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This thesis explores research into new distributed circuit design techniques and topologies, developed to extend the bandwidth of amplifiers operating in the mm and sub-mm wave regimes, and in optical and visible light communication systems. Theoretical, mathematical modelling and simulation-based studies are presented, with detailed designs of new circuits based on distributed amplifier (DA) principles, and constructed using a double heterojunction bipolar transistor (DHBT) indium phosphide (InP) process with fT =fmax of 350/600 GHz. A single stage DA (SSDA) with bandwidth of 345 GHz and 8 dB gain, based on novel techniques developed in this work, shows 140% bandwidth improvement over the conventional DA design. Furthermore, the matrix-single stage DA (M-SSDA) is proposed for higher gain than both the conventional DA and matrix amplifier. A two-tier M-SSDA with 14 dB gain at 300 GHz bandwidth, and a three-tier M-SSDA with a gain of 20 dB at 324 GHz bandwidth, based on a cascode gain cell and optimized for bandwidth and gain flatness, are presented based on full foundry simulation tests. Analytical and simulation-based studies of the noise performance peculiarities of the SSDA and its multiplicative derivatives are also presented. The newly proposed circuits are fabricated as monolithic microwave integrated circuits (MMICs), with measurements showing 7.1 dB gain and 200 GHz bandwidth for the SSDA and 12 dB gain at 170 GHz bandwidth for the three-tier M-SSDA. Details of layout, fabrication and testing; and discussion of performance limiting factors and layout optimization considerations are presented. Drawing on the concept of artificial transmission line synthesis in distributed amplification, a new technique to achieve up to three-fold improvement in the modulation bandwidth of light emitting diodes (LEDs) for visible light communication (VLC) is introduced. The thesis also describes the design and application of analogue pre-emphasis to improve signal-to-noise ratio in bandwidth limited optical transceivers.