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Effective Dielectric Constant of Substrate Formula

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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. Check FAQs

E eff = \frac{E r + 1}{2} + (\frac{E r - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{h}{W p})}})

E_eff - Effective Dielectric Constant of Substrate?E_r - Dielectric Constant of Substrate?h - Thickness of the Substrate?W_p - Width of Microstrip Patch?

Effective Dielectric Constant of Substrate Example

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Here is how the Effective Dielectric Constant of Substrate equation looks like with Values.

Here is how the Effective Dielectric Constant of Substrate equation looks like with Units.

Here is how the Effective Dielectric Constant of Substrate equation looks like.

4.0901 = \frac{4.4 + 1}{2} + (\frac{4.4 - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{1.57}{38.01})}})

4.0901 = \frac{4.4 + 1}{2} + (\frac{4.4 - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{1.57mm}{38.01mm})}})

4.0901 = \frac{4.4 + 1}{2} + (\frac{4.4 - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{1.57}{38.01})}})

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Effective Dielectric Constant of Substrate Solution

Follow our step by step solution on how to calculate Effective Dielectric Constant of Substrate?

FIRST Step Consider the formula

E eff = \frac{E r + 1}{2} + (\frac{E r - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{h}{W p})}})

Next Step Substitute values of Variables

∴

E eff = \frac{4.4 + 1}{2} + (\frac{4.4 - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{1.57mm}{38.01mm})}})

Next Step Convert Units

∴

E eff = \frac{4.4 + 1}{2} + (\frac{4.4 - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{0.0016m}{0.038m})}})

Next Step Prepare to Evaluate

∴

E eff = \frac{4.4 + 1}{2} + (\frac{4.4 - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{0.0016}{0.038})}})

Next Step Evaluate

∴

E eff = 4.09005704026773

LAST Step Rounding Answer

∴

E eff = 4.0901

Effective Dielectric Constant of Substrate Formula Elements

Variables

Functions

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.

Symbol: E_eff

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Effective Dielectric Constant of Substrate

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.

Symbol: E_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Dielectric Constant of Substrate

Thickness of the Substrate

The thickness of the Substrate refers to the thickness of the dielectric substrate on which the microstrip antenna is fabricated.

Symbol: h

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of the Substrate

Width of Microstrip Patch

The Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.

Symbol: W_p

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Microstrip Patch

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.

Syntax: sqrt(Number)

Other formulas in Microstrip Antenna category

Go Width of Microstrip Patch

W p = \frac{[c]}{2 \cdot f res \cdot (\sqrt{\frac{E r + 1}{2}})}

Go Effective Length of Patch

L eff = \frac{[c]}{2 \cdot f res \cdot (\sqrt{E eff})}

Go Length Extention of Patch

ΔL = 0.412 \cdot h \cdot (\frac{(E eff + 0.3) \cdot (\frac{W p}{h} + 0.264)}{(E eff - 0.264) \cdot (\frac{W p}{h} + 0.8)})

Go Resonating Frequency of Microstrip Antenna

f r = \frac{[c]}{2 \cdot L eff \cdot \sqrt{E eff}}

How to Evaluate Effective Dielectric Constant of Substrate?

Effective Dielectric Constant of Substrate evaluator 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 evaluate 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 evaluate Effective Dielectric Constant of Substrate using this online evaluator? To use this online evaluator 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.

FAQs on Effective Dielectric Constant of Substrate

What is the formula to find Effective Dielectric Constant of Substrate?

The formula of Effective Dielectric Constant of Substrate is expressed as 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))). Here is an example- 4.090057 = (4.4+1)/2+((4.4-1)/2)*(1/sqrt(1+12*(0.00157/0.03801))).

How to calculate Effective Dielectric Constant of Substrate?

With Dielectric Constant of Substrate (E_r), Thickness of the Substrate (h) & Width of Microstrip Patch (W_p) we can find Effective Dielectric Constant of Substrate using the formula - 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))). This formula also uses Square Root (sqrt) function(s).

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Effective Dielectric Constant of Substrate Formula

Effective Dielectric Constant of Substrate Example

Effective Dielectric Constant of Substrate Solution

Effective Dielectric Constant of Substrate Formula Elements

Other formulas in Microstrip Antenna category

How to Evaluate Effective Dielectric Constant of Substrate?

FAQs on Effective Dielectric Constant of Substrate

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