Physical Radius of Circular Microstrip Patch Calculator

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Special Antennas

Antenna Theory Parameters

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✖The Normalized Wavenumber typically refers to a dimensionless quantity that characterizes the propagation of electromagnetic waves along the microstrip structure.ⓘ Normalized Wavenumber [F_n]			+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%

✖The Actual Radius of Circular Microstrip Patch depends on the specific design parameters and requirements of the patch antenna.ⓘ Physical Radius of Circular Microstrip Patch [a_c]

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Formula

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Physical Radius of Circular Microstrip Patch

Formula

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

Example

`"174.538cm"="1.746227005"/((1+(2*"0.157cm"/(pi*"1.746227005"*"4.4"))*(ln(pi*"1.746227005"/(2*"0.157cm")+1.7726)))^(1/2))`

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Physical Radius of Circular Microstrip Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
a_c = F_n/((1+(2*h_o/(pi*F_n*E_r))*(ln(pi*F_n/(2*h_o)+1.7726)))^(1/2))
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

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.
Normalized Wavenumber - The Normalized Wavenumber typically refers to a dimensionless quantity that characterizes the propagation of electromagnetic waves along the microstrip structure.
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

Normalized Wavenumber: 1.746227005 --> No Conversion Required
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_c = F_n/((1+(2*h_o/(pi*F_n*E_r))*(ln(pi*F_n/(2*h_o)+1.7726)))^(1/2)) --> 1.746227005/((1+(2*0.00157/(pi*1.746227005*4.4))*(ln(pi*1.746227005/(2*0.00157)+1.7726)))^(1/2))

Evaluating ... ...

a_c = 1.74537955995848

STEP 3: Convert Result to Output's Unit

1.74537955995848 Meter -->174.537955995848 Centimeter (Check conversion here)

FINAL ANSWER

174.537955995848 ≈ 174.538 Centimeter <-- Actual 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 » Physical Radius of Circular Microstrip Patch

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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

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

Physical Radius of Circular Microstrip Patch Formula

What is the significance of physical radius of circular microstrip patch ?

The design and performance of a circular microstrip patch antenna are greatly influenced by its physical radius. This parameter has a direct impact on the radiation properties, impedance matching, and resonance frequency of the antenna. The physical radius is a critical factor in establishing the ideal operating frequency and overall efficiency of an antenna by dictating its size and form. It is an essential geometric dimension that contributes to the definition of the antenna's electrical behavior together with other elements like substrate characteristics. Achieving the best possible antenna performance requires precise management of the physical radius, which is why it is a crucial factor to take into account throughout the design phase. Engineers can customize the antenna for a certain application by fine-tuning the physical radius. This ensures that the radiation pattern features and impedance matching are correct for dependable and effective communication systems.

How to Calculate Physical Radius of Circular Microstrip Patch?

Physical Radius of Circular Microstrip Patch calculator uses 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)) to calculate the Actual Radius of Circular Microstrip Patch, The Physical Radius of Circular Microstrip Patch is vital in determining size, resonance frequency, impedance matching, and radiation characteristics. Precise control is essential for optimal performance in diverse communication systems. Actual Radius of Circular Microstrip Patch is denoted by a_c symbol.

How to calculate Physical Radius of Circular Microstrip Patch using this online calculator? To use this online calculator for Physical Radius of Circular Microstrip Patch, enter Normalized Wavenumber (F_n), Thickness of Substrate Microstrip (h_o) & Dielectric Constant of Substrate (E_r) and hit the calculate button. Here is how the Physical Radius of Circular Microstrip Patch calculation can be explained with given input values -> 17453.8 = 1.746227005/((1+(2*0.00157/(pi*1.746227005*4.4))*(ln(pi*1.746227005/(2*0.00157)+1.7726)))^(1/2)).

FAQ

What is Physical Radius of Circular Microstrip Patch?

The Physical Radius of Circular Microstrip Patch is vital in determining size, resonance frequency, impedance matching, and radiation characteristics. Precise control is essential for optimal performance in diverse communication systems and is represented as a_c = F_n/((1+(2*h_o/(pi*F_n*E_r))*(ln(pi*F_n/(2*h_o)+1.7726)))^(1/2)) or 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)). The Normalized Wavenumber typically refers to a dimensionless quantity that characterizes the propagation of electromagnetic waves along the microstrip structure, 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 Physical Radius of Circular Microstrip Patch?

The Physical Radius of Circular Microstrip Patch is vital in determining size, resonance frequency, impedance matching, and radiation characteristics. Precise control is essential for optimal performance in diverse communication systems is calculated using 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)). To calculate Physical Radius of Circular Microstrip Patch, you need Normalized Wavenumber (F_n), Thickness of Substrate Microstrip (h_o) & Dielectric Constant of Substrate (E_r). With our tool, you need to enter the respective value for Normalized Wavenumber, 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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