Time Delay when NMOS Operates in Linear Region Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
tdelay = -2*Cj*int(1/(kn*(2*(Vi-VT)*x-x^2)),x,V1,V2)
This formula uses 1 Functions, 7 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
Linear Region in Time Delay - (Measured in Second) - Linear Region in Time Delay is defined as the delay that arises from charging and discharging of capacitors connected to the NMOS during switching events.
Junction Capacitance - (Measured in Farad) - Junction Capacitance refers to the capacitance arising from the depletion region between the source/drain terminals and the substrate.
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.
Input Voltage - (Measured in Volt) - Input Voltage is the electrical potential difference applied to the input terminals of a component or system.
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.
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.
Final Voltage - (Measured in Volt) - Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event.
STEP 1: Convert Input(s) to Base Unit
Junction Capacitance: 95009 Farad --> 95009 Farad No Conversion Required
Transconductance Process Parameter: 4.553 Ampere per Square Volt --> 4.553 Ampere per Square Volt No Conversion Required
Input Voltage: 2.25 Volt --> 2.25 Volt No Conversion Required
Threshold Voltage: 5.91 Volt --> 5.91 Volt No Conversion Required
Initial Voltage: 5.42 Nanovolt --> 5.42E-09 Volt (Check conversion here)
Final Voltage: 6.135 Nanovolt --> 6.135E-09 Volt (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tdelay = -2*Cj*int(1/(kn*(2*(Vi-VT)*x-x^2)),x,V1,V2) --> -2*95009*int(1/(4.553*(2*(2.25-5.91)*x-x^2)),x,5.42E-09,6.135E-09)
Evaluating ... ...
tdelay = 706.520454377221
STEP 3: Convert Result to Output's Unit
706.520454377221 Second --> No Conversion Required
FINAL ANSWER
706.520454377221 706.5205 Second <-- Linear Region in Time Delay
(Calculation completed in 00.004 seconds)

Credits

Created by Vignesh Naidu
Vellore Institute of Technology (VIT), Vellore,Tamil Nadu
Vignesh Naidu has created this Calculator and 25+ more calculators!
Verified by Dipanjona Mallick
Heritage Insitute of technology (HITK), Kolkata
Dipanjona Mallick has verified this Calculator and 50+ more calculators!

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

Time Delay when NMOS Operates in Linear Region Formula

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)
tdelay = -2*Cj*int(1/(kn*(2*(Vi-VT)*x-x^2)),x,V1,V2)

What are the Applications of Time Delay when NMOS Operates in Linear Region ?

1. Analog Signal Processing Circuits: Certain analog circuits, like integrators or differentiators, rely on the charging and discharging characteristics of capacitors. By using an NMOS transistor in the linear region as part of the charging/discharging path, the gate voltage can control the rate of this process. This can indirectly influence the overall time delay experienced by the signal within the circuit.

2. Voltage-Controlled Oscillators (VCOs): Some VCO designs incorporate NMOS transistors in their control circuitry. By adjusting the gate voltage of the NMOS, we can affect the charging/discharging of capacitors within the oscillator loop. This can influence the oscillation frequency, which is indirectly related to the time delay between cycles.

How to Calculate Time Delay when NMOS Operates in Linear Region?

Time Delay when NMOS Operates in Linear Region calculator uses 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) to calculate the Linear Region in Time Delay, The Time Delay when NMOS Operates in Linear Region formula is defined as the delay that arises from charging and discharging of capacitors connected to the NMOS during switching events. Linear Region in Time Delay is denoted by tdelay symbol.

How to calculate Time Delay when NMOS Operates in Linear Region using this online calculator? To use this online calculator for Time Delay when NMOS Operates in Linear Region, enter Junction Capacitance (Cj), Transconductance Process Parameter (kn), Input Voltage (Vi), Threshold Voltage (VT), Initial Voltage (V1) & Final Voltage (V2) and hit the calculate button. Here is how the Time Delay when NMOS Operates in Linear Region calculation can be explained with given input values -> 706.5205 = -2*95009*int(1/(4.553*(2*(2.25-5.91)*x-x^2)),x,5.42E-09,6.135E-09).

FAQ

What is Time Delay when NMOS Operates in Linear Region?
The Time Delay when NMOS Operates in Linear Region formula is defined as the delay that arises from charging and discharging of capacitors connected to the NMOS during switching events and is represented as tdelay = -2*Cj*int(1/(kn*(2*(Vi-VT)*x-x^2)),x,V1,V2) or 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). Junction Capacitance refers to the capacitance arising from the depletion region between the source/drain terminals and the substrate, 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, Input Voltage is the electrical potential difference applied to the input terminals of a component or system, Threshold Voltage is the minimum gate-to-source voltage required in a MOSFET to turn it "on" and allow a significant current to flow, 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 & Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event.
How to calculate Time Delay when NMOS Operates in Linear Region?
The Time Delay when NMOS Operates in Linear Region formula is defined as the delay that arises from charging and discharging of capacitors connected to the NMOS during switching events is calculated using 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). To calculate Time Delay when NMOS Operates in Linear Region, you need Junction Capacitance (Cj), Transconductance Process Parameter (kn), Input Voltage (Vi), Threshold Voltage (VT), Initial Voltage (V1) & Final Voltage (V2). With our tool, you need to enter the respective value for Junction Capacitance, Transconductance Process Parameter, Input Voltage, Threshold Voltage, Initial Voltage & Final 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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