Rectifier is an electrical circuit that converts AC to DC. It is either half wave or full wave. A half wave rectifier consists of a single diode only. There are two types of full wave rectifier. One is the bridge type and the other one is the center tap type.

Bridge rectifiers have four identical diodes connected in bridge. On the other hand, a center tap rectifier consists of two identical diodes but also utilizes a transformer winding.

A bridge rectifier is often used in primary circuits of a power supply (AC section). On the other hand, a center tap is common in secondary side wherein it is making use of the transformer secondary winding.

The main component of a rectifier is diode. Rectifier is often partnered with a capacitor on its output wherein its purpose is to elevate the DC and RMS values.

Almost all appliances or gadgets that we used every day have rectifier on it. For instance, a cell phone adapter or charger. It uses a rectifier to convert the ac power from the wall outlet to DC level that is usable by electronic components.

Another example is computer and TV. They both use ac power from the wall outlet, but their internal circuits need DC power. Thus, it needs a rectifier.

## Half Wave Rectifier

Below is a half wave rectifier circuit. It is a very simple circuit with just a diode on it. The resistor symbolizes the load or the recipient of the rectified waveform. The output wave shape is just half of the input, thus called it a half wave rectifier.

#### Details of Operation – Half Wave Rectifier

At positive half cycle of the AC waveform, the diode is forward biased. A forward biased diode is comparable to an ideal closed switch, and its path is just a short circuit connection. This will allow current flow. During this time, the output waveform is identical to the input waveform.

During the negative half cycle on the other hand, the diode is reverse biased. A reverse biased diode is analogous to an open switch or simply an open circuit. Thus, there is no current flow. The voltage in output side is zero.

Take note: A diode is forward biased when the potential difference applied to anode with respect to cathode is higher than the forward voltage drop (V_{F}) specification of the diode. It is reverse biased if otherwise.

## Full Wave Rectifier – Bridge Type

There are two types of full wave rectifier; bridge and center tap and below circuit is a bridge type. It has four identical diodes connected like a bridge (thus called a bridge rectifier). A pair of diodes will work at the same time.

#### Details of Operation – Bridge Rectifier

At positive half cycle, both D1 and D4 are forward biased while both D2 and D3 are reverse biased. The current flow is from the source, going to D1, to the load (RL), then returning to D4 and finally going back to the source. The waveform in the output is ideally the same as the input waveform.

At negative half cycle, both D2 and D3 are forward biased while D1 and D4 are reverse biased. The current flow is from the source, going to D3, to the load, then returning to D2 and finally to the source. The rectified waveform is the same in shape as the input but with a positive polarity.

## Full Wave Rectifier – Center Tap

A center tap rectifier is also a full wave rectifier. It can be constructed as below. There are two diodes and a transformer. In this circuit, the center of the transformer secondary winding is tapped to ground.

#### Details of Operation – Center Tap Rectifier

As you can see, the transformer winding has dots on it. This means that whatever the polarity of the dot side of the primary winding is also the polarity of the dot side of the secondary winding.

At the positive half cycle, the primary dot is positive and the secondary dots as well. This will forward bias the diode D1 and reverse bias the diode D2. The current flow will be from the upper secondary winding, going to D1 and to the load RL. This gives an output waveform of ideally the same shape as the input.

During the negative half cycle, the diode D2 is the one forward biased while this time it is the diode D1 is reverse biased. The current flow is from the lower secondary winding, going to diode D2 and to the load RL.

