Effective Dielectric Constant of Substrate Calculator

✖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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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 00.004 seconds)

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Created by Souradeep Dey

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

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Chandigarh University (CU), Punjab

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< Microstrip Antenna Calculators

Length Extention of Patch

LaTeX 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

LaTeX 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)))

Effective Length of Patch

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

Width of Microstrip Patch

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

Effective Dielectric Constant of Substrate Formula

LaTeX Go

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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