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The discovery of neighbouring active nodes is one of the most challenging problems in asynchronous ad hoc networks. Since time synchronization is extremely costly in these networks, application of asynchronous methods like quorum-based protocols have attracted increased interest for their suitability. This is because Quorum-based protocols can guarantee that two nodes with differing clock times have an intersection within at least one timeslot. A higher neighbour discovery rate of active nodes is desired, but it also results in a higher active ratio and consequently and adversely more overall power consumption of the nodes and a shorter network lifetime. There must be a trade-off between extensive neighbour discovery and active ratio in order to design high-performance and efficient protocols. In this paper, two novel asynchronous quorum-based protocols to maximize the neighbour discovery and minimize the active ratio have been designed and presented. A new metric (Quorum Efficiency Ratio: QER) has also been designed to evaluate and compare the performance of quorum-based protocols in terms of their neighbour discovery (the Expected Quorum Overlap Size: EQOS) and the active ratio. The EQOS has been theoretically derived, along with the Active Ratio and the QER values for the proposed novel protocols and the other contemporary protocols. Finally, the proposed methods have been evaluated and compared against the other methods based on the current metrics and the new metric.