What is the physical meaning of Propagation constant beta in a signal ?

[electronic_guy]

Hi,

I’ve seen the propagation constant defined in many RF signals when we use the phasors. Sin(Omega*t - Beta*z) when the wave propagates in z direction, Omega being the angular frequency. Beta is defined as 2*Pi / Wavelength. What is the physical meaning of this constant ? How does it relates to the phase of the signal and propagation of the wave through the transmission line? Please explain in a basic sense of it.

Thank you.

[mag_therm]

I think you refer to the imaginary part of P
P is one of the 3  secondary line coefficients
P = sqrt( (R+jwL)*(G+jwC) )
 where R,L,G,C are the primary line characteristics measurable/length

Re(P) is the attenuation Coefficient
Im(P) is the wavelength Coefficient (2*pi/Lamdba)  *****op's query***

Im(P) gives the distance along the line where the phase has changed by 2*pi)
and practically related to calculating line (eg coax) velocity factor.

Someone may be able to give current reference to the secondary coeficients. My book is too old.

[radiogeek381]

The equation you’ve posted describes the propagation of a real wave in space. (No imaginary parts needed.)

As you know, the omega t part is the time varying aspect of the wave. If you were standing in one place, the amplitude of the wave would vary as sin omega t.

But the wave is propagating through space — in the z direction in this case.  So it will vary there too, since the instantaneous change in amplitude at the source can’t appear everywhere at the same time — the speed of light says the oscillation must take time to propagate from z0 = 0 to some other z.  That’s where the beta z comes in.  Notice that the units of beta are in radians per meter. (omega = radians / second  c = meters / second) so radians per meter.  That makes sense because radians per meter times meters gets us radians.  Just like 2 pi f t gets us radians.

So the beta term accounts for the propagation of the wave through a distance.