TEM plane waves, decay and attenuation

[FrankJ777]

I've been trying to get reantiquated with electormagnetics to understand RF communications better. I have a question about TEM plane waves. The funtions which describe the plane waves in the z dirrection are:

e^-α cos(ωt-βz) ; in the time domain

where is the rate of decay.

In free space α is 0, so the plane wave function does not account for free space loss which from what I understand accounts for the fields spreading out is a sphere and the distribution of the fields across the surface of the sphere. Hence it is an inverse square law.

My questions is, is it only appropriate to use the plane wave function, e^-α cos(ωt-βz), for very short distances of travel, i.e. in a circuit, or through a shielding? Is it ever appropriate to use over long distances? Hope my question is making sense. Thanks.

 

[yungman]

My questions is, is it only appropriate to use the plane wave function, e^-α cos(ωt-βz), for very short distances of travel, i.e. in a circuit, or through a shielding? Is it ever appropriate to use over long distances? Hope my question is making sense. Thanks.

That's is my understanding: The term plane wave is the approximation of the wave front from a source at large distance, that the small surface area is approx a flat plane rather a concave shape. So for a short distant travel, the wave is in a plane perpendicular to the direction of propagation.

So for short distance, the propagation is assume to be at a constant direction, where, in a lot of books, assumed to be in the z direction ( for no better reason than just picking one!). So the basic formula of of the E wave is:

$$\vec E(z)= \hat x E_{(0)} e^{-\alpha z}Re[e^{j\omega t} e^{-j\beta z+ \phi}]$$

Where the inverse square thing is ignored. For EM wave in guided structure like coax or other type of tx line, there is no inverse square thing as it is not spreading like a sphere, it is in only one direction.

 

[FrankJ777]

Thanks. That's pretty much what i was assuming, but in the texts I've been reading they really don't specify.

 

[yungman]

Thanks. That's pretty much what i was assuming, but in the texts I've been reading they really don't specify.

There are a lot of things the EM textbooks do not explain very clearly. I resort to repeat studying three different times with different books to try to understand the material. It was not until the third time studying that I realize signal in electronics does not travel as current, it is really the EM wave that travel and current is the consequence of the boundary condition between the dielectric and the conductor surface. To me, that's the real "light bulb" moment where a lot of things start to make sense.
Another thing that is so not explained clearly is the "free charge" vs "bounded charge" application in the Maxwell's equations. I actually learned from the video lecture done by the India Institute of Technology.

Every time I study back, I learn something new!

 

[FrankJ777]

Yeah, I'm using Wentorth's Electromagnetics, Pozar's Microwave text, and Dan Fliesch's book on Maxwell's equations.