Length Extention of Patch Calculator

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⤿

Special Antennas

Antenna Theory Parameters

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✖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 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]			+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%

✖Length Extension of Microstrip Patch refers to a modification or adjustment made to the physical length of the patch.ⓘ Length Extention of Patch [ΔL]

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Formula

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Length Extention of Patch

Formula

`"ΔL" = 0.412*"h"*((("E"_{"eff"}+0.3)*("W"_{"p"}/"h"+0.264))/(("E"_{"eff"}-0.264)*("W"_{"p"}/"h"+0.8)))`

Example

`"0.726285mm"=0.412*"1.57mm"*((("4.09005704"+0.3)*("38.01mm"/"1.57mm"+0.264))/(("4.09005704"-0.264)*("38.01mm"/"1.57mm"+0.8)))`

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Length Extention of Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
ΔL = 0.412*h*(((E_eff+0.3)*(W_p/h+0.264))/((E_eff-0.264)*(W_p/h+0.8)))
This formula uses 4 Variables

Variables Used

Length Extension of Microstrip Patch - (Measured in Meter) - Length Extension of Microstrip Patch refers to a modification or adjustment made to the physical length of the patch.
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.
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.
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

Thickness of the Substrate: 1.57 Millimeter --> 0.00157 Meter (Check conversion here)
Effective Dielectric Constant of Substrate: 4.09005704 --> No Conversion Required
Width of Microstrip Patch: 38.01 Millimeter --> 0.03801 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔL = 0.412*h*(((E_eff+0.3)*(W_p/h+0.264))/((E_eff-0.264)*(W_p/h+0.8))) --> 0.412*0.00157*(((4.09005704+0.3)*(0.03801/0.00157+0.264))/((4.09005704-0.264)*(0.03801/0.00157+0.8)))

Evaluating ... ...

ΔL = 0.00072628475428001

STEP 3: Convert Result to Output's Unit

0.00072628475428001 Meter -->0.72628475428001 Millimeter (Check conversion here)

FINAL ANSWER

0.72628475428001 ≈ 0.726285 Millimeter <-- Length Extension of Microstrip Patch

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Antenna & Wave Propogation » Special Antennas » Microstrip Antenna » Length Extention of Patch

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Created by Souradeep Dey

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

Souradeep Dey has created this Calculator and 25+ more calculators!

Verified by Parminder Singh

Chandigarh University (CU), Punjab

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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

Length Extention of Patch Formula

what is the significance of Length extention?

A patch antenna's length extension is crucial for adjusting the antenna's performance to fulfill particular design goals. For antenna engineers and designers, this intentional adjusting or changing of the radiating element's physical length is a useful tool. A crucial aspect is resonance tuning, in which length extensions are employed to precisely modify the resonant frequency in order to achieve maximum efficiency at the intended operating frequency. Furthermore, length adjustments are essential for impedance matching, which makes it possible for the antenna and the linked transmission line to transfer energy efficiently.

How to Calculate Length Extention of Patch?

Length Extention of Patch calculator uses 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))) to calculate the Length Extension of Microstrip Patch, The Length Extention of Patch formula is refers to the deliberate modification or adjustment made to the physical length of the patch element in order to achieve specific design goals and improve the antenna's performance. Length Extension of Microstrip Patch is denoted by ΔL symbol.

How to calculate Length Extention of Patch using this online calculator? To use this online calculator for Length Extention of Patch, enter Thickness of the Substrate (h), Effective Dielectric Constant of Substrate (E_eff) & Width of Microstrip Patch (W_p) and hit the calculate button. Here is how the Length Extention of Patch calculation can be explained with given input values -> 726.2848 = 0.412*0.00157*(((4.09005704+0.3)*(0.03801/0.00157+0.264))/((4.09005704-0.264)*(0.03801/0.00157+0.8))).

FAQ

What is Length Extention of Patch?

The Length Extention of Patch formula is refers to the deliberate modification or adjustment made to the physical length of the patch element in order to achieve specific design goals and improve the antenna's performance and is represented as ΔL = 0.412*h*(((E_eff+0.3)*(W_p/h+0.264))/((E_eff-0.264)*(W_p/h+0.8))) or 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))). The thickness of the Substrate refers to the thickness of the dielectric substrate on which the microstrip antenna is fabricated, 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 & The Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.

How to calculate Length Extention of Patch?

The Length Extention of Patch formula is refers to the deliberate modification or adjustment made to the physical length of the patch element in order to achieve specific design goals and improve the antenna's performance is calculated using 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))). To calculate Length Extention of Patch, you need Thickness of the Substrate (h), Effective Dielectric Constant of Substrate (E_eff) & Width of Microstrip Patch (W_p). With our tool, you need to enter the respective value for Thickness of the Substrate, Effective Dielectric Constant of 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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