Skin Depth or Depth of Penetration Calculator

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Wave Propagation

Antenna Theory Parameters

Special Antennas

✖The Conductivity of antenna refers to the electrical conductivity of the subsurface of the antenna.ⓘ Conductivity of Antenna [σ]			+10% -10%
✖Relative Permeability is a fundamental parameter used to characterize the response of a material to magnetic fields.ⓘ Relative Permeability [μ_r]			+10% -10%
✖The Frequency of conductor loop the rate at which something occurs over a particular period of time or in a given sample.ⓘ Frequency of Conductor Loop [f]			+10% -10%

✖Skin Depth refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material.ⓘ Skin Depth or Depth of Penetration [δ]

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Formula

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Skin Depth or Depth of Penetration

Formula

`"δ" = 1/"σ"*sqrt(pi*"μ"_{"r"}*"[Permeability-vacuum]"*"f")`

Example

`"0.006479m"=1/"0.96mho/m"*sqrt(pi*"0.98H/m"*"[Permeability-vacuum]"*"10Hz")`

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Skin Depth or Depth of Penetration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop)
δ = 1/σ*sqrt(pi*μ_r*[Permeability-vacuum]*f)
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[Permeability-vacuum] - Permeability of vacuum Value Taken As 1.2566E-6
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Skin Depth - (Measured in Meter) - Skin Depth refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material.
Conductivity of Antenna - (Measured in Siemens per Meter) - The Conductivity of antenna refers to the electrical conductivity of the subsurface of the antenna.
Relative Permeability - (Measured in Henry per Meter) - Relative Permeability is a fundamental parameter used to characterize the response of a material to magnetic fields.
Frequency of Conductor Loop - (Measured in Hertz) - The Frequency of conductor loop the rate at which something occurs over a particular period of time or in a given sample.

STEP 1: Convert Input(s) to Base Unit

Conductivity of Antenna: 0.96 Mho per Meter --> 0.96 Siemens per Meter (Check conversion here)
Relative Permeability: 0.98 Henry per Meter --> 0.98 Henry per Meter No Conversion Required
Frequency of Conductor Loop: 10 Hertz --> 10 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = 1/σ*sqrt(pi*μ_r*[Permeability-vacuum]*f) --> 1/0.96*sqrt(pi*0.98*[Permeability-vacuum]*10)

Evaluating ... ...

δ = 0.00647920428481428

STEP 3: Convert Result to Output's Unit

0.00647920428481428 Meter --> No Conversion Required

FINAL ANSWER

0.00647920428481428 ≈ 0.006479 Meter <-- Skin Depth

(Calculation completed in 00.004 seconds)

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< 16 Wave Propagation Calculators

Field Strength of Space Wave

Go Field Strength = (4*pi*Electric Field*Height of Receiving Antenna*Height of Transmitting Antenna)/(Wavelength*Antenna Distance^2)

Skin Depth or Depth of Penetration

Go Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop)

Phase Difference between Radio Waves

Go Phase Difference = 4*pi*Height of Receiving Antenna*Height of Transmitting Antenna/(Antenna Distance*Wavelength)

Height of Layer

Go Ionospheric Layer Height = Skip Distance/(2*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1))

Maximum Usable Frequency

Go Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height))^2)

Propagation Distance

Go Skip Distance = 2*Ionospheric Layer Height*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1)

Line of Sight

Go Line of Sight = 3577*(sqrt(Height of Receiving Antenna)+sqrt(Height of Transmitting Antenna))

Skip Distance

Go Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1)

Refractive Index of Ionosphere

Go Refractive Index = sqrt(1-((81*Electron Density)/Operating Frequency^2))

Maximum Usable Frequency in F-region

Go Maximum Usable Frequency = Critical Frequency/cos(Angle of Incidence)

Normal of Reflecting Plane

Go Normal of Reflecting Plane = Wavelength/cos(Theta)

Wavelength of Plane

Go Wavelength = Normal of Reflecting Plane*cos(Theta)

Parallel of Reflecting Plane

Go Parallel of Reflecting = Wavelength/sin(Theta)

Electron Density

Go Electron Density = ((1-Refractive Index^2)*Operating Frequency^2)/81

Critical Frequency of Ionosphere

Go Critical Frequency of Ionosphere = 9*sqrt(Electron Density)

Antenna Beamwidth

Go Antenna Beamwidth = (70*Wavelength)/Antenna Diameter

Skin Depth or Depth of Penetration Formula

Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop)
δ = 1/σ*sqrt(pi*μ_r*[Permeability-vacuum]*f)

What is skin effect?

For very high conductivity the induced current also attenuated in the conductor. The current density associated a wave is maximum along the surface of a conductor known as skin effect.

What are the applications of skin effect?

Based upon the skin effect the conductor in antenna system is preferred to operate as large outer diameter hollow tube.

How to Calculate Skin Depth or Depth of Penetration?

Skin Depth or Depth of Penetration calculator uses Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop) to calculate the Skin Depth, Skin Depth or Depth of Penetration refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material. It quantifies how deeply the electromagnetic wave can penetrate into the material before its intensity is significantly attenuated. Skin Depth is denoted by δ symbol.

How to calculate Skin Depth or Depth of Penetration using this online calculator? To use this online calculator for Skin Depth or Depth of Penetration, enter Conductivity of Antenna (σ), Relative Permeability (μ_r) & Frequency of Conductor Loop (f) and hit the calculate button. Here is how the Skin Depth or Depth of Penetration calculation can be explained with given input values -> 0.006479 = 1/0.96*sqrt(pi*0.98*[Permeability-vacuum]*10).

FAQ

What is Skin Depth or Depth of Penetration?

Skin Depth or Depth of Penetration refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material. It quantifies how deeply the electromagnetic wave can penetrate into the material before its intensity is significantly attenuated and is represented as δ = 1/σ*sqrt(pi*μ_r*[Permeability-vacuum]*f) or Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop). The Conductivity of antenna refers to the electrical conductivity of the subsurface of the antenna, Relative Permeability is a fundamental parameter used to characterize the response of a material to magnetic fields & The Frequency of conductor loop the rate at which something occurs over a particular period of time or in a given sample.

How to calculate Skin Depth or Depth of Penetration?

Skin Depth or Depth of Penetration refers to the distance at which the amplitude of an electromagnetic wave decreases to approximately 1/e (about 37%) of its initial value as it propagates through a conductive material. It quantifies how deeply the electromagnetic wave can penetrate into the material before its intensity is significantly attenuated is calculated using Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop). To calculate Skin Depth or Depth of Penetration, you need Conductivity of Antenna (σ), Relative Permeability (μ_r) & Frequency of Conductor Loop (f). With our tool, you need to enter the respective value for Conductivity of Antenna, Relative Permeability & Frequency of Conductor Loop 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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