** Rectifiers**

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Half wave Rectifier

A rectifier is nothing but a simple diode__ __or group of diodes which converts the Alternating Current (AC) into Direct Current (DC).We know that a diode allows electric current in one direction and blocks electric current in another direction. We are using this principle to construct various types of rectifiers. Rectifiers are classified into different types based on the number of diodes used in the circuit or arrangement of diodes in the circuit. The basic types of rectifiers are: half wave rectifier and full wave rectifier.

Half wave rectifier definition

A half wave rectifier is a type of rectifier which converts the positive half cycle (positive current) of the input signal into pulsating DC (Direct Current) output signal.

or

A half wave rectifier is a type of rectifier which allows only half cycle (either positive half cycle or negative half cycle) of the input AC signal while another half cycle is blocked.

For example, if the positive half cycle is allowed then the negative half cycle is blocked. Similarly, if the negative half cycle is allowed then the positive half cycle is blocked. However, a half wave rectifier will not allow both positive and negative half cycles at the same time.

Therefore, the half cycle (either positive or negative) of the input signal is wasted.

What is half wave rectifier?

The half wave rectifier is the simplest form of the rectifier. We use only a single diode to construct the half wave rectifier.

The half wave rectifier is made up of an AC source, transformer (step-down), diode, and __resistor __(load). The diode is placed between the transformer and resistor (load).

AC source

The AC source supplies Alternating Current to the circuit. The alternating current is often represented by a sinusoidal waveform.

Half wave rectifier operation

When high AC voltage (60 Hz) is applied, the step-down transformer reduces this high voltage into low voltage. Thus, a low voltage is produced at the secondary winding of the transformer. The low voltage produced at the secondary winding of the transformer is called secondary voltage (V_{S}). The AC voltage or AC signal applied to the transformer is nothing but an input AC signal or input AC voltage.

The low AC voltage produced by the step-down transformer is directly applied to the diode.

When low AC voltage is applied to the diode (D), during the positive half cycle of the signal, the diode is __forward biased__ and allows electric current whereas, during the negative half cycle, the diode is __reverse biased__ and blocks electric current. In simple words, the diode allows the positive half-cycle of the input AC signal and blocks the negative half-cycle of the input AC signal.

The positive half-cycle of the input AC signal or AC voltage applied to the diode is analogous to the forward DC voltage applied to the p-n junction diode similarly the negative half-cycle of the input AC signal applied to the diode is analogous to the reverse DC voltage applied to the p-n junction diode.

We know that diode allows electric current when it is forward biased and blocks electric current when it is reverse biased. Similarly, in an AC circuit, the diode allows electric current during the positive half cycle (forward biased) and blocks electric current during the negative half cycle (reverse biased).

The positive half wave rectifier does not completely block the negative half cycles. It allows a small portion of negative half cycles or small negative current. This current is produced by the minority carriers in the diode.

The current produced by the minority carriers is very small. So it is neglected. We can’t visually see the small portion of negative half cycles at the output.

In an ideal diode, the negative half cycles or negative current is zero.

The resistor placed at the output consumes the DC current generated by the diode. Hence, the resistor is also known as an electrical load. The output DC voltage or DC current is measured across the load resistor R_{L}.

The electrical load is nothing but an electrical component of a circuit that consumes electric current. In half wave rectifier, the resistor consumes the DC current generated by the diode. So the resistor in half wave rectifier is known as a load.

Sometimes, the load is also refers to the power consumed by the circuit.

The load resistors are used in half wave rectifiers to restrict or block the unusual excess DC current produced by the diode.

Thus, the half wave rectifier allows positive half cycles and blocks negative half cycles. The half wave rectifier which allows positive half cycles and blocks negative half cycles is called a positive half wave rectifier. The output DC current or DC signal produced by a positive half wave rectifier is a series of positive half cycles or positive sinusoidal pulses.

Now let’s take a look at the negative half wave rectifier……..

Negative half wave rectifier

The construction and working of negative half wave rectifier is almost similar to the positive half wave rectifier. The only thing we change here is the direction of a diode.

When AC voltage is applied, the step-down transformer reduces the high voltage to low voltage. This low voltage is applied to the diode.

Unlike the positive half wave rectifier, the negative half wave rectifier allows electric current during the negative half-cycle of input AC signal and blocks electric current during the positive half-cycle of the input AC signal.

During the negative half cycle, the diode is forward biased and during the positive half cycle the diode is reverse biased, so the negative half wave rectifier allows electric current only during the negative half cycle.

Thus, the negative half wave rectifier allows negative half cycles and blocks positive half cycles.

The negative half wave rectifier does not completely block the positive half cycles. It allows a small portion of positive half cycles or small positive current. This current is produced by the minority carriers in the diode.

The current produced by the minority carriers is very small. So it is neglected. We can’t visually see this small positive half cycles at the output.

