## Pull down Current in Linear Region Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
ID(linear) = sum(x,0,n,(μn*Cox/2)*(W/L)*(2*(VGS-VT)*Vout-Vout^2))
This formula uses 1 Functions, 9 Variables
Functions Used
sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)
Variables Used
Linear Region Pull Down Current - (Measured in Ampere) - Linear Region Pull Down Current is the current through the resistor is when a pull-down resistor is used with an N-channel MOSFET in linear mode.
Number of Parallel Driver Transistors - Number of Parallel Driver Transistors refers to the number of parallel driver transistors in the circuit.
Electron Mobility - (Measured in Square Meter per Volt per Second) - Electron Mobility in MOSFET describes how easily electrons can move through the channel, directly impacting the current flow for a given voltage.
Oxide Capacitance - (Measured in Farad) - Oxide Capacitance refers to the capacitance associated with the insulating oxide layer in a Metal-Oxide-Semiconductor (MOS) structure, such as in MOSFETs.
Channel Width - (Measured in Meter) - Channel Width represents the width of the conducting channel within a MOSFET, directly affecting the amount of current it can handle.
Channel Length - (Measured in Meter) - Channel Length in a MOSFET is the distance between the source and drain regions, determining how easily current flows and impacting transistor performance.
Gate Source Voltage - (Measured in Volt) - Gate Source Voltage is the voltage applied between the gate and source terminals of a MOSFET.
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.
Output Voltage - (Measured in Volt) - Output Voltage in an n-channel MOSFET circuit with a pull-down resistor, Vout (output voltage) refers to the voltage at the drain terminal of the MOSFET.
STEP 1: Convert Input(s) to Base Unit
Number of Parallel Driver Transistors: 11 --> No Conversion Required
Electron Mobility: 9.92 Square Meter per Volt per Second --> 9.92 Square Meter per Volt per Second No Conversion Required
Channel Width: 2.678 Meter --> 2.678 Meter No Conversion Required
Channel Length: 3.45 Meter --> 3.45 Meter No Conversion Required
Gate Source Voltage: 29.65 Volt --> 29.65 Volt No Conversion Required
Threshold Voltage: 5.91 Volt --> 5.91 Volt No Conversion Required
Output Voltage: 4.89 Volt --> 4.89 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ID(linear) = sum(x,0,n,(μn*Cox/2)*(W/L)*(2*(VGS-VT)*Vout-Vout^2)) --> sum(x,0,11,(9.92*3.9/2)*(2.678/3.45)*(2*(29.65-5.91)*4.89-4.89^2))
Evaluating ... ...
ID(linear) = 37526.2792793155
STEP 3: Convert Result to Output's Unit
37526.2792793155 Ampere --> No Conversion Required
37526.2792793155 37526.28 Ampere <-- Linear Region Pull Down Current
(Calculation completed in 00.020 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
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))
Node Voltage at Given Instance
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
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

## Pull down Current in Linear Region Formula

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))
ID(linear) = sum(x,0,n,(μn*Cox/2)*(W/L)*(2*(VGS-VT)*Vout-Vout^2))

## What are the Applications of Pull Down Current in Linear Region ?

1. Defining Default State in Logic Circuits: Pull-down resistors with N-channel MOSFETs set the default output state to logic low (0V) in digital circuits when no external signal is applied.

2. Biasing for Analog Amplification: In some analog amplifier circuits, a pull-down resistor can bias the MOSFET in the linear region for proper signal amplification.

## How to Calculate Pull down Current in Linear Region?

Pull down Current in Linear Region calculator uses 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)) to calculate the Linear Region Pull Down Current, The Pull down Current in Linear Region formula is defined as the current through the resistor is when a pull-down resistor is used with an N-channel MOSFET in linear mode. Linear Region Pull Down Current is denoted by ID(linear) symbol.

How to calculate Pull down Current in Linear Region using this online calculator? To use this online calculator for Pull down Current in Linear Region, enter Number of Parallel Driver Transistors (n), Electron Mobility n), Oxide Capacitance (Cox), Channel Width (W), Channel Length (L), Gate Source Voltage (VGS), Threshold Voltage (VT) & Output Voltage (Vout) and hit the calculate button. Here is how the Pull down Current in Linear Region calculation can be explained with given input values -> 37526.28 = sum(x,0,11,(9.92*3.9/2)*(2.678/3.45)*(2*(29.65-5.91)*4.89-4.89^2)).

### FAQ

What is Pull down Current in Linear Region?
The Pull down Current in Linear Region formula is defined as the current through the resistor is when a pull-down resistor is used with an N-channel MOSFET in linear mode and is represented as ID(linear) = sum(x,0,n,(μn*Cox/2)*(W/L)*(2*(VGS-VT)*Vout-Vout^2)) or 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)). Number of Parallel Driver Transistors refers to the number of parallel driver transistors in the circuit, Electron Mobility in MOSFET describes how easily electrons can move through the channel, directly impacting the current flow for a given voltage, Oxide Capacitance refers to the capacitance associated with the insulating oxide layer in a Metal-Oxide-Semiconductor (MOS) structure, such as in MOSFETs, Channel Width represents the width of the conducting channel within a MOSFET, directly affecting the amount of current it can handle, Channel Length in a MOSFET is the distance between the source and drain regions, determining how easily current flows and impacting transistor performance, Gate Source Voltage is the voltage applied between the gate and source terminals of a MOSFET, Threshold Voltage is the minimum gate-to-source voltage required in a MOSFET to turn it "on" and allow a significant current to flow & Output Voltage in an n-channel MOSFET circuit with a pull-down resistor, Vout (output voltage) refers to the voltage at the drain terminal of the MOSFET.
How to calculate Pull down Current in Linear Region?
The Pull down Current in Linear Region formula is defined as the current through the resistor is when a pull-down resistor is used with an N-channel MOSFET in linear mode is calculated using 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)). To calculate Pull down Current in Linear Region, you need Number of Parallel Driver Transistors (n), Electron Mobility n), Oxide Capacitance (Cox), Channel Width (W), Channel Length (L), Gate Source Voltage (VGS), Threshold Voltage (VT) & Output Voltage (Vout). With our tool, you need to enter the respective value for Number of Parallel Driver Transistors, Electron Mobility, Oxide Capacitance, Channel Width, Channel Length, Gate Source Voltage, Threshold Voltage & Output 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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