Effective Dielectric Constant of Substrate Calculator

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Special Antennas

Antenna Theory Parameters

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✖The Dielectric Constant of Substrate measures the amount that the material's electric field is lowered in relation to its value in a vacuum.ⓘ Dielectric Constant of Substrate [E_r]			+10% -10%
✖The thickness of the Substrate refers to the thickness of the dielectric substrate on which the microstrip antenna is fabricated.ⓘ Thickness of the Substrate [h]			+10% -10%
✖The Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.ⓘ Width of Microstrip Patch [W_p]			+10% -10%

✖The Effective Dielectric Constant of Substrate also known as the effective relative permittivity is a concept used in the analysis and design of microstrip and other planar antennas.ⓘ Effective Dielectric Constant of Substrate [E_eff]

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Formula

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Effective Dielectric Constant of Substrate

Formula

`"E"_{"eff"} = ("E"_{"r"}+1)/2+(("E"_{"r"}-1)/2)*(1/sqrt(1+12*("h"/"W"_{"p"})))`

Example

`"4.090057"=("4.4"+1)/2+(("4.4"-1)/2)*(1/sqrt(1+12*("1.57mm"/"38.01mm")))`

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Effective Dielectric Constant of Substrate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Dielectric Constant of Substrate = (Dielectric Constant of Substrate+1)/2+((Dielectric Constant of Substrate-1)/2)*(1/sqrt(1+12*(Thickness of the Substrate/Width of Microstrip Patch)))
E_eff = (E_r+1)/2+((E_r-1)/2)*(1/sqrt(1+12*(h/W_p)))
This formula uses 1 Functions, 4 Variables

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

Effective Dielectric Constant of Substrate - The Effective Dielectric Constant of Substrate also known as the effective relative permittivity is a concept used in the analysis and design of microstrip and other planar antennas.
Dielectric Constant of Substrate - The Dielectric Constant of Substrate measures the amount that the material's electric field is lowered in relation to its value in a vacuum.
Thickness of the Substrate - (Measured in Meter) - The thickness of the Substrate refers to the thickness of the dielectric substrate on which the microstrip antenna is fabricated.
Width of Microstrip Patch - (Measured in Meter) - The Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.

STEP 1: Convert Input(s) to Base Unit

Dielectric Constant of Substrate: 4.4 --> No Conversion Required
Thickness of the Substrate: 1.57 Millimeter --> 0.00157 Meter (Check conversion here)
Width of Microstrip Patch: 38.01 Millimeter --> 0.03801 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_eff = (E_r+1)/2+((E_r-1)/2)*(1/sqrt(1+12*(h/W_p))) --> (4.4+1)/2+((4.4-1)/2)*(1/sqrt(1+12*(0.00157/0.03801)))

Evaluating ... ...

E_eff = 4.09005704026773

STEP 3: Convert Result to Output's Unit

4.09005704026773 --> No Conversion Required

FINAL ANSWER

4.09005704026773 ≈ 4.090057 <-- Effective Dielectric Constant of Substrate

(Calculation completed in 00.020 seconds)

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Created by Souradeep Dey

National Institute of Technology Agartala (NITA), Agartala, Tripura

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< 16 Microstrip Antenna Calculators

Effective Radius of Circular Microstrip Patch

Go Effective Radius of Circular Microstrip Patch = Actual Radius of Circular Microstrip Patch*(1+((2*Thickness of Substrate Microstrip)/(pi*Actual Radius of Circular Microstrip Patch*Dielectric Constant of Substrate))*(ln((pi*Actual Radius of Circular Microstrip Patch)/(2*Thickness of Substrate Microstrip)+1.7726)))^0.5

Physical Radius of Circular Microstrip Patch

Go Actual Radius of Circular Microstrip Patch = Normalized Wavenumber/((1+(2*Thickness of Substrate Microstrip/(pi*Normalized Wavenumber*Dielectric Constant of Substrate))*(ln(pi*Normalized Wavenumber/(2*Thickness of Substrate Microstrip)+1.7726)))^(1/2))

Length Extention of Patch

Go Length Extension of Microstrip Patch = 0.412*Thickness of the Substrate*(((Effective Dielectric Constant of Substrate+0.3)*(Width of Microstrip Patch/Thickness of the Substrate+0.264))/((Effective Dielectric Constant of Substrate-0.264)*(Width of Microstrip Patch/Thickness of the Substrate+0.8)))

Effective Dielectric Constant of Substrate

Go Effective Dielectric Constant of Substrate = (Dielectric Constant of Substrate+1)/2+((Dielectric Constant of Substrate-1)/2)*(1/sqrt(1+12*(Thickness of the Substrate/Width of Microstrip Patch)))

Resonating Frequency of Microstrip Antenna

Go Resonant Frequency = [c]/(2*Effective Length of Microstrip Patch*sqrt(Effective Dielectric Constant of Substrate))

Resonating Frequency of Equilateral Triangular Patch

Go Resonant Frequency = 2*[c]/(3*Side Length of Equilateral Triangular Patch*sqrt(Dielectric Constant of Substrate))

