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Node Voltage at Given Instance Formula

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Node Voltage at Given Instance refers to the electrical potential (voltage) at a specific point or junction within the circuit, known as a node. Check FAQs

V y [t] = (\frac{β}{C y}) \cdot \int (\exp (- (\frac{1}{R y \cdot C y}) \cdot (T - x)) \cdot I dd [x] \cdot x, x, 0, T)

V_y[t] - Node Voltage at Given Instance?β - Transconductance Factor?C_y - Node Capacitance?R_y - Node Resistance?T - Time Period?I_dd[x] - Current Flowing into Node?

Node Voltage at Given Instance Example

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Here is how the Node Voltage at Given Instance equation looks like with Values.

Here is how the Node Voltage at Given Instance equation looks like with Units.

Here is how the Node Voltage at Given Instance equation looks like.

0.0786 = (\frac{0.432}{237}) \cdot \int (\exp (- (\frac{1}{43 \cdot 237}) \cdot (5.61 - x)) \cdot 2.74 \cdot x, x, 0, 5.61)

0.0786V = (\frac{0.432S}{237μF}) \cdot \int (\exp (- (\frac{1}{43kΩ \cdot 237μF}) \cdot (5.61ms - x)) \cdot 2.74A \cdot x, x, 0, 5.61ms)

0.0786 = (\frac{0.432}{237}) \cdot \int (\exp (- (\frac{1}{43 \cdot 237}) \cdot (5.61 - x)) \cdot 2.74 \cdot x, x, 0, 5.61)

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Node Voltage at Given Instance Solution

Follow our step by step solution on how to calculate Node Voltage at Given Instance?

FIRST Step Consider the formula

V y [t] = (\frac{β}{C y}) \cdot \int (\exp (- (\frac{1}{R y \cdot C y}) \cdot (T - x)) \cdot I dd [x] \cdot x, x, 0, T)

Next Step Substitute values of Variables

∴

V y [t] = (\frac{0.432S}{237μF}) \cdot \int (\exp (- (\frac{1}{43kΩ \cdot 237μF}) \cdot (5.61ms - x)) \cdot 2.74A \cdot x, x, 0, 5.61ms)

Next Step Convert Units

∴

V y [t] = (\frac{0.432S}{0.0002F}) \cdot \int (\exp (- (\frac{1}{43000Ω \cdot 0.0002F}) \cdot (0.0056s - x)) \cdot 2.74A \cdot x, x, 0, 0.0056s)

Next Step Prepare to Evaluate

∴

V y [t] = (\frac{0.432}{0.0002}) \cdot \int (\exp (- (\frac{1}{43000 \cdot 0.0002}) \cdot (0.0056 - x)) \cdot 2.74 \cdot x, x, 0, 0.0056)

Next Step Evaluate

∴

V y [t] = 0.0785790880040371V

LAST Step Rounding Answer

∴

V y [t] = 0.0786V

Node Voltage at Given Instance Formula Elements

Variables

Functions

Node Voltage at Given Instance

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

Symbol: V_y[t]

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Node Voltage at Given Instance

Transconductance Factor

Transconductance Factor is a measure of how much the output current of a device changes in response to a change in the input voltage.

Symbol: β

Measurement: TransconductanceUnit: S

Note: Value should be greater than 0.

Formulas to find Transconductance Factor

Node Capacitance

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.

Symbol: C_y

Measurement: CapacitanceUnit: μF

Note: Value can be positive or negative.

Formulas to find Node Capacitance

Node Resistance

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.

Symbol: R_y

Measurement: Electric ResistanceUnit: kΩ

Note: Value should be greater than 0.

Formulas to find Node Resistance

Time Period

Time Period refers to the duration of one complete cycle of a periodic waveform.

Symbol: T

Measurement: TimeUnit: ms

Note: Value can be positive or negative.

Formulas to find Time Period

Current Flowing into Node

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.

Symbol: I_dd[x]

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Current Flowing into Node

exp

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

Syntax: 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.

Syntax: int(expr, arg, from, to)

Other formulas in MOS Transistor category

Go Zero Bias Sidewall Junction Capacitance per Unit Length

C jsw = C j0sw \cdot x j

Go Equivalent Large Signal Junction Capacitance

C eq(sw) = P \cdot C jsw \cdot K eq(sw)

Go Fermi Potential for P Type

Φ Fp = \frac{[BoltZ] \cdot T a}{[Charge-e]} \cdot \ln (\frac{n i}{N A})

Go Sidewall Voltage Equivalence Factor

K eq(sw) = - (2 \cdot \frac{\sqrt{Φ osw}}{V 2 - V 1} \cdot (\sqrt{Φ osw - V 2} - \sqrt{Φ osw - V 1}))

How to Evaluate Node Voltage at Given Instance?

Node Voltage at Given Instance evaluator 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 evaluate 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 evaluate Node Voltage at Given Instance using this online evaluator? To use this online evaluator 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.

FAQs on Node Voltage at Given Instance

What is the formula to find Node Voltage at Given Instance?

The formula of Node Voltage at Given Instance is expressed as 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). Here is an example- 0.078579 = (0.432/0.000237)*int(exp(-(1/(43000*0.000237))*(0.00561-x))*2.74*x,x,0,0.00561).

How to calculate Node Voltage at Given Instance?

With Transconductance Factor (β), Node Capacitance (C_y), Node Resistance (R_y), Time Period (T) & Current Flowing into Node (I_dd[x]) we can find Node Voltage at Given Instance using the 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). This formula also uses Exponential Growth (exp), Definite Integral (int) function(s).

Can the Node Voltage at Given Instance be negative?

No, the Node Voltage at Given Instance, measured in Electric Potential cannot be negative.

Which unit is used to measure Node Voltage at Given Instance?

Node Voltage at Given Instance is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which Node Voltage at Given Instance can be measured.

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Node Voltage at Given Instance Formula

Node Voltage at Given Instance Example

Node Voltage at Given Instance Solution

Node Voltage at Given Instance Formula Elements

Other formulas in MOS Transistor category

How to Evaluate Node Voltage at Given Instance?

FAQs on Node Voltage at Given Instance

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