NMOS as Linear Resistance Solution

STEP 0: Pre-Calculation Summary
Formula Used
Linear Resistance = Length of the Channel/(Mobility of Electrons at Surface of Channel*Oxide Capacitance*Width of Channel*(Gate Source Voltage-Threshold Voltage))
rDS = L/(μn*Cox*Wc*(Vgs-VT))
This formula uses 7 Variables
Variables Used
Linear Resistance - (Measured in Ohm) - Linear resistance acts as a variable resistor in the linear region and as a current source in the saturation region.
Length of the Channel - (Measured in Meter) - Length of the channel can be defined as the distance between its start and end points, and can vary greatly depending on its purpose and location.
Mobility of Electrons at Surface of Channel - (Measured in Square Meter per Volt per Second) - The mobility of electrons at surface of channel refers to the ability of electrons to move or conduct within a material's surface layer when subjected to an electric field.
Oxide Capacitance - (Measured in Farad) - Oxide capacitance is an important parameter that affects the performance of MOS devices, such as the speed and power consumption of integrated circuits.
Width of Channel - (Measured in Meter) - The width of channel refers to the amount of bandwidth available for transmitting data within a communication channel.
Gate Source Voltage - (Measured in Volt) - The Gate Source Voltage is the voltage that falls across the gate-source terminal of the transistor.
Threshold Voltage - (Measured in Volt) - Threshold voltage, also known as the gate threshold voltage or simply Vth, is a critical parameter in the operation of field-effect transistors, which are fundamental components in modern electronics.
STEP 1: Convert Input(s) to Base Unit
Length of the Channel: 3 Micrometer --> 3E-06 Meter (Check conversion here)
Mobility of Electrons at Surface of Channel: 2.2 Square Meter per Volt per Second --> 2.2 Square Meter per Volt per Second No Conversion Required
Oxide Capacitance: 2.02 Microfarad --> 2.02E-06 Farad (Check conversion here)
Width of Channel: 10 Micrometer --> 1E-05 Meter (Check conversion here)
Gate Source Voltage: 10.3 Volt --> 10.3 Volt No Conversion Required
Threshold Voltage: 1.82 Volt --> 1.82 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rDS = L/(μn*Cox*Wc*(Vgs-VT)) --> 3E-06/(2.2*2.02E-06*1E-05*(10.3-1.82))
Evaluating ... ...
rDS = 7960.70173055041
STEP 3: Convert Result to Output's Unit
7960.70173055041 Ohm -->7.96070173055041 Kilohm (Check conversion here)
FINAL ANSWER
7.96070173055041 7.960702 Kilohm <-- Linear Resistance
(Calculation completed in 00.020 seconds)

Credits

Created by Payal Priya
Birsa Institute of Technology (BIT), Sindri
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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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17 N-Channel Enhancement Calculators

Current Entering Drain-Source in Triode Region of NMOS
Go Drain Current in NMOS = Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*((Gate Source Voltage-Threshold Voltage)*Drain Source Voltage-1/2*(Drain Source Voltage)^2)
Current Entering Drain Terminal of NMOS given Gate Source Voltage
Go Drain Current in NMOS = Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*((Gate Source Voltage-Threshold Voltage)*Drain Source Voltage-1/2*Drain Source Voltage^2)
Body Effect in NMOS
Go Change in Threshold Voltage = Threshold Voltage+Fabrication Process Parameter*(sqrt(2*Physical Parameter+Voltage between Body and Source)-sqrt(2*Physical Parameter))
Current Entering Drain Terminal of NMOS
Go Drain Current in NMOS = Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*Drain Source Voltage*(Overdrive Voltage in NMOS-1/2*Drain Source Voltage)
NMOS as Linear Resistance
Go Linear Resistance = Length of the Channel/(Mobility of Electrons at Surface of Channel*Oxide Capacitance*Width of Channel*(Gate Source Voltage-Threshold Voltage))
Drain Current when NMOS Operates as Voltage-Controlled Current Source
Go Drain Current in NMOS = 1/2*Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*(Gate Source Voltage-Threshold Voltage)^2
Current Entering Drain-Source at Saturation Region of NMOS
Go Drain Current in NMOS = 1/2*Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*(Gate Source Voltage-Threshold Voltage)^2
Fabrication Process Parameter of NMOS
Go Fabrication Process Parameter = sqrt(2*[Charge-e]*Doping Concentration of P Substrate*[Permitivity-vacuum])/Oxide Capacitance
Current Entering Drain-Source at Saturation Region of NMOS given Effective Voltage
Go Saturation Drain Current = 1/2*Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*(Overdrive Voltage in NMOS)^2
Current Entering Drain Source at Boundary of Saturation and Triode Region of NMOS
Go Drain Current in NMOS = 1/2*Process Transconductance Parameter in NMOS*Width of Channel/Length of the Channel*(Drain Source Voltage)^2
Electron Drift Velocity of Channel in NMOS Transistor
Go Electron Drift Velocity = Mobility of Electrons at Surface of Channel*Electric Field across Length of Channel
Total Power Supplied in NMOS
Go Power Supplied = Supply Voltage*(Drain Current in NMOS+Current)
Drain Current given NMOS Operates as Voltage-Controlled Current Source
Go Transconductance Parameter = Process Transconductance Parameter in PMOS*Aspect Ratio
Output Resistance of Current Source NMOS given Drain Current
Go Output Resistance = Device Parameter/Drain Current without Channel Length Modulation
Total Power Dissipated in NMOS
Go Power Dissipated = Drain Current in NMOS^2*ON Channel Resistance
Positive Voltage given Channel Length in NMOS
Go Voltage = Device Parameter*Length of the Channel
Oxide Capacitance of NMOS
Go Oxide Capacitance = (3.45*10^(-11))/Oxide Thickness

