## 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)
Vy[t] = (β/Cy)*int(exp(-(1/(Ry*Cy))*(T-x))*Idd[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 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
Vy[t] = (β/Cy)*int(exp(-(1/(Ry*Cy))*(T-x))*Idd[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 ... ...
Vy[t] = 0.0785790880040371
STEP 3: Convert Result to Output's Unit
0.0785790880040371 Volt --> No Conversion Required
0.0785790880040371 0.078579 Volt <-- Node Voltage at Given Instance
(Calculation completed in 00.004 seconds)
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## Credits

Created by banuprakash
Dayananda Sagar College of Engineering (DSCE), Bangalore
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Verified by Dipanjona Mallick
Heritage Insitute of technology (HITK), Kolkata
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## <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)))
Fermi Potential for P Type
​ Go Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)
Equivalent Large Signal Junction Capacitance
​ Go Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor
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

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)
Vy[t] = (β/Cy)*int(exp(-(1/(Ry*Cy))*(T-x))*Idd[x]*x,x,0,T)

## 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 Vy[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 (Cy), Node Resistance (Ry), Time Period (T) & Current Flowing into Node (Idd[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 Vy[t] = (β/Cy)*int(exp(-(1/(Ry*Cy))*(T-x))*Idd[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 (Cy), Node Resistance (Ry), Time Period (T) & Current Flowing into Node (Idd[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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