Algebraic Relation between Sensitivities and Impedance (More Complicated with Inductive Reactance)

[Sha1rholder]

I used to write a post How and Why to Convert Headphone Sensitivity to Make a Rough Estimate of Headphones' Driving Difficulty.

Recently I realized that as headphone drivers are not simple resistance, there must be a lot of fun facts buried in those Peaks in those impedance curves. BUT, before diving into another article introducing impedance and impedance curve, I decided to fix the previous post which would have been completely wrong considering reactance! Also, I left a little puzzle for you, which... may add a little interestingness.

BTW, here's non-profit advertisement. Have a glance at my GitHub repository Sha1rholder/Sound-Library: Your Acoustics Knowledge Base (github.com) which dedicates to helping audiophiles and those interested in high-quality audio learn the knowledge of sound : )

Let's start with conclusion​

Basic Background Knowledge​

Preliminary Derivation​

Understanding the following derivation requires knowledge of logarithmic operations and Junior high school level electrical principles.

Advanced Background Knowledge​

Advanced Derivation​

Understanding the following derivation requires knowledge of complex number operations and the distinction between visible power and actual power

Happy solving the problem at beginning!​