FULL WAVE RECTIFIER

               We know that, converting a.c alternating voltage into d.c pulsating voltage is called rectification. The rectifier which converts both the half cycles of the a.c input voltage into the d.c output voltage is called as full wave rectifier.

TYPES:
 There are two types of full wave rectifier they are:
                                    (i)center tapped transformer based rectifier
                                   (ii)bridge rectifier
(i)CENTER TAPPED TRANSFORMER BASED RECTIFIER:

CONSTRUCTION:
                
                         The center tapped transformer as the name says it has center tapped secondary coil.
Hence it got the name as center tapped rectifier.  All the other parts are the same, it has two pn junction diodes, a load resistor, a capacitor for filtering the output, and a fuse if necessary.

CIRCUIT DIAGRAM:

WORKING:
                      As seen from the circuit diagram the transformer has a center tapped structure in the secondary coil. The usage of the step down transformer is that the diode works only at the lower voltage conditions hence there is a necessary to convert the high voltage input to lower voltage output. The usage of diode is that it acts as a switch hence it rectifies the oscillating input signal.
 But the full wave rectifier works in two different cycles, viz
                                           (i) during positive half cycle(ie from angle 0 to 90degrees)
                                          (ii)during the negative half cycle(ie from angle 90 to 180 degrees)
(i) during positive half cycle:
                     During the positive half cycle the diode at the upper part of the circuit ie (diode 2) become forward biased whereas the diode at the lower part of the circuit (ie diode 1) is reverse biased resulting in no output from the diode 1 but diode 2 only conducts which results in the output.  In this case for a ideal diode (resistance is zero) Vin=Vo across the load.

(ii)during negative half cycle:
                      During the negative half cycle the diode at the lower part of the circuit ie(diode 1) become forward biased whereas the diode at the upper part of the circuit(ie diode 2) become reverse resulting in no output from the diode 2 whereas the diode 1 only conducts which results in the output. For a ideal diode Vin=Vo across the load.


INPUT AND OUTPUT WAVEFORM OF THE FULL WAVE RECTIFIER:


note: the upper waveform is input and the lower waveform is the output.

AVERAGE OUTPUT VALUE OR Vdc:

                  Vdc=(1/π)∫Vm sinwt dwt
                         =(Vm/π)[-coswt]lim 0-π
                   Vdc=2Vm/π
                    Idc=2Im/π

RMS OUTPUT VOLTAGE:
                     Vrms=(1/π)√[∫Vm^2 sin^2(wt) dwt]
                              =(Vm/√2√π)√[∫1-cos2wt dwt]
                              =(Vm/√2√π)√[wt-(sin2wt/2)]
                      Vrms =Vm/√2
                       Irms=Im/√2
 

RIPPLE FACTOR:
                   
                     τ=√((Vrms-Vdc)-1)
                       =√((π/2√2)^2-1)
                     τ = 0.483
EFFICIENCY:
                Effiency is given as the total power output to the total power input.
                       η=Vdc^2/Vrms^2
                         =8/π^2
                       η=81.2%
Tuf of full wave rectifier:
                    Tuf=power output /power rating of the transformer
                          =pac/Vrms.Irms
                          =8/√π^2
                   Tuf=0.8105 
MATLAB SIMULATION CIRCUIT DIAGRAM:















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