Quality Factor and Inductance in Differential IC Implementations

Voltage-controlled oscillators (VCOs) are critical components for signal generation and frequency selection in RF/microwave transceivers. Recently, there has been considerable interest in monolithic integration of inductance-capacitance (LC) tank oscillators for highly integrated RF transceivers [1]. Technologies such as Si complimentary metal-oxide-semiconductor (CMOS) and Si/SiGe BiCMOS are of interest in light of the potential for integration with digital functions. The operation of an oscillator can be described using the concept of “negative resistance.” In an oscillator, an active network with negative transconductance, −GM, is connected to an LC-tank circuit with an equivalent parallel resistance, RP. The equivalent negative resistance (1/−GM) looking back into the transconductor is chosen to cancel the equivalent parallel resistance of the tank circuit. RP is obviously related to the quality factor Q of the L and C components. In Si technologies, the Q of the inductor is usually the limiting factor. Differential topologies are advantageous in integrated circuits (ICs) because they offer common-mode rejection. Therefore, differential circuits are less susceptible to supply noise present in on-chip power rails. Many RF integrated circuits (RFICs) utilize double-balanced Gilbert-cell mixers because they offer conversion gain while minimizing local oscillator (LO)/intermediate frequency (IF) feedthrough and even-order mixing products. Differential VCO topologies avoid the need for single-ended to differential conversion circuitry for the LO drive of a Gilbert-cell mixer. Figure 1 shows a differential CMOS complementary −GM oscillator [2], [3]. In this case, the negative resistance seen by the tank is given by