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Effective Radius of Circular Microstrip Patch Formula

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Effective Radius of Circular Microstrip Patch is related to the physical radius of the circular patch but is adjusted to account for the fringing fields affecting the performance of the antenna. Check FAQs

a eff = a c \cdot {(1 + (\frac{2 \cdot h o}{π \cdot a c \cdot E r}) \cdot (\ln (\frac{π \cdot a c}{2 \cdot h o} + 1.7726)))}^{0.5}

a_eff - Effective Radius of Circular Microstrip Patch?a_c - Actual Radius of Circular Microstrip Patch?h_o - Thickness of Substrate Microstrip?E_r - Dielectric Constant of Substrate?π - Archimedes' constant?

Effective Radius of Circular Microstrip Patch Example

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Here is how the Effective Radius of Circular Microstrip Patch equation looks like with Values.

Here is how the Effective Radius of Circular Microstrip Patch equation looks like with Units.

Here is how the Effective Radius of Circular Microstrip Patch equation looks like.

174.6228 = 174.538 \cdot {(1 + (\frac{2 \cdot 0.157}{3.1416 \cdot 174.538 \cdot 4.4}) \cdot (\ln (\frac{3.1416 \cdot 174.538}{2 \cdot 0.157} + 1.7726)))}^{0.5}

174.6228cm = 174.538cm \cdot {(1 + (\frac{2 \cdot 0.157cm}{3.1416 \cdot 174.538cm \cdot 4.4}) \cdot (\ln (\frac{3.1416 \cdot 174.538cm}{2 \cdot 0.157cm} + 1.7726)))}^{0.5}

174.6228 = 174.538 \cdot {(1 + (\frac{2 \cdot 0.157}{3.1416 \cdot 174.538 \cdot 4.4}) \cdot (\ln (\frac{3.1416 \cdot 174.538}{2 \cdot 0.157} + 1.7726)))}^{0.5}

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Effective Radius of Circular Microstrip Patch Solution

Follow our step by step solution on how to calculate Effective Radius of Circular Microstrip Patch?

FIRST Step Consider the formula

a eff = a c \cdot {(1 + (\frac{2 \cdot h o}{π \cdot a c \cdot E r}) \cdot (\ln (\frac{π \cdot a c}{2 \cdot h o} + 1.7726)))}^{0.5}

Next Step Substitute values of Variables

∴

a eff = 174.538cm \cdot {(1 + (\frac{2 \cdot 0.157cm}{π \cdot 174.538cm \cdot 4.4}) \cdot (\ln (\frac{π \cdot 174.538cm}{2 \cdot 0.157cm} + 1.7726)))}^{0.5}

Next Step Substitute values of Constants

∴

a eff = 174.538cm \cdot {(1 + (\frac{2 \cdot 0.157cm}{3.1416 \cdot 174.538cm \cdot 4.4}) \cdot (\ln (\frac{3.1416 \cdot 174.538cm}{2 \cdot 0.157cm} + 1.7726)))}^{0.5}

Next Step Convert Units

∴

a eff = 1.7454m \cdot {(1 + (\frac{2 \cdot 0.0016m}{3.1416 \cdot 1.7454m \cdot 4.4}) \cdot (\ln (\frac{3.1416 \cdot 1.7454m}{2 \cdot 0.0016m} + 1.7726)))}^{0.5}

Next Step Prepare to Evaluate

∴

a eff = 1.7454 \cdot {(1 + (\frac{2 \cdot 0.0016}{3.1416 \cdot 1.7454 \cdot 4.4}) \cdot (\ln (\frac{3.1416 \cdot 1.7454}{2 \cdot 0.0016} + 1.7726)))}^{0.5}

Next Step Evaluate

∴

a eff = 1.74622780138498m

Next Step Convert to Output's Unit

∴

a eff = 174.622780138498cm

LAST Step Rounding Answer

∴

a eff = 174.6228cm

Effective Radius of Circular Microstrip Patch Formula Elements

Variables

Constants

Functions

Effective Radius of Circular Microstrip Patch

Effective Radius of Circular Microstrip Patch is related to the physical radius of the circular patch but is adjusted to account for the fringing fields affecting the performance of the antenna.

Symbol: a_eff

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Effective Radius of Circular Microstrip Patch

Actual Radius of Circular Microstrip Patch

The Actual Radius of Circular Microstrip Patch depends on the specific design parameters and requirements of the patch antenna.

Symbol: a_c

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Actual Radius of Circular Microstrip Patch

Thickness of Substrate Microstrip

The Thickness of Substrate Microstrip defines the height of the dielectric substrate.

Symbol: h_o

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Thickness of Substrate Microstrip

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.

Symbol: E_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Dielectric Constant of Substrate

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(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 Effective Length of Patch

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

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)})

How to Evaluate Effective Radius of Circular Microstrip Patch?

Effective Radius of Circular Microstrip Patch evaluator uses 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 to evaluate the Effective Radius of Circular Microstrip Patch, The Effective Radius of Circular Microstrip Patch is a critical parameter. It is connected to the circular patch's physical radius but is modified to take fringing fields and other elements that affect the antenna's performance into account. Effective Radius of Circular Microstrip Patch is denoted by a_eff symbol.

How to evaluate Effective Radius of Circular Microstrip Patch using this online evaluator? To use this online evaluator for Effective Radius of Circular Microstrip Patch, enter Actual Radius of Circular Microstrip Patch (a_c), Thickness of Substrate Microstrip (h_o) & Dielectric Constant of Substrate (E_r) and hit the calculate button.

FAQs on Effective Radius of Circular Microstrip Patch

What is the formula to find Effective Radius of Circular Microstrip Patch?

The formula of Effective Radius of Circular Microstrip Patch is expressed as 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. Here is an example- 1751.245 = 1.74538*(1+((2*0.00157)/(pi*1.74538*4.4))*(ln((pi*1.74538)/(2*0.00157)+1.7726)))^0.5.

How to calculate Effective Radius of Circular Microstrip Patch?

With Actual Radius of Circular Microstrip Patch (a_c), Thickness of Substrate Microstrip (h_o) & Dielectric Constant of Substrate (E_r) we can find Effective Radius of Circular Microstrip Patch using the formula - 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. This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

Can the Effective Radius of Circular Microstrip Patch be negative?

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

Which unit is used to measure Effective Radius of Circular Microstrip Patch?

Effective Radius of Circular Microstrip Patch is usually measured using the Centimeter[cm] for Length. Meter[cm], Millimeter[cm], Kilometer[cm] are the few other units in which Effective Radius of Circular Microstrip Patch can be measured.

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Effective Radius of Circular Microstrip Patch Formula

Effective Radius of Circular Microstrip Patch Example

Effective Radius of Circular Microstrip Patch Solution

Effective Radius of Circular Microstrip Patch Formula Elements

Other formulas in Microstrip Antenna category

How to Evaluate Effective Radius of Circular Microstrip Patch?

FAQs on Effective Radius of Circular Microstrip Patch

Variable Name