The effective ISFs of differential LC oscillators are derived under the assumption that the drain-to-source current is linearly dependent on the gate-to-source voltage for transistors operated in saturation. Moreover, a new interpretation of phase noise is given by examining the real vector diagram of the carrier signal, upon which the noise voltage induced by the impulse noise current is superimposed. The distinct feature of our vector diagram lies in that the noise voltage is always parallel with the horizontal axis. From the Fourier transformations of the derived effective ISFs, the phase noise of differential LC oscillators can be formulated with physical meanings in the frequency domain. The proposed theory can well describe the translation of the noise spectra when the noises from the LC-tank, the switching transistors, and the tail current source are converted into the phase noise. Theoretical predictions from our formulas agree well with the simulation results.

A LNA, an RF front-end and a 6th–order complex BPF for reconfigurable low-IF receivers are demonstrated in this work. Due to the noise cancellation, the two-stage LNA presents a low NF of 2.8 to 3.3 dB from 0.8 to 6 GHz. Moreover, the LNA delivers two kinds of gain curves with IIP3 of -2.6 dBm by employing the capacitive degeneration and the resistive gain-curve shaping in the second stage. The flicker noise corner frequency of the down-converter has been considered and the measured fC of the RF front-end is 200 kHz. The RF front-end also provides two kinds of gain curves. For the low-frequency mode, the conversion gain is 28.831.1 dB from 800 MHz to 2.4 GHz. For the high-frequency mode, the conversion gain is 26.827.4 dB from 3 to 5 GHz. The complex BPF is realized with gm-C LPFs by shifting the low-pass frequency response. With variable transconductances and capacitors, a fixed ratio of the centre frequency to the bandwidth (2) is achieved by varying the bandwidth and the centre frequency of the LPF simultaneously. The complex BPF has a variable bandwidth from 200 kHz to 6.4 MHz while achieving an image rejection of 44 dB.