Radian Cutoff Angular Frequency Calculator

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Guided Waves in Field Theory

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✖Mode Number the mode number indicates the number of half-wavelengths that fit into the given space.ⓘ Mode Number [m]			+10% -10%
✖Refractive index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.ⓘ Refractive Index [n_r]			+10% -10%
✖Plate Distance typically refers to the separation between the conductive elements.ⓘ Plate Distance [p_d]			+10% -10%

✖Cutoff Angular Frequency representing the maximum frequency for which a particular mode of a waveguide or transmission line can be supported.ⓘ Radian Cutoff Angular Frequency [ω_cm]

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Formula

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Radian Cutoff Angular Frequency

Formula

`"ω"_{"cm"} = ("m"*pi*"[c]")/("n"_{"r"}*"p"_{"d"})`

Example

`"8.9E^9rad/s"=("4"*pi*"[c]")/("2"*"21.23cm")`

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Radian Cutoff Angular Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)
ω_cm = (m*pi*[c])/(n_r*p_d)
This formula uses 2 Constants, 4 Variables

Constants Used

[c] - Light speed in vacuum Value Taken As 299792458.0
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Cutoff Angular Frequency - (Measured in Radian per Second) - Cutoff Angular Frequency representing the maximum frequency for which a particular mode of a waveguide or transmission line can be supported.
Mode Number - Mode Number the mode number indicates the number of half-wavelengths that fit into the given space.
Refractive Index - Refractive index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.
Plate Distance - (Measured in Meter) - Plate Distance typically refers to the separation between the conductive elements.

STEP 1: Convert Input(s) to Base Unit

Mode Number: 4 --> No Conversion Required
Refractive Index: 2 --> No Conversion Required
Plate Distance: 21.23 Centimeter --> 0.2123 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_cm = (m*pi*[c])/(n_r*p_d) --> (4*pi*[c])/(2*0.2123)

Evaluating ... ...

ω_cm = 8872593345.77887

STEP 3: Convert Result to Output's Unit

8872593345.77887 Radian per Second --> No Conversion Required

FINAL ANSWER

8872593345.77887 ≈ 8.9E+9 Radian per Second <-- Cutoff Angular Frequency

(Calculation completed in 00.004 seconds)

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Credits

Created by Gowthaman N

Vellore Institute of Technology (VIT University), Chennai

Gowthaman N has created this Calculator and 25+ more calculators!

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Chandigarh University (CU), Punjab

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< 12 Guided Waves in Field Theory Calculators

Characteristic Impedance of Line

Go Characteristic Impedance = sqrt(Magnetic Permeability*pi*10^-7/Dielectric Permitivitty)*(Plate Distance/Plate Width)

Total Resistance of Coaxial Cable

Go Total Resistance of Coaxial Cable = 1/(2*pi*Skin Depth*Electrical Conductivity)*(1/Inner Radius of Coaxial Cable+1/Outer Radius of Coaxial Cable)

Inductance per unit Length of Coaxial Cable

Go Inductance per unit length of Coaxial Cable = Magnetic Permeability/2*pi*ln(Outer Radius of Coaxial Cable/Inner Radius of Coaxial Cable)

Conductance of Coaxial Cable

Go Conductance of Coaxial Cable = (2*pi*Electrical Conductivity)/ln(Outer Radius of Coaxial Cable/Inner Radius of Coaxial Cable)

Radian Cutoff Angular Frequency

Go Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)

Inner Resistance of Coaxial Cable

Go Inner Resistance of Coaxial Cable = 1/(2*pi*Inner Radius of Coaxial Cable*Skin Depth*Electrical Conductivity)

Outer Resistance of Coaxial Cable

Go Outer Resistance of Coaxial Cable = 1/(2*pi*Skin Depth*Outer Radius of Coaxial Cable*Electrical Conductivity)

Inductance between Conductors

Go Conductor Inductance = Magnetic Permeability*pi*10^-7*Plate Distance/(Plate Width)

Magnitude of Wavevector

Go Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty)

Skin Effect Resistivity

Go Skin Effect Resistivity = 2/(Electrical Conductivity*Skin Depth*Plate Width)

Cutoff Wavelength

Go Cutoff Wavelength = (2*Refractive Index*Plate Distance)/Mode Number

Phase Velocity in Microstrip Line

Go Phase Velocity = [c]/sqrt(Dielectric Permitivitty)

Radian Cutoff Angular Frequency Formula

Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)
ω_cm = (m*pi*[c])/(n_r*p_d)

How does the mode number affect the angular frequency of a wave in a waveguide?

As the mode number increases, the angular frequency of a wave in a waveguide also increases. This is because higher mode numbers correspond to shorter wavelengths, which in turn require higher frequencies for propagation within the waveguide's confined dimensions.

How to Calculate Radian Cutoff Angular Frequency?

Radian Cutoff Angular Frequency calculator uses Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance) to calculate the Cutoff Angular Frequency, The Radian Cutoff Angular Frequency formula is a fundamental relationship in waveguiding and transmission line theory. It allows us to calculate the angular frequency of a wave propagating within a waveguide or transmission line, given its mode number, the speed of light, the refractive index of the medium, and the waveguide's characteristic dimension. Cutoff Angular Frequency is denoted by ω_cm symbol.

How to calculate Radian Cutoff Angular Frequency using this online calculator? To use this online calculator for Radian Cutoff Angular Frequency, enter Mode Number (m), Refractive Index (n_r) & Plate Distance (p_d) and hit the calculate button. Here is how the Radian Cutoff Angular Frequency calculation can be explained with given input values -> 8.9E+9 = (4*pi*[c])/(2*0.2123).

FAQ

What is Radian Cutoff Angular Frequency?

The Radian Cutoff Angular Frequency formula is a fundamental relationship in waveguiding and transmission line theory. It allows us to calculate the angular frequency of a wave propagating within a waveguide or transmission line, given its mode number, the speed of light, the refractive index of the medium, and the waveguide's characteristic dimension and is represented as ω_cm = (m*pi*[c])/(n_r*p_d) or Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance). Mode Number the mode number indicates the number of half-wavelengths that fit into the given space, Refractive index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum & Plate Distance typically refers to the separation between the conductive elements.

How to calculate Radian Cutoff Angular Frequency?

The Radian Cutoff Angular Frequency formula is a fundamental relationship in waveguiding and transmission line theory. It allows us to calculate the angular frequency of a wave propagating within a waveguide or transmission line, given its mode number, the speed of light, the refractive index of the medium, and the waveguide's characteristic dimension is calculated using Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance). To calculate Radian Cutoff Angular Frequency, you need Mode Number (m), Refractive Index (n_r) & Plate Distance (p_d). With our tool, you need to enter the respective value for Mode Number, Refractive Index & Plate Distance 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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