🚀 go-pugleaf

References are sought for two transmission line impedance problems.

As part of some work I am doing on broadband antenna design the following 
problems in transmission line theory appeared. They look to be standard
enough problems that someone somewhere has probably published a solution.
Since I don't wish to reinvent wheels or fail to reference others work,
could anyone please advise me of appropriate references.
Replies via email.  Thanks.
 
                          PROBLEM 1. 

Does anybody know the formula for the common mode impedance
of a 2 wire transmission line above ground?

ie         +   +            not          +   -

        ___________                  _____________
        ///////////                  /////////////
         ground                         ground


in terms of wire diameter "d" , spacing "D" and height "h"?

Also, can this be generalised to 3, 4 or "N" evenly spaced coplanar wires.
 
ie        +  +  +            and        +  +  +  +

       _____________                 ________________
       /////////////                 ////////////////

It would be expected that for d << D << h (which is all I need)
that the formula would be similar to the single wire case:
                                 4.h
                  Zo = 138 log( ----- )
                                  d
except that "d" would be replaced with a formula describing the "equivalent"
single wire diameter of the multiple wires.
 
                             PROBLEM 2.

A transmission line (assumed lossless, since the problem is probably not
solvable otherwise) of known electrical length and with a known termination
has its natural impedance vary in an unknown way along its length.
The complex input impedance of the line is measured at "N" (evenly spaced?)
frequencies.  The line is then modelled as the joining of N equal length
transmission line segments, each of unknown natural impedance. 
The problem is to find these unknown impedances.
 
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