Rectifier: Line commutated 1 phase and 3 phase half (semi) & fully controlled bridge converters
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### Rectifiers: Line Commutated 1-Phase and 3-Phase Half (Semi) & Fully Controlled Bridge Converters

#### Introduction
Rectifiers are power electronic devices that convert alternating current (AC) into direct current (DC). They are widely used in power supplies, motor drives, and other electronic devices that require DC power. There are two main types of rectifiers:
- **Half-controlled (semi-controlled) rectifiers**: Consist of both diodes and thyristors (SCRs). They allow control over only part of the AC cycle.
- **Fully-controlled rectifiers**: Composed entirely of thyristors, providing full control over the AC waveform.

Both types can be implemented in single-phase and three-phase systems and are known as bridge converters.

### 1-Phase Half and Fully Controlled Bridge Converters

#### 1-Phase Half-Controlled Bridge Converter

A **half-controlled bridge converter** in a 1-phase system consists of two diodes and two thyristors arranged in a bridge configuration.

##### Working:
- **Positive half-cycle**: During the positive half-cycle of the AC input, one thyristor and one diode conduct, allowing current to flow through the load.
- **Negative half-cycle**: During the negative half-cycle, the other thyristor and diode conduct, allowing current in the reverse direction.
- **Control of output voltage**: The thyristors are controlled by firing at a specific angle (called the **firing angle α**) during the positive and negative cycles. The diodes automatically conduct based on the polarity of the input voltage.

##### Output:
- The output voltage is pulsating DC with some control over the magnitude, depending on the firing angle of the thyristors.

##### Applications:
- Used in applications requiring simple control of DC power but where full control over the entire waveform is not necessary, such as battery chargers.

#### 1-Phase Fully Controlled Bridge Converter

A **fully-controlled bridge converter** in a 1-phase system consists of four thyristors instead of diodes.

##### Working:
- **Positive half-cycle**: During the positive half-cycle, two thyristors (T1 and T2) are triggered at the appropriate firing angle (α).
- **Negative half-cycle**: During the negative half-cycle, the other two thyristors (T3 and T4) are triggered at the same firing angle.

##### Output:
- The output voltage is fully controlled, depending on the firing angle of all thyristors. By adjusting the firing angle, the average output voltage can be varied from positive maximum to negative maximum.
- The output is a controlled DC waveform with reduced ripple compared to a half-controlled converter.

##### Applications:
- Used in applications where precise control of DC output is needed, such as motor drives, industrial power supplies, and variable DC sources.

### 3-Phase Half and Fully Controlled Bridge Converters

#### 3-Phase Half-Controlled Bridge Converter

A **3-phase half-controlled bridge converter** consists of three thyristors and three diodes arranged in a bridge configuration.

##### Working:
- **Positive half-cycle**: During each positive half-cycle of the AC input from any phase, one thyristor and one diode conduct.
- **Negative half-cycle**: During the negative half-cycle of the AC input from any phase, a different thyristor and diode conduct.
- **Control of output voltage**: The thyristors can be triggered at a specific firing angle to control the output DC voltage.

##### Output:
- The output voltage is a pulsating DC waveform with reduced ripple compared to a 1-phase system due to the three-phase input.
- The magnitude of the DC voltage depends on the firing angle of the thyristors.

##### Applications:
- Used in high-power applications like DC motor drives and large rectifier systems where full control over the waveform is not required.

#### 3-Phase Fully Controlled Bridge Converter

A **3-phase fully controlled bridge converter** consists of six thyristors arranged in a bridge configuration, with each phase having two thyristors.

##### Working:
- **Operation per phase**: Each phase of the AC input is controlled by two thyristors. During the positive half-cycle of each phase, one thyristor is triggered, and during the negative half-cycle, the other thyristor is triggered.
- **Control of output voltage**: The firing angle of each thyristor can be adjusted to control the average DC output voltage. The firing sequence is synchronized with the AC waveform.

##### Output:
- The output is a fully controlled DC waveform with low ripple. By varying the firing angle of the thyristors, the output voltage can be adjusted over a wide range.
- The ripple in the output voltage is smaller compared to the single-phase converters due to the three-phase input, which improves the quality of the output.

##### Applications:
- Widely used in high-power applications like industrial motor drives, power supplies for large equipment, and HVDC power transmission systems.

### Key Concepts

- **Firing Angle (α)**: The angle at which a thyristor is triggered in each cycle of the AC waveform. By delaying the firing angle, the average DC output voltage can be controlled.
  - For a **half-controlled converter**, the firing angle only affects part of the AC cycle.
  - For a **fully controlled converter**, the firing angle affects the entire AC cycle.

- **Commutation**: In line-commutated rectifiers, the thyristors turn off automatically when the current reaches zero in the AC cycle, known as natural commutation.

### Comparison of Half and Fully Controlled Converters

| Feature                      | Half-Controlled Converter           | Fully Controlled Converter         |
|------------------------------|-------------------------------------|-----------------------------------|
| **Control Elements**          | Thyristors + Diodes                 | Thyristors only                   |
| **Control**                   | Partial control of the waveform     | Full control of the waveform      |
| **Output Voltage Control**    | Limited control via firing angle    | Complete control via firing angle |
| **Applications**              | Simpler control applications        | Precision control applications    |
| **Cost**                      | Lower due to fewer thyristors       | Higher due to more thyristors     |

### Conclusion

Line-commutated rectifiers, both half and fully controlled, play a critical role in power electronics, allowing for the conversion and control of AC to DC power. The choice between half-controlled and fully controlled rectifiers depends on the application's need for control, complexity, and cost.

- **1-phase** rectifiers are simpler but produce more ripple in the output.
- **3-phase** rectifiers offer better performance with less ripple and are more suitable for high-power applications.

Understanding the difference between these configurations helps in choosing the right rectifier for specific industrial and electronic applications.
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