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This letter presents the design and implementation of a Ka-band low noise amplifier (LNA). The LNA is based on a cascode amplifier using 0.12 mum SiGe heterojunction bipolar transistors (HBT). A new design procedure for simultaneous noise and input power matching is developed considering the collector-base feedback capacitance . At 33-34 GHz, the LNA results in a measured gain of 23.5 dB, a return loss of <-20 dB and a noise figure (NF) of 2.9 dB. The input return loss is <-10 dB and the NF is 2.6-3.2 dB for the entire Ka-band frequency range. The LNA is 300times300 mum2, consuming 6 mA from 1.8 V supply (11 mW). The output 1 dB compression power is -6 dBm. To our knowledge, these are state-of-the-art results and show the validity of the design technique.