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
- <math>\gamma = \alpha +i \beta \,</math>
where
- α, the real part, is the attenuation constant
- β, the imaginary part, is the phase constant
- i = <math>\sqrt{-1}</math>
Source: Federal Standard 1037C. As input and output impedences are equal under zo termination ie, zo 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 zo 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) => eγ1 × eγ2 × ... × = eγ The over all propagation constant γ = γ1+γ2+....+γn