NMOS as Linear Resistance Formula

Linear Resistance = Length of the Channel/(Mobility of Electrons at Surface of Channel*Oxide Capacitance*Width of Channel*(Gate Source Voltage-Threshold Voltage))
rDS = L/(μn*Cox*Wc*(Vgs-VT))

What is the condition to use the MOSFET as a linear resistor?

When you slowly increase the gate voltage the MOSFET slowly starts conducting by entering the linear region where it starts developing a voltage across it which we call V DS . In this region, the MOSFET acts as a resistance of finite value.

How to Calculate NMOS as Linear Resistance?

NMOS as Linear Resistance calculator uses Linear Resistance = Length of the Channel/(Mobility of Electrons at Surface of Channel*Oxide Capacitance*Width of Channel*(Gate Source Voltage-Threshold Voltage)) to calculate the Linear Resistance, The NMOS as linear resistance acts as a variable resistor in the linear region and as a current source in the saturation region. Unlike a BJT, to use a MOSFET as a switch, you need to operate within the linear region. Linear Resistance is denoted by rDS symbol.

How to calculate NMOS as Linear Resistance using this online calculator? To use this online calculator for NMOS as Linear Resistance, enter Length of the Channel (L), Mobility of Electrons at Surface of Channel n), Oxide Capacitance (Cox), Width of Channel (Wc), Gate Source Voltage (Vgs) & Threshold Voltage (VT) and hit the calculate button. Here is how the NMOS as Linear Resistance calculation can be explained with given input values -> 0.007961 = 3E-06/(2.2*2.02E-06*1E-05*(10.3-1.82)).

FAQ

What is NMOS as Linear Resistance?
The NMOS as linear resistance acts as a variable resistor in the linear region and as a current source in the saturation region. Unlike a BJT, to use a MOSFET as a switch, you need to operate within the linear region and is represented as rDS = L/(μn*Cox*Wc*(Vgs-VT)) or Linear Resistance = Length of the Channel/(Mobility of Electrons at Surface of Channel*Oxide Capacitance*Width of Channel*(Gate Source Voltage-Threshold Voltage)). Length of the channel can be defined as the distance between its start and end points, and can vary greatly depending on its purpose and location, The mobility of electrons at surface of channel refers to the ability of electrons to move or conduct within a material's surface layer when subjected to an electric field, Oxide capacitance is an important parameter that affects the performance of MOS devices, such as the speed and power consumption of integrated circuits, The width of channel refers to the amount of bandwidth available for transmitting data within a communication channel, The Gate Source Voltage is the voltage that falls across the gate-source terminal of the transistor & Threshold voltage, also known as the gate threshold voltage or simply Vth, is a critical parameter in the operation of field-effect transistors, which are fundamental components in modern electronics.
How to calculate NMOS as Linear Resistance?
The NMOS as linear resistance acts as a variable resistor in the linear region and as a current source in the saturation region. Unlike a BJT, to use a MOSFET as a switch, you need to operate within the linear region is calculated using Linear Resistance = Length of the Channel/(Mobility of Electrons at Surface of Channel*Oxide Capacitance*Width of Channel*(Gate Source Voltage-Threshold Voltage)). To calculate NMOS as Linear Resistance, you need Length of the Channel (L), Mobility of Electrons at Surface of Channel n), Oxide Capacitance (Cox), Width of Channel (Wc), Gate Source Voltage (Vgs) & Threshold Voltage (VT). With our tool, you need to enter the respective value for Length of the Channel, Mobility of Electrons at Surface of Channel, Oxide Capacitance, Width of Channel, Gate Source 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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