Because of symmetric configuration, the equivalent circuit of the 2n + 1-way BPPD can be equivalent to that in Figure 1(b).
Here, the value of [Z.sub.b] has no effect on matching of the proposed multi-way BPPD, and it is usual to make the value of [Z.sub.b] equal to the value of [Z.sub.m].
Therefore, the procedure to design the multi-way BPPD with arbitrary complex terminated impedances is briefly summarized as follows:
In order to verify the proposed design and analysis theory in Section 2, we take the 3-way BPPD as an example (n = 1).
When [Z.sub.S] = [Z.sub.0] & [Z.sub.L] = [Z.sub.0], this proposed 3-way BPPD becomes the conventional one as , and the design Equations (8) and (9) can be simplified as (13) and (14), respectively.
The BPPD has 180[degrees] phase difference between any two adjacent output ports and 0[degrees] phase difference between two symmetrical output ports.
When [Z.sub.S] = [Z.sub.0] & [Z.sub.L] = [R.sub.L] + j[X.sub.L], this proposed 3-way BPPD can be reduced to the input terminated impedance as real impedance [Z.sub.0], and the output terminated impedances are arbitrary complex impedances [Z.sub.L] = [R.sub.L] + j[X.sub.L].
From Figure 5, in Case B proposed 3-way BPPD shows an excellent performance with the return loss of input port and insertion loss.
The principal characteristics of NLD have been refined (e.g., Casey, Rourke, & Picard, 1991; Harnadek & Rourke, 1994; Rourke & Tsatsanis, 1996), and the NLD and BPPD subtypes more fully explored (Rourke, 1995a, 1995b; Rourke et al., 2002).
We have also developed rules of classification for NLD and BPPD (e.g., Drummond, Ahmad, & Rourke, in press; Pelletier, Ahmad, & Rourke, 2001), which have been shown to have clear external validity with respect to types of psychosocial dysfunction for children (Pelletier et al., 2001) and adults (Ahmad, Rourke, & Drummond, under review).
For example, we have demonstrated several times that children with NLD are particularly and increasingly prone to serious forms of psychosocial dysfunction over the course of development, whereas those with BPPD are not (e.g., Tsatsanis et al., 1997).
Perhaps most intriguing is the evidence that brain changes in a normalizing direction are observed after the application of intensive phonological training of children with deficits in phonology (as evident in children with BPPD).