Resonating Frequency of Microstrip Antenna Calculator

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Special Antennas

Antenna Theory Parameters

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✖The Effective Length of Microstrip Patch takes into account the physical length and the influence of the dielectric substrate on the propagation of electromagnetic waves.ⓘ Effective Length of Microstrip Patch [L_eff]			+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 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 Microstrip Antenna [f_r]

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Formula

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Resonating Frequency of Microstrip Antenna

Formula

`"f"_{"r"} = "[c]"/(2*"L"_{"eff"}*sqrt("E"_{"eff"}))`

Example

`"2.398323GHz"="[c]"/(2*"30.90426103mm"*sqrt("4.09005704"))`

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Resonating Frequency of Microstrip Antenna Solution

STEP 0: Pre-Calculation Summary

Formula Used

Resonant Frequency = [c]/(2*Effective Length of Microstrip Patch*sqrt(Effective Dielectric Constant of Substrate))
f_r = [c]/(2*L_eff*sqrt(E_eff))
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.
Effective Length of Microstrip Patch - (Measured in Meter) - The Effective Length of Microstrip Patch takes into account the physical length and the influence of the dielectric substrate on the propagation of electromagnetic waves.
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.

STEP 1: Convert Input(s) to Base Unit

Effective Length of Microstrip Patch: 30.90426103 Millimeter --> 0.03090426103 Meter (Check conversion here)
Effective Dielectric Constant of Substrate: 4.09005704 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_r = [c]/(2*L_eff*sqrt(E_eff)) --> [c]/(2*0.03090426103*sqrt(4.09005704))

Evaluating ... ...

f_r = 2398322940.07791

STEP 3: Convert Result to Output's Unit

2398322940.07791 Hertz -->2.39832294007791 Gigahertz (Check conversion here)

FINAL ANSWER

2.39832294007791 ≈ 2.398323 Gigahertz <-- Resonant Frequency

(Calculation completed in 00.007 seconds)

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Created by Souradeep Dey

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

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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

Resonating Frequency of Microstrip Antenna Formula

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

What is resonating frequency with respect to microstrip patch antenna?

A microstrip patch antenna's resonance frequency indicates the precise frequency at which it responds best and radiates electromagnetic waves with the greatest efficiency. The physical dimensions of the patch, such as its length, width, and substrate thickness, as well as the substrate material's dielectric characteristics, dictate this crucial parameter.

How to Calculate Resonating Frequency of Microstrip Antenna?

Resonating Frequency of Microstrip Antenna calculator uses Resonant Frequency = [c]/(2*Effective Length of Microstrip Patch*sqrt(Effective Dielectric Constant of Substrate)) to calculate the Resonant Frequency, The Resonating Frequency of Microstrip Antenna refers to the specific frequency at which the antenna exhibits maximum efficiency in radiating or receiving electromagnetic signals. For a microstrip patch antenna, the resonant frequency is a crucial parameter that determines when the antenna is most responsive to the applied signal. Resonant Frequency is denoted by f_r symbol.

How to calculate Resonating Frequency of Microstrip Antenna using this online calculator? To use this online calculator for Resonating Frequency of Microstrip Antenna, enter Effective Length of Microstrip Patch (L_eff) & Effective Dielectric Constant of Substrate (E_eff) and hit the calculate button. Here is how the Resonating Frequency of Microstrip Antenna calculation can be explained with given input values -> 2.4E-9 = [c]/(2*0.03090426103*sqrt(4.09005704)).

FAQ

What is Resonating Frequency of Microstrip Antenna?

The Resonating Frequency of Microstrip Antenna refers to the specific frequency at which the antenna exhibits maximum efficiency in radiating or receiving electromagnetic signals. For a microstrip patch antenna, the resonant frequency is a crucial parameter that determines when the antenna is most responsive to the applied signal and is represented as f_r = [c]/(2*L_eff*sqrt(E_eff)) or Resonant Frequency = [c]/(2*Effective Length of Microstrip Patch*sqrt(Effective Dielectric Constant of Substrate)). The Effective Length of Microstrip Patch takes into account the physical length and the influence of the dielectric substrate on the propagation of electromagnetic waves & 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.

How to calculate Resonating Frequency of Microstrip Antenna?

The Resonating Frequency of Microstrip Antenna refers to the specific frequency at which the antenna exhibits maximum efficiency in radiating or receiving electromagnetic signals. For a microstrip patch antenna, the resonant frequency is a crucial parameter that determines when the antenna is most responsive to the applied signal is calculated using Resonant Frequency = [c]/(2*Effective Length of Microstrip Patch*sqrt(Effective Dielectric Constant of Substrate)). To calculate Resonating Frequency of Microstrip Antenna, you need Effective Length of Microstrip Patch (L_eff) & Effective Dielectric Constant of Substrate (E_eff). With our tool, you need to enter the respective value for Effective Length of Microstrip Patch & Effective 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 Effective Length of Microstrip Patch & Effective Dielectric Constant of Substrate. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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