## DC (Average) and RMS of Half Wave and Full Wave Rectifiers

Half wave rectifiers have lower DC and RMS values compared to full wave rectifiers. This makes the half wave rectifier less popular. Below table summarizes the DC and RMS values of half wave and full wave rectifiers.

where Vpeak and Ipeak are the peak level of the rectified voltage or current

## Half Wave and Full Wave Rectifier Ripple

Ripple is the amount of AC component present in the output of the rectifier. The RMS of this ripple is

*Vr(rms) = sqrt (Vrms ^{2 }– Vdc^{2})*

#### Half Wave Rectifier

*Vr(rms) (HW) = sqrt [(Peak/2) ^{2 }– (0.318 x Peak)^{2}]*

*Vr(rms) (HW) = sqrt [Peak ^{2} x (0.5^{2} – 0.318^{2})]*

*Vr(rms) (HW) = sqrt [Peak ^{2} x (0.1489)]*

**Vr(rms) (HW) = 0.386 x Peak**

#### Full Wave Rectifier

*Vr(rms) (FW) = sqrt [Peak ^{2} x (0.707^{2} – 0.636^{2})]*

*Vr(rms) (FW) = sqrt [ (0.707 x Peak) ^{2 }– (0.636 x Peak)^{2} ]*

*Vr(rms) (FW) = sqrt [Peak ^{2 }x (0.096)]*

**Vr(rms) (FW) = 0.31 x Peak**

## Half Wave and Full Wave Rectifier Ripple Factor

Ripple factor is an indicator on how effective a rectifier is in converting AC into DC. It is defined as the ratio of the RMS of the ripple (Vr(rms)) to the DC or average value.

*Ripple Factor = Vr(rms) / Vdc*

#### Half Wave Rectifier

*Ripple Factor (HW) = 0.386 x Peak / 0.318 x Peak*

**Ripple Factor (HW) = 0.386 / 0.318 = 1.214**

#### Full Wave Rectifier

*Ripple Factor (FW) = 0.31 x Peak / 0.636 x Peak*

**Ripple Factor (FW) = 0.31 / 0.636 = 0.487**

A good rectifier must have a very low ripple factor. Capacitors are added to the output of a rectifier to decrease the ripple content and make the ripple factor dramatically low.

## Half Wave and Full Wave Rectifier Efficiency

Efficiency is the ratio of output power to input power. Efficiency relates to power losses.

*Efficiency = Output Power / Input Power*

The output power is DC (Pdc) while the input power is ac (Pac).

*Efficiency = Pdc / Pac*

Pdc is Vdc x Idc, while Pac is Vrms x Irms, so

*Efficiency = (Vdc x Idc / Vrms x Irms)*

#### Half Wave Rectifier

*Efficiency (HW) = (Vpeak/pi x Ipeak/pi) / (Vpeak/2 x Ipeak/2)*

**Efficiency (HW) =4 / pi ^{2} = 40.53%**

#### Full Wave Rectifier

*Efficiency (FW) = [ (2 x Vpeak/pi) x (2 x Ipeak/pi) ] / [ (Vpeak/sqrt 2) x (Ipeak/sqrt 2) ]*

**Efficiency (FW) = 8 / pi ^{2} = 81.06%**

Take note that the derived efficiency numbers above are ideal. It is not considering the power losses of the diodes.

## Half Wave and Full Wave Rectifier Form Factor

Form factor of a rectifier is defined as the ratio of RMS load voltage to the average load voltage. It is used to get information about a waveform

*Form factor = Vrms / Vdc*

#### Half Wave Rectifier

**Form factor (HW) = 0.5 x Vpeak / (Vpeak / pi) = pi / 2 = 1.57**

#### Full Wave Rectifier

**Form factor (FW) = ( Vpeak / sqrt 2 ) / (2 x Vpeak / pi ) = pi / ( 2 x sqrt 2 ) = 1.11**

## Half Wave and Full Wave Rectifier Peak Factor

Peak factor is the ratio of the peak value of the output voltage to the RMS value of the output voltage. Peak factor is also called as crest factor.

*Peak factor = Vpeak / Vrms*

#### Half Wave Rectifier

**Peak factor (HW) = Vpeak / ( Vpeak / 2 ) = 2**

#### Full Wave Rectifier

**Peak factor (FW) = Vpeak / ( Vpeak / sqrt 2 ) = sqrt 2= 1.41**

## Peak Inverse Voltage (PIV) of a Rectifier

Peak inverse voltage is the voltage measured across the diode in a rectifier circuit when it is reverse biased. It is also called a peak reverse voltage (PRV).

