Side Length of Equilateral Triangular Patch Calculator

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Special Antennas

Antenna Theory Parameters

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✖Frequency refers to the number of waves that pass a fixed point in unit time.ⓘ Frequency [f_res]			+10% -10%
✖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 Side Length of Equilateral Triangular Patch defines the dimensional parameter of the triangle if we know one side, all other two sides will be the same.ⓘ Side Length of Equilateral Triangular Patch [S_tng]

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Formula

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Side Length of Equilateral Triangular Patch

Formula

`"S"_{"tng"} = 2*"[c]"/(3*"f"_{"res"}*sqrt("E"_{"r"}))`

Example

`"39.70012mm"=2*"[c]"/(3*"2.4GHz"*sqrt("4.4"))`

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Side Length of Equilateral Triangular Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

Side Length of Equilateral Triangular Patch = 2*[c]/(3*Frequency*sqrt(Dielectric Constant of Substrate))
S_tng = 2*[c]/(3*f_res*sqrt(E_r))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[c] - Light speed in vacuum Value Taken As 299792458.0

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 Equilateral Triangular Patch - (Measured in Meter) - The Side Length of Equilateral Triangular Patch defines the dimensional parameter of the triangle if we know one side, all other two sides will be the same.
Frequency - (Measured in Hertz) - Frequency refers to the number of waves that pass a fixed point in unit time.
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.

STEP 1: Convert Input(s) to Base Unit

Frequency: 2.4 Gigahertz --> 2400000000 Hertz (Check conversion here)
Dielectric Constant of Substrate: 4.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_tng = 2*[c]/(3*f_res*sqrt(E_r)) --> 2*[c]/(3*2400000000*sqrt(4.4))

Evaluating ... ...

S_tng = 0.0397001240612473

STEP 3: Convert Result to Output's Unit

0.0397001240612473 Meter -->39.7001240612473 Millimeter (Check conversion here)

FINAL ANSWER

39.7001240612473 ≈ 39.70012 Millimeter <-- Side Length of Equilateral Triangular Patch

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electronics » Antenna & Wave Propogation » Special Antennas » Microstrip Antenna » Side Length of Equilateral Triangular Patch

Credits

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

Santhosh Yadav has verified this Calculator and 50+ more calculators!

< 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 Equilateral Triangular Patch Formula

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

What is the significance ?

One of the key factors controlling the electrical and radiation properties of a microstrip antenna is the side length of the equilateral triangle patch. This dimension has a major impact on the antenna's bandwidth, radiation pattern, and resonant frequency. To attain resonance within particular frequency bands, we meticulously adjust the side length, customize radiation patterns for peak efficiency, and ascertain the antenna's bandwidth to meet communication needs. The selected side length also affects the microstrip antenna's size and compactness, therefore it is important in applications where space is limited. Furthermore, side length is critical to impedance matching, which guarantees effective power transfer.

How to Calculate Side Length of Equilateral Triangular Patch?

Side Length of Equilateral Triangular Patch calculator uses Side Length of Equilateral Triangular Patch = 2*[c]/(3*Frequency*sqrt(Dielectric Constant of Substrate)) to calculate the Side Length of Equilateral Triangular Patch, The Side Length of Equilateral Triangular Patch is the distance between any two vertices (corners) of the triangle. In an equilateral triangle, all three sides are of equal length. This means that if you measure the distance from one vertex to any other vertex along the edge of the triangle, that distance is the side length. Side Length of Equilateral Triangular Patch is denoted by S_tng symbol.

How to calculate Side Length of Equilateral Triangular Patch using this online calculator? To use this online calculator for Side Length of Equilateral Triangular Patch, enter Frequency (f_res) & Dielectric Constant of Substrate (E_r) and hit the calculate button. Here is how the Side Length of Equilateral Triangular Patch calculation can be explained with given input values -> 39700.12 = 2*[c]/(3*2400000000*sqrt(4.4)).

FAQ

What is Side Length of Equilateral Triangular Patch?

The Side Length of Equilateral Triangular Patch is the distance between any two vertices (corners) of the triangle. In an equilateral triangle, all three sides are of equal length. This means that if you measure the distance from one vertex to any other vertex along the edge of the triangle, that distance is the side length and is represented as S_tng = 2*[c]/(3*f_res*sqrt(E_r)) or Side Length of Equilateral Triangular Patch = 2*[c]/(3*Frequency*sqrt(Dielectric Constant of Substrate)). Frequency refers to the number of waves that pass a fixed point in unit time & The Dielectric Constant of Substrate measures the amount that the material's electric field is lowered in relation to its value in a vacuum.

How to calculate Side Length of Equilateral Triangular Patch?

The Side Length of Equilateral Triangular Patch is the distance between any two vertices (corners) of the triangle. In an equilateral triangle, all three sides are of equal length. This means that if you measure the distance from one vertex to any other vertex along the edge of the triangle, that distance is the side length is calculated using Side Length of Equilateral Triangular Patch = 2*[c]/(3*Frequency*sqrt(Dielectric Constant of Substrate)). To calculate Side Length of Equilateral Triangular Patch, you need Frequency (f_res) & Dielectric Constant of Substrate (E_r). With our tool, you need to enter the respective value for Frequency & Dielectric Constant of Substrate 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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