Half-Wave Rectifiers
Important Points of This Lecture
• Calculation of output voltage using
appropriate piecewise models for diode for
simple (unfiltered) half-wave rectifier
• Differences between calculations using
piecewise models and ideal diode equation
and PSpice simulation results
• Diode selection criteria
• Filtered half-wave rectifier
– Ripple voltage
AC to DC Conversion
• AC to DC conversion (ADC)
– Used to change 120V 60Hz to direct current
• Charging batteries in laptops, ipods, cell phones, etc.
• Used to supply logic levels in desktop computers
• The need for ADC
– A number of electronic devices operate under forward bias
or zero bias and can only withstand very small reverse bias
conductions without sustaining permanent damage.
• Example: LEDs and semiconductor lasers
– Circuits may be designed such that only positive d.c.
voltages are used.
• Example: Digital logic circuits
Design Criteria
• Conversion efficiency
– Average DC power delivered to load compared to
the available AC power
• Maximum voltage and current rating of the
load
• Ripple voltage (Vr)
– Maximum range of fluctuations of the “DC”
voltage
Three types of rectifiers
• Half wave rectifier
• Full wave rectifying bridge
• Full wave rectifier
Components
• All rectifiers use one or more diodes
• A transformer may be used in the half-wave
rectifier and full-wave rectifying bridge; must
be used in a full-wave rectifier circuit
Half-Wave Rectifier
Approach to Solution
• Assume that the frequency of the AC power supply is
low in comparison to the frequency response of the
diode circuit
– I.e., the parasitic capacitance and inductance of the diode
and the resistor do not affect the magnitude or phase of
the output voltage
• This allows us
– to use the DC models for the diode
– to replace the AC power supply with a variable DC power
supply
– To calculate the output voltage for specific set of input
voltages and interpolate the value of output voltage in
between.
What do you need to know?
• AC power supply
– Minimum and maximum voltages
• Diode
– Turn-on voltage, Vg
– Breakdown voltage, VBR or the Zener voltage at a
particular reverse bias current and Zener
resistance, VZ and RZ
Solution
• Three to four calculations
1. When the diode is at its maximum forward bias
condition
2. When the diode voltage is equal to its turn-on
voltage, but the diode current is zero
3. When the diode is at its maximum reverse bias
condition
4. When the diode is just entering breakdown
NOTE: This is not a desired condition for the half-wave
rectifier, but may accidently occur if an incorrect diode is
selected for the AC power supply connected to the circuit.
Example
Decisions on Diode Models
• Since the maximum voltage is +10V, there is
probably is enough voltage available to turn the
diode on. So, the ON model for the diode will
likely be used.
• Since the minimum voltage is -10V which is much
less than -VZ, we do not need to use the
BREAKDOWN model.
• As the voltage of the AC power supply can be
negative, it is likely that the OFF model for the
diode will be used.
Calculation 1:
The magnitude of the AC voltage is at its maximum
 10V  0.7V  200  I D  0
I D  46.5mA
Vo  200  I D  9.3V
Calculation 2:
The magnitude of the AC voltage just turns on the diode
 Vdc  0.7V  200  I D  0
I D  0mA
Vdc  0.7V
Vo  200  I D  0V
Calculation 3:
The magnitude of the AC voltage is at its minimum
 10V  VD  200  I D  0
I D  0mA
VD  10V
Vo  200  I D  0V
Output Voltage as a Function of Time
• Since the input voltage was actually an AC
power supply, the output voltage must vary
with time.
– The maximum output voltage is 9.3V.
– The output voltage is 0V when the input voltage is
0.7V.
– The minimum output voltage is 0V.
Vo vs. Time
Voltage Transfer Characteristic
Vg 
If one used the Ideal Diode equation to
determine Vo
• There will be a nonlinear dependence between the
power supply voltage and the output voltage
because of the nonlinear dependence of ID with VD
when the diode is forward biased.
• There will be a voltage drop when the diode is
reverse biased because of the reverse saturation
current.

