Propagation Constant Calculator

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✖Angular Frequency is a steadily recurring phenomenon expressed in radians per second.ⓘ Angular Frequency [ω₀]			+10% -10%
✖Magnetic Permeability is a property of a magnetic material which supports the formation of a magnetic field.ⓘ Magnetic Permeability [μ]			+10% -10%
✖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.ⓘ Dielectric Permittivity [ε]			+10% -10%
✖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.ⓘ Cut-off Frequency [f_c]			+10% -10%
✖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.ⓘ Frequency [f]			+10% -10%

✖Propagation Constant of Rectangular Waveguide represents as a change in the amplitude or phase.ⓘ Propagation Constant [β_g]

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Formula

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Propagation Constant

Formula

`"β"_{"g"} = "ω"_{"0"}*(sqrt("μ"*"ε"))*(sqrt(1-(("f"_{"c"}/"f")^2)))`

Example

`"15.43994"="5.75rad/s"*(sqrt("1.3H/m"*"5.56F/m"))*(sqrt(1-(("2.72Hz"/"55.02Hz")^2)))`

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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)))
β_g = ω₀*(sqrt(μ*ε))*(sqrt(1-((f_c/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

β_g = ω₀*(sqrt(μ*ε))*(sqrt(1-((f_c/f)^2))) --> 5.75*(sqrt(1.3*5.56))*(sqrt(1-((2.72/55.02)^2)))

Evaluating ... ...

β_g = 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 00.004 seconds)

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Created by Sai Sudha Vani Priya Lanka

Dayananda Sagar University (DSU), Bengaluru, Karnataka, India-560100

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< 17 Microwave Devices Calculators

Propagation Constant

Go Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2)))

Attenuation for TEmn mode

Go Attenuation for the TEmn mode = (Conductivity*Intrinsic Impedance)/(2*sqrt(1-((Cut-off Frequency)/(Frequency))^2))

Attenuation for TMmn mode

Go Attenuation for the TMmn mode = ((Conductivity*Intrinsic Impedance)/2)*sqrt(1-(Cut-off Frequency/Frequency)^2)

Cut-off Frequency of Rectangular Waveguide

Go Cut-off Frequency = (1/(2*pi*sqrt(Magnetic Permeability*Dielectric Permittivity)))*Cut-off Wave Number

Surface Resistance of Guide Walls

Go Surface Resistance = sqrt((pi*Frequency*Magnetic Permeability)/(Conductivity))

Power Density of Spherical Wave

Go Power Density = (Power Transmitted*Transmitting Gain)/(4*pi*Distance between Antennas)

Wavelength for TEmn Modes

Go Wavelength for TEmn modes = (Wavelength)/(sqrt(1-(Cut-off Frequency/Frequency)^2))

Force Exerted on Particle

Go Force Exerted on Particle = (Charge of a Particle*Velocity of a Charged Particle)*Magnetic Flux Density

Cut-off Frequency of Circular Waveguide in Transverse Electric 11 Mode

Go Cut-off Frequency Circular Waveguide TE11 = ([c]*1.841)/(2*pi*Radius of Circular Waveguide)

Cut-off Frequency of Circular Waveguide in Transverse Magnetic 01 Mode

Go Cut-off Frequency Circular Waveguide TM01 = ([c]*2.405)/(2*pi*Radius of Circular Waveguide)

Characteristic Wave Impedance

Go Characteristic Wave Impedance = (Angular Frequency*Magnetic Permeability)/(Phase Constant)

Quality Factor

Go Quality Factor = (Angular Frequency*Maximum Stored Energy)/(Average Power Loss)

Maximum Stored Energy

Go Maximum Stored Energy = (Quality Factor*Average Power Loss)/Angular Frequency

Power Received by Antenna

Go Power Received by Antenna = Power Density of Antenna*Effective Area Antenna

Power Losses for TEM Mode

Go Power Losses for the TEM Mode = 2*Attenuation Constant*Transmitting Power

Critical Frequency for Vertical Incidence

Go Critical Frequency = 9*sqrt(Maximum Electron Density)

Phase Velocity of Rectangular Waveguide

Go Phase Velocity = Angular Frequency/Phase Constant

Propagation Constant Formula

Propagation Constant = Angular Frequency*(sqrt(Magnetic Permeability*Dielectric Permittivity))*(sqrt(1-((Cut-off Frequency/Frequency)^2)))
β_g = ω₀*(sqrt(μ*ε))*(sqrt(1-((f_c/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 β_g symbol.

How to calculate Propagation Constant using this online calculator? To use this online calculator 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. 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 β_g = ω₀*(sqrt(μ*ε))*(sqrt(1-((f_c/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 (ω₀), Magnetic Permeability (μ), Dielectric Permittivity (ε), Cut-off Frequency (f_c) & 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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