Analytical phase noise study of a back-gate coupled colpitts quadrature VCO

Abstract

This paper presents a detailed study of phase noise of an LC Quadrature Voltage-Controlled Oscillator (QVCO). This QVCO is made of coupling two identical cross-connected Colpitts oscillators as core oscillators. MOSFETs are used as varactors, the substrates of which are used for coupling the two core Colpitts oscillators. Phase noise improvement resulted from substrate coupling is not only due to elimination of noise sources (as no extra passive or active coupling devices are used) but also due to lower effective thermal noise of the substrates. To verify this, a rigorous phase noise analysis of the circuit using the Linear Time Variant (LTV) model is performed for the 1/f2 region. It indicates that the improvement is not only due to lower thermal noise of the substrate, but also a better noise modulating factor (NMF). The proposed QVCO was designed and simulated in a 0.18 ​μm RF-CMOS Technology at frequency of 5.35 ​GHz with a power consumption of 8 ​mW, tuning range of 18% and phase noise of −142.8 ​dBc/Hz at 5 ​MHz frequency offset. The presented analysis indicates a phase noise of −143 ​dBc/Hz at an offset of 5 ​MHz, which shows a good agreement with the simulation. The difference between the simulated and calculated phase noise at high frequency offsets is less than 0.2 ​dB.