A dual-band impedance transformer for achieving very high impedance transformation (k) and frequency ratio (r) is presented in this paper. The design is accompanied by a thorough analysis and systematic design procedure for facilitating the rapid development of the prototypes. A number of case studies show the excellent design flexibility of the proposed design in regards to achieving ultra-high k and r. Two prototypes, with very high design specifications, working at concurrent r = 5, k = 8.04 and r = 15, k = 20 are fabricated to validate the proposed architecture and the design procedure. Subsequently, the application of the proposed impedance transformer is demonstrated in the design of a dual-band balun architecture with inherent impedance transformation capability. To evaluate the performance and the presented concept, an impedance transforming balun prototype is fabricated and the excellent agreement between the simulation and experimental results is a testament to the effectiveness of the proposed design. INDEX TERMS closed-form equations, dual-band, high frequency ratio, impedance matching, impedance transformer, microstrip line, ultra-high impedance transformation.