[TowerTalk] Dielectrically lenghtening the boom

[jimlux]

David J. Sourdis - HK1A wrote:
> 
> Maybe it has already been applied to the cellphone technology or elsewhere, or it is just not feasible because dielectric losses...
> 
> Dielectric material, lossy in some extent, sets a velocity factor (VF) for wave propagation in cables.
> 
> This makes the physical lenght of the line shorter than freespace size.
> 
> Take a Yagi, and fill the space between elements with a material which its dielectric constant is less than 1.0 (air's). 
> 
> Would the element spacing, hence the boom lenght, have to be adjusted by a shortening factor equal to the VF?
> 

To restate your question in different way, are you asking if you took a 
Yagi-Uda design, and immersed it in something with a different 
permittivity, would all the dimensions need to change?

Yes. And yes, in general, the boom would be shorter.  You'd have to do a 
bit more analysis to figure out just how much shorter, it's not 
necessarily a uniform scaling.

If you are asking about surrounding just the elements, but most of 
what's in between is air, then most of the field is in air, so the 
dimensions wouldn't change all that much.

there's really two things going on in a Yagi:
1) It's a phased array, with the phases and amplitudes in each of the 
elements arranged to get the right far field pattern.  From this 
standpoint, the physical distance between elements (in a dielectric or 
not) makes a difference, because eventually you'd transition from 
dielectric into free space, and there's some refraction effects at the 
boundary you'd have to deal with.  So the relative phases and amplitudes 
needed for the far field pattern would be different with the 
dielectrically immersed antenna.

2) It's a passive phased array, where the currents in most of the 
elements of the array get there by mutual coupling from the driven 
element. The relative length and distance between the elements sets the 
relative phase and amplitude of the curent in the elements. The presence 
of a dielectric changes that coupling, so you'd need to adjust the 
lengths and spacings to make that come out "right".


Yagi design, in concept, works by figuring out what pattern you want, 
then what element currents you need, given a particular spacing.  You 
then adjust the lengths of the elements to get the right current/phase. 
It's a matter of solving a set of simultaneous equations: in a 3 element 
array, there's a 3x3 matrix of coupling (each a complex number), and you 
adjust the spacing and length (which determines the values in that 
matrix) until the solution comes out right. (if you change the spacing, 
then you have to go back to your pattern calculation to figure out the 
needed currents)

It's a tough problem to solve algebraically (because of the 
interactions), so today, everyone uses an iterative approach with some 
sort of finite element model to get the performance.

There are some good approximations for free space and limited numbers of 
elements that get you pretty close without doing the modeling/iteration 
scheme.

But if you throw in dielectrics, you're going to want an appropriate 
modeling code (or spend a LOT of time rejiggering the analytical 
formulae to account for dielectrics:  there's copious literature on this 
in places like IEEE Trans. on Ant and Prop, but much of it is for 
special cases, and the math gets pretty hairy, pretty fast, especially 
once you get away from simple cases like infinite extent of dielectric)