Width of Microstrip 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 Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.ⓘ Width of Microstrip Patch [W_p]

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Formula

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Width of Microstrip Patch

Formula

`"W"_{"p"} = "[c]"/(2*"f"_{"res"}*(sqrt(("E"_{"r"}+1)/2)))`

Example

`"38.00997mm"="[c]"/(2*"2.4GHz"*(sqrt(("4.4"+1)/2)))`

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Width of Microstrip Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

Width of Microstrip Patch = [c]/(2*Frequency*(sqrt((Dielectric Constant of Substrate+1)/2)))
W_p = [c]/(2*f_res*(sqrt((E_r+1)/2)))
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

Width of Microstrip Patch - (Measured in Meter) - The Width of Microstrip Patch antenna plays a critical role in determining its electrical characteristics and performance.
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

W_p = [c]/(2*f_res*(sqrt((E_r+1)/2))) --> [c]/(2*2400000000*(sqrt((4.4+1)/2)))

Evaluating ... ...

W_p = 0.0380099749575278

STEP 3: Convert Result to Output's Unit

0.0380099749575278 Meter -->38.0099749575278 Millimeter (Check conversion here)

FINAL ANSWER

38.0099749575278 ≈ 38.00997 Millimeter <-- Width of Microstrip Patch

(Calculation completed in 00.004 seconds)

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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 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

Width of Microstrip Patch Formula

Width of Microstrip Patch = [c]/(2*Frequency*(sqrt((Dielectric Constant of Substrate+1)/2)))
W_p = [c]/(2*f_res*(sqrt((E_r+1)/2)))

What is the significance of width of microstrip patch ?

An essential factor that greatly affects a microstrip patch antenna's resonant frequency, impedance matching, bandwidth, radiation pattern, effective dielectric constant, size, and overall performance is its width. By varying the width, antenna designers can enhance impedance matching, customize the antenna for certain frequencies, and get desired radiation characteristics.

How to Calculate Width of Microstrip Patch?

Width of Microstrip Patch calculator uses Width of Microstrip Patch = [c]/(2*Frequency*(sqrt((Dielectric Constant of Substrate+1)/2))) to calculate the Width of Microstrip Patch, The Width of Microstrip Patch formula is derived from the microstrip transmission line theory and is used to determine the physical width of the rectangular patch that forms the radiating element of the antenna. Width of Microstrip Patch is denoted by W_p symbol.

How to calculate Width of Microstrip Patch using this online calculator? To use this online calculator for Width of Microstrip Patch, enter Frequency (f_res) & Dielectric Constant of Substrate (E_r) and hit the calculate button. Here is how the Width of Microstrip Patch calculation can be explained with given input values -> 38009.97 = [c]/(2*2400000000*(sqrt((4.4+1)/2))).

FAQ

What is Width of Microstrip Patch?

The Width of Microstrip Patch formula is derived from the microstrip transmission line theory and is used to determine the physical width of the rectangular patch that forms the radiating element of the antenna and is represented as W_p = [c]/(2*f_res*(sqrt((E_r+1)/2))) or Width of Microstrip Patch = [c]/(2*Frequency*(sqrt((Dielectric Constant of Substrate+1)/2))). 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 Width of Microstrip Patch?

The Width of Microstrip Patch formula is derived from the microstrip transmission line theory and is used to determine the physical width of the rectangular patch that forms the radiating element of the antenna is calculated using Width of Microstrip Patch = [c]/(2*Frequency*(sqrt((Dielectric Constant of Substrate+1)/2))). To calculate Width of Microstrip 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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