# Half-Wave Rectifier

```Half-Wave Rectifier
Ideal diode model
T
Vout
Vin
Vout
Vdc
Diode conducts only for positive input
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.
The “conduction angle” θc is that part of
the cycle during which the diode is
conducting.
Vin
Vout
Constant voltage drop model
vd
Vdc
The average DC component is given by
1
Vdc 
T
&copy; Bob York, 2006-2009

T
V (t ) dt
θc
Vin
0
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Half-Wave Rectifier
T
Assume constant voltage drop model
V (t )  vd
Vout (t )   in
0

Vin  vd
otherwise
Vdc
θc
Conduction Angle
 vd 

 Vm 
 ton  sin 1 
 vd 

 Vm 
 vd 

V
 m
c   

0
1
Vout (t ) dt 
T

toff
for vd  Vm
Ideal rectifier:
vd  0
Vm sin t  vd  dt
Vdc 
ton
Vm 
vd2  c vd 

 1 2 

 
2 Vm 
Vm
&copy; Bob York, 2006-2009
2vd
Vm
c  
Average DC Value
T
Vin
 toff    sin 1 
 c   (toff  ton )    2sin 1 
1
Vdc 
T
vd
Vout
Vin (t )  Vm sin t
Vm

 0.318Vm
Vm   vd
vd2 
Vdc 

1 
 for vd  Vm
  2 Vm 2Vm2 
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Half-Wave Rectifier
Ideal diode model
Suppose we reverse the diode: now
only the negative portion of the input
signal passes through
Vin
Vdc
Vout
Vin
Vout
θc
Other than the poarity reversal, all
math on conduction angle and DC
magnitude is identical
Vdc
vd
Constant voltage drop model
&copy; Bob York, 2006-2009
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Peak Detector
Vin
&copy; Bob York, 2006-2009
Vout
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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.
Vin
C
Vout
For
For
C = 100 nF
τ=T
C = 1000 nF
τ = 10 T
T = 1 mS
τ &laquo; T, circuit acts like an ideal rectifier
τ &raquo; T, circuit acts like an ideal peak detector
&copy; Bob York, 2006-2009
τ = 0.1 T
10 kΩ
The plots at right consider the various
cases for the simple circuit above with
a 1kHz, 5V sinusoidal input
τ = RC
C = 10 nF
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Peak-Detector as an AM Demodulator
Output of detector
Amplitude-modulated signal
&copy; Bob York, 2006-2009
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```