Question

Give the concept of firing angle and conduction angle with a neat waveform.

Answer 1

Sure, let's dive into the concepts of firing angle and conduction angle, which are crucial in understanding the operation of phase-controlled devices like TRIACs and SCRs in power electronics.

### **1. Firing Angle**

**Definition:** The firing angle (\(\alpha\)) is the phase angle at which the gate of a thyristor (like SCR or TRIAC) is triggered to start conducting. It is measured with respect to the zero crossing of the input AC signal.

**Concept:**
- In a phase-controlled rectifier circuit, such as a phase-controlled rectifier or a TRIAC-based dimmer, the firing angle determines the portion of the AC cycle during which the device is triggered to conduct.
- By adjusting the firing angle, you can control the amount of power delivered to the load. A larger firing angle means less power is delivered, and vice versa.

### **2. Conduction Angle**

**Definition:** The conduction angle (\(\beta\)) is the duration of the AC cycle during which the device (e.g., SCR or TRIAC) remains in the conducting state after being triggered.

**Concept:**
- After the thyristor is triggered, it remains conducting until the current through it drops below a certain threshold (typically zero in an AC cycle).
- The conduction angle is the part of the AC cycle during which the device is actually conducting current.

### **Waveform Explanation**

To illustrate these concepts, consider a typical waveform of an AC voltage and the resulting voltage waveform across the load in a phase-controlled rectifier circuit.

#### **AC Voltage Input**

This waveform is a standard sinusoidal waveform with a peak voltage and a zero crossing every half cycle.

  
*Note: This is a general sinusoidal waveform for reference.*

#### **Triggered Conduction**

When the SCR or TRIAC is triggered at a firing angle (\(\alpha\)), it starts conducting at that phase angle.

- **Firing Angle (\(\alpha\)):** The angle at which the SCR or TRIAC starts conducting. For instance, if \(\alpha\) is 60°, the SCR is triggered 60° after the zero crossing of the AC waveform.

- **Conduction Angle (\(\beta\)):** The angle from the firing angle to the point where the SCR or TRIAC stops conducting. If the device conducts for 120°, then the conduction angle is 120°.

Here’s a representation of the waveforms:

1. **AC Input Voltage Waveform:**
   \[
   V_{in} = V_{peak} \sin(\omega t)
   \]

2. **Voltage Across the Load (with Firing Angle and Conduction Angle):**
   \[
   V_{load} =
   \begin{cases}
   V_{peak} \sin(\omega t) & \text{for } \alpha \leq \omega t \leq \alpha + \beta \\
   0 & \text{otherwise}
   \end{cases}
   \]

**Illustrative Waveform:**

```
        AC Input Voltage
        ___________________
       |         |         |
       |         |         |
       |         |         |
       |_________|_________|__________
              |               |        
              |               |
       Firing Angle    Conduction Angle
```

In this waveform:
- The **firing angle** is the phase angle from the start of the AC cycle to the point where the SCR or TRIAC starts conducting.
- The **conduction angle** is the duration for which the device remains conducting before it stops.

### **Summary**

- **Firing Angle (\(\alpha\))**: The phase angle at which the SCR or TRIAC begins conducting.
- **Conduction Angle (\(\beta\))**: The duration of conduction from the firing angle until the device stops conducting.

By adjusting the firing angle and conduction angle, you can control the power delivered to the load in AC power control applications.

Answer 2

Could you specify which type of waveform you're referring to—AC or DC?