Equivalent Large Signal Capacitance Calculator

✖Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event.ⓘ Final Voltage [V₂]			+10% -10%
✖Initial Voltage refer to the voltage present at a specific point in a circuit at the beginning of a certain operation or under specific conditions.ⓘ Initial Voltage [V₁]			+10% -10%
✖Junction Capacitance refers to the capacitance arising from the depletion region between the source/drain terminals and the substrate.ⓘ Junction Capacitance [C_j]			+10% -10%

✖Equivalent Large Signal Capacitance is a simplified model used to represent the combined effect of the junction capacitances at low frequencies (large signal regime).ⓘ Equivalent Large Signal Capacitance [C_eq]

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Formula

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Equivalent Large Signal Capacitance

Formula

`"C"_{"eq"} = (1/("V"_{"2"}-"V"_{"1"}))*int("C"_{"j"}*x,x,"V"_{"1"},"V"_{"2"})`

Example

`"0.000549F"=(1/("6.135nV"-"5.42nV"))*int("95009F"*x,x,"5.42nV","6.135nV")`

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Equivalent Large Signal Capacitance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)
C_eq = (1/(V₂-V₁))*int(C_j*x,x,V₁,V₂)
This formula uses 1 Functions, 4 Variables

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Equivalent Large Signal Capacitance - (Measured in Farad) - Equivalent Large Signal Capacitance is a simplified model used to represent the combined effect of the junction capacitances at low frequencies (large signal regime).
Final Voltage - (Measured in Volt) - Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event.
Initial Voltage - (Measured in Volt) - Initial Voltage refer to the voltage present at a specific point in a circuit at the beginning of a certain operation or under specific conditions.
Junction Capacitance - (Measured in Farad) - Junction Capacitance refers to the capacitance arising from the depletion region between the source/drain terminals and the substrate.

STEP 1: Convert Input(s) to Base Unit

Final Voltage: 6.135 Nanovolt --> 6.135E-09 Volt (Check conversion here)
Initial Voltage: 5.42 Nanovolt --> 5.42E-09 Volt (Check conversion here)
Junction Capacitance: 95009 Farad --> 95009 Farad No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_eq = (1/(V₂-V₁))*int(C_j*x,x,V₁,V₂) --> (1/(6.135E-09-5.42E-09))*int(95009*x,x,5.42E-09,6.135E-09)

Evaluating ... ...

C_eq = 0.0005489144975

STEP 3: Convert Result to Output's Unit

0.0005489144975 Farad --> No Conversion Required

FINAL ANSWER

0.0005489144975 ≈ 0.000549 Farad <-- Equivalent Large Signal Capacitance

(Calculation completed in 00.008 seconds)

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Created by Vignesh Naidu

Vellore Institute of Technology (VIT), Vellore,Tamil Nadu

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< 21 MOS Transistor Calculators

Sidewall Voltage Equivalence Factor

Go Sidewall Voltage Equivalence Factor = -(2*sqrt(Built in Potential of Sidewall Junctions)/(Final Voltage-Initial Voltage)*(sqrt(Built in Potential of Sidewall Junctions-Final Voltage)-sqrt(Built in Potential of Sidewall Junctions-Initial Voltage)))

Pull down Current in Linear Region

Go Linear Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(2*(Gate Source Voltage-Threshold Voltage)*Output Voltage-Output Voltage^2))

Node Voltage at Given Instance

Go Node Voltage at Given Instance = (Transconductance Factor/Node Capacitance)*int(exp(-(1/(Node Resistance*Node Capacitance))*(Time Period-x))*Current Flowing into Node*x,x,0,Time Period)

Pull down Current in Saturation Region

Go Saturation Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(Gate Source Voltage-Threshold Voltage)^2)

Saturation Time

Go Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage)

Drain Current Flowing through MOS Transistor

Go Drain Current = (Channel Width/Channel Length)*Electron Mobility*Oxide Capacitance*int((Gate Source Voltage-x-Threshold Voltage),x,0,Drain Source Voltage)

