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A technique for the design of broadband microwave transistor power amplifiers is presented that utilises the powerful methods of network synthesis to achieve optimum large-signal performance. Only two large-signal transistor measurements per frequency are required to achieve a good analytic model of the transistor's variation of added power with load impedance, and a mapping function is presented that translates this added-power characteristic into an equivalent linear-circuit reflection-coefficient characteristic. With this representation, methods of linear-network synthesis are used to obtain circuits which optimise the amplifier's added-power efficiency over a broad range of frequencies. The design technique has been experimentally verified by the characterisation, design and construction of a b.j.t. amplifier of near-octave bandwidth centred at 1 GHz, with the large-signal performance in good agreement with that predicted by the design theory.