Optimal impedance matching uses geometric mean intermediate steps

Evidence

Suppose the impedance must change from Z1 at one place to Z3 at another. We are allowed to insert an intermediate impedance Z2. What is the optimum Z2 for maximum transmission? We want the intermediate step to be the geometric mean of the impedances of adjacent steps. If Z1 and Z3 are the impedances of regions 1 and 3 surrounding region 2, then the impedance of region 2 that will lead to the highest throughput of energy from 1 to 3 is the geometric mean One of the engineer’s favorite tricks is lumping properties of objects that are connected together, combining their individual responses into a response of a single system. — Eric J. Heller, Why You Hear What You Hear- An…, 551

Categorization

• DEFINE: Introduces the geometric-mean impedance-matching rule that motivates the exponential horn profile.
• XREF: Generalizes to any transmission-line problem — electrical, optical, acoustic — where impedance matching matters. — connects to: A soundboard must avoid too-perfect impedance matching to not drain the strings
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 551

Broader Connections

• A soundboard must avoid too-perfect impedance matching to not drain the strings #complicates (0.72)