## Total Power Lost in Spiral Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance)
Ptot = sum(x,1,K,((Iu,n)^2)*KRs)
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
Total Power Lost in Spiral - (Measured in Watt) - Total Power Lost in Spiral can be calculated based on factors such as the resistance of the spiral, the current flowing through it, and the voltage across it.
Number of Inductors - Number of Inductors which are connected in the circuit model of inductor's distributed capacitance.
Corresponding RC Branch Current - (Measured in Ampere) - Corresponding RC Branch Current refers to the current flowing through the corresponding RC branch.
Substrate Resistance - (Measured in Ohm) - Substrate Resistance refers to the inherent resistance present in the semiconductor substrate material.
STEP 1: Convert Input(s) to Base Unit
Number of Inductors: 2 --> No Conversion Required
Corresponding RC Branch Current: 4 Ampere --> 4 Ampere No Conversion Required
Substrate Resistance: 5 Ohm --> 5 Ohm No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ptot = sum(x,1,K,((Iu,n)^2)*KRs) --> sum(x,1,2,((4)^2)*5)
Evaluating ... ...
Ptot = 160
STEP 3: Convert Result to Output's Unit
160 Watt --> No Conversion Required
160 Watt <-- Total Power Lost in Spiral
(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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Heritage Insitute of technology (HITK), Kolkata
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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

## Total Power Lost in Spiral Formula

Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance)
Ptot = sum(x,1,K,((Iu,n)^2)*KRs)

## What is the purpose of calculating the Total Power Lost in Spiral?

Calculating the distributed model of a spiral inductor to estimate power loss in the substrate is essential for accurate performance analysis, optimization, and ensuring the reliability of integrated circuits, particularly in high-frequency and high-performance applications.

## How to Calculate Total Power Lost in Spiral?

Total Power Lost in Spiral calculator uses Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance) to calculate the Total Power Lost in Spiral, The Total Power Lost in Spiral formula is defined as the sum of the power dissipated in all substrate resistors in the circuit such that current flowing through the respective branch is considered when calculating the total power lost in the spiral. Total Power Lost in Spiral is denoted by Ptot symbol.

How to calculate Total Power Lost in Spiral using this online calculator? To use this online calculator for Total Power Lost in Spiral, enter Number of Inductors (K), Corresponding RC Branch Current (Iu,n) & Substrate Resistance (KRs) and hit the calculate button. Here is how the Total Power Lost in Spiral calculation can be explained with given input values -> 160 = sum(x,1,2,((4)^2)*5).

### FAQ

What is Total Power Lost in Spiral?
The Total Power Lost in Spiral formula is defined as the sum of the power dissipated in all substrate resistors in the circuit such that current flowing through the respective branch is considered when calculating the total power lost in the spiral and is represented as Ptot = sum(x,1,K,((Iu,n)^2)*KRs) or Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance). Number of Inductors which are connected in the circuit model of inductor's distributed capacitance, Corresponding RC Branch Current refers to the current flowing through the corresponding RC branch & Substrate Resistance refers to the inherent resistance present in the semiconductor substrate material.
How to calculate Total Power Lost in Spiral?
The Total Power Lost in Spiral formula is defined as the sum of the power dissipated in all substrate resistors in the circuit such that current flowing through the respective branch is considered when calculating the total power lost in the spiral is calculated using Total Power Lost in Spiral = sum(x,1,Number of Inductors,((Corresponding RC Branch Current)^2)*Substrate Resistance). To calculate Total Power Lost in Spiral, you need Number of Inductors (K), Corresponding RC Branch Current (Iu,n) & Substrate Resistance (KRs). With our tool, you need to enter the respective value for Number of Inductors, Corresponding RC Branch Current & Substrate Resistance 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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