DC-DC converters can be found in three basic forms which are the linear regulators, the switch-mode power supplies (SMPSs) and the charge pumps. The combinations of these topologies are prevalent in power management circuits where the designers try to achieve cost-effectiveness, low output noise, high end-to-end efficiency and predictable transient response in these converters to make them suitable for a steady and constant power supply with regulation and multiple outputs. Combining an array of low equivalent series resistance (ESR) supercapacitors (SCs) and a linear low-dropout (LDO) regulator, a unique DC-DC converter topology has been developed over the past nine years; this technique is called the supercapacitor-assisted low-dropout (SCALDO) regulator. In the SCALDO approach, one or more supercapacitors are used in the series path of a LDO regulator as a lossless dropper and the excess energy accumulated in the SCs is re-circulated at a very low frequency to increase the end-to-end efficiency by a multiplication factor in the range of 1.33 to 3. During the past several years, the SCALDO technique was further developed into many applications by introducing the reduced-switch topology and DC-UPS capability. Also, this technique has been identified as a potential area where further research can be carried out to match various power management requirements. After a comprehensive investigation of feasible SCALDO implementation scenarios for multiple outputs, it was found possible to narrow them down to a detailed analysis of two output stages in a single converter which is substantial research for a PhD thesis. This dual-output converter is called the dual-output SCALDO (DO-SCALDO) regulator. In this method, dual-polarity voltage levels are generated from a single input voltage source whilst maintaining the useful characteristics of the original SCALDO approach such as high efficiency, low noise, fast dynamic response and low EMI/RFI issues. This thesis describes the conceptual background of the DO-SCALDO technique together with the working principles related to the different modes of operation. The theoretical concept is validated by the experimental results of a prototype version of a 12 V to ±5 V DO-SCALDO regulator. The steady-state and transient responses are investigated. The end-to-end efficiencies and the losses are also determined, and the unique characteristics and potential advantages are compared with the commercial dual-output DC-DC converters. In addition to the DO-SCALDO concept, the stability analysis of the single-stage SCALDO regulator is also considered as another potential area for further research. Since the SCALDO approach works based on a low-frequency SC circulation technique at the front end of a LDO regulator, the stability of the LDO regulator might be affected due to this external SC circulation network. Therefore, the overall circuit should be analysed for stability. The outcomes of this study can be used to stabilise the discrete SCALDO regulators or SoC (System on a Chip) designs. This thesis explores the design parameters and constraints regarding the stability of the fundamental SCALDO topology with the aid of the small-signal model. The open-loop transfer function is derived, and the possible frequency compensation techniques are identified. The theoretical small-signal model is validated from the simulated and experimental results of a 12 V to 5 V discrete SCALDO regulator, and the conclusions are made accordingly.