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Duty Cycle for Boost Regulator (DCM) Formula

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A Duty Cycle of Boost DCM or power cycle is the fraction of one period in which a signal or system is active in a voltage regulator circuit. Check FAQs

D bo_dcm = \sqrt{(2 \cdot L x(bo_dcm) \cdot \frac{i o(bo_dcm)}{V i(bo_dcm) \cdot t c(bo_dcm)}) \cdot ((\frac{V o(bo_dcm)}{V i(bo_dcm)}) - 1)}

D_{bo_dcm} - Duty Cycle of Boost DCM?L_{x(bo_dcm)} - Critical Inductance of Boost DCM?i_{o(bo_dcm)} - Output Current of Boost DCM?V_{i(bo_dcm)} - Input Voltage of Boost DCM?t_{c(bo_dcm)} - Time Commutation of Boost DCM?V_{o(bo_dcm)} - Output Voltage of Boost DCM?

Duty Cycle for Boost Regulator (DCM) Example

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Here is how the Duty Cycle for Boost Regulator (DCM) equation looks like with Values.

Here is how the Duty Cycle for Boost Regulator (DCM) equation looks like with Units.

Here is how the Duty Cycle for Boost Regulator (DCM) equation looks like.

0.0359 = \sqrt{(2 \cdot 0.4191 \cdot \frac{1.9899}{9.71 \cdot 4.063}) \cdot ((\frac{10.006}{9.71}) - 1)}

0.0359 = \sqrt{(2 \cdot 0.4191H \cdot \frac{1.9899A}{9.71V \cdot 4.063s}) \cdot ((\frac{10.006V}{9.71V}) - 1)}

0.0359 = \sqrt{(2 \cdot 0.4191 \cdot \frac{1.9899}{9.71 \cdot 4.063}) \cdot ((\frac{10.006}{9.71}) - 1)}

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Duty Cycle for Boost Regulator (DCM) Solution

Follow our step by step solution on how to calculate Duty Cycle for Boost Regulator (DCM)?

FIRST Step Consider the formula

D bo_dcm = \sqrt{(2 \cdot L x(bo_dcm) \cdot \frac{i o(bo_dcm)}{V i(bo_dcm) \cdot t c(bo_dcm)}) \cdot ((\frac{V o(bo_dcm)}{V i(bo_dcm)}) - 1)}

Next Step Substitute values of Variables

∴

D bo_dcm = \sqrt{(2 \cdot 0.4191H \cdot \frac{1.9899A}{9.71V \cdot 4.063s}) \cdot ((\frac{10.006V}{9.71V}) - 1)}

Next Step Prepare to Evaluate

∴

D bo_dcm = \sqrt{(2 \cdot 0.4191 \cdot \frac{1.9899}{9.71 \cdot 4.063}) \cdot ((\frac{10.006}{9.71}) - 1)}

Next Step Evaluate

∴

D bo_dcm = 0.0358998528719057

LAST Step Rounding Answer

∴

D bo_dcm = 0.0359

Duty Cycle for Boost Regulator (DCM) Formula Elements

Variables

Functions

Duty Cycle of Boost DCM

A Duty Cycle of Boost DCM or power cycle is the fraction of one period in which a signal or system is active in a voltage regulator circuit.

Symbol: D_{bo_dcm}

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Duty Cycle of Boost DCM

Critical Inductance of Boost DCM

Critical Inductance of Boost DCM refers to the minimum value of the inductance required in these converters to maintain discontinuous current flow through the inductor.

Symbol: L_{x(bo_dcm)}

Measurement: InductanceUnit: H

Note: Value should be greater than 0.

Formulas to find Critical Inductance of Boost DCM

Output Current of Boost DCM

Output Current of Boost DCM is the current the amplifier draws from the signal source.

Symbol: i_{o(bo_dcm)}

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Output Current of Boost DCM

Input Voltage of Boost DCM

Input Voltage of Boost DCM is the voltage supplied to the voltage regulator circuit.

Symbol: V_{i(bo_dcm)}

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Input Voltage of Boost DCM

Time Commutation of Boost DCM

The Time Commutation of Boost DCM is the process of transferring current from one connection to another within an electric circuit such as voltage regulator circuit.

Symbol: t_{c(bo_dcm)}

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Commutation of Boost DCM

Output Voltage of Boost DCM

Output Voltage of Boost DCM signifies the voltage of the signal after it has been regulated by a voltage regulator circuit.

