Binary Connection Tree Parallel Adaptor

To interconnect three or more adaptors in a wave digital filter, it is now typical to use a Binary Connection Tree (BCT) [152,364], in which only three-port adapters are needed. Three-port adaptors can handle any combination of parallel and series connections.

For example, suppose we wish two connect adaptors $B$ and $C$ in parallel using a new three-port parallel adaptor $A$ , as shown in Fig.F.6. Adaptors $B$ and $C$ are normally themselves three-port adaptors in a BCT, but they can be any kind of adaptor (scattering junction). All that matters from the point of view of adaptor $A$ is the connecting port wave impedances $R_B$ and $R_C$ . Then to make the top port of adaptor $A$ reflection free, we choose its wave impedance $R_A$ to be the parallel combination of all other connected adaptors, i.e., $R_A=R_B\Vert R_C=R_BR_C/(R_B+R_C)$ in this case. We mark the top outgoing port of $A$ as being reflection-free using the `$\perp$ ' symbol.

Figure F.6: Parallel connection of adaptors $B$ and $C$ using a reflection-free three-port parallel adaptor $A$ .