# Phase Factor in wave propagation (lossy medium): does the distance matters?

1. Jan 6, 2010

### Ionito

In the electromagnetism theory, the phase factor or constant (usually BETA) in wave propagation for lossy medium has the unit rad/m.

I understood that it must be interpreted as the amount of phase shift that occurs as the wave travels one meter.

However, differently of the attenuation factor (usually ALFA), I cannot see examples relating the phase factor to the distance. In other words, we can see the signal attenuation as the form of 8.69*ALFA*d, where d is the distance between the sender and the receiver. However, this distance "d" is not used in conjunction with the phase factor BETA. Is it right?

Can anyone provide me a complete example of the total attenuation (in dBs), given ALFA, BETA, frequency, and distance d, for a plane wave propagating in a lossy medium?

Thanks

2. Dec 17, 2010

### ZunairaMaryam

Yes, the phase factor appears in the wave equation as beta(phase shift) multiplied with the distance in the direction of wave propagation.i.e if wave is travelling along z direction then phase factor = beta(z)
along with the time dependence wt.

beta is radians per meter,this multiplied with distance gives the phase shift in radians.

3. Dec 17, 2010

### Bob S

See the Definitions section of

http://en.wikipedia.org/wiki/Phase_constant#Phase_constant

The propagator in transmission lines is complex; γ = α +iβ. Alpha (α) has dimensions of nepers per meter. Beta (β) has dimensions of radians per meter. The attenuation in dB is 8.686·α·d.

Bob S