This thesis presents the research progress in practically utilising memristors to enhance the performance of conventional analogue circuits and developing an on-chip characterisation platform for accessing a large number of devices. A methodology of employing memristive devices in current-mode circuit design is proposed by realising an on-chip memristor-controlled current conveyor. Two CMOS circuits: a memristor-controlled active inductor and a tuneable delay element, are developed to investigate whether this emerging device could significantly improve the reconfigurability of current-controlled analogue circuits. The experiment results show that the tuning range for desired parameters is increased significantly compared to conventional designs. In addition, the advantages and disadvantages of the proposed method are discussed to share some insights into the current challenges in practically utilising memristive devices.

During the programming and measurement phase of the memristor device, its non-ideal behaviours regarding the noisy transient programming progress are observed. Although the underlying physics behind this phenomenon is still unclear, this noise is captured by developing a behaviour memristor model.
A transient memristor model is constructed using a data-driven approach, which computes the alteration of the resistive state based on the current resistive state and the amplitude of stimulus pulses. The noise components are incorporated, which are randomly generated according to the modelled distribution of the resistive state alteration.

With a more mature understanding of memristive devices, two CMOS characterisation platforms are designed for programming and measuring on-chip memristors. The first characterisation platform is a scalable 16x16 array designed in high-voltage CMOS technology, which is a prototype array for CMOS-memristor technology integration...