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RMS Harmonic Current for PWM Control Formula

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RMS nth Harmonic Current is the Effective Value of the Harmonic Component of the Current Waveform at a Frequency that is an Integer Multiple (n) of the Fundamental Frequency of the PWM Signal. Check FAQs

I n = (\frac{\sqrt{2} \cdot I a}{π}) \cdot \sum (x, 1, p, (\cos (n \cdot α k)) - (\cos (n \cdot β k)))

I_n - RMS nth Harmonic Current?I_a - Armature Current?p - Number of Pulse in Half-cycle of PWM?n - Harmonic Order?α_k - Excitation Angle?β_k - Symmetrical Angle?π - Archimedes' constant?

RMS Harmonic Current for PWM Control Example

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Here is how the RMS Harmonic Current for PWM Control equation looks like with Values.

Here is how the RMS Harmonic Current for PWM Control equation looks like with Units.

Here is how the RMS Harmonic Current for PWM Control equation looks like.

2.971 = (\frac{\sqrt{2} \cdot 2.2}{3.1416}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 30)) - (\cos (3 \cdot 60)))

2.971A = (\frac{\sqrt{2} \cdot 2.2A}{3.1416}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 30°)) - (\cos (3 \cdot 60°)))

2.971 = (\frac{\sqrt{2} \cdot 2.2}{3.1416}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 30)) - (\cos (3 \cdot 60)))

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RMS Harmonic Current for PWM Control Solution

Follow our step by step solution on how to calculate RMS Harmonic Current for PWM Control?

FIRST Step Consider the formula

I n = (\frac{\sqrt{2} \cdot I a}{π}) \cdot \sum (x, 1, p, (\cos (n \cdot α k)) - (\cos (n \cdot β k)))

Next Step Substitute values of Variables

∴

I n = (\frac{\sqrt{2} \cdot 2.2A}{π}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 30°)) - (\cos (3 \cdot 60°)))

Next Step Substitute values of Constants

∴

I n = (\frac{\sqrt{2} \cdot 2.2A}{3.1416}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 30°)) - (\cos (3 \cdot 60°)))

Next Step Convert Units

∴

I n = (\frac{\sqrt{2} \cdot 2.2A}{3.1416}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 0.5236rad)) - (\cos (3 \cdot 1.0472rad)))

Next Step Prepare to Evaluate

∴

I n = (\frac{\sqrt{2} \cdot 2.2}{3.1416}) \cdot \sum (x, 1, 3, (\cos (3 \cdot 0.5236)) - (\cos (3 \cdot 1.0472)))

Next Step Evaluate

∴

I n = 2.97104384331933A

LAST Step Rounding Answer

∴

I n = 2.971A

RMS Harmonic Current for PWM Control Formula Elements

Variables

Constants

Functions

RMS nth Harmonic Current

RMS nth Harmonic Current is the Effective Value of the Harmonic Component of the Current Waveform at a Frequency that is an Integer Multiple (n) of the Fundamental Frequency of the PWM Signal.

Symbol: I_n

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find RMS nth Harmonic Current

Armature Current

Armature Current DC motor is defined as the armature current developed in an electrical dc motor due to the rotation of rotor.

Symbol: I_a

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Armature Current

Number of Pulse in Half-cycle of PWM

Number of Pulse in Half-cycle of PWM (Pulse Width Modulation) converter refers to the count of pulses generated within half of the waveform period.

Symbol: p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Pulse in Half-cycle of PWM

Harmonic Order

Harmonic Order is Defined as the the Integer Multiple of the Fundamental Frequency (f) of the PWM Signal. It indicates which Harmonic Component of the Current Waveform is being analyzed.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Harmonic Order

Excitation Angle

Excitation Angle is the angle at which the PWM Converter begins to Produce Output Voltage or Current.

Symbol: α_k

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Excitation Angle

Symmetrical Angle

Symmetrical Angle is the Angle at which the PWM Converter produces Symmetrical Output Waveforms with respect to the AC Input Waveform.

Symbol: β_k

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Symmetrical Angle

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

cos

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

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

sum

Summation or sigma (∑) notation is a method used to write out a long sum in a concise way.

Syntax: sum(i, from, to, expr)

Other formulas in Power Converter Characteristics category

Go DC Output Voltage for First Converter

V out(first) = \frac{2 \cdot V in(dual) \cdot (\cos (α 1(dual)))}{π}

Go DC Output Voltage of Second Converter

V out(second) = \frac{2 \cdot V in(dual) \cdot (\cos (α 2(dual)))}{π}

Go Average DC Output Voltage of Single Phase Full Converter

V avg-dc(full) = \frac{2 \cdot V m-dc(full) \cdot \cos (α full)}{π}

Go RMS Output Voltage of Single Phase Full Converter

V rms(full) = \frac{V m(full)}{\sqrt{2}}

How to Evaluate RMS Harmonic Current for PWM Control?

RMS Harmonic Current for PWM Control evaluator uses RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle))) to evaluate the RMS nth Harmonic Current, The RMS Harmonic Current for PWM Control formula is defined as the effective value of the harmonic component of the current waveform at a frequency that is an integer multiple (n) of the fundamental frequency of the PWM signal. RMS nth Harmonic Current is denoted by I_n symbol.

How to evaluate RMS Harmonic Current for PWM Control using this online evaluator? To use this online evaluator for RMS Harmonic Current for PWM Control, enter Armature Current (I_a), Number of Pulse in Half-cycle of PWM (p), Harmonic Order (n), Excitation Angle (α_k) & Symmetrical Angle (β_k) and hit the calculate button.

FAQs on RMS Harmonic Current for PWM Control

What is the formula to find RMS Harmonic Current for PWM Control?

The formula of RMS Harmonic Current for PWM Control is expressed as RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle))). Here is an example- -4.058521 = ((sqrt(2)*2.2)/pi)*sum(x,1,3,(cos(3*0.5235987755982))-(cos(3*1.0471975511964))).

How to calculate RMS Harmonic Current for PWM Control?

With Armature Current (I_a), Number of Pulse in Half-cycle of PWM (p), Harmonic Order (n), Excitation Angle (α_k) & Symmetrical Angle (β_k) we can find RMS Harmonic Current for PWM Control using the formula - RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle))). This formula also uses Archimedes' constant and , Cosine (cos), Square Root (sqrt), Summation Notation (sum) function(s).

Can the RMS Harmonic Current for PWM Control be negative?

Yes, the RMS Harmonic Current for PWM Control, measured in Electric Current can be negative.

Which unit is used to measure RMS Harmonic Current for PWM Control?

RMS Harmonic Current for PWM Control is usually measured using the Ampere[A] for Electric Current. Milliampere[A], Microampere[A], Centiampere[A] are the few other units in which RMS Harmonic Current for PWM Control can be measured.

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RMS Harmonic Current for PWM Control Formula

RMS Harmonic Current for PWM Control Example

RMS Harmonic Current for PWM Control Solution

RMS Harmonic Current for PWM Control Formula Elements

Other formulas in Power Converter Characteristics category

How to Evaluate RMS Harmonic Current for PWM Control?

FAQs on RMS Harmonic Current for PWM Control

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