## Energy Stored in all Unit Capacitances Solution

STEP 0: Pre-Calculation Summary
Formula Used
Energy Stored in All Unit Capacitances = (1/2)*Value of Unit capacitance*(sum(x,1,Number of Inductors,((Value of Node N/Number of Inductors)^2)*((Input Voltage)^2)))
Etot = (1/2)*Cu*(sum(x,1,K,((n/K)^2)*((V1)^2)))
This formula uses 1 Functions, 5 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
Energy Stored in All Unit Capacitances - (Measured in Joule) - Energy Stored in All Unit Capacitances is the total energy of the unit capacitors which are connected by the interwinding.
Value of Unit capacitance - (Measured in Farad) - Value of Unit capacitance is the value of the fringe capacitors which are connected in parallel with the inductor of the circuit model of inductor's distributed capacitance.
Number of Inductors - Number of Inductors which are connected in the circuit model of inductor's distributed capacitance.
Value of Node N - Value of Node N is the at which the voltage across the capacitance is calculated for the circuit model of inductor's distributed capacitance.
Input Voltage - (Measured in Volt) - Input Voltage is the required voltage to be given for the circuit model of an inductor’s distributed capacitance.
STEP 1: Convert Input(s) to Base Unit
Value of Unit capacitance: 6 Farad --> 6 Farad No Conversion Required
Number of Inductors: 2 --> No Conversion Required
Value of Node N: 2 --> No Conversion Required
Input Voltage: 2.5 Volt --> 2.5 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Etot = (1/2)*Cu*(sum(x,1,K,((n/K)^2)*((V1)^2))) --> (1/2)*6*(sum(x,1,2,((2/2)^2)*((2.5)^2)))
Evaluating ... ...
Etot = 37.5
STEP 3: Convert Result to Output's Unit
37.5 Joule --> No Conversion Required
37.5 Joule <-- Energy Stored in All Unit Capacitances
(Calculation completed in 00.004 seconds)
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## Credits

Created by Zaheer Sheik
Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru
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## < 18 RF Microelectronics Calculators

Energy Stored in all Unit Capacitances
Energy Stored in All Unit Capacitances = (1/2)*Value of Unit capacitance*(sum(x,1,Number of Inductors,((Value of Node N/Number of Inductors)^2)*((Input Voltage)^2)))
Equivalent Capacitance for n Stacked Spirals
Equivalent Capacitance of N Stacked Spirals = 4*((sum(x,1,Number of Stacked Spirals-1,Inter Spiral Capacitance+Substrate Capacitance)))/(3*((Number of Stacked Spirals)^2))
Total Noise Power Introduced by Interferer
Total Noise Power of Interferer = int(Broadened Spectrum of Interferer*x,x,Lower End of the Desired Channel,Higher End of the Desired Channel)
Feedback Factor of Low Noise Amplifier
Feedback Factor = (Transconductance*Source Impedance-1)/(2*Transconductance*Source Impedance*Voltage Gain)
Return Loss of Low-Noise Amplifier
Return Loss = modulus((Input Impedance-Source Impedance)/(Input Impedance+Source Impedance))^2
Total Power Lost in Spiral
Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance)
Noise Figure of Low Noise Amplifier
Noise Figure = 1+((4*Source Impedance)/Feedback Resistance)+Noise Factor of Transistor
Gate to Source Voltage of Low Noise Amplifier
Gate to Source Voltage = ((2*Drain Current)/(Transconductance))+Threshold Voltage
Threshold Voltage of Low Noise Amplifier
Threshold Voltage = Gate to Source Voltage-(2*Drain Current)/(Transconductance)
Transconductance of Low Noise Amplifier
Transconductance = (2*Drain Current)/(Gate to Source Voltage-Threshold Voltage)
Drain Current of Low Noise Amplifier
Drain Current = (Transconductance*(Gate to Source Voltage-Threshold Voltage))/2
Voltage Gain of Low Noise Amplifier given DC Voltage Drop
Voltage Gain = 2*DC Voltage Drop/(Gate to Source Voltage-Threshold Voltage)
Load Impedance of Low Noise Amplifier
Load Impedance = (Input Impedance-(1/Transconductance))/Feedback Factor
Input Impedance of Low Noise Amplifier
Input Impedance = (1/Transconductance)+Feedback Factor*Load Impedance
Output Impedance of Low Noise Amplifier
Output Impedance = (1/2)*(Feedback Resistance+Source Impedance)
Source Impedance of Low Noise Amplifier
Source Impedance = 2*Output Impedance-Feedback Resistance
Drain Resistance of Low Noise Amplifier
Drain Resistance = Voltage Gain/Transconductance
Voltage Gain of Low Noise Amplifier
Voltage Gain = Transconductance*Drain Resistance

