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Propagation Constant Formula

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Propagation Constant of Rectangular Waveguide represents as a change in the amplitude or phase. Check FAQs

β g = ω 0 \cdot (\sqrt{μ \cdot ε}) \cdot (\sqrt{1 - ({(\frac{f c}{f})}^{2})})

β_g - Propagation Constant?ω₀ - Angular Frequency?μ - Magnetic Permeability?ε - Dielectric Permittivity?f_c - Cut-off Frequency?f - Frequency?

Propagation Constant Example

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Here is how the Propagation Constant equation looks like with Values.

Here is how the Propagation Constant equation looks like with Units.

Here is how the Propagation Constant equation looks like.

15.4399 = 5.75 \cdot (\sqrt{1.3 \cdot 5.56}) \cdot (\sqrt{1 - ({(\frac{2.72}{55.02})}^{2})})

15.4399 = 5.75rad/s \cdot (\sqrt{1.3H/m \cdot 5.56F/m}) \cdot (\sqrt{1 - ({(\frac{2.72Hz}{55.02Hz})}^{2})})

15.4399 = 5.75 \cdot (\sqrt{1.3 \cdot 5.56}) \cdot (\sqrt{1 - ({(\frac{2.72}{55.02})}^{2})})

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Propagation Constant Solution

Follow our step by step solution on how to calculate Propagation Constant?

FIRST Step Consider the formula

β g = ω 0 \cdot (\sqrt{μ \cdot ε}) \cdot (\sqrt{1 - ({(\frac{f c}{f})}^{2})})

Next Step Substitute values of Variables

∴

β g = 5.75rad/s \cdot (\sqrt{1.3H/m \cdot 5.56F/m}) \cdot (\sqrt{1 - ({(\frac{2.72Hz}{55.02Hz})}^{2})})

Next Step Prepare to Evaluate

∴

β g = 5.75 \cdot (\sqrt{1.3 \cdot 5.56}) \cdot (\sqrt{1 - ({(\frac{2.72}{55.02})}^{2})})

Next Step Evaluate

∴

β g = 15.439938452176

LAST Step Rounding Answer

∴

β g = 15.4399

Propagation Constant Formula Elements

Variables

Functions

Propagation Constant

Propagation Constant of Rectangular Waveguide represents as a change in the amplitude or phase.

Symbol: β_g

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Propagation Constant

Angular Frequency

Angular Frequency is a steadily recurring phenomenon expressed in radians per second.

Symbol: ω₀

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency

Magnetic Permeability

Magnetic Permeability is a property of a magnetic material which supports the formation of a magnetic field.

Symbol: μ

Measurement: Magnetic PermeabilityUnit: H/m

Note: Value should be greater than 0.

Formulas to find Magnetic Permeability

Dielectric Permittivity

Dielectric Permittivity is a diagnostic physical property which characterizes the degree of electrical polarization a material experiences under the influence of an external electric field.

Symbol: ε

Measurement: PermittivityUnit: F/m

Note: Value should be greater than 0.

Formulas to find Dielectric Permittivity

Cut-off Frequency

Cut-off Frequency of rectangular waveguide defines wave propagation modes in the rectangular waveguide, and this frequency is dependent on the dimensions of the waveguide.

Symbol: f_c

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Cut-off Frequency

Frequency

Frequency the number of waves that pass a fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion in a waveguide.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Frequency

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 Microwave Devices category

Go Force Exerted on Particle

F e = (q \cdot v cp) \cdot B

Go Power Losses for TEM Mode

P loss = 2 \cdot α \cdot P t

Go Quality Factor

Q = \frac{ω 0 \cdot E max}{P avg}

Go Characteristic Wave Impedance

Z = \frac{ω 0 \cdot μ}{β}

How to Evaluate Propagation Constant?

Propagation Constant evaluator uses Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2))) to evaluate the Propagation Constant, Propagation Constant of Rectangular Waveguide represented as a change in the amplitude or phase. It is a dimensionless quantity and is represented by the units of change per unit length. Propagation Constant is denoted by β_g symbol.

How to evaluate Propagation Constant using this online evaluator? To use this online evaluator for Propagation Constant, enter Angular Frequency (ω₀), Magnetic Permeability (μ), Dielectric Permittivity (ε), Cut-off Frequency (f_c) & Frequency (f) and hit the calculate button.

FAQs on Propagation Constant

What is the formula to find Propagation Constant?

The formula of Propagation Constant is expressed as Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2))). Here is an example- 15.43994 = 5.75*(sqrt(1.3*5.56))*(sqrt(1-((2.72/55.02)^2))).

How to calculate Propagation Constant?

With Angular Frequency (ω₀), Magnetic Permeability (μ), Dielectric Permittivity (ε), Cut-off Frequency (f_c) & Frequency (f) we can find Propagation Constant using the formula - Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2))). This formula also uses Square Root (sqrt) function(s).

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Propagation Constant Formula

Propagation Constant Example

Propagation Constant Solution

Propagation Constant Formula Elements

Other formulas in Microwave Devices category

How to Evaluate Propagation Constant?

FAQs on Propagation Constant

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