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Form Factor of Half Wave Thyristor Rectifier with R Load Formula

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Form Factor is defined as is the ratio of the RMS value to the average value. Check FAQs

FF = \frac{{(\frac{1}{π} \cdot ((π - α r) + \frac{\sin (2 \cdot α d)}{2}))}^{\frac{1}{2}}}{\frac{1}{π} \cdot (1 + \cos (α d))}

FF - Form Factor?α_r - Trigger Angle in Radians?α_d - Trigger Angle in Degree?π - Archimedes' constant?

Form Factor of Half Wave Thyristor Rectifier with R Load Example

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Here is how the Form Factor of Half Wave Thyristor Rectifier with R Load equation looks like with Values.

Here is how the Form Factor of Half Wave Thyristor Rectifier with R Load equation looks like with Units.

Here is how the Form Factor of Half Wave Thyristor Rectifier with R Load equation looks like.

1.7379 = \frac{{(\frac{1}{3.1416} \cdot ((3.1416 - 0.84) + \frac{\sin (2 \cdot 45)}{2}))}^{\frac{1}{2}}}{\frac{1}{3.1416} \cdot (1 + \cos (45))}

1.7379 = \frac{{(\frac{1}{3.1416} \cdot ((3.1416 - 0.84rad) + \frac{\sin (2 \cdot 45°)}{2}))}^{\frac{1}{2}}}{\frac{1}{3.1416} \cdot (1 + \cos (45°))}

1.7379 = \frac{{(\frac{1}{3.1416} \cdot ((3.1416 - 0.84) + \frac{\sin (2 \cdot 45)}{2}))}^{\frac{1}{2}}}{\frac{1}{3.1416} \cdot (1 + \cos (45))}

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Form Factor of Half Wave Thyristor Rectifier with R Load Solution

Follow our step by step solution on how to calculate Form Factor of Half Wave Thyristor Rectifier with R Load?

FIRST Step Consider the formula

FF = \frac{{(\frac{1}{π} \cdot ((π - α r) + \frac{\sin (2 \cdot α d)}{2}))}^{\frac{1}{2}}}{\frac{1}{π} \cdot (1 + \cos (α d))}

Next Step Substitute values of Variables

∴

FF = \frac{{(\frac{1}{π} \cdot ((π - 0.84rad) + \frac{\sin (2 \cdot 45°)}{2}))}^{\frac{1}{2}}}{\frac{1}{π} \cdot (1 + \cos (45°))}

Next Step Substitute values of Constants

∴

FF = \frac{{(\frac{1}{3.1416} \cdot ((3.1416 - 0.84rad) + \frac{\sin (2 \cdot 45°)}{2}))}^{\frac{1}{2}}}{\frac{1}{3.1416} \cdot (1 + \cos (45°))}

Next Step Convert Units

∴

FF = \frac{{(\frac{1}{3.1416} \cdot ((3.1416 - 0.84rad) + \frac{\sin (2 \cdot 0.7854rad)}{2}))}^{\frac{1}{2}}}{\frac{1}{3.1416} \cdot (1 + \cos (0.7854rad))}

Next Step Prepare to Evaluate

∴

FF = \frac{{(\frac{1}{3.1416} \cdot ((3.1416 - 0.84) + \frac{\sin (2 \cdot 0.7854)}{2}))}^{\frac{1}{2}}}{\frac{1}{3.1416} \cdot (1 + \cos (0.7854))}

Next Step Evaluate

∴

FF = 1.73786782926578

LAST Step Rounding Answer

∴

FF = 1.7379

Form Factor of Half Wave Thyristor Rectifier with R Load Formula Elements

Variables

Constants

Functions

Form Factor

Form Factor is defined as is the ratio of the RMS value to the average value.

Symbol: FF

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Form Factor

Trigger Angle in Radians

Trigger Angle in Radians is defined as the firing angle of a thyristor in radians.

Symbol: α_r

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Trigger Angle in Radians

Trigger Angle in Degree

Trigger Angle in Degree it gives the firing angle of thyristor in degree.

Symbol: α_d

Measurement: AngleUnit: °

Note: Value should be less than 181.

Formulas to find Trigger Angle in Degree

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Half Wave Controlled Rectifiers category

Go RMS Output Voltage of Half Wave Thyristor Rectifier with R Load

V rms(half) = \frac{V o(max) \cdot \sqrt{π - α r + (0.5 \cdot \sin (2 \cdot α d))}}{2 \cdot \sqrt{π}}

Go Average Voltage of Half Wave Thyristor Rectifier with RL Load

V avg(half) = (\frac{V o(max)}{2 \cdot π}) \cdot (\cos (α d) - \cos (β d))

Go Voltage Ripple Factor of Half Wave Thyristor Rectifier with R Load

RF = \sqrt{{FF}^{2} - 1}

Go Average Load Voltage of Half Wave Thyristor Rectifier with RLE Load

V L(half) = (\frac{V o(max)}{2 \cdot π}) \cdot (\cos (α d) + \cos (β d)) + (\frac{E b}{2}) \cdot (1 + (\frac{θ r + α r}{π}))

How to Evaluate Form Factor of Half Wave Thyristor Rectifier with R Load?

Form Factor of Half Wave Thyristor Rectifier with R Load evaluator uses Form Factor = ((1/pi*((pi-Trigger Angle in Radians)+sin(2*Trigger Angle in Degree)/2))^(1/2))/(1/pi*(1+cos(Trigger Angle in Degree))) to evaluate the Form Factor, The Form Factor of Half Wave Thyristor Rectifier with R Load formula is defined as degree of closeness of rectified voltage to ideal dc voltage waveform in half wave rectifier. Form Factor is denoted by FF symbol.

How to evaluate Form Factor of Half Wave Thyristor Rectifier with R Load using this online evaluator? To use this online evaluator for Form Factor of Half Wave Thyristor Rectifier with R Load, enter Trigger Angle in Radians (α_r) & Trigger Angle in Degree (α_d) and hit the calculate button.

FAQs on Form Factor of Half Wave Thyristor Rectifier with R Load

What is the formula to find Form Factor of Half Wave Thyristor Rectifier with R Load?

The formula of Form Factor of Half Wave Thyristor Rectifier with R Load is expressed as Form Factor = ((1/pi*((pi-Trigger Angle in Radians)+sin(2*Trigger Angle in Degree)/2))^(1/2))/(1/pi*(1+cos(Trigger Angle in Degree))). Here is an example- 1.737868 = ((1/pi*((pi-0.84)+sin(2*0.785398163397301)/2))^(1/2))/(1/pi*(1+cos(0.785398163397301))).

How to calculate Form Factor of Half Wave Thyristor Rectifier with R Load?

With Trigger Angle in Radians (α_r) & Trigger Angle in Degree (α_d) we can find Form Factor of Half Wave Thyristor Rectifier with R Load using the formula - Form Factor = ((1/pi*((pi-Trigger Angle in Radians)+sin(2*Trigger Angle in Degree)/2))^(1/2))/(1/pi*(1+cos(Trigger Angle in Degree))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

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