# 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

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