Symbol: V_{o(bo_dcm)}

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Output Voltage of Boost DCM

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)

Other formulas in Discontinuous Conduction Mode category

Go Output Voltage for Boost Regulator (DCM)

V o(bo_dcm) = V i(bo_dcm) + (\frac{{V i(bo_dcm)}^{2} \cdot {D bo_dcm}^{2} \cdot t c(bo_dcm)}{2 \cdot L x(bo_dcm) \cdot i o(bo_dcm)})

Go Commutation Period for Boost Regulator (DCM)

t c(bo_dcm) = (\frac{2 \cdot L x(bo_dcm) \cdot i o(bo_dcm)}{({D bo_dcm}^{2}) \cdot V i(bo_dcm)}) \cdot ((\frac{V o(bo_dcm)}{V i(bo_dcm)}) - 1)

Go Inductor Value for Boost Regulator (DCM)

L x(bo_dcm) = \frac{({V i(bo_dcm)}^{2}) \cdot ({D bo_dcm}^{2}) \cdot t c(bo_dcm)}{2 \cdot (V o(bo_dcm) - V i(bo_dcm)) \cdot i o(bo_dcm)}

Go Output Current for Boost Regulator (DCM)

i o(bo_dcm) = \frac{({V i(bo_dcm)}^{2}) \cdot {D bo_dcm}^{2} \cdot t c(bo_dcm)}{2 \cdot L x(bo_dcm) \cdot (V o(bo_dcm) - V i(bo_dcm))}

How to Evaluate Duty Cycle for Boost Regulator (DCM)?

Duty Cycle for Boost Regulator (DCM) evaluator uses Duty Cycle of Boost DCM = sqrt((2*Critical Inductance of Boost DCM*Output Current of Boost DCM/(Input Voltage of Boost DCM*Time Commutation of Boost DCM))*((Output Voltage of Boost DCM/Input Voltage of Boost DCM)-1)) to evaluate the Duty Cycle of Boost DCM, The Duty Cycle for Boost Regulator (DCM) formula is defined as the ratio of time a load or circuit is ON compared to the time the load or circuit is Off. Duty Cycle of Boost DCM is denoted by D_{bo_dcm} symbol.

How to evaluate Duty Cycle for Boost Regulator (DCM) using this online evaluator? To use this online evaluator for Duty Cycle for Boost Regulator (DCM), enter Critical Inductance of Boost DCM (L_{x(bo_dcm)}), Output Current of Boost DCM (i_{o(bo_dcm)}), Input Voltage of Boost DCM (V_{i(bo_dcm)}), Time Commutation of Boost DCM (t_{c(bo_dcm)}) & Output Voltage of Boost DCM (V_{o(bo_dcm)}) and hit the calculate button.

FAQs on Duty Cycle for Boost Regulator (DCM)

What is the formula to find Duty Cycle for Boost Regulator (DCM)?

The formula of Duty Cycle for Boost Regulator (DCM) is expressed as Duty Cycle of Boost DCM = sqrt((2*Critical Inductance of Boost DCM*Output Current of Boost DCM/(Input Voltage of Boost DCM*Time Commutation of Boost DCM))*((Output Voltage of Boost DCM/Input Voltage of Boost DCM)-1)). Here is an example- 0.03581 = sqrt((2*0.4191*1.9899/(9.71*4.063))*((10.006/9.71)-1)).

How to calculate Duty Cycle for Boost Regulator (DCM)?

With Critical Inductance of Boost DCM (L_{x(bo_dcm)}), Output Current of Boost DCM (i_{o(bo_dcm)}), Input Voltage of Boost DCM (V_{i(bo_dcm)}), Time Commutation of Boost DCM (t_{c(bo_dcm)}) & Output Voltage of Boost DCM (V_{o(bo_dcm)}) we can find Duty Cycle for Boost Regulator (DCM) using the formula - Duty Cycle of Boost DCM = sqrt((2*Critical Inductance of Boost DCM*Output Current of Boost DCM/(Input Voltage of Boost DCM*Time Commutation of Boost DCM))*((Output Voltage of Boost DCM/Input Voltage of Boost DCM)-1)). This formula also uses Square Root (sqrt) function(s).

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Duty Cycle for Boost Regulator (DCM) Formula

Duty Cycle for Boost Regulator (DCM) Example

Duty Cycle for Boost Regulator (DCM) Solution

Duty Cycle for Boost Regulator (DCM) Formula Elements

Other formulas in Discontinuous Conduction Mode category

How to Evaluate Duty Cycle for Boost Regulator (DCM)?

FAQs on Duty Cycle for Boost Regulator (DCM)

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