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Equivalent Capacitance for n Stacked Spirals Calculator

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✖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).ⓘ Number of Stacked Spirals [N]			+10% -10%
✖Inter Spiral Capacitance refers to the capacitance between adjacent spiral inductors on an integrated circuit.ⓘ Inter Spiral Capacitance [C_m]			+10% -10%
✖Substrate Capacitance, also known as parasitic substrate capacitance, refers to the capacitance that exists between conductive elements in an integrated circuit.ⓘ Substrate Capacitance [C_s]			+10% -10%

✖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.ⓘ Equivalent Capacitance for n Stacked Spirals [C_eq]

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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))
C_eq = 4*((sum(x,1,N-1,C_m+C_s)))/(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

C_eq = 4*((sum(x,1,N-1,C_m+C_s)))/(3*((N)^2)) --> 4*((sum(x,1,2-1,4.5+3.5)))/(3*((2)^2))

Evaluating ... ...

C_eq = 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 00.020 seconds)

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Equivalent Capacitance for n Stacked Spirals Formula

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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 C_eq 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 (C_m) & Substrate Capacitance (C_s) 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 C_eq = 4*((sum(x,1,N-1,C_m+C_s)))/(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 (C_m) & Substrate Capacitance (C_s). 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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