Average Load Voltage for Calculus Function Calculator

Formula Used:

\[ V_{avg(thy)} = \frac{1}{2\pi} \int_{\alpha_{f(thy)}}^{\pi} V_{in(thy)} \cdot \sin(x) \, dx \]

Average Voltage Thyristor Converter:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Average Load Voltage Formula?

The Average Load Voltage formula calculates the average output voltage of a thyristor-based converter circuit over one complete cycle. It considers the peak input voltage and the firing angle at which the thyristor is triggered.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ V_{avg(thy)} = \frac{1}{2\pi} \int_{\alpha_{f(thy)}}^{\pi} V_{in(thy)} \cdot \sin(x) \, dx \]

Where:

\( V_{avg(thy)} \) — Average Voltage Thyristor Converter (Volt)
\( V_{in(thy)} \) — Peak Input Voltage Thyristor Converter (Volt)
\( \alpha_{f(thy)} \) — Firing Angle of Thyristor Converter (Radian)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula integrates the sinusoidal voltage waveform from the firing angle to π radians, then averages it over the full cycle.

3. Importance of Average Voltage Calculation

Details: Calculating average load voltage is essential for designing and analyzing thyristor-based power converters, determining output power characteristics, and ensuring proper circuit operation in AC-DC conversion applications.

4. Using the Calculator

Tips: Enter peak input voltage in volts and firing angle in radians. The firing angle should be between 0 and π radians (0-180 degrees). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of firing angle values?
A: The firing angle typically ranges from 0 to π radians (0-180 degrees) for half-wave thyristor converters.

Q2: How does firing angle affect the average voltage?
A: As the firing angle increases, the average output voltage decreases. At 0 radians, maximum voltage is obtained; at π radians, output voltage is zero.

Q3: Can this formula be used for full-wave converters?
A: This specific formula is for half-wave converters. Full-wave converters use a modified formula that integrates over a different range.

Q4: What are typical applications of thyristor converters?
A: Thyristor converters are used in motor speed control, power supplies, lighting control, and various industrial AC-DC conversion applications.

Q5: Why is the integration performed from firing angle to π?
A: The thyristor conducts only during the positive half-cycle from the firing angle to π radians, when the anode voltage is positive relative to the cathode.