#### Half Wave Rectifier

*– Vpeak – PIV – Vrectified = 0*

Where Vrectified is zero when the diode is at reverse bias condition. So,

*– Vpeak – PIV = 0*

*PIV = – Vpeak*

The negative sign can be neglected as it is only telling that this voltage is going to happen when the diode is at reverse bias state. Thus, PIV for half wave rectifier is simply equal to the peak level of the output voltage.

**PIV (HW) = Vpeak**

#### Bridge Rectifier

By doing KVL on the loop indicated,

*Vpeak + PIV = 0*

*PIV = – Vpeak*

or simply PIV is

**PIV (bridge rectifier) = Vpeak**

#### Center Tap Rectifier

*Vpeak + PIV + Vpeak = 0*

*PIV = – 2 x Vpeak*

Simply, the PIV of a center tap rectifier is

**PIV (center tap) = 2 x Vpeak**

PIV is very important in selecting diode for a rectifier. If the diode rating is lower than the computed value or the actual measured PIV, it will damage right away. Keeping the PIV stress to less than 80% will prolong the life of the diodes in a rectifier circuit.

*PIV Stress = ( actual PIV / diode PIV rating ) x 100%*

*PIV Stress < 80% (will prolong diode life)*

## Current Stress

Aside from PIV, diodes in rectifier circuits are rated in terms of current. The actual current that flows to the diode should not exceed the device rating. Otherwise, it will get damaged in no time. Keeping the current stress below 80% will prolong the diode life.

*Current Stress = ( actual forward current / diode current rating ) x 100%*

*Current Stress < 80% (will prolong diode life)*

## Power and Thermal Considerations

The power dissipation in diode is the product of the forward current and the forward voltage. In ideal scenario, once the diode is forward biased, there is no voltage drop (the same analysis we used above). However, in real situations, diode has forward voltage when it is conducting.

*Power dissipation = V _{F} x I_{F}*

where V_{F} and I_{F} are forward voltage and current respectively

The power dissipation will result to heat generation. This heat must be dealt accordingly to ensure the diode will not get damaged. In high power applications, diode is mounted to a heat sink or cooled by fans.

For detailed analysis about diode selection, read How to Select a Diode for Circuit Design.

## Advantages of Half Wave Rectifier

- It is very simple

- Cheap up front cost, since it is using the lowest number of components

- The diode PIV is just half of a center tap full wave rectifier

## Disadvantages of Half Wave Rectifier

- Only the half cycle of the input is utilized which result to very low efficiency

- It produces low output voltage (both RMS and DC values)
- Both the voltage and current it produces are far from pure DC and it has lot of ripples (it has high ripple factor)

## Advantages of a Bridge Full Wave Rectifier

- It utilizes both the input half cycles; thus provides higher conversion efficiency than the half wave rectifier. Higher conversion efficiency also means that the power loss is low.
- Lower output ripple voltage compared to half wave rectifiers

## Disadvantages of a Bridge Full Wave Rectifier

- It is complex than half wave rectifiers in terms of construction

- It is expensive since using 4 diodes
- Occupy bigger space than the half wave rectifiers

## Advantages of a Center Tap Full Wave Rectifier

- It utilizes both the input half cycles; thus provides higher conversion efficiency than the half wave rectifier. Higher conversion efficiency also means that the power loss is low
- Lower output ripple voltage compared to half wave rectifiers

## Disadvantages of Center Tap Full Wave Rectifier

- It is complex than half wave rectifiers in terms of construction
- It is expensive since using 2 diodes and needs to have a transformer
- Occupy bigger space than the half wave rectifiers
- It has the highest PIV which means a high voltage diode is necessary. High voltage diode means physically big and expensive.