Describe the operation of single phase fully controlled bridge converter with R-load.
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A single-phase fully controlled bridge converter, also known as a single-phase full-wave controlled rectifier, is a type of power electronic circuit used to convert AC (alternating current) to DC (direct current) with the ability to control the output voltage. When connected to a resistive load (R-load), its operation can be described as follows:

### Circuit Configuration

1. **Components**:
   - Four thyristors (often SCRs - Silicon Controlled Rectifiers) arranged in a bridge configuration.
   - A resistive load (R) connected across the output.
   - An AC supply (V_s) connected to the input terminals.

2. **Operation**:
   - The thyristors are controlled by gate signals that determine when each thyristor conducts.
   - The AC supply voltage is applied to the input terminals of the converter.
   - The load is connected across the output terminals.

### Operation Phases

1. **Firing Angle Control**:
   - The firing angle (α) is the delay after the zero crossing of the AC input voltage at which the thyristors are triggered into conduction.
   - By adjusting the firing angle, the duration for which each thyristor conducts within a half-cycle of the AC supply is controlled.

2. **Positive Half-Cycle**:
   - During the positive half-cycle of the AC input voltage, two thyristors (T1 and T2) are triggered into conduction.
   - The output voltage is the same as the input voltage minus any voltage drops across the conducting thyristors.
   - The resistive load experiences a voltage that is proportional to the input voltage, adjusted by the firing angle.

3. **Negative Half-Cycle**:
   - During the negative half-cycle, the other two thyristors (T3 and T4) conduct.
   - Similarly, the output voltage is the same as the input voltage but with the opposite polarity, minus the voltage drops across the thyristors.
   - The load voltage and current during this phase are also controlled by the firing angle.

4. **Average Output Voltage**:
   - The average output voltage (\( V_{dc} \)) across the load can be expressed as:
     \[
     V_{dc} = \frac{2V_m}{\pi} \cdot \cos(\alpha)
     \]
     where \( V_m \) is the peak value of the AC input voltage and \( \alpha \) is the firing angle.
   - By varying the firing angle, the average DC output voltage can be controlled.

### Key Points

- **Controllability**: The output voltage can be controlled by adjusting the firing angle of the thyristors. This allows for smooth control of the DC output.
- **Conducting States**: Each thyristor conducts for 180° of the input AC cycle, alternating between pairs of thyristors.
- **Ripple**: The output voltage will have some ripple due to the nature of the AC to DC conversion, but the ripple is typically smoothed by additional filtering if needed.

In summary, the single-phase fully controlled bridge converter with an R-load uses four thyristors to convert AC to DC while allowing the output voltage to be adjusted by controlling the firing angle of the thyristors.
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A Single-Phase Fully Controlled Bridge Converter (also known as a Single-Phase Thyristor Bridge Converter) with an R-load (resistive load) is a type of power electronic circuit used to convert alternating current (AC) from a single-phase source into a controlled direct current (DC). This converter utilizes thyristors (such as SCRs, Silicon Controlled Rectifiers) as the main switching components. Let's break down the operation step by step:

### Basic Configuration

The single-phase fully controlled bridge converter consists of four thyristors arranged in a bridge configuration, and the load is connected across the output.

**Schematic:**

```
      AC Source
        ~
        |
       | |
     T1   T2
      |     |
      |     |
      +----+----+
           |
           | R-Load
           |
      +----+----+
      |     |    |
     T3   T4
      |     |
      |     |
       ~
```

**Where:**
- **T1, T2, T3, T4** are the thyristors.
- **R-Load** is a resistive load.

### Operation

1. **Triggering Thyristors:**
   - In a fully controlled bridge converter, each thyristor can be individually triggered to control the conduction angle, which in turn controls the output voltage and current.
   - The thyristors are typically triggered by a gate pulse. The angle at which they are triggered (known as the firing angle, α) determines the amount of power delivered to the load.

2. **Conduction Phases:**
   - **Positive Half-Cycle (AC Source Positive):** During the positive half-cycle of the AC input, thyristors T1 and T2 conduct, while T3 and T4 are off. This allows current to flow through T1, the load (R), and T2, producing a positive voltage across the load.
   - **Negative Half-Cycle (AC Source Negative):** During the negative half-cycle, T3 and T4 conduct, while T1 and T2 are off. This allows current to flow through T3, the load (R), and T4, resulting in a negative voltage across the load.

3. **Controlled Rectification:**
   - By varying the firing angles of the thyristors, the converter can adjust the average DC output voltage across the resistive load. A firing angle of 0° means the thyristors are conducting for the entire half-cycle of the AC source, delivering maximum DC output voltage. As the firing angle increases, the conduction period of the thyristors decreases, reducing the average output voltage.

4. **Waveform and Output Voltage:**
   - **Output Voltage (V_DC):** The average DC voltage across the load depends on the firing angle. For a resistive load, the output voltage is directly proportional to the average value of the rectified output waveform.
   - **Output Current (I_DC):** The current through the load is given by Ohm’s law: \( I_{DC} = \frac{V_{DC}}{R} \).

5. **Harmonics and Filtering:**
   - The output waveform of a fully controlled bridge converter is not pure DC; it contains harmonics due to the non-sinusoidal nature of the rectified output. Typically, filtering is required to smooth out the voltage and reduce the harmonics.

### Key Points

- **Firing Angle Control:** The firing angle of the thyristors is crucial in determining the output voltage. A phase control technique is used to vary this angle.
- **Efficiency and Heat:** Thyristors, being semiconductor devices, have losses associated with their operation. Proper heat management and cooling are essential to ensure reliable performance.
- **Protection:** Protection mechanisms such as snubber circuits, fuses, and circuit breakers are important to safeguard the converter and load from potential damage.

In summary, the single-phase fully controlled bridge converter with an R-load effectively converts AC to DC with controllable output voltage by varying the firing angles of the thyristors. It is widely used in various applications where precise control of DC output is required.
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