Height of Equilateral Triangular Patch

Go Height of Equilateral Triangular Patch = sqrt(Side Length of Equilateral Triangular Patch^2-(Side Length of Equilateral Triangular Patch/2)^2)

Effective Length of Patch

Go Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate)))

Side Length of Equilateral Triangular Patch

Go Side Length of Equilateral Triangular Patch = 2*[c]/(3*Frequency*sqrt(Dielectric Constant of Substrate))

Side Length of Hexagonal Patch

Go Side Length of Hexagonal Patch = (sqrt(2*pi)*Effective Radius of Circular Microstrip Patch)/sqrt(5.1962)

Width of Microstrip Patch

Go Width of Microstrip Patch = [c]/(2*Frequency*(sqrt((Dielectric Constant of Substrate+1)/2)))

Normalized Wavenumber

Go Normalized Wavenumber = (8.791*10^9)/(Frequency*sqrt(Dielectric Constant of Substrate))

Actual Length of Microstrip Patch

Go Actual Length of Microstrip Patch = Effective Length of Microstrip Patch-2*Length Extension of Microstrip Patch

Radiation Resistance of Infinitesimal Dipole

Go Radiation Resistance of Infinitesimal Dipole = 80*pi^2*(Length of Infinitesimal Dipole/Wavelength of Dipole)^2

Length of Ground Plate

Go Length of Ground Plate = 6*Thickness of the Substrate+Actual Length of Microstrip Patch

Width of Ground Plate

Go Width of Ground Plate = 6*Thickness of the Substrate+Width of Microstrip Patch

Effective Dielectric Constant of Substrate Formula

What is the significance of effective dielectric constant of substrate ?

In microstrip antennas, the effective dielectric constant has a major impact on a number of antenna performance parameters. It is essential for figuring out the microstrip transmission line's characteristic impedance, which guarantees appropriate impedance matching and effective power transfer. The effective dielectric constant also influences the antenna's resonant frequency, which helps designers adjust the antenna to function at desired frequencies. This parameter affects the electrical length and resonant behavior of the antenna by influencing the velocity at which electromagnetic waves propagate within the microstrip construction.

How to Calculate Effective Dielectric Constant of Substrate?

Effective Dielectric Constant of Substrate calculator uses Effective Dielectric Constant of Substrate = (Dielectric Constant of Substrate+1)/2+((Dielectric Constant of Substrate-1)/2)*(1/sqrt(1+12*(Thickness of the Substrate/Width of Microstrip Patch))) to calculate the Effective Dielectric Constant of Substrate, The Effective Dielectric Constant of Substrate refers to an equivalent or effective permittivity that takes into account the substrate's influence on the electrical characteristics of the microstrip transmission line. This idea makes the design and analysis of microstrip structures simpler. Effective Dielectric Constant of Substrate is denoted by E_eff symbol.

How to calculate Effective Dielectric Constant of Substrate using this online calculator? To use this online calculator for Effective Dielectric Constant of Substrate, enter Dielectric Constant of Substrate (E_r), Thickness of the Substrate (h) & Width of Microstrip Patch (W_p) and hit the calculate button. Here is how the Effective Dielectric Constant of Substrate calculation can be explained with given input values -> 4.090057 = (4.4+1)/2+((4.4-1)/2)*(1/sqrt(1+12*(0.00157/0.03801))).

FAQ

What is Effective Dielectric Constant of Substrate?

The Effective Dielectric Constant of Substrate refers to an equivalent or effective permittivity that takes into account the substrate's influence on the electrical characteristics of the microstrip transmission line. This idea makes the design and analysis of microstrip structures simpler and is represented as E_eff = (E_r+1)/2+((E_r-1)/2)*(1/sqrt(1+12*(h/W_p))) or Effective Dielectric Constant of Substrate = (Dielectric Constant of Substrate+1)/2+((Dielectric Constant of Substrate-1)/2)*(1/sqrt(1+12*(Thickness of the Substrate/Width of Microstrip Patch))). The Dielectric Constant of Substrate measures the amount that the material's electric field is lowered in relation to its value in a vacuum, The thickness of the Substrate refers to the thickness of the dielectric substrate on which the microstrip antenna is fabricated & The Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.

How to calculate Effective Dielectric Constant of Substrate?

The Effective Dielectric Constant of Substrate refers to an equivalent or effective permittivity that takes into account the substrate's influence on the electrical characteristics of the microstrip transmission line. This idea makes the design and analysis of microstrip structures simpler is calculated using Effective Dielectric Constant of Substrate = (Dielectric Constant of Substrate+1)/2+((Dielectric Constant of Substrate-1)/2)*(1/sqrt(1+12*(Thickness of the Substrate/Width of Microstrip Patch))). To calculate Effective Dielectric Constant of Substrate, you need Dielectric Constant of Substrate (E_r), Thickness of the Substrate (h) & Width of Microstrip Patch (W_p). With our tool, you need to enter the respective value for Dielectric Constant of Substrate, Thickness of the Substrate & Width of Microstrip Patch 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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