A question about the phase of the response function fo the simple 3-loop circuit system

[jiajiasun]

The response function can be written as \frac{\alpha^2 + i \alpha}{1+\alpha^2}. The phase lag is $\phi/2 + tan^{-1}(\alpha)$.

Therefore, if \alpha is very small, say, 1e-4 (for example, in the case of a very poor conductor), then the phase lag is 90 degrees. Conversely, if \alpha is very large, say, 1e+4 (e.g., in the case of a very good conductor), the phase is 180 degrees. And, the phase lag should monotonically increase from 90 to 180 degrees as \alpha increases from 0 to positive infinity.

However, that is not what the following figure on https://em.geosci.xyz/content/maxwell3_fdem/circuitmodel_for_eminduction/understanding_harmonicEMresponse.html shows.

The red curve in the right panel, i.e., the phase values, show values from 0 to 90 degrees. Also, it shows a monotonic decreasing behavior.

Could you please double check the red curve in the right panel?

(Looks like my equations won't show up properly. Sorry about that. I need to figure out how to type equations properly in github)