## Saturation Time Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
This formula uses 1 Functions, 5 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
Saturation Time - (Measured in Second) - Saturation Time is the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal.
Load Capacitance - (Measured in Farad) - Load Capacitance is the total capacitance connected to the transistor's output terminal, including external components and the MOSFET's own parasitic capacitance.
Transconductance Process Parameter - (Measured in Ampere per Square Volt) - Transconductance Process Parameter is a device-specific constant that characterizes the transistor's ability to convert a change in gate voltage to a change in output current.
High Output Voltage - (Measured in Volt) - High Output Voltage is the maximum voltage level the transistor can reach at its output terminal when fully turned on (operating in saturation).
Threshold Voltage - (Measured in Volt) - Threshold Voltage is the minimum gate-to-source voltage required in a MOSFET to turn it "on" and allow a significant current to flow.
STEP 1: Convert Input(s) to Base Unit
Transconductance Process Parameter: 4.553 Ampere per Square Volt --> 4.553 Ampere per Square Volt No Conversion Required
High Output Voltage: 3.789 Volt --> 3.789 Volt No Conversion Required
Threshold Voltage: 5.91 Volt --> 5.91 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Evaluating ... ...
Tsat = 5.63810361511811
STEP 3: Convert Result to Output's Unit
5.63810361511811 Second --> No Conversion Required
5.63810361511811 ā 5.638104 Second <-- Saturation Time
(Calculation completed in 00.021 seconds)
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Created by Vignesh Naidu
Vellore Institute of Technology (VIT), Vellore,Tamil Nadu
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## < 20 MOS Transistor Calculators

Sidewall Voltage Equivalence Factor
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
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))
Pull down Current in Saturation Region
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
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
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
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
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
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
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
Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)
Maximum Depletion Depth
Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))
Fermi Potential for N Type
Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)
Equivalent Large Signal Capacitance
Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)
Built in Potential at Depletion Region
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
Source's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*Built in Junction Potential)/([Charge-e]*Doping Concentration of Acceptor))
Substrate Bias Coefficient
Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance
Average Power Dissipated over Period of Time
Average Power = (1/Total Time Taken)*int(Voltage*Current,x,0,Total Time Taken)
Equivalent Large Signal Junction Capacitance
Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor
Work Function in MOSFET
Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)
Zero Bias Sidewall Junction Capacitance per Unit Length
Sidewall Junction Capacitance = Zero Bias Sidewall Junction Potential*Depth of Sidewall

## Saturation Time Formula

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)

## What are the Applications of Saturation Time ?

1. Circuit Speed Estimation: tsat helps estimate the propagation delay of a digital circuit. It represents the time it takes for the output voltage of a transistor to reach a specific level after receiving an input signal. Knowing this delay is crucial for understanding how fast the circuit can operate and make decisions.

2. Design Optimization: By considering tsat, circuit designers can optimize circuits for speed. Techniques like choosing transistors with higher transconductance or reducing the load capacitance can lead to faster switching and shorter saturation times.

## How to Calculate Saturation Time?

Saturation Time calculator uses 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) to calculate the Saturation Time, The Saturation Time formula is defined as the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal. Saturation Time is denoted by Tsat symbol.

How to calculate Saturation Time using this online calculator? To use this online calculator for Saturation Time, enter Load Capacitance (Cload), Transconductance Process Parameter (kn), High Output Voltage (VOH) & Threshold Voltage (VT) and hit the calculate button. Here is how the Saturation Time calculation can be explained with given input values -> 5.638104 = -2*9.77/(4.553*(3.789-5.91)^2)*int(1,x,3.789,3.789-5.91).

### FAQ

What is Saturation Time?
The Saturation Time formula is defined as the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal and is represented as Tsat = -2*Cload/(kn*(VOH-VT)^2)*int(1,x,VOH,VOH-VT) or 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). Load Capacitance is the total capacitance connected to the transistor's output terminal, including external components and the MOSFET's own parasitic capacitance, Transconductance Process Parameter is a device-specific constant that characterizes the transistor's ability to convert a change in gate voltage to a change in output current, High Output Voltage is the maximum voltage level the transistor can reach at its output terminal when fully turned on (operating in saturation) & Threshold Voltage is the minimum gate-to-source voltage required in a MOSFET to turn it "on" and allow a significant current to flow.
How to calculate Saturation Time?
The Saturation Time formula is defined as the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal is calculated using 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). To calculate Saturation Time, you need Load Capacitance (Cload), Transconductance Process Parameter (kn), High Output Voltage (VOH) & Threshold Voltage (VT). With our tool, you need to enter the respective value for Load Capacitance, Transconductance Process Parameter, High Output Voltage & Threshold Voltage 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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