Resonating Frequency of Equilateral Triangular Patch Calculator

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Special Antennas

Antenna Theory Parameters

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✖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]			+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 Resonant Frequency is the specific frequency at which an antenna naturally oscillates most efficiently. It maximizes electromagnetic wave interaction, crucial for optimal antenna performance.ⓘ Resonating Frequency of Equilateral Triangular Patch [f_r]

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Formula

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Resonating Frequency of Equilateral Triangular Patch

Formula

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

Example

`"2.39834GHz"=2*"[c]"/(3*"39.7276mm"*sqrt("4.4"))`

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Resonating Frequency of Equilateral Triangular Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Resonant Frequency - (Measured in Hertz) - The Resonant Frequency is the specific frequency at which an antenna naturally oscillates most efficiently. It maximizes electromagnetic wave interaction, crucial for optimal antenna performance.
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.
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

Side Length of Equilateral Triangular Patch: 39.7276 Millimeter --> 0.0397276 Meter (Check conversion here)
Dielectric Constant of Substrate: 4.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_r = 2*[c]/(3*S_tng*sqrt(E_r)) --> 2*[c]/(3*0.0397276*sqrt(4.4))

Evaluating ... ...

f_r = 2398340140.02843

STEP 3: Convert Result to Output's Unit

2398340140.02843 Hertz -->2.39834014002843 Gigahertz (Check conversion here)

FINAL ANSWER

2.39834014002843 ≈ 2.39834 Gigahertz <-- Resonant Frequency

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Antenna & Wave Propogation » Special Antennas » Microstrip Antenna » Resonating Frequency 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

Resonating Frequency of Equilateral Triangular Patch Formula

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

What is the significance resonating frequency of equilateral triangular patch ?

An equilateral triangular microstrip patch antenna's resonance frequency is a crucial factor that affects many aspects of its operation. This frequency indicates the point at which the antenna produces electromagnetic energy efficiently; it is influenced by the side length of the triangular patch. Engineers may carefully adjust the resonance frequency and line it with particular communication bands by tailoring the side length. This parameter is essential for maximizing the antenna's performance and making sure it runs at the frequencies needed for uses like radar systems and wireless communication. The resonant frequency of the equilateral triangle patch is an important factor to take into account when designing and implementing microstrip antennas in a variety of technical areas, as achieving resonance is essential for effective energy transfer and transmission.

How to Calculate Resonating Frequency of Equilateral Triangular Patch?

Resonating Frequency of Equilateral Triangular Patch calculator uses Resonant Frequency = 2*[c]/(3*Side Length of Equilateral Triangular Patch*sqrt(Dielectric Constant of Substrate)) to calculate the Resonant Frequency, The Resonating Frequency of Equilateral Triangular Patch is the frequency at which the antenna is most efficient in radiating or receiving electromagnetic waves. Resonant Frequency is denoted by f_r symbol.

How to calculate Resonating Frequency of Equilateral Triangular Patch using this online calculator? To use this online calculator for Resonating Frequency of Equilateral Triangular Patch, enter Side Length of Equilateral Triangular Patch (S_tng) & Dielectric Constant of Substrate (E_r) and hit the calculate button. Here is how the Resonating Frequency of Equilateral Triangular Patch calculation can be explained with given input values -> 2.4E-9 = 2*[c]/(3*0.0397276*sqrt(4.4)).

FAQ

What is Resonating Frequency of Equilateral Triangular Patch?

The Resonating Frequency of Equilateral Triangular Patch is the frequency at which the antenna is most efficient in radiating or receiving electromagnetic waves and is represented as f_r = 2*[c]/(3*S_tng*sqrt(E_r)) or Resonant Frequency = 2*[c]/(3*Side Length of Equilateral Triangular Patch*sqrt(Dielectric Constant of Substrate)). 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 & 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 Resonating Frequency of Equilateral Triangular Patch?

The Resonating Frequency of Equilateral Triangular Patch is the frequency at which the antenna is most efficient in radiating or receiving electromagnetic waves is calculated using Resonant Frequency = 2*[c]/(3*Side Length of Equilateral Triangular Patch*sqrt(Dielectric Constant of Substrate)). To calculate Resonating Frequency of Equilateral Triangular Patch, you need Side Length of Equilateral Triangular Patch (S_tng) & Dielectric Constant of Substrate (E_r). With our tool, you need to enter the respective value for Side Length of Equilateral Triangular Patch & 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.

How many ways are there to calculate Resonant Frequency?

In this formula, Resonant Frequency uses Side Length of Equilateral Triangular Patch & Dielectric Constant of Substrate. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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