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I asked Gemini to clarify a question I had about the response to 6 and got the following. I have highlighted the part at the end that

The source¹ is here.

Prompt: Please explain "Because a passive, lossless impedance match from 50 Ω to 400 Ω naturally increases voltage by a factor of square root of 400 / 50 = square root of 8 = about 2.83

This comes down to one of the most fundamental rules of physics: **Conservation of Energy**.

[... deleted description of conservation of energy in a lossless system ...]

The Physical Takeaway

If you have a fixed amount of power, you cannot change the resistance without also changing the voltage and current to compensate.

The useful part came as a footnote

*(Note: Because a resistor-based L-pad actually dissipates heat, it is strictly **lossy**. The theoretical ~2.83x voltage increase only happens in a perfectly lossless network, like an ideal transformer or a perfect LC circuit. In the real-world resistor pad designed in the previous step, that theoretical gain is immediately eaten by the resistors' inherent losses, which is why the actual output voltage dropped to 0.3536 mV).*