OF HALF WAVE RECTIFIER:

note:the first waveform is the output and the second is the a.c input
                                                     MATLAB STIMULATION MODEL

TO find Vdc:
     
                   Vdc=(1/2π)∫Vm sinwt dwt
                          =(Vm/2π)[-cosπ+cos0]
                          =(Vm/2π).2
                          =Vm/π
wkt:Vrms=Vm/2


RIPPLE FACTOR

                                             τ=√((Vrms/Vdc)^2-1)

                                             τ=(√π^2/4)-1

                                             τ=1.211

EFFICIENCY:
      The ratio of DC output power to the AC input power is known as rectifier efficiency.

                                        η=(Vdc^2/Rl)/(Vrms^2/Rl)
                                           =4/π^2
                                         η=40.60%

TRANSFORMER UTILISATION FACTOR:
       The ratio of the dc power delivered to the load to the AC rating of the transformer secondary.

                                     Tuf=DCpower delivered to the load/AC rating of the transformer


                                     Tuf=Vdc.Idc/Vrms.Irms
                                           =2√2/π^2
                                           =0.287
NOTE:Here the Irms is taken as Im/2 because the circuit works only on one half of the cycle of the input a.c voltage. 
















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