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Physical Radius of Circular Microstrip Patch Formula

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

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

a_c - Actual Radius of Circular Microstrip Patch?F_n - Normalized Wavenumber?h_o - Thickness of Substrate Microstrip?E_r - Dielectric Constant of Substrate?π - Archimedes' constant?

Physical Radius of Circular Microstrip Patch Example

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

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

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

174.538 = \frac{1.7462}{{(1 + (2 \cdot \frac{0.157}{3.1416 \cdot 1.7462 \cdot 4.4}) \cdot (\ln (3.1416 \cdot \frac{1.7462}{2 \cdot 0.157} + 1.7726)))}^{\frac{1}{2}}}

174.538cm = \frac{1.7462}{{(1 + (2 \cdot \frac{0.157cm}{3.1416 \cdot 1.7462 \cdot 4.4}) \cdot (\ln (3.1416 \cdot \frac{1.7462}{2 \cdot 0.157cm} + 1.7726)))}^{\frac{1}{2}}}

174.538 = \frac{1.7462}{{(1 + (2 \cdot \frac{0.157}{3.1416 \cdot 1.7462 \cdot 4.4}) \cdot (\ln (3.1416 \cdot \frac{1.7462}{2 \cdot 0.157} + 1.7726)))}^{\frac{1}{2}}}

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Physical Radius of Circular Microstrip Patch Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

a c = \frac{1.7462}{{(1 + (2 \cdot \frac{0.157cm}{π \cdot 1.7462 \cdot 4.4}) \cdot (\ln (π \cdot \frac{1.7462}{2 \cdot 0.157cm} + 1.7726)))}^{\frac{1}{2}}}

Next Step Substitute values of Constants

∴

a c = \frac{1.7462}{{(1 + (2 \cdot \frac{0.157cm}{3.1416 \cdot 1.7462 \cdot 4.4}) \cdot (\ln (3.1416 \cdot \frac{1.7462}{2 \cdot 0.157cm} + 1.7726)))}^{\frac{1}{2}}}

Next Step Convert Units

∴

a c = \frac{1.7462}{{(1 + (2 \cdot \frac{0.0016m}{3.1416 \cdot 1.7462 \cdot 4.4}) \cdot (\ln (3.1416 \cdot \frac{1.7462}{2 \cdot 0.0016m} + 1.7726)))}^{\frac{1}{2}}}

Next Step Prepare to Evaluate

∴

a c = \frac{1.7462}{{(1 + (2 \cdot \frac{0.0016}{3.1416 \cdot 1.7462 \cdot 4.4}) \cdot (\ln (3.1416 \cdot \frac{1.7462}{2 \cdot 0.0016} + 1.7726)))}^{\frac{1}{2}}}

Next Step Evaluate

∴

a c = 1.74537955995848m

Next Step Convert to Output's Unit

∴

a c = 174.537955995848cm

LAST Step Rounding Answer

∴

a c = 174.538cm

Physical Radius of Circular Microstrip Patch Formula Elements

Variables

Constants

Functions

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

Normalized Wavenumber

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

Symbol: F_n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Normalized Wavenumber

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 Physical Radius of Circular Microstrip Patch?

Physical Radius of Circular Microstrip Patch evaluator uses 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)) to evaluate the Actual Radius of Circular Microstrip Patch, The Physical Radius of Circular Microstrip Patch is vital in determining size, resonance frequency, impedance matching, and radiation characteristics. Precise control is essential for optimal performance in diverse communication systems. Actual Radius of Circular Microstrip Patch is denoted by a_c symbol.

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

FAQs on Physical Radius of Circular Microstrip Patch

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

The formula of Physical Radius of Circular Microstrip Patch is expressed as 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)). Here is an example- 17453.8 = 1.746227005/((1+(2*0.00157/(pi*1.746227005*4.4))*(ln(pi*1.746227005/(2*0.00157)+1.7726)))^(1/2)).

How to calculate Physical Radius of Circular Microstrip Patch?

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

Can the Physical Radius of Circular Microstrip Patch be negative?

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

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

Physical 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 Physical Radius of Circular Microstrip Patch can be measured.

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Physical Radius of Circular Microstrip Patch Formula

Physical Radius of Circular Microstrip Patch Example

Physical Radius of Circular Microstrip Patch Solution

Physical Radius of Circular Microstrip Patch Formula Elements

Other formulas in Microstrip Antenna category

How to Evaluate Physical Radius of Circular Microstrip Patch?

FAQs on Physical Radius of Circular Microstrip Patch

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