Effective Radius of Circular Microstrip Patch Calculator

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Special Antennas

Antenna Theory Parameters

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✖The Actual Radius of Circular Microstrip Patch depends on the specific design parameters and requirements of the patch antenna.ⓘ Actual Radius of Circular Microstrip Patch [a_c]			+10% -10%
✖The Thickness of Substrate Microstrip defines the height of the dielectric substrate.ⓘ Thickness of Substrate Microstrip [h_o]			+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%

✖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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Formula

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Effective Radius of Circular Microstrip Patch

Formula

`"a"_{"eff"} = "a"_{"c"}*(1+((2*"h"_{"o"})/(pi*"a"_{"c"}*"E"_{"r"}))*(ln((pi*"a"_{"c"})/(2*"h"_{"o"})+1.7726)))^0.5`

Example

`"174.6228cm"="174.538cm"*(1+((2*"0.157cm")/(pi*"174.538cm"*"4.4"))*(ln((pi*"174.538cm")/(2*"0.157cm")+1.7726)))^0.5`

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Effective Radius of Circular Microstrip Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
a_eff = a_c*(1+((2*h_o)/(pi*a_c*E_r))*(ln((pi*a_c)/(2*h_o)+1.7726)))^0.5
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

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.
Actual Radius of Circular Microstrip Patch - (Measured in Meter) - The Actual Radius of Circular Microstrip Patch depends on the specific design parameters and requirements of the patch antenna.
Thickness of Substrate Microstrip - (Measured in Meter) - The Thickness of Substrate Microstrip defines the height of the dielectric substrate.
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

Actual Radius of Circular Microstrip Patch: 174.538 Centimeter --> 1.74538 Meter (Check conversion here)
Thickness of Substrate Microstrip: 0.157 Centimeter --> 0.00157 Meter (Check conversion here)
Dielectric Constant of Substrate: 4.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_eff = a_c*(1+((2*h_o)/(pi*a_c*E_r))*(ln((pi*a_c)/(2*h_o)+1.7726)))^0.5 --> 1.74538*(1+((2*0.00157)/(pi*1.74538*4.4))*(ln((pi*1.74538)/(2*0.00157)+1.7726)))^0.5

Evaluating ... ...

a_eff = 1.74622780138498

STEP 3: Convert Result to Output's Unit

1.74622780138498 Meter -->174.622780138498 Centimeter (Check conversion here)

FINAL ANSWER

174.622780138498 ≈ 174.6228 Centimeter <-- Effective Radius of Circular Microstrip Patch

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Antenna & Wave Propogation » Special Antennas » Microstrip Antenna » Effective Radius of Circular Microstrip Patch

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Created by Souradeep Dey

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

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GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI

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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

Effective Radius of Circular Microstrip Patch Formula

Where does effective radius of circular patch antenna used?

For circular microstrip patches, the effective radius is frequently utilized in the context of impedance calculations. Because of the distribution of the electric field near the edges, the effective radius of a circular patch is usually smaller than its physical radius.

How to Calculate Effective Radius of Circular Microstrip Patch?

Effective Radius of Circular Microstrip Patch calculator uses 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 to calculate the Effective Radius of Circular Microstrip Patch, The Effective Radius of Circular Microstrip Patch is a critical parameter. It is connected to the circular patch's physical radius but is modified to take fringing fields and other elements that affect the antenna's performance into account. Effective Radius of Circular Microstrip Patch is denoted by a_eff symbol.

How to calculate Effective Radius of Circular Microstrip Patch using this online calculator? To use this online calculator for Effective Radius of Circular Microstrip Patch, enter Actual Radius of Circular Microstrip Patch (a_c), Thickness of Substrate Microstrip (h_o) & Dielectric Constant of Substrate (E_r) and hit the calculate button. Here is how the Effective Radius of Circular Microstrip Patch calculation can be explained with given input values -> 1751.245 = 1.74538*(1+((2*0.00157)/(pi*1.74538*4.4))*(ln((pi*1.74538)/(2*0.00157)+1.7726)))^0.5.

FAQ

What is Effective Radius of Circular Microstrip Patch?

The Effective Radius of Circular Microstrip Patch is a critical parameter. It is connected to the circular patch's physical radius but is modified to take fringing fields and other elements that affect the antenna's performance into account and is represented as a_eff = a_c*(1+((2*h_o)/(pi*a_c*E_r))*(ln((pi*a_c)/(2*h_o)+1.7726)))^0.5 or 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. The Actual Radius of Circular Microstrip Patch depends on the specific design parameters and requirements of the patch antenna, The Thickness of Substrate Microstrip defines the height of the dielectric 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.

How to calculate Effective Radius of Circular Microstrip Patch?

The Effective Radius of Circular Microstrip Patch is a critical parameter. It is connected to the circular patch's physical radius but is modified to take fringing fields and other elements that affect the antenna's performance into account is calculated using 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. To calculate Effective Radius of Circular Microstrip Patch, you need Actual Radius of Circular Microstrip Patch (a_c), Thickness of Substrate Microstrip (h_o) & Dielectric Constant of Substrate (E_r). With our tool, you need to enter the respective value for Actual Radius of Circular Microstrip Patch, Thickness of Substrate Microstrip & 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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