In an ideal diode, the positive half cycle or positive current is zero.

The DC current or DC voltage produced by the negative half wave rectifier is measured across the load resistor R_{L}. The output DC current or DC signal produced by a negative half wave rectifier is a series of negative half cycles or negative sinusoidal pulses.

Thus, a negative half wave rectifier produces a series of negative sinusoidal pulses.

In a perfect or ideal diode, the positive half cycle or negative half cycle at the output is exactly same as the input positive half cycle or negative half cycle. However, in practice, the positive half cycle or negative half cycle at the output is slightly different from the input positive half cycle or negative half cycle. But this difference is negligible. So we can’t see the difference with our eyes.

Thus, the half wave rectifier produces a series of positive sinusoidal pulses or negative sinusoidal pulses. This series of positive pulses or negative pulses is not a pure direct current. It is a pulsating direct current.

The pulsating direct current changes its value over a short period of time. But our aim is to produce a direct current which does not change its value over a short period of time. Therefore, the pulsating direct current is not much useful.

Half wave rectifier with capacitor filter

A filter converts the pulsating direct current into pure direct current. In half wave rectifiers, a __capacitor __or inductor is used as a filter to convert the pulsating DC to pure DC.

The output voltage produced by a half wave rectifier is not constant; it varies with respect to time. In practical applications, a constant DC supply voltage is needed.

In order to produce a constant DC voltage, we need to suppress the ripples of a DC voltage. This can be achieved by using either a capacitor filter or inductor filter at the output side. In the below circuit, we are using the capacitor filter. The capacitor placed at the output side smoothen the pulsating DC to pure DC.

Characteristics of half wave rectifier

Ripple factor

The direct current (DC) produced by a half wave rectifier is not a pure DC but a pulsating DC. In the output pulsating DC signal, we find ripples. These ripples in the output DC signal can be reduced by using filters such capacitors and inductors.

In order to measure how much ripples are there in the output DC signal we use a factor known as ripple factor. The ripple factor is denoted by **γ**.

The ripple factor tells us the amount of ripples present in the output DC signal.

A large ripple factor indicates a high pulsating DC signal while a low ripple factor indicates a low pulsating DC signal.

If the ripple factor is very low then it indicates that the output DC current is closer to the pure DC current. In simple words, the lower the ripple factor the smoother the output DC signal.

Ripple factor can be mathematically defined as the ratio of rms value of AC component of the output voltage to the DC component of the output voltage.

Ripples factor = rms value of AC component of the output voltage / DC component of the output voltage

Where, rms = root mean square

or

The ripple factor is also simply defined as the ratio of ripple voltage to the DC voltage

Ripple factor = Ratio of ripple voltage / DC voltage

The ripple factor should be kept as minimum as possible to construct a good rectifier.

The ripple factor is given as

Finally, we get

**γ = 1.21**

The unwanted ripple present in the output along with the DC voltage is 121% of the DC magnitude. This indicates that the half wave rectifier is not an efficient AC to DC converter. The high ripples in the half wave rectifier can be reduced by using filters.

DC current

The DC current is given by,

Where,

I_{max} = maximum DC load current

Output DC voltage (V_{DC})

The output DC voltage (V_{DC}) is the voltage appeared at the load resistor (R_{L}). This voltage is obtained by multiplying the output DC current with load resistance R_{L}.

It can be mathematically written as,

V_{DC} = I_{DC} R_{L}

The output DC voltage is given by,

Where, V_{Smax} = Maximum secondary voltage

Peak inverse voltage (PIV)

Peak inverse voltage is the maximum reverse bias voltage up to which a diode can withstand. If the applied voltage is greater than the peak inverse voltage, the diode will be destroyed.

During the positive half cycle, the diode is forward biased and allow electric current. This current is dropped at the resistor load (RL). However, during the negative half cycle, the diode is reverse biased and does not allows electric current, so the input AC current or AC voltage is dropped at the diode.

The maximum voltage dropped at the diode is nothing but an input voltage.

Therefore, peak inverse voltage (PIV) of diode = V_{Smax}

_{Rectifier efficiency}

Rectifier efficiency is defined as the ratio of output DC power to the input AC power.

The rectifier efficiency of a half wave rectifier is 40.6%

Root mean square (RMS) value of load current I_{RMS}

The root mean square (RMS) value of load current in a half wave rectifier is

Root mean square (RMS) value of output load voltage V_{RMS}

The root mean square (RMS) value of output load voltage in a half wave rectifier is

**Form factor**

Form factor is defined as the ratio of RMS value to the DC value

It can be mathematically written as

F.F = RMS value / DC value

The form factor of a half wave rectifier is

F.F = 1.57

**Advantages of half wave rectifier**

- We use very few components to construct the half wave rectifier. So the cost is very low.
- Easy to construct

**Disadvantages of half wave rectifier**

- Power loss

The half wave rectifier either allows the positive half cycle or negative half cycle. So the remaining half cycle is wasted. Approximately half of the applied voltage is wasted in half wave rectifier.

