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

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Formula

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Normalized Wavenumber

Formula

`"F"_{"n"} = (8.791*10^9)/("f"_{"res"}*sqrt("E"_{"r"}))`

Example

`"1.746227"=(8.791*10^9)/("2.4GHz"*sqrt("4.4"))`

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Normalized Wavenumber Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normalized Wavenumber = (8.791*10^9)/(Frequency*sqrt(Dielectric Constant of Substrate))
F_n = (8.791*10^9)/(f_res*sqrt(E_r))
This formula uses 1 Functions, 3 Variables

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

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

F_n = (8.791*10^9)/(f_res*sqrt(E_r)) --> (8.791*10^9)/(2400000000*sqrt(4.4))

Evaluating ... ...

F_n = 1.74622700459542

STEP 3: Convert Result to Output's Unit

1.74622700459542 --> No Conversion Required

FINAL ANSWER

1.74622700459542 ≈ 1.746227 <-- Normalized Wavenumber

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Antenna & Wave Propogation » Special Antennas » Microstrip Antenna » Normalized Wavenumber

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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

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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

Normalized Wavenumber Formula

Normalized Wavenumber = (8.791*10^9)/(Frequency*sqrt(Dielectric Constant of Substrate))
F_n = (8.791*10^9)/(f_res*sqrt(E_r))

What is the significance of normalized wavenumber?

In the realm of microwave engineering, the normalized wavenumber in microstrip transmission lines is very important. It offers a dimensionless measure of the propagation of electromagnetic waves along the microstrip structure and is represented by the symbol β. Engineers can evaluate and construct microstrip circuits without regard to particular physical dimensions by normalizing the wavenumber, which allows for a flexible knowledge over a range of frequencies and substrate materials. This dimensionless quantity is an important metric for effective design and analysis in high-frequency applications since it helps to optimize the performance of microstrip components and makes comparisons across various contexts easier.

How to Calculate Normalized Wavenumber?

Normalized Wavenumber calculator uses Normalized Wavenumber = (8.791*10^9)/(Frequency*sqrt(Dielectric Constant of Substrate)) to calculate the Normalized Wavenumber, The Normalized Wavenumber in microstrip, denoted as F_normalized , represents the dimensionless ratio of guided wave wavenumber to free-space wavenumber, aiding in the analysis and design of microstrip transmission lines at different frequencies and substrate materials. Normalized Wavenumber is denoted by F_n symbol.

How to calculate Normalized Wavenumber using this online calculator? To use this online calculator for Normalized Wavenumber, enter Frequency (f_res) & Dielectric Constant of Substrate (E_r) and hit the calculate button. Here is how the Normalized Wavenumber calculation can be explained with given input values -> 1.746227 = (8.791*10^9)/(2400000000*sqrt(4.4)).

FAQ

What is Normalized Wavenumber?

The Normalized Wavenumber in microstrip, denoted as F_normalized , represents the dimensionless ratio of guided wave wavenumber to free-space wavenumber, aiding in the analysis and design of microstrip transmission lines at different frequencies and substrate materials and is represented as F_n = (8.791*10^9)/(f_res*sqrt(E_r)) or Normalized Wavenumber = (8.791*10^9)/(Frequency*sqrt(Dielectric Constant of Substrate)). 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 Normalized Wavenumber?

The Normalized Wavenumber in microstrip, denoted as F_normalized , represents the dimensionless ratio of guided wave wavenumber to free-space wavenumber, aiding in the analysis and design of microstrip transmission lines at different frequencies and substrate materials is calculated using Normalized Wavenumber = (8.791*10^9)/(Frequency*sqrt(Dielectric Constant of Substrate)). To calculate Normalized Wavenumber, 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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