Maximum Usable Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height) )^2)
Fmuf = fc*sqrt(1+(Pd/(2*h) )^2)
This formula uses 1 Functions, 4 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
Maximum Usable Frequency - (Measured in Hertz) - Maximum Usable frequency is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere.
Critical Frequency - (Measured in Hertz) - Critical frequency is the highest magnitude of frequency above which the waves penetrate the ionosphere and below which the waves are reflected back from the ionosphere.
Skip Distance - (Measured in Meter) - Skip distance is defined as the distance b/w transmitting antenna and a point where that wave is first received after reflection from ionosphere.
Ionospheric Layer Height - (Measured in Meter) - Ionospheric Layer Height is defined as the height of ionospheric layer.
STEP 1: Convert Input(s) to Base Unit
Critical Frequency: 45 Hertz --> 45 Hertz No Conversion Required
Skip Distance: 21714 Meter --> 21714 Meter No Conversion Required
Ionospheric Layer Height: 1169.985 Meter --> 1169.985 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fmuf = fc*sqrt(1+(Pd/(2*h) )^2) --> 45*sqrt(1+(21714/(2*1169.985) )^2)
Evaluating ... ...
Fmuf = 419.999949774394
STEP 3: Convert Result to Output's Unit
419.999949774394 Hertz --> No Conversion Required
FINAL ANSWER
419.999949774394 419.9999 Hertz <-- Maximum Usable Frequency
(Calculation completed in 00.004 seconds)

Credits

Created by Shobhit Dimri
Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat
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16 Wave Propagation Calculators

Field Strength of Space Wave
Go Field Strength = (4*pi*Electric Field*Height of Receiving Antenna*Height of Transmitting Antenna)/(Wavelength*Antenna Distance^2)
Skin Depth or Depth of Penetration
Go Skin Depth = 1/Conductivity of Antenna*sqrt(pi*Relative Permeability*[Permeability-vacuum]*Frequency of Conductor Loop)
Phase Difference between Radio Waves
Go Phase Difference = 4*pi*Height of Receiving Antenna*Height of Transmitting Antenna/(Antenna Distance*Wavelength)
Height of Layer
Go Ionospheric Layer Height = Skip Distance/(2*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1))
Maximum Usable Frequency
Go Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height) )^2)
Propagation Distance
Go Skip Distance = 2*Ionospheric Layer Height*sqrt((Maximum Usable Frequency^2/Critical Frequency^2)-1)
Line of Sight
Go Line of Sight = 3577*(sqrt(Height of Receiving Antenna)+sqrt(Height of Transmitting Antenna))
Skip Distance
Go Skip Distance = 2*Reflection Height*sqrt((Maximum Usable Frequency/Critical Frequency)^2-1)
Refractive Index of Ionosphere
Go Refractive Index = sqrt(1-((81*Electron Density)/Operating Frequency^2))
Maximum Usable Frequency in F-region
Go Maximum Usable Frequency = Critical Frequency/cos(Angle of Incidence)
Normal of Reflecting Plane
Go Normal of Reflecting Plane = Wavelength/cos(Theta)
Wavelength of Plane
Go Wavelength = Normal of Reflecting Plane*cos(Theta)
Parallel of Reflecting Plane
Go Parallel of Reflecting = Wavelength/sin(Theta)
Electron Density
Go Electron Density = ((1-Refractive Index^2)*Operating Frequency^2)/81
Critical Frequency of Ionosphere
Go Critical Frequency of Ionosphere = 9*sqrt(Electron Density)
Antenna Beamwidth
Go Antenna Beamwidth = (70*Wavelength)/Antenna Diameter

Maximum Usable Frequency Formula

Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height) )^2)
Fmuf = fc*sqrt(1+(Pd/(2*h) )^2)

What are the critical frequencies?

Critical frequency is the highest magnitude of frequency above which the waves penetrate the ionosphere and below which the waves are reflected back from the ionosphere. It is denoted by "fc". Its value is not fixed and it depends upon the electron density of the ionosphere.

How to Calculate Maximum Usable Frequency?

Maximum Usable Frequency calculator uses Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height) )^2) to calculate the Maximum Usable Frequency, The Maximum Usable Frequency formula is defined as is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere. Maximum Usable Frequency is denoted by Fmuf symbol.

How to calculate Maximum Usable Frequency using this online calculator? To use this online calculator for Maximum Usable Frequency, enter Critical Frequency (fc), Skip Distance (Pd) & Ionospheric Layer Height (h) and hit the calculate button. Here is how the Maximum Usable Frequency calculation can be explained with given input values -> 419.9999 = 45*sqrt(1+(21714/(2*1169.985) )^2).

FAQ

What is Maximum Usable Frequency?
The Maximum Usable Frequency formula is defined as is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere and is represented as Fmuf = fc*sqrt(1+(Pd/(2*h) )^2) or Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height) )^2). Critical frequency is the highest magnitude of frequency above which the waves penetrate the ionosphere and below which the waves are reflected back from the ionosphere, Skip distance is defined as the distance b/w transmitting antenna and a point where that wave is first received after reflection from ionosphere & Ionospheric Layer Height is defined as the height of ionospheric layer.
How to calculate Maximum Usable Frequency?
The Maximum Usable Frequency formula is defined as is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere is calculated using Maximum Usable Frequency = Critical Frequency*sqrt(1+(Skip Distance/(2*Ionospheric Layer Height) )^2). To calculate Maximum Usable Frequency, you need Critical Frequency (fc), Skip Distance (Pd) & Ionospheric Layer Height (h). With our tool, you need to enter the respective value for Critical Frequency, Skip Distance & Ionospheric Layer Height and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Maximum Usable Frequency?
In this formula, Maximum Usable Frequency uses Critical Frequency, Skip Distance & Ionospheric Layer Height. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Maximum Usable Frequency = Critical Frequency/cos(Angle of Incidence)
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