A modified low-pass filter with progressively diminishing ripples

A modified low-pass filter functions are proposed. A modified inverse Chebyshev function possesses progressively diminishing ripples in the stopband whereas the modified Chebyshev function exhibits ripples diminishing toward = 0 in the passband.Both are realizable in the doubly-terminated ladder structures for the ordern even or odd, thus lending themselves amenable to high-quality activeRC or switched capacitor filters through the simulation techniques.     

Metal Ions versus Protons: Tracking of Charge-Carrier Insertion into a Cathode Oxide in Aqueous Rechargeable Batteries

Protons in aqueous electrolytes can perform as an additional type of charge carrier for insertion/extraction in addition to the primary carrier cations in aqueous rechargeable batteries. Despite many diverse claims regarding the effect of protons, mutually conflicting experimental results and their interpretations without direct evidence have been reported over the last decade. Systematic examinations and analyses are thus imperative to clarify the conditions of proton insertion in aqueous rechargeable batteries. Utilizing V₂O₅ as a model cathode and beaker-type cells with a sufficient amount of ZnSO₄ aqueous electrolytes in this work, it is demonstrated that protons are inserted into the cathode prior to Zn-ions in low-pH conditions (pH ≤ 3.0). In stark contrast, the influence of protons on the discharge voltage and capacity is insignificant, when either the pH becomes higher (pH ≥ 4.0) or the electrolyte volume is considerably low in coin-type cells. Similar behavior of pH-dependent proton insertion is also verified in Na–, Mg–, and Al-ion electrolytes. Providing a resolution to the controversy regarding proton insertion, the present study emphasizes that the influence of protons substantially varies depending on the pH and relative volume of electrolytes in aqueous batteries.