Time Delay when NMOS Operates in Linear Region

Go Linear Region in Time Delay = -2*Junction Capacitance*int(1/(Transconductance Process Parameter*(2*(Input Voltage-Threshold Voltage)*x-x^2)),x,Initial Voltage,Final Voltage)

Depletion Region Charge Density

Go Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential)))

Depth of Depletion Region Associated with Drain

Go Drain's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*(Built in Junction Potential+Drain Source Voltage))/([Charge-e]*Doping Concentration of Acceptor))

Drain Current in Saturation Region in MOS Transistor

Go Saturation Region Drain Current = Channel Width*Saturation Electron Drift Velocity*int(Charge*Short Channel Parameter,x,0,Effective Channel Length)

Fermi Potential for P Type

Go Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)

Maximum Depletion Depth

Go Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))

Fermi Potential for N Type

Go Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)

Equivalent Large Signal Capacitance

Go Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)

Built in Potential at Depletion Region

Go Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential)))

Depth of Depletion Region Associated with Source

Go Source's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*Built in Junction Potential)/([Charge-e]*Doping Concentration of Acceptor))

Substrate Bias Coefficient

Go Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance

Average Power Dissipated over Period of Time

Go Average Power = (1/Total Time Taken)*int(Voltage*Current,x,0,Total Time Taken)

Equivalent Large Signal Junction Capacitance

Go Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor

Work Function in MOSFET

Go Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)

Zero Bias Sidewall Junction Capacitance per Unit Length

Go Sidewall Junction Capacitance = Zero Bias Sidewall Junction Potential*Depth of Sidewall

Equivalent Large Signal Capacitance Formula

Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)
C_eq = (1/(V₂-V₁))*int(C_j*x,x,V₁,V₂)

What are the Applications of Equivalent Large Signal Capacitance ?

1. Circuit analysis and design: It simplifies calculations of charging and discharging times in MOSFET circuits, aiding in predicting switching speeds and transient behavior.

2. SPICE simulations: SPICE (Simulation Program with Integrated Circuit Emphasis) is a widely used software for circuit analysis. SPICE models for MOSFETs often include this as a parameter to represent the low-frequency capacitance.

How to Calculate Equivalent Large Signal Capacitance?

Equivalent Large Signal Capacitance calculator uses Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage) to calculate the Equivalent Large Signal Capacitance, The Equivalent Large Signal Capacitance formula is defined as a simplified model used to represent the combined effect of the junction capacitances at low frequencies (large signal regime). Equivalent Large Signal Capacitance is denoted by C_eq symbol.

How to calculate Equivalent Large Signal Capacitance using this online calculator? To use this online calculator for Equivalent Large Signal Capacitance, enter Final Voltage (V₂), Initial Voltage (V₁) & Junction Capacitance (C_j) and hit the calculate button. Here is how the Equivalent Large Signal Capacitance calculation can be explained with given input values -> 0.000549 = (1/(6.135E-09-5.42E-09))*int(95009*x,x,5.42E-09,6.135E-09).

FAQ

What is Equivalent Large Signal Capacitance?

The Equivalent Large Signal Capacitance formula is defined as a simplified model used to represent the combined effect of the junction capacitances at low frequencies (large signal regime) and is represented as C_eq = (1/(V₂-V₁))*int(C_j*x,x,V₁,V₂) or Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage). Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event, Initial Voltage refer to the voltage present at a specific point in a circuit at the beginning of a certain operation or under specific conditions & Junction Capacitance refers to the capacitance arising from the depletion region between the source/drain terminals and the substrate.

How to calculate Equivalent Large Signal Capacitance?

The Equivalent Large Signal Capacitance formula is defined as a simplified model used to represent the combined effect of the junction capacitances at low frequencies (large signal regime) is calculated using Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage). To calculate Equivalent Large Signal Capacitance, you need Final Voltage (V₂), Initial Voltage (V₁) & Junction Capacitance (C_j). With our tool, you need to enter the respective value for Final Voltage, Initial Voltage & Junction Capacitance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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