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None of the previously reported third-order and fourth-order operational transconductance amplifier and capacitor (OTA-C) elliptic filter structures use the minimum number of active and passive components. After an innovative algebraic decomposition for a complicated transfer function, i.e., a new analytical synthesis method, a current-mode odd-nth-order and a current-mode even-nth-order OTA-C elliptic filter structure having the following advantages are presented: 1) all the OTAs have single-ended inputs; 2) all the capacitors are grounded; 3) the minimum active and passive components are used. An equal-capacitance-type structure is designed taking into account the difficulty of precisely fabricating capacitances in integrated circuits. Although the above three advantages lead to the lowest total parasitics and to the most precise output response, the small deviations (such as the 3.5159% error in fp) of the four parameters of the new third-order OTA-C elliptic filter can be drastically reduced (for example, to 0.1553% error in fp) by only slightly tuning the four transconductances, but fixing the ratio of the given three capacitances, and without adding any other active and passive components. H-spice high-pass and low-pass simulations with 0.35-mum process are provided to demonstrate the theoretical results.