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

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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

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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.

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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.

• For the minimum power loss while the diode is off, the reverse saturation current should be low.

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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

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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

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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