Negative capacitance or inductive loop? - A general assessment of a common low frequency impedance feature

Impedance analysis is not an easy task. This becomes even more obvious if unusual shapes appear in the impedance diagram. Here, a low frequency hook with positive imaginary part is discussed that often leaves researchers clueless of how to handle it, especially if there is no common model for the device under test that includes the hook, which is actually true for most electrochemical systems. The low frequency hook is explained from a systems theory perspective and a very basic explanation is given of what has to happen phenomenologically for this feature to appear. The most common equivalent circuit model (ECM) for such a low frequency hook is reviewed and the relation to a general empirical low-pass filter type model is discussed. A common electrochemical example and an abstract minimal example are introduced to facilitate the interpretation of the low frequency hook for an arbitrary (photo-) electrochemical system.