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This paper presents a general analysis of the third-order nonlinearity of a differential common-emitter RF amplifier and an improved technique to cancel the third-order nonlinearity. A thorough analysis of the mechanisms leading to the second-order nonlinearity of bipolar double-balanced active mixers is also presented. An SiGe BiCMOS WCDMA direct-conversion mixer is designed based on the third- and the second-order cancellation schemes. The mixer achieves +6-dBm third-order input intercept point, +49-dBm second-order input intercept point, 16-dB gain and 7.2-dB double-sideband noise figure with only 2.2-mA current at 2.1 GHz.