Propagation constant

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It has been suggested that Attenuation constant be merged into this article or section. (Discuss)

It has been suggested that Phase constant be merged into this article or section. (Discuss)

For an electromagnetic field mode varying sinusoidally with time at a given frequency, the propagation constant is the logarithmic rate of change, with respect to distance in a given direction, of the complex amplitude of any field component.

The propagation constant, γ, is a complex quantity given by

where

α, the real part, is the attenuation constant

β, the imaginary part, is the phase constant

i =

Source: Federal Standard 1037C.

As input and output impedences are equal under z_o termination ie, z_o termination = V₁/I₁ = V₂/(-I₂)

   V1/V2 = I1/I2 = eγ

where γ is a complex number and is defined as

 γ = α+i β 

where

α, the real part, is the attenuation constant

β, the imaginary part, is the phase constant

For 'n' number of sections cascaded' with all of them having the same z_o value' the ratio of currents can be written as

(I ₁/ -I ₂) × (-I ₂ / -I ₃) × ..... × (-I _n-1 / -I _n) = (I ₁ / -I _n)

=> e^γ₁ × e^γ₂ × ... × = e^γ

The over all propagation constant γ = γ₁+γ₂+....+γ_n