Equivalent Capacitance for n Stacked Spirals Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Ceq = 4*((sum(x,1,N-1,Cm+Cs)))/(3*((N)^2))
This formula uses 1 Functions, 4 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
Equivalent Capacitance of N Stacked Spirals - (Measured in Farad) - Equivalent Capacitance of N Stacked Spirals is calculated by considering the capacitance between each pair of adjacent spirals and the capacitance between each spiral and the substrate.
Number of Stacked Spirals - Number of Stacked Spirals in an inductor design depends on various factors such as the desired inductance value, the available space on the integrated circuit (IC).
Inter Spiral Capacitance - (Measured in Farad) - Inter Spiral Capacitance refers to the capacitance between adjacent spiral inductors on an integrated circuit.
Substrate Capacitance - (Measured in Farad) - Substrate Capacitance, also known as parasitic substrate capacitance, refers to the capacitance that exists between conductive elements in an integrated circuit.
STEP 1: Convert Input(s) to Base Unit
Number of Stacked Spirals: 2 --> No Conversion Required
Inter Spiral Capacitance: 4.5 Farad --> 4.5 Farad No Conversion Required
Substrate Capacitance: 3.5 Farad --> 3.5 Farad No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ceq = 4*((sum(x,1,N-1,Cm+Cs)))/(3*((N)^2)) --> 4*((sum(x,1,2-1,4.5+3.5)))/(3*((2)^2))
Evaluating ... ...
Ceq = 2.66666666666667
STEP 3: Convert Result to Output's Unit
2.66666666666667 Farad --> No Conversion Required
FINAL ANSWER
2.66666666666667 2.666667 Farad <-- Equivalent Capacitance of N Stacked Spirals
(Calculation completed in 00.004 seconds)

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
Go 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
Go 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
Go 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
Go Feedback Factor = (Transconductance*Source Impedance-1)/(2*Transconductance*Source Impedance*Voltage Gain)
Return Loss of Low-Noise Amplifier
Go Return Loss = modulus((Input Impedance-Source Impedance)/(Input Impedance+Source Impedance))^2
Total Power Lost in Spiral
Go Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance)
Noise Figure of Low Noise Amplifier
Go Noise Figure = 1+((4*Source Impedance)/Feedback Resistance)+Noise Factor of Transistor
Gate to Source Voltage of Low Noise Amplifier
Go Gate to Source Voltage = ((2*Drain Current)/(Transconductance))+Threshold Voltage
Threshold Voltage of Low Noise Amplifier
Go Threshold Voltage = Gate to Source Voltage-(2*Drain Current)/(Transconductance)
Transconductance of Low Noise Amplifier
Go Transconductance = (2*Drain Current)/(Gate to Source Voltage-Threshold Voltage)
Drain Current of Low Noise Amplifier
Go Drain Current = (Transconductance*(Gate to Source Voltage-Threshold Voltage))/2
Voltage Gain of Low Noise Amplifier given DC Voltage Drop
Go Voltage Gain = 2*DC Voltage Drop/(Gate to Source Voltage-Threshold Voltage)
Load Impedance of Low Noise Amplifier
Go Load Impedance = (Input Impedance-(1/Transconductance))/Feedback Factor
Input Impedance of Low Noise Amplifier
Go Input Impedance = (1/Transconductance)+Feedback Factor*Load Impedance
Output Impedance of Low Noise Amplifier
Go Output Impedance = (1/2)*(Feedback Resistance+Source Impedance)
Source Impedance of Low Noise Amplifier
Go Source Impedance = 2*Output Impedance-Feedback Resistance
Drain Resistance of Low Noise Amplifier
Go Drain Resistance = Voltage Gain/Transconductance
Voltage Gain of Low Noise Amplifier
Go Voltage Gain = Transconductance*Drain Resistance

Equivalent Capacitance for n Stacked Spirals Formula

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))
Ceq = 4*((sum(x,1,N-1,Cm+Cs)))/(3*((N)^2))

What is purpose of calculating the Equivalent Capacitance for n Stacked Spirals?

Calculating the equivalent capacitance of n stacked spiral inductors is essential for optimizing the performance, power consumption, signal integrity, and noise immunity of integrated circuits, especially in high-frequency and RF applications. It provides valuable insights for circuit design, layout optimization, and performance analysis, ultimately leading to more efficient and reliable electronic systems.

How to Calculate Equivalent Capacitance for n Stacked Spirals?

Equivalent Capacitance for n Stacked Spirals calculator uses 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)) to calculate the Equivalent Capacitance of N Stacked Spirals, The Equivalent Capacitance for n Stacked Spirals formula is defined as the equivalent capacitance which is calculated by considering the inter-spiral capacitance and substrate capacitance. Equivalent Capacitance of N Stacked Spirals is denoted by Ceq symbol.

How to calculate Equivalent Capacitance for n Stacked Spirals using this online calculator? To use this online calculator for Equivalent Capacitance for n Stacked Spirals, enter Number of Stacked Spirals (N), Inter Spiral Capacitance (Cm) & Substrate Capacitance (Cs) and hit the calculate button. Here is how the Equivalent Capacitance for n Stacked Spirals calculation can be explained with given input values -> 2.666667 = 4*((sum(x,1,2-1,4.5+3.5)))/(3*((2)^2)).

FAQ

What is Equivalent Capacitance for n Stacked Spirals?
The Equivalent Capacitance for n Stacked Spirals formula is defined as the equivalent capacitance which is calculated by considering the inter-spiral capacitance and substrate capacitance and is represented as Ceq = 4*((sum(x,1,N-1,Cm+Cs)))/(3*((N)^2)) or 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)). Number of Stacked Spirals in an inductor design depends on various factors such as the desired inductance value, the available space on the integrated circuit (IC), Inter Spiral Capacitance refers to the capacitance between adjacent spiral inductors on an integrated circuit & Substrate Capacitance, also known as parasitic substrate capacitance, refers to the capacitance that exists between conductive elements in an integrated circuit.
How to calculate Equivalent Capacitance for n Stacked Spirals?
The Equivalent Capacitance for n Stacked Spirals formula is defined as the equivalent capacitance which is calculated by considering the inter-spiral capacitance and substrate capacitance is calculated using 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)). To calculate Equivalent Capacitance for n Stacked Spirals, you need Number of Stacked Spirals (N), Inter Spiral Capacitance (Cm) & Substrate Capacitance (Cs). With our tool, you need to enter the respective value for Number of Stacked Spirals, Inter Spiral Capacitance & Substrate Capacitance 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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