Rectifiers
Linear Integrated Circuit Applications
20201120 01:02:17
The Rectifiers
AC and DC are two common terms you come across while studying the flow shock. Alternating current (AC) has the property of changing its state continuously. For example, if we consider a sine wave, current flows in one direction for a positive half cycle and in the opposite direction for a negative half cycle. On the other hand, direct current (DC) only flows in one direction.
An electronic circuit, which produces either a DC signal or a pulsed DC signal, when an AC signal is applied to it is called as a rectifier . This chapter deals in detail with rectifiers based on an operational amplifier.
Types of rectifiers
Rectifiers are classified into two types: Halfwave rectifier and Fullwave rectifier . This section discusses these two types in detail.
Halfwave rectifier
Un rhalfwave rectifier is a rectifier which produces positive half cycles of output for one half cycle of the input and zero of the output for the other half cycle of the input.
The electrical diagram of a halfwave rectifier is shown in the following figure.
Observe that the electrical diagram of a halfwave rectifier shown above looks like an inverting amplifier, with two D diodes _{ 1 } and D _{ 2 } in addition.
The operation of the halfwave rectifier circuit shown above is explained below

For the positive half cycle of the sine input, the output of the opamp will be negative. Therefore, diode D _{ 1 } will be forward biased.

When diode D _{ 1 } is forward biased, the output voltage of the op amp will be 0.7 V. Thus, the diode D _{ 2 } will be reverse biased. Therefore, the output voltage of the above circuit is zero volt s.

By cTherefore, there is no (zero) half wave rectifier output for the positive half cycle of a sine wave input.

For the negative half cycle of the sine input, the output of the opamp will be positive. Thus, the D _{ 1 } and D _{ 2 } diodes will be reverse biased and forward biased respectively. So the output voltage of the above circuit will be 
$$ V_0 =  left (frac {R_f} {R_1} right) V_1 $ $
Waveforms
The input and waveforms of output of a halfwave rectifier are shown in the following figure
As you can see from the graphic above, the circuit diagram of the half wave rectifier we have discussed will produce positive half cycles for the half sine input and zero output negative cycles for po half cyclessine wave input sitive
Full wave rectifier
A full wave rectifier produces positive output half cycles for the two half cycles of the entrance.
The electrical diagram of a full wave rectifier is indicated in the due figure 
The diagram above consists of two operational amplifiers, two diodes, D _{ 1 } & D _{ 2 } and five resistors, R _{ 1 } to R _{ 5 }. The operation of the full wave rectifier circuit shown above is explained below 

For the positive half cycle of a sinusoidal input, the output of the first opamp will be negative, therefore the D _{ 1 } and D _{ 2 } diodes will be forward biased and inverted respectively.

Then the output voltage of the first opamp will be 
$$ V_ {01} =  left (frac {R_2} {R_1} right) V_i $$

Observe that the output of the first opamp is connected to a resistornce R _{ 4 }, which is connected to the inverting terminal of the second op amp. The voltage present at the noninverting terminal of the second opamp is 0 V. Thus, the second opamp with resistors, R _{ 4 } and R _{ 4 } acts as a inverting amplifier .

The output voltage of the second op amp will be
$$ V_0 =  left (frac {R_5} {R_4} right) V_ {01} $$
By replacing the value of $ V_ {01} $ in the equation above, we get 
$$ => V_ {0} =  left (frac {R_5} {R_4} right) left { left (frac {R_2} {R_1} right) V_ {i} right} $$
$$ => V_ {0} = left (frac {R_2R_5} {R_1R_4} right) V_ {i} $$

Therefore, the output of a full wave rectifier will be a positive half cycle for the positive half cycle of a sinusoidal input. In this case, the gain of the output is $ frac {R_2R_5} {R_1R_4} $. If we consider $ R_ {1}= R_ {2} = R_ {4} = R_ {5} = R $, then the gain of the output will be one.

For the negative half cycle of a sinusoidal input, the output of the first opamp will be positive. Therefore, the D _{ 1 } and D _{ 2 } diodes will be reverse biased and forward biased respectively.

The output voltage of the first opamp will be 
$$ V_ {01} =  left (frac {R_3} {R_1} right) V_ {i} $$

The output of the first opamp is directly connected to the noninverting terminal of the second opamp. Now the second opamp with resistors, R _{ 4 } and R _{ 5 } acts as a noninverting amplifier .
The output voltage of the second op amp will be 
$$ V_ {0} = left (1 + frac {R_5} {R_4} right) V_ {01} $$
By replacing the value of $ V_ {01} $ in the equation above, we get
$$ => V_{0} = left (1 + frac {R_5} {R_4} right) left { left (frac {R_3} {R_1} right) V_ {i} right} $$
$$ => V_ {0} =  left (frac {R_3} {R_1} right) left (1 + frac {R_5} {R_4} right) V_ {i} $$

Therefore, the output of a full wave rectifier will be a positive half cycle for the negative half cycle of the sine input as well. In this case, the amplitude of the output gain is $ left (frac {R_3} {R_1} right) left (1 + frac {R_5} {R_4} right) $. If we consider $ R_ {1} = 2R_ {3} = R_ {4} = R_ {5} = R $ then the gain of the output will be one .
The input and output waveforms of a full wave rectifier are illustrated in the following figure
As you can see in the figure above, the circuit diagram of the full wave rectifier that we have considered will only produce positive half cycles for the positive and negative half cycles of a sinusoidal input.