## Energy Stored in all Unit Capacitances Formula

Energy Stored in All Unit Capacitances = (1/2)*Value of Unit capacitance*(sum(x,1,Number of Inductors,((Value of Node N/Number of Inductors)^2)*((Input Voltage)^2)))
Etot = (1/2)*Cu*(sum(x,1,K,((n/K)^2)*((V1)^2)))

## What is the purpose of calculating the Energy Stored in all Unit Capacitances?

The Energy Stored in all Unit Capacitances formula is used to calculate the energy stored by the capacitors which are connected in parallel with inductors of the circuit model of inductor's distributed capacitance. And also to obtain the lumped model of the parasitic capacitances of the substrate.

## How to Calculate Energy Stored in all Unit Capacitances?

Energy Stored in all Unit Capacitances calculator uses Energy Stored in All Unit Capacitances = (1/2)*Value of Unit capacitance*(sum(x,1,Number of Inductors,((Value of Node N/Number of Inductors)^2)*((Input Voltage)^2))) to calculate the Energy Stored in All Unit Capacitances, The Energy Stored in all Unit Capacitances formula is defined as the energy stored by the capacitors which are connected in parallel with inductors of the circuit model of inductor's distributed capacitance. Energy Stored in All Unit Capacitances is denoted by Etot symbol.

How to calculate Energy Stored in all Unit Capacitances using this online calculator? To use this online calculator for Energy Stored in all Unit Capacitances, enter Value of Unit capacitance (Cu), Number of Inductors (K), Value of Node N (n) & Input Voltage (V1) and hit the calculate button. Here is how the Energy Stored in all Unit Capacitances calculation can be explained with given input values -> 37.5 = (1/2)*6*(sum(x,1,2,((2/2)^2)*((2.5)^2))).

### FAQ

What is Energy Stored in all Unit Capacitances?
The Energy Stored in all Unit Capacitances formula is defined as the energy stored by the capacitors which are connected in parallel with inductors of the circuit model of inductor's distributed capacitance and is represented as Etot = (1/2)*Cu*(sum(x,1,K,((n/K)^2)*((V1)^2))) or Energy Stored in All Unit Capacitances = (1/2)*Value of Unit capacitance*(sum(x,1,Number of Inductors,((Value of Node N/Number of Inductors)^2)*((Input Voltage)^2))). Value of Unit capacitance is the value of the fringe capacitors which are connected in parallel with the inductor of the circuit model of inductor's distributed capacitance, Number of Inductors which are connected in the circuit model of inductor's distributed capacitance, Value of Node N is the at which the voltage across the capacitance is calculated for the circuit model of inductor's distributed capacitance & Input Voltage is the required voltage to be given for the circuit model of an inductor’s distributed capacitance.
How to calculate Energy Stored in all Unit Capacitances?
The Energy Stored in all Unit Capacitances formula is defined as the energy stored by the capacitors which are connected in parallel with inductors of the circuit model of inductor's distributed capacitance is calculated using Energy Stored in All Unit Capacitances = (1/2)*Value of Unit capacitance*(sum(x,1,Number of Inductors,((Value of Node N/Number of Inductors)^2)*((Input Voltage)^2))). To calculate Energy Stored in all Unit Capacitances, you need Value of Unit capacitance (Cu), Number of Inductors (K), Value of Node N (n) & Input Voltage (V1). With our tool, you need to enter the respective value for Value of Unit capacitance, Number of Inductors, Value of Node N & Input 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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