Effective Length of 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 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 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 Patch [L_eff]

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Formula

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Effective Length of Patch

Formula

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

Example

`"30.88267mm"="[c]"/(2*"2.4GHz"*(sqrt("4.09005704")))`

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Effective Length of Patch Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Frequency - (Measured in Hertz) - Frequency refers to the number of waves that pass a fixed point in unit time.
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

Frequency: 2.4 Gigahertz --> 2400000000 Hertz (Check conversion here)
Effective Dielectric Constant of Substrate: 4.09005704 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_eff = [c]/(2*f_res*(sqrt(E_eff))) --> [c]/(2*2400000000*(sqrt(4.09005704)))

Evaluating ... ...

L_eff = 0.0308826659060019

STEP 3: Convert Result to Output's Unit

0.0308826659060019 Meter -->30.8826659060019 Millimeter (Check conversion here)

FINAL ANSWER

30.8826659060019 ≈ 30.88267 Millimeter <-- Effective Length of Microstrip Patch

(Calculation completed in 00.004 seconds)

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

Credits

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

Parminder Singh has verified this Calculator and 600+ 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

Effective Length of Patch Formula

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

What is the significance of effective length of patch?

An important factor that greatly affects a microstrip patch antenna's electrical performance is its effective length. This parameter affects the frequency at which the antenna radiates electromagnetic energy efficiently and is crucial in defining the resonant frequency of the antenna. The effective length plays a crucial role in attaining appropriate impedance matching since it affects the microstrip antenna's total impedance. Engineers can control and modify the form and orientation of the radiation pattern in accordance with design requirements since changes in the effective length also have a significant impact on the radiation pattern. Furthermore, the effective length is affected by the substrate material's dielectric characteristics and is intimately linked to the antenna's gain and bandwidth.

How to Calculate Effective Length of Patch?

Effective Length of Patch calculator uses Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate))) to calculate the Effective Length of Microstrip Patch, The Effective Length of Patch antenna is not typically expressed by a simple formula, as it involves complex electromagnetic interactions and is influenced by various factors, including the physical dimensions of the patch, the dielectric properties of the substrate, and the frequency of operation. Effective Length of Microstrip Patch is denoted by L_eff symbol.

How to calculate Effective Length of Patch using this online calculator? To use this online calculator for Effective Length of Patch, enter Frequency (f_res) & Effective Dielectric Constant of Substrate (E_eff) and hit the calculate button. Here is how the Effective Length of Patch calculation can be explained with given input values -> 30882.67 = [c]/(2*2400000000*(sqrt(4.09005704))).

FAQ

What is Effective Length of Patch?

The Effective Length of Patch antenna is not typically expressed by a simple formula, as it involves complex electromagnetic interactions and is influenced by various factors, including the physical dimensions of the patch, the dielectric properties of the substrate, and the frequency of operation and is represented as L_eff = [c]/(2*f_res*(sqrt(E_eff))) or Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate))). Frequency refers to the number of waves that pass a fixed point in unit time & 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 Effective Length of Patch?

The Effective Length of Patch antenna is not typically expressed by a simple formula, as it involves complex electromagnetic interactions and is influenced by various factors, including the physical dimensions of the patch, the dielectric properties of the substrate, and the frequency of operation is calculated using Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate))). To calculate Effective Length of Patch, you need Frequency (f_res) & Effective Dielectric Constant of Substrate (E_eff). With our tool, you need to enter the respective value for Frequency & 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.

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