All possible gyrator circuits using the minimum number of voltage and current unity-gain cells are extracted, as a result of generalizing the unity gains, such that a unity gain can be +1 or -1. Since second-generation current conveyors (CCIIs), possessing both voltage and current unity-gain cells, are very suitable for such gyrators, it is shown that inclusion of the recently proposed 'inverting second-generation current conveyor' (ICCII) in the design enables implementation of all types of extracted gyrators. The number of possible gyrator configurations is eight, one of them being the well-known Sedra-Smith gyrator and another its x-input counterpart; both utilize only CCIIs. The remaining possible six gyrators are new and utilize ICCIIs as well. Like the Sedra-Smith gyrator, all the circuits employ a minimum number of passive elements and similar types of active components, namely CCIIs and/or ICCIIs. The effects of current conveyor non-idealities and parasitics on important gyrator applications are also investigated. A high performance dual-output CMOS ICCII is designed and used in SPICE simulations of two important gyrator applications in order to verify the theoretical results. Also, as a design example: an elliptic filter is realized and simulated.