- Pulsating direct current

The direct current produced by the half wave rectifier is not a pure direct current; it is a pulsating direct current which is not much useful.

- Produces low output voltage.

** ****Full Wave Rectifier**

Like the half wave circuit, a full wave rectifier circuit produces an output voltage or current which is purely DC or has some specified DC component. Full wave rectifiers have some fundamental advantages over their half wave rectifier counterparts. The average (DC) output voltage is higher than for half wave, the output of the full wave rectifier has much less ripple than that of the half wave rectifier producing a smoother output waveform.

In a **Full Wave Rectifier** circuit two diodes are now used, one for each half of the cycle. A multiple winding transformer is used whose secondary winding is split equally into two halves with a common centre tapped connection, (C). This configuration results in each diode conducting in turn when its anode terminal is positive with respect to the transformer centre point C producing an output during both half-cycles, twice that for the half wave rectifier so it is 100% efficient as shown below.

### Full Wave Rectifier Circuit

The full wave rectifier circuit consists of two *power diodes* connected to a single load resistance (R_{L}) with each diode taking it in turn to supply current to the load. When point A of the transformer is positive with respect to point C, diode D_{1} conducts in the forward direction as indicated by the arrows.

When point B is positive (in the negative half of the cycle) with respect to point C, diode D_{2} conducts in the forward direction and the current flowing through resistor R is in the same direction for both half-cycles. As the output voltage across the resistor R is the phasor sum of the two waveforms combined, this type of full wave rectifier circuit is also known as a “bi-phase” circuit.

Partsim Simulation Waveform

As the spaces between each half-wave developed by each diode is now being filled in by the other diode the average DC output voltage across the load resistor is now double that of the single half-wave rectifier circuit and is about 0.637V_{max} of the peak voltage, assuming no losses.

Where: V_{MAX} is the maximum peak value in one half of the secondary winding and V_{RMS} is the rms value.

The peak voltage of the output waveform is the same as before for the half-wave rectifier provided each half of the transformer windings have the same rms voltage value. To obtain a different DC voltage output different transformer ratios can be used.

The main disadvantage of this type of full wave rectifier circuit is that a larger transformer for a given power output is required with two separate but identical secondary windings making this type of full wave rectifying circuit costly compared to the “Full Wave Bridge Rectifier” circuit equivalent.

## The Full Wave Bridge Rectifier

Another type of circuit that produces the same output waveform as the full wave rectifier circuit above, is that of the **Full Wave Bridge Rectifier**. This type of single phase rectifier uses four individual rectifying diodes connected in a closed loop “bridge” configuration to produce the desired output.

The main advantage of this bridge circuit is that it does not require a special centre tapped transformer, thereby reducing its size and cost. The single secondary winding is connected to one side of the diode bridge network and the load to the other side as shown below.

### The Diode Bridge Rectifier

The four diodes labelled D_{1} to D_{4} are arranged in “series pairs” with only two diodes conducting current during each half cycle. During the positive half cycle of the supply, diodes D1 and D2 conduct in series while diodes D3 and D4 are reverse biased and the current flows through the load as shown below.

### The Positive Half-cycle

During the negative half cycle of the supply, diodes D3 and D4 conduct in series, but diodes D1 and D2 switch “OFF” as they are now reverse biased. The current flowing through the load is the same direction as before.

### The Negative Half-cycle

As the current flowing through the load is unidirectional, so the voltage developed across the load is also unidirectional the same as for the previous two diode full-wave rectifier, therefore the average DC voltage across the load is 0.637V_{max}.

However in reality, during each half cycle the current flows through two diodes instead of just one so the amplitude of the output voltage is two voltage drops ( 2*0.7 = 1.4V ) less than the input V_{MAX} amplitude. The ripple frequency is now twice the supply frequency (e.g. 100Hz for a 50Hz supply or 120Hz for a 60Hz supply.)

Although we can use four individual power diodes to make a full wave bridge rectifier, pre-made bridge rectifier components are available “off-the-shelf” in a range of different voltage and current sizes that can be soldered directly into a PCB circuit board or be connected by spade connectors.

The image to the right shows a typical single phase bridge rectifier with one corner cut off. This cut-off corner indicates that the terminal nearest to the corner is the positive or +ve output terminal or lead with the opposite (diagonal) lead being the negative or -ve output lead. The other two connecting leads are for the input alternating voltage from a transformer secondary winding.

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**Reference:**

https://www.tutorialspoint.com/electronic_circuits/electronic_circuits_rectifiers.htm

https://www.electronics-tutorials.ws/diode/diode_6.html

http://www.visionics.a.se/Full%20Wave%20Rectifier1.aspx