Nathan Raymond
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But, I do not know what a typical headphone's impedance looks like, nor what sort of output impedance most headphones amplifiers exhibit.
It depends. Some headphones have consistent impedance across their frequency response, some have small variations, and some have giant swings up and down. Today it's often the multi-driver IEMs that can have very uneven impedance, but it's also true for dynamic headphones (see my links to the Innerfidelity test results for the Audio Technica ATH-R70x above for instance). Innerfidelity is a good resource for looking at test results from a wide range of headphones and seeing what their actual measured impedance is:
https://www.innerfidelity.com/headphone-measurements
Regarding headphone amps, it depends on the amp in terms of it's output impedance. Some are 5 ohms, 10 ohms, 30 ohms, or 50 ohms. The Objective 2 is one of the lowest ones at 0.54 ohms. Some amps don't readily publish their output impedance and you're left to measure it yourself or try to derive it from other specs.
For those who haven't read it, this is a good resource on the topic of headphone/amp impedance and why it matters:
https://nwavguy.blogspot.com/2011/02/headphone-amp-impedance.html