Propagation Constant Solution

STEP 0: Pre-Calculation Summary
Formula Used
Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2)))
βg = ω0*(sqrt(μ*ε))*(sqrt(1-((fc/f)^2)))
This formula uses 1 Functions, 6 Variables
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
Propagation Constant - Propagation Constant of Rectangular Waveguide represents as a change in the amplitude or phase.
Angular Frequency - (Measured in Radian per Second) - Angular Frequency is a steadily recurring phenomenon expressed in radians per second.
Magnetic Permeability - (Measured in Henry per Meter) - Magnetic Permeability is a property of a magnetic material which supports the formation of a magnetic field.
Dielectric Permittivity - (Measured in Farad per Meter) - 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.
Cut-off Frequency - (Measured in Hertz) - 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.
Frequency - (Measured in Hertz) - 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.
STEP 1: Convert Input(s) to Base Unit
Angular Frequency: 5.75 Radian per Second --> 5.75 Radian per Second No Conversion Required
Magnetic Permeability: 1.3 Henry per Meter --> 1.3 Henry per Meter No Conversion Required
Dielectric Permittivity: 5.56 Farad per Meter --> 5.56 Farad per Meter No Conversion Required
Cut-off Frequency: 2.72 Hertz --> 2.72 Hertz No Conversion Required
Frequency: 55.02 Hertz --> 55.02 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
βg = ω0*(sqrt(μ*ε))*(sqrt(1-((fc/f)^2))) --> 5.75*(sqrt(1.3*5.56))*(sqrt(1-((2.72/55.02)^2)))
Evaluating ... ...
βg = 15.439938452176
STEP 3: Convert Result to Output's Unit
15.439938452176 --> No Conversion Required
FINAL ANSWER
15.439938452176 15.43994 <-- Propagation Constant
(Calculation completed in 00.020 seconds)

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Propagation Constant Formula

​LaTeX ​Go
Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2)))
βg = ω0*(sqrt(μ*ε))*(sqrt(1-((fc/f)^2)))

What is a lossless rectangular waveguide?

In a lossless rectangular waveguide, the propagation constant γ is equal to the phase constant β. One of the major uses of a rectangular waveguide is when losses must be kept to a minimum, so that a rectangular waveguide is used in very high-power situations such as radar, and at a few tens of gigahertz and above.

How to Calculate Propagation Constant?

Propagation Constant calculator uses Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2))) to calculate 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 βg symbol.

How to calculate Propagation Constant using this online calculator? To use this online calculator for Propagation Constant, enter Angular Frequency 0), Magnetic Permeability (μ), Dielectric Permittivity (ε), Cut-off Frequency (fc) & Frequency (f) and hit the calculate button. Here is how the Propagation Constant calculation can be explained with given input values -> 15.43994 = 5.75*(sqrt(1.3*5.56))*(sqrt(1-((2.72/55.02)^2))).

FAQ

What is 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 and is represented as βg = ω0*(sqrt(μ*ε))*(sqrt(1-((fc/f)^2))) or Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2))). Angular Frequency is a steadily recurring phenomenon expressed in radians per second, Magnetic Permeability is a property of a magnetic material which supports the formation of a magnetic field, 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, 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 & 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.
How to calculate 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 is calculated using Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2))). To calculate Propagation Constant, you need Angular Frequency 0), Magnetic Permeability (μ), Dielectric Permittivity (ε), Cut-off Frequency (fc) & Frequency (f). With our tool, you need to enter the respective value for Angular Frequency, Magnetic Permeability, Dielectric Permittivity, Cut-off Frequency & Frequency 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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