Phase Noise in CMOS Differential LC Oscillators

An analysis of phase noise in differential cross-coupled tuned tank voltage controlled oscillators is presented. The effect of active device noise sources as well as the noise due to the passive elements are taken into account. The predictions are in good agreement with the measurements for different tail currents and supply voltages. The effect of the complementary cross-coupled pair is analyzed and verified experimentally. A 1.8GHz LC oscillator with a phase noise of -121dBc/Hz at 600kHz is demonstrated, dissipating 6mW of power using spiral inductors. Introduction Due to their relatively good phase noise, ease of implementation and differential operation, cross-coupled LC voltage controlled oscillators play an important role in high frequency circuit design. In this paper we apply the time variant phase noise model presented in [1] to these oscillators. We start with a very brief introduction to this model. Then we calculate the relation between the tank amplitude, the tail current source and the supply voltage. We will continue by analyzing the effect of the active device noise sources as well as the noise sources in the resistive loss in the tank. Finally, we present the experimental results which constitute measurements of the phase noise for different tail currents and supply voltages, showing good agreement with theory. We will analyze the effect of the complementary cross-coupled pair on phase noise and demonstrate it experimentally. The Time Variant Phase Impulse Response The phase noise of an oscillator can be characterized by its phase impulse response [1]. This impulse response characterizes the amount of phase shift caused by a given voltage (or current) impulse. To illustrate this concept we consider the ideal LC oscillator shown in Fig. 1. Assume it is already oscillating with a maximum voltage amplitude of Vmax. The current source in parallel with the tank has a value of zero at all times except at τ, when a current impulse of area ∆q is injected. All of this current goes through C as it shows the lowest impedance path for the current and the current through L cannot change instantly. This will cause a sudden change of in the capacitor voltage. Depending on the time of injection, τ, the resultant change in the capacitor voltage, ∆V, can cause the oscillator to oscillate with a different amplitude and phase. Fig. 1 demonstrates two extreme illustrative cases. If the impulse is injected when the tank voltage is at its maximum it will cause the tank voltage to change immediately without affecting the excess phase. By excess phase we mean φ(t) in the argument of sin[ωt+φ(t)] and not the whole argument of the sine. The second extreme case shown in Fig. 1 corresponds to an impulse injected close to a zero crossing of the tank voltage. This time, the change in the tank voltage introduces ∆V ∆q C ⁄ = some phase shift and a minimal change in amplitude. The resulting phase shift clearly depends on the instant of injection, τ. It is noteworthy that unlike the amplitude response, once the phase shift is introduced, the oscillator will oscillate with this new phase and will not go back to its previous phase. The phase shift depends on the instance of injection and is proportional to the injected charge, ∆q, for , where . Since the system is linear for small injections [1], we can characterize the phase response completely using a time-variant impulse response, . This is the impulse response of a system with current (or voltage) as the input and the phase as the output. This impulse response can be written in the following form