Half wave rectifier and equivalent circuit with piece-wise linear model

v i   = VM  sin (?t)
Half Wave Rectifier
We initially consider the diode to be ideal, such that VC =0 and Rf =0
Half Wave Rectifier
• The (ideal) diode conducts for vi >0 and since Rf =0  
v0 ? vi

• For vi < 0 the (ideal) diode is an open circuit (it doesn’t conduct) and
v0 ? 0.

Half Wave Rectifier
In this simplified (ideal diode) case the input and output waveforms are as shown



Half Wave Rectifier
The average d.c. value of this half-wave-rectified sine wave is

Half Wave Rectifier
So far this rectifier is not very useful.
Even though the output does not change polarity it has a lot of ripple, i.e. variations in output voltage about a steady value.
To generate an output voltage that more closely resembles a true d.c. voltage we can use a reservoir or smoothing capacitor in parallel with the output (load) resistance.

Smoothed Half Wave Rectifier
Circuit with reservoir capacitor
Output voltage
The capacitor charges over the period t1 to t2 when the diode is on and discharges from t2 to t3 when the diode is off.
Smoothed Half Wave Rectifier
When the supply voltage exceeds the output voltage the (ideal) diode conducts. During the charging period (t1 < t< t2)
vo = VM  sin (?t)
(The resistance in the charging circuit is strictly Rf which we have assumed to be zero. Even for a practical diode RfC will be very small)
Smoothed Half Wave Rectifier
When the supply voltage falls below the output voltage the diode switches off and the capacitor discharges through the load.
During the discharge period (t2 < t< t3 ) and
            
 vo = VM  exp {- t’ /RC}                                    

where t’= t- t2
At time t3 the supply voltage once again exceeds the load voltage and the cycle repeats

Smoothed Half Wave Rectifier
The resistance in the discharge phase is the load resistance R.
RC can be made large compared to the wave period.
The change in output voltage (or ripple) can then be estimated using a linear approximation to the exponential discharge.
Smoothed Half Wave Rectifier
 vo = VM  exp {- t’ /RC} ? VM  [ 1- (t’ /RC)]
The change in voltage ?V is therefore approximately given by  VM t’ /RC
For a the half wave rectifier this discharge occurs for a time (t3  - t2 ) close to the period T = 1/f, with f= frequency.
Giving the required result:
Smoothed Half Wave Rectifier
We can define a ripple factor as



    where Vd.c.  = (VM - ?V/2)

The lower the ripple factor the better

Half Wave Rectifier
If we don’t consider the diode to be ideal  then from the equivalent circuit we obtain, for vi >Vc:
       vi – Vc – i Rf  - iR =0
  i.e.

Giving
Non-Ideal Half Wave Rectifier

Non-Ideal Half Wave Rectifier
A plot of v0  against vi  is known as the transfer characteristic


Non-Ideal Half Wave Rectifier
• We usually have R>> Rf  so that Rf can be neglected in comparison to R.
• Often VM  >> Vc  so Vc can also be neglected.

The transfer characteristic then reduces to
v0 ? vi

Full-Wave (Bridge) Rectifier
We initially consider the diodes to be ideal, such that VC =0 and Rf =0
The four-diode bridge can be bought as a package
Full-Wave (Bridge) Rectifier
During positive half cycles vi is positive.
Current is conducted through diodes D1, resistor R and diode D2
Meanwhile diodes D3 and D4 are reverse biased.

Full-Wave (Bridge) Rectifier
During negative half cycles vi is negative.
Current is conducted through diodes D3, resistor R and diode D4
Meanwhile diodes D1 and D2 are reverse biased.

Full-Wave (Bridge) Rectifier
Current always flows the same way through the load R.
Show for yourself that the average d.c. value of this full-wave-rectified sine wave is VAV  = 2VM/? (i.e. twice the half-wave value)


Full-Wave (Bridge) Rectifier
Two diodes are in the conduction path.
Thus in the case of non-ideal diodes vo will be lower than vi by 2VC.
As for the half-wave rectifier a reservoir capacitor can be used. In the full wave case the discharge time is T/2 and
Diode Clipper Circuits
These circuits clip off portions of signal voltages above or below certain limits, i.e. the circuits limit the range of the output signal.
Such a circuit may be used to protect the input of a CMOS logic gate against static.
Diode Clipper Circuits

Diode Clipper Circuits
When the diode is off the output of these circuits resembles a voltage divider



Diode Clipper Circuits
If RS << RL

The level at which the signal is clipped can be adjusted by adding a d.c. bias voltage in series with the diode.

v0 ? vi
For instance see example sheet 1, Q11

Diode Clipper Circuits
Let’s look at a few other examples of clipper circuits.
Diode Clamper Circuits
The following circuit acts as a d.c. restorer.
 see Q9, example sheet1.


Diode Clamper Circuits
A bias voltage can  be added to pin the output to a level other than zero.

Posted in Posted by waytofeed at 9:30 AM