Question

Draw a neat diagram of 1φ half wave controlled converter with RL load. Give its operation.

Answer 1

I can't draw diagrams directly, but I can describe how to create one and explain the operation of a single-phase half-wave controlled converter with an RL load.

### Diagram Description

1. **Input Source**: Draw an AC voltage source (V_s) connected to a diode (or thyristor for control).
2. **Thyristor/Diode**: Connect a thyristor (SCR) in series with the AC source. This will control the current flow.
3. **Load**: After the thyristor, connect an RL load (resistor R and inductor L) in series.
4. **Output Voltage**: Show the output voltage across the load.

### Operation

1. **Phase Control**: The thyristor is triggered at a specific angle (α) during the positive half-cycle of the AC waveform. This angle determines how much of the input waveform will appear across the load.

2. **Conduction Period**: Once the thyristor is triggered, it conducts for the remainder of the positive half-cycle until the current through it falls to zero. The output voltage across the RL load is essentially the portion of the AC input waveform that starts from the firing angle α to the peak of the waveform.

3. **Load Behavior**:
   - **Inductor Charging**: As the current flows through the inductor, it stores energy in the magnetic field.
   - **Continuous Current**: In an RL circuit, the current does not drop to zero immediately when the thyristor turns off, due to the inductor's stored energy. The current continues to flow until it gradually decays.

4. **Negative Half-Cycle**: During the negative half-cycle, the thyristor is reverse-biased and does not conduct. The current through the load will continue to flow in the same direction because of the inductor's stored energy, but it will gradually decrease until the next positive half-cycle.

### Key Points

- The output voltage waveform will be a series of pulses corresponding to the conduction period determined by the firing angle α.
- The current waveform will be more continuous due to the inductor.
- The average output voltage and current can be calculated based on the firing angle and load parameters.

This setup is commonly used in applications requiring controlled DC output from an AC source, such as in power supplies and motor control systems. If you need more details on specific calculations or waveforms, let me know!

Answer 2

A 1-phase half-wave controlled converter with an RL load is a type of power electronic circuit used for controlled rectification. It converts AC to DC and is particularly useful in applications where precise control of the output voltage is required. Here’s a detailed explanation of the circuit and its operation:

### Diagram of 1-Phase Half-Wave Controlled Converter

Here's how you can visualize the circuit:

1. **AC Source:** Represents the input AC voltage source, which typically consists of a transformer if voltage adjustment is needed.
2. **Thyristor (SCR):** A semiconductor device used for control. The gate of the SCR is used to trigger it at the desired phase angle.
3. **RL Load:** A resistor (R) in series with an inductor (L), representing the load of the converter.

```
   AC Source
     |
     |
     |
     |----|>|---+--- R --- L ---|
     |           |
     |           |
     |           |
   Thyristor     |
     |
     |
   Ground
```

In this diagram:
- The **AC Source** provides the input voltage.
- The **Thyristor** (SCR) is connected in series with the AC source and the RL load.
- The **RL Load** consists of a resistor and inductor in series.

### Operation of 1-Phase Half-Wave Controlled Converter

#### 1. **Triggering of Thyristor**

The thyristor (SCR) is a semiconductor device that conducts when it is triggered with a gate signal. The timing of this trigger signal determines the conduction angle of the thyristor. The angle at which the SCR is triggered is known as the firing angle (α).

- **Firing Angle (α):** The angle after the zero-crossing of the AC voltage at which the SCR is turned on. If α = 0°, the SCR conducts as soon as the AC voltage is positive, providing maximum output voltage. If α is greater than 0°, the SCR conducts later, reducing the average output voltage.

#### 2. **Conduction Phase**

When the SCR is triggered, it starts conducting and allows current to flow through the RL load. This conduction continues until the AC voltage drops to zero.

- **Positive Half-Cycle:** During the positive half of the AC cycle, the SCR conducts and allows current through the load. The voltage across the load is essentially the same as the input AC voltage minus the forward voltage drop of the SCR.

- **Negative Half-Cycle:** During the negative half-cycle, the SCR is reverse-biased and does not conduct. The current through the RL load is zero, and the voltage across the load is zero.

#### 3. **Output Voltage and Current**

The output voltage (V_out) across the RL load is a rectified waveform with a DC component. The waveform is pulsating DC due to the nature of the half-wave rectification. The average output voltage depends on the firing angle (α) of the SCR.

- **Average Output Voltage (V_avg):** It can be approximated by integrating the rectified waveform over one period and depends on the firing angle. The output voltage decreases as the firing angle increases.

- **Load Current (I_load):** The current through the RL load also pulsates. During the positive half-cycle, the current builds up through the inductor and flows through the resistor. During the negative half-cycle, the inductor tries to maintain current flow, leading to a decaying current in the circuit.

#### 4. **Effects of RL Load**

The presence of the inductor in the RL load smooths out the current waveform. The inductor resists changes in current, causing the current through the load to have a smoother waveform compared to the voltage waveform.

- **Inductor Behavior:** The inductor stores energy during the conduction phase and releases it when the SCR is off. This results in a continuous current flow through the load, although the current waveform is still pulsating.

- **Resistor Behavior:** The resistor causes a voltage drop proportional to the current, and together with the inductor, affects the overall shape of the output voltage and current waveforms.

### Summary

The 1-phase half-wave controlled converter with an RL load provides controlled rectification of AC voltage. By adjusting the firing angle of the SCR, the average output voltage can be controlled, which is useful in various applications requiring controlled DC power. The presence of the RL load affects the current waveform and overall performance of the converter.