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Gates on Critical Path Formula

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Gates on Critical Path are defined as the total number of the logic gate required during one cycle time in CMOS. Check FAQs

N g = D \cdot \frac{i off \cdot (10^{V bc})}{C g \cdot [BoltZ] \cdot V bc}

N_g - Gates on Critical Path?D - Duty Cycle?i_off - Off Current?V_bc - Base Collector Voltage?C_g - Capacitance of Gate to Channel?[BoltZ] - Boltzmann constant?

Gates on Critical Path Example

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Here is how the Gates on Critical Path equation looks like with Values.

Here is how the Gates on Critical Path equation looks like with Units.

Here is how the Gates on Critical Path equation looks like.

0.001 = 1.3E-25 \cdot \frac{0.01 \cdot (10^{2.02})}{5.1 \cdot 1.4E-23 \cdot 2.02}

0.001 = 1.3E-25 \cdot \frac{0.01mA \cdot (10^{2.02V})}{5.1mF \cdot 1.4E-23J/K \cdot 2.02V}

0.001 = 1.3E-25 \cdot \frac{0.01 \cdot (10^{2.02})}{5.1 \cdot 1.4E-23 \cdot 2.02}

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Gates on Critical Path Solution

Follow our step by step solution on how to calculate Gates on Critical Path?

FIRST Step Consider the formula

N g = D \cdot \frac{i off \cdot (10^{V bc})}{C g \cdot [BoltZ] \cdot V bc}

Next Step Substitute values of Variables

∴

N g = 1.3E-25 \cdot \frac{0.01mA \cdot (10^{2.02V})}{5.1mF \cdot [BoltZ] \cdot 2.02V}

Next Step Substitute values of Constants

∴

N g = 1.3E-25 \cdot \frac{0.01mA \cdot (10^{2.02V})}{5.1mF \cdot 1.4E-23J/K \cdot 2.02V}

Next Step Convert Units

∴

N g = 1.3E-25 \cdot \frac{1E-5A \cdot (10^{2.02V})}{0.0051F \cdot 1.4E-23J/K \cdot 2.02V}

Next Step Prepare to Evaluate

∴

N g = 1.3E-25 \cdot \frac{1E-5 \cdot (10^{2.02})}{0.0051 \cdot 1.4E-23 \cdot 2.02}

Next Step Evaluate

∴

N g = 0.000957058919420363

LAST Step Rounding Answer

∴

N g = 0.001

Gates on Critical Path Formula Elements

Variables

Constants

Gates on Critical Path

Gates on Critical Path are defined as the total number of the logic gate required during one cycle time in CMOS.

Symbol: N_g

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Gates on Critical Path

Duty Cycle

A Duty cycle or power cycle is the fraction of one period in which a signal or system is active.

Symbol: D

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Duty Cycle

Off Current

Off Current of a switch is a non-exist value in the reality. Real switches have normally very small off current which some times called the leakage current.

Symbol: i_off

Measurement: Electric CurrentUnit: mA

Note: Value should be greater than 0.

Formulas to find Off Current

Base Collector Voltage

Base Collector Voltage is a crucial parameter in transistor biasing. It refers to the voltage difference between the base and collector terminals of the transistor when it is in its active state.

Symbol: V_bc

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Base Collector Voltage

Capacitance of Gate to Channel

Capacitance of Gate to Channel is the capacitance due to the overlap of the source and the channel regions by the polysilicon gate and is independent of applied voltage.

Symbol: C_g

Measurement: CapacitanceUnit: mF

Note: Value should be greater than 0.

Formulas to find Capacitance of Gate to Channel

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

Other formulas in CMOS Power Metrics category

Go Activity Factor

α = \frac{P s}{C \cdot {V bc}^{2} \cdot f}

Go Switching Power

P s = α \cdot (C \cdot {V bc}^{2} \cdot f)

Go Dynamic Power in CMOS

P dyn = P sc + P s

Go Short-Circuit Power in CMOS

P sc = P dyn - P s

How to Evaluate Gates on Critical Path?

Gates on Critical Path evaluator uses Gates on Critical Path = Duty Cycle*(Off Current*(10^Base Collector Voltage))/(Capacitance of Gate to Channel*[BoltZ]*Base Collector Voltage) to evaluate the Gates on Critical Path, The Gates on critical path formula is defined as the total number of the logic gate required during one cycle time in CMOS. Gates on Critical Path is denoted by N_g symbol.

How to evaluate Gates on Critical Path using this online evaluator? To use this online evaluator for Gates on Critical Path, enter Duty Cycle (D), Off Current (i_off), Base Collector Voltage (V_bc) & Capacitance of Gate to Channel (C_g) and hit the calculate button.

FAQs on Gates on Critical Path

What is the formula to find Gates on Critical Path?

The formula of Gates on Critical Path is expressed as Gates on Critical Path = Duty Cycle*(Off Current*(10^Base Collector Voltage))/(Capacitance of Gate to Channel*[BoltZ]*Base Collector Voltage). Here is an example- 0.957059 = 1.3E-25*(1E-05*(10^2.02))/(5.1E-06*[BoltZ]*2.02).

How to calculate Gates on Critical Path?

With Duty Cycle (D), Off Current (i_off), Base Collector Voltage (V_bc) & Capacitance of Gate to Channel (C_g) we can find Gates on Critical Path using the formula - Gates on Critical Path = Duty Cycle*(Off Current*(10^Base Collector Voltage))/(Capacitance of Gate to Channel*[BoltZ]*Base Collector Voltage). This formula also uses Boltzmann constant .

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Gates on Critical Path Formula

Gates on Critical Path Example

Gates on Critical Path Solution

Gates on Critical Path Formula Elements

Other formulas in CMOS Power Metrics category

How to Evaluate Gates on Critical Path?

FAQs on Gates on Critical Path

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