Impedance overcoupled

Inspection of (D.IO) shows that the embedded stick impedance Zemb stk consists of the stick self impedance Z° ° for the center array plus two terms representing the overcoupled impedances from the two outer arrays. 

It can be shown that the embedded stick impedance for any size finite array is structured the same way—that is, as a sum of the stick self-impedance Z° ° plus overcoupled terms associated with all the other parasitically excited stick arrays. 

Comparing Z° ° in Fig. D.5 and Zemb stk in Fig. D.6 shows that they are in fact very similar except that the latter has a larger loop at the middle frequencies as caused by the overcoupled terms observed in (D.IO). At the lower and upper frequencies, Z° ° and Zemb stk are practically identical. More comments about this subject will be given in the conclusion section. [A parametric study (not shown) reveals that the impedance loop of Zemb stk becomes larger for smaller values of Zi and vice versa. See also comments in the Postscript section of this chapter.]... 

A typical example was to estimate the overcoupled impedance as given by the first and last term in (D.IO). Making the rather gross approximation that... 

Fig. D.15 How to estimate the overcoupled impedance from the two outer stick arrets. See text for details.

When the overcoupled impedances (remember we have two) are added to Z° ° as suggested by (D.IO), we readily see that the embedded stick impedance Zemb stk will have a larger loop than the one present in Z° ° (see Fig. D.5). This is of course exactly what Jonothan later calculated (see Fig. D.6). 

We may also conclude from (D.18) that a larger Zl produces a smaller overcoupled impedance and vice versa. 

---