Enter the attenuation constant (α) and the phase constant (β) into the calculator to determine the propagation constant (γ). This calculator helps in understanding the complex propagation constant in transmission line theory.
Propagation Constant Formula
The following formula is used to calculate the propagation constant (γ):
γ = √(α² + β²)
Variables:
- γ is the propagation constant (Np/m or rad/m)
- α is the attenuation constant (Np/m)
- β is the phase constant (rad/m)
To calculate the propagation constant, take the square root of the sum of the squares of the attenuation constant and the phase constant.
What is a Propagation Constant?
The propagation constant is a complex number that describes the change in amplitude and phase of an electromagnetic wave as it propagates through a medium. The real part of the propagation constant is the attenuation constant (α), which represents the exponential decay of the wave’s amplitude. The imaginary part is the phase constant (β), which represents the phase shift of the wave per unit length. The propagation constant is a fundamental parameter in the analysis of transmission lines and waveguides.
How to Calculate Propagation Constant?
The following steps outline how to calculate the Propagation Constant.
- First, determine the attenuation constant (α) in Nepers per meter (Np/m).
- Next, determine the phase constant (β) in radians per meter (rad/m).
- Next, gather the formula from above = γ = √(α² + β²).
- Finally, calculate the Propagation Constant (γ) in Np/m or rad/m.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Attenuation Constant (α) = 0.1 Np/m
Phase Constant (β) = 2 rad/m
