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Effective Length of Patch Formula

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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. Check FAQs

L eff = \frac{[c]}{2 \cdot f res \cdot (\sqrt{E eff})}

L_eff - Effective Length of Microstrip Patch?f_res - Frequency?E_eff - Effective Dielectric Constant of Substrate?[c] - Light speed in vacuum?

Effective Length of Patch Example

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Here is how the Effective Length of Patch equation looks like with Values.

Here is how the Effective Length of Patch equation looks like with Units.

Here is how the Effective Length of Patch equation looks like.

30.8827 = \frac{3E+8}{2 \cdot 2.4 \cdot (\sqrt{4.0901})}

30.8827mm = \frac{3E+8m/s}{2 \cdot 2.4GHz \cdot (\sqrt{4.0901})}

30.8827 = \frac{3E+8}{2 \cdot 2.4 \cdot (\sqrt{4.0901})}

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Effective Length of Patch Solution

Follow our step by step solution on how to calculate Effective Length of Patch?

FIRST Step Consider the formula

L eff = \frac{[c]}{2 \cdot f res \cdot (\sqrt{E eff})}

Next Step Substitute values of Variables

∴

L eff = \frac{[c]}{2 \cdot 2.4GHz \cdot (\sqrt{4.0901})}

Next Step Substitute values of Constants

∴

L eff = \frac{3E+8m/s}{2 \cdot 2.4GHz \cdot (\sqrt{4.0901})}

Next Step Convert Units

∴

L eff = \frac{3E+8m/s}{2 \cdot 2.4E+9Hz \cdot (\sqrt{4.0901})}

Next Step Prepare to Evaluate

∴

L eff = \frac{3E+8}{2 \cdot 2.4E+9 \cdot (\sqrt{4.0901})}

Next Step Evaluate

∴

L eff = 0.0308826659060019m

Next Step Convert to Output's Unit

∴

L eff = 30.8826659060019mm

LAST Step Rounding Answer

∴

L eff = 30.8827mm

Effective Length of Patch Formula Elements

Variables

Constants

Functions

Effective Length of Microstrip Patch

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.

Symbol: L_eff

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Microstrip Patch

Frequency

Frequency refers to the number of waves that pass a fixed point in unit time.

Symbol: f_res

Measurement: FrequencyUnit: GHz

Note: Value should be greater than 0.

Formulas to find Frequency

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.

Symbol: E_eff

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Effective Dielectric Constant of Substrate

Light speed in vacuum

Light speed in vacuum is a fundamental physical constant representing the speed at which light propagates through a vacuum.

Symbol: [c]

Value: 299792458.0 m/s

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.

Syntax: sqrt(Number)

Other formulas in Microstrip Antenna category

Go Width of Microstrip Patch

W p = \frac{[c]}{2 \cdot f res \cdot (\sqrt{\frac{E r + 1}{2}})}

Go Effective Dielectric Constant of Substrate

E eff = \frac{E r + 1}{2} + (\frac{E r - 1}{2}) \cdot (\frac{1}{\sqrt{1 + 12 \cdot (\frac{h}{W p})}})

Go Length Extention of Patch

ΔL = 0.412 \cdot h \cdot (\frac{(E eff + 0.3) \cdot (\frac{W p}{h} + 0.264)}{(E eff - 0.264) \cdot (\frac{W p}{h} + 0.8)})

Go Resonating Frequency of Microstrip Antenna

f r = \frac{[c]}{2 \cdot L eff \cdot \sqrt{E eff}}

How to Evaluate Effective Length of Patch?

Effective Length of Patch evaluator uses Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate))) to evaluate 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 evaluate Effective Length of Patch using this online evaluator? To use this online evaluator for Effective Length of Patch, enter Frequency (f_res) & Effective Dielectric Constant of Substrate (E_eff) and hit the calculate button.

FAQs on Effective Length of Patch

What is the formula to find Effective Length of Patch?

The formula of Effective Length of Patch is expressed as Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate))). Here is an example- 30882.67 = [c]/(2*2400000000*(sqrt(4.09005704))).

How to calculate Effective Length of Patch?

With Frequency (f_res) & Effective Dielectric Constant of Substrate (E_eff) we can find Effective Length of Patch using the formula - Effective Length of Microstrip Patch = [c]/(2*Frequency*(sqrt(Effective Dielectric Constant of Substrate))). This formula also uses Light speed in vacuum constant(s) and Square Root (sqrt) function(s).

Can the Effective Length of Patch be negative?

No, the Effective Length of Patch, measured in Length cannot be negative.

Which unit is used to measure Effective Length of Patch?

Effective Length of Patch is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Effective Length of Patch can be measured.

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Effective Length of Patch Formula

Effective Length of Patch Example

Effective Length of Patch Solution

Effective Length of Patch Formula Elements

Other formulas in Microstrip Antenna category

How to Evaluate Effective Length of Patch?

FAQs on Effective Length of Patch

Variable Name