I D  I o  e

qVD
nkT

 1

PSpice
• Simple diode model uses the Ideal Diode
equation.
• The models based on real diode parts are
more complex, incorporating parasitic
resistances, capacitances, and temperature
dependences
– Hence, your hand calculations are not going to
match the answers obtained when simulating the
circuit using Pspice. However, they should be
roughly the same.
Voltage Transfer Characteristic
Frequency Response
• Though the output voltage is plotted incorrectly in Pspice, there
is a maximum frequency of operation at which the diode no
longer operates via any of the models we have discussed thus far.
Output voltage when input power
supply is operating at 1GHz
Criteria for Diode Selection
• For maximum power to the load while the
diode is conducting, the diode should have a
small turn-on voltage.
kT  N d N a 
Vbi 
ln  2 
q  ni 
• For the minimum power loss while the diode
is off, the reverse saturation current should be
low.
 Dn ni 2 D p ni 2 

I o  qA

L N

L
N
p
d 
 n a
Last Criteria
• The breakdown voltage must be greater than
the magnitude of the larger reverse bias
applied to the diode.
– VBR is inversely proportional to the doping level of
the most lightly doped side of the p-n junction
• The maximum reverse bias voltage is called the peak
inverse voltage (PIV).
Alternative Circuit:
Half-Wave Rectifier
Smoothing the output voltage
Example
• Transformer steps down the input voltage to
+/- 12V
• Diode used is a D1N4002
• 1k resistor
• 10mF capacitor
VP
VM
Vr
VL
-VP
T’
Tp
Wait – that statement about the diode selection
criteria needs to be modified for this circuit!
• Let’s assume that the capacitor doesn’t have a chance to
discharge before the voltage of the input power supply is at
its minimum value.
– The diode is reverse biased at twice the magnitude of the peak
input voltage
• So, the criteria on the breakdown voltage is even more severe
• Now, assume that the reverse saturation current is large.
– This current will help speed the discharge rate of the capacitor,
causing the ripple voltage to be larger than expected.
• So, the criteria on the reverse breakdown voltage is still important.
However, it can be ignored if the reverse saturation current is less
than 10% of the minimum current through the load resistor while the
capacitor is discharging.
Ripple Voltage
• If you assume that the diode turns off (becomes
an open) as soon as the input voltage begins to
drop from its maximum value
– Then the output voltage is the voltage across the
capacitor (10mF) as it discharges through the resistor
(1k)
• Until the input voltage equals the output voltage
plus the turn-on voltage of the diode
– When the diode turns on and the capacitor begins to
be recharged.
Ripple Voltage
Vr  VM  VL  VM (1  e
T ' RC
T'
Vr  VM
RC
if T  Tp , then Vr  VM
'
1
Tp 
f
VM
Vr 
fRC
Tp
RC
)
Power Conversion Efficiency
1  VM
  
2  VP
2

 for a half - wave rectifier

2
1 

2
V

 (VM  VL )   M 2 Vr 
 for a filtered half - wave rectifier
  
  

 2VP   VP



if you assume that T'  T and the voltage drop across
the capacitor can assumed to be linearly decreasing .
Things to Know From This Lecture
• Optimal diode is a lightly doped p-n junction
– For a properly designed circuit, ON and OFF piecewise
models are used
– Reverse saturation current of a lightly doped p-n junction
is not ideal for this application
• Three calculations are needed to map the output
voltage using piecewise model
– Max. input voltage, minimum input voltage, and input
voltage at which the diode model switches between ON
and OFF
– Output voltage when diode is on varies linearly with input
voltage: Vo = Vin – Vg
– A transformer is used to step down (or up) the input
voltage as needed for the application.
• Results using Ideal Diode Equation
– Current does flow whenever Vin is not equal to zero
– Vo does not vary linearly with Vin
• Pspice Simulation
– Uses a more complex model based on the Ideal Diode
Equation
• Inclusion of parasitic capacitances means there is a
frequency dependence to the circuit operation
• Not shown was the temperature dependence of the
operation (but you can do this at home).
• Not all of the answers obtained from the simulation are
correct.
– First cycle in transient response is different because initial charge
on capacitors (external and parasitic) was zero.
• Filtered half-wave rectifier results in a better
“dc” output voltage
– Ripple voltage is a function of the maximum
voltage on the capacitor, the frequency of the
input voltage, and the RC time constant of the
load.
– Better power conversion than simple half-wave
rectifier circuit
– Significantly increases the maximum reverse bias
voltage on the diode
– Reverse saturation current of the diode may
influence ripple voltage