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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$ .

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University