Node Voltage at Given Instance Calculator

✖Transconductance Factor is a measure of how much the output current of a device changes in response to a change in the input voltage.ⓘ Transconductance Factor [β]			+10% -10%
✖Node Capacitance refers to the total capacitance associated with a specific node in an electrical circuit. In circuit analysis, a node is a point where two or more circuit elements connect.ⓘ Node Capacitance [C_y]			+10% -10%
✖Node Resistance refers to the equivalent resistance associated with a specific node in an electrical circuit. In circuit analysis, a node is a point where two or more circuit elements connect.ⓘ Node Resistance [R_y]			+10% -10%
✖Time Period refers to the duration of one complete cycle of a periodic waveform.ⓘ Time Period [T]			+10% -10%
✖Current Flowing into Node refers to the net flow of electric current entering that specific node. A node is a point within the circuit where two or more circuit elements.ⓘ Current Flowing into Node [I_dd[x]]			+10% -10%

✖Node Voltage at Given Instance refers to the electrical potential (voltage) at a specific point or junction within the circuit, known as a node.ⓘ Node Voltage at Given Instance [V_y[t]]

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Formula

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Node Voltage at Given Instance

Formula

`("V"_{"y"}"[t]") = ("β"/"C"_{"y"})*int(exp(-(1/("R"_{"y"}*"C"_{"y"}))*("T"-x))*("I"_{"dd"}"[x]")*x,x,0,"T")`

Example

`"0.078579V"=("0.432S"/"237μF")*int(exp(-(1/("43kΩ"*"237μF"))*("5.61ms"-x))*"2.74A"*x,x,0,"5.61ms")`

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Node Voltage at Given Instance Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V_y[t] = (β/C_y)*int(exp(-(1/(R_y*C_y))*(T-x))*I_dd[x]*x,x,0,T)
This formula uses 2 Functions, 6 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
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

Node Voltage at Given Instance - (Measured in Volt) - Node Voltage at Given Instance refers to the electrical potential (voltage) at a specific point or junction within the circuit, known as a node.
Transconductance Factor - (Measured in Siemens) - Transconductance Factor is a measure of how much the output current of a device changes in response to a change in the input voltage.
Node Capacitance - (Measured in Farad) - Node Capacitance refers to the total capacitance associated with a specific node in an electrical circuit. In circuit analysis, a node is a point where two or more circuit elements connect.
Node Resistance - (Measured in Ohm) - Node Resistance refers to the equivalent resistance associated with a specific node in an electrical circuit. In circuit analysis, a node is a point where two or more circuit elements connect.
Time Period - (Measured in Second) - Time Period refers to the duration of one complete cycle of a periodic waveform.
Current Flowing into Node - (Measured in Ampere) - Current Flowing into Node refers to the net flow of electric current entering that specific node. A node is a point within the circuit where two or more circuit elements.

STEP 1: Convert Input(s) to Base Unit

Transconductance Factor: 0.432 Siemens --> 0.432 Siemens No Conversion Required
Node Capacitance: 237 Microfarad --> 0.000237 Farad (Check conversion here)
Node Resistance: 43 Kilohm --> 43000 Ohm (Check conversion here)
Time Period: 5.61 Millisecond --> 0.00561 Second (Check conversion here)
Current Flowing into Node: 2.74 Ampere --> 2.74 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_y[t] = (β/C_y)*int(exp(-(1/(R_y*C_y))*(T-x))*I_dd[x]*x,x,0,T) --> (0.432/0.000237)*int(exp(-(1/(43000*0.000237))*(0.00561-x))*2.74*x,x,0,0.00561)

Evaluating ... ...

V_y[t] = 0.0785790880040371

STEP 3: Convert Result to Output's Unit

0.0785790880040371 Volt --> No Conversion Required

FINAL ANSWER

0.0785790880040371 ≈ 0.078579 Volt <-- Node Voltage at Given Instance

(Calculation completed in 00.004 seconds)

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Dayananda Sagar College of Engineering (DSCE), Bangalore

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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

Node Voltage at Given Instance Formula

What is the significance of node voltage?

Node voltage analysis is fundamental in circuit analysis and design. It helps determine the distribution of voltages and currents in a circuit, aiding in the understanding of circuit behavior and performance.

How to Calculate Node Voltage at Given Instance?

Node Voltage at Given Instance calculator uses 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) to calculate the Node Voltage at Given Instance, The Node Voltage at Given Instance formula is defined as refers to the voltage potential at a specific node within the circuit at a particular moment in time. Node Voltage at Given Instance is denoted by V_y[t] symbol.

How to calculate Node Voltage at Given Instance using this online calculator? To use this online calculator for Node Voltage at Given Instance, enter Transconductance Factor (β), Node Capacitance (C_y), Node Resistance (R_y), Time Period (T) & Current Flowing into Node (I_dd[x]) and hit the calculate button. Here is how the Node Voltage at Given Instance calculation can be explained with given input values -> 0.078579 = (0.432/0.000237)*int(exp(-(1/(43000*0.000237))*(0.00561-x))*2.74*x,x,0,0.00561).

FAQ

What is Node Voltage at Given Instance?

The Node Voltage at Given Instance formula is defined as refers to the voltage potential at a specific node within the circuit at a particular moment in time and is represented as V_y[t] = (β/C_y)*int(exp(-(1/(R_y*C_y))*(T-x))*I_dd[x]*x,x,0,T) or 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). Transconductance Factor is a measure of how much the output current of a device changes in response to a change in the input voltage, Node Capacitance refers to the total capacitance associated with a specific node in an electrical circuit. In circuit analysis, a node is a point where two or more circuit elements connect, Node Resistance refers to the equivalent resistance associated with a specific node in an electrical circuit. In circuit analysis, a node is a point where two or more circuit elements connect, Time Period refers to the duration of one complete cycle of a periodic waveform & Current Flowing into Node refers to the net flow of electric current entering that specific node. A node is a point within the circuit where two or more circuit elements.

How to calculate Node Voltage at Given Instance?

The Node Voltage at Given Instance formula is defined as refers to the voltage potential at a specific node within the circuit at a particular moment in time is calculated using 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). To calculate Node Voltage at Given Instance, you need Transconductance Factor (β), Node Capacitance (C_y), Node Resistance (R_y), Time Period (T) & Current Flowing into Node (I_dd[x]). With our tool, you need to enter the respective value for Transconductance Factor, Node Capacitance, Node Resistance, Time Period & Current Flowing into Node 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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