Side Length of Hexagonal Patch Calculator

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Special Antennas

Antenna Theory Parameters

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✖Effective Radius of Circular Microstrip Patch is related to the physical radius of the circular patch but is adjusted to account for the fringing fields affecting the performance of the antenna.ⓘ Effective Radius of Circular Microstrip Patch [a_eff]

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✖The Side Length of Hexagonal Patch refers to the length of one of the sides of the hexagon.ⓘ Side Length of Hexagonal Patch [S_hex]

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Formula

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Side Length of Hexagonal Patch

Formula

`"S"_{"hex"} = (sqrt(2*pi)*"a"_{"eff"})/sqrt(5.1962)`

Example

`"192.1471mm"=(sqrt(2*pi)*"17.47378cm")/sqrt(5.1962)`

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Side Length of Hexagonal Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

Side Length of Hexagonal Patch = (sqrt(2*pi)*Effective Radius of Circular Microstrip Patch)/sqrt(5.1962)
S_hex = (sqrt(2*pi)*a_eff)/sqrt(5.1962)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

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

Side Length of Hexagonal Patch - (Measured in Meter) - The Side Length of Hexagonal Patch refers to the length of one of the sides of the hexagon.
Effective Radius of Circular Microstrip Patch - (Measured in Meter) - Effective Radius of Circular Microstrip Patch is related to the physical radius of the circular patch but is adjusted to account for the fringing fields affecting the performance of the antenna.

STEP 1: Convert Input(s) to Base Unit

Effective Radius of Circular Microstrip Patch: 17.47378 Centimeter --> 0.1747378 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_hex = (sqrt(2*pi)*a_eff)/sqrt(5.1962) --> (sqrt(2*pi)*0.1747378)/sqrt(5.1962)

Evaluating ... ...

S_hex = 0.192147115128304

STEP 3: Convert Result to Output's Unit

0.192147115128304 Meter -->192.147115128304 Millimeter (Check conversion here)

FINAL ANSWER

192.147115128304 ≈ 192.1471 Millimeter <-- Side Length of Hexagonal Patch

(Calculation completed in 00.020 seconds)

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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 Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

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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

Side Length of Hexagonal Patch Formula

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

What is the significance of side length of hexagonal patch antenna?

One important factor that greatly affects the effectiveness of a microstrip antenna is the side length of a hexagonal patch. Compared to other designs, the hexagonal shape is chosen because of its capacity to offer a wider bandwidth. The side length, represented by the letter "S_hex" controls the antenna's size and resonance frequency. It has a direct impact on electrical properties including radiation pattern and impedance matching. Achieving the required antenna requirements, such as radiation efficiency and resonance frequency, requires optimizing the side length. Additionally, the hexagonal form contributes to a more effective and reliable antenna design by reducing edge effects that are found in square patches. Therefore, the careful selection and tuning of the side length play a pivotal role in designing microstrip antennas with optimal performance for specific applications.

How to Calculate Side Length of Hexagonal Patch?

Side Length of Hexagonal Patch calculator uses Side Length of Hexagonal Patch = (sqrt(2*pi)*Effective Radius of Circular Microstrip Patch)/sqrt(5.1962) to calculate the Side Length of Hexagonal Patch, The Side Length of Hexagonal Patch refers to the length of one of the sides of the hexagon. The hexagonal shape is chosen for various reasons, including its ability to provide a wider bandwidth compared to a square or circular patch. Side Length of Hexagonal Patch is denoted by S_hex symbol.

How to calculate Side Length of Hexagonal Patch using this online calculator? To use this online calculator for Side Length of Hexagonal Patch, enter Effective Radius of Circular Microstrip Patch (a_eff) and hit the calculate button. Here is how the Side Length of Hexagonal Patch calculation can be explained with given input values -> 19214.71 = (sqrt(2*pi)*0.01747378)/sqrt(5.1962).

FAQ

What is Side Length of Hexagonal Patch?

The Side Length of Hexagonal Patch refers to the length of one of the sides of the hexagon. The hexagonal shape is chosen for various reasons, including its ability to provide a wider bandwidth compared to a square or circular patch and is represented as S_hex = (sqrt(2*pi)*a_eff)/sqrt(5.1962) or Side Length of Hexagonal Patch = (sqrt(2*pi)*Effective Radius of Circular Microstrip Patch)/sqrt(5.1962). Effective Radius of Circular Microstrip Patch is related to the physical radius of the circular patch but is adjusted to account for the fringing fields affecting the performance of the antenna.

How to calculate Side Length of Hexagonal Patch?

The Side Length of Hexagonal Patch refers to the length of one of the sides of the hexagon. The hexagonal shape is chosen for various reasons, including its ability to provide a wider bandwidth compared to a square or circular patch is calculated using Side Length of Hexagonal Patch = (sqrt(2*pi)*Effective Radius of Circular Microstrip Patch)/sqrt(5.1962). To calculate Side Length of Hexagonal Patch, you need Effective Radius of Circular Microstrip Patch (a_eff). With our tool, you need to enter the respective value for Effective Radius of Circular 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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