基於開迴路注入鎖定之 CMOS 可調式倍頻器

Abstract

本論文目標是實現一個開迴路的可調式倍頻器，為了實現開迴路的倍頻鎖定，本文採取了注入鎖定的方式。然而使用注入鎖定首先就要面對的是次諧波注入鎖定的鎖定範圍過窄的問題，無法單獨由該方式應付自振頻率的變異，再來是注入強度過強會導致振盪器波形受到強烈的干涉，會使得些微的自振頻率與注入頻率的偏差就會導致後續嚴重的問題。因此，本論文中先使用同頻的注入鎖定產生多相位，再用多相位合成出倍率為相位數量因數的訊號，以此避開了次諧波注入鎖定過窄的問題。另外，本文使用的一些電路機制克服了相位雜訊與相位誤差的取捨，使得在很大的注入強度下，既可以保有良好的對相位雜訊抑制效果，又不會使得振盪器波形破壞過於嚴重而導致後續合成出來的倍頻訊號有嚴重的確定性抖動(deterministic jitter)/突波(spur)。此外，本文所使用的多相位產生方式，相較延遲鎖定迴路，可以節省許多功耗，並且此架構可以在不過多消耗額外功耗情況下，產生更多相位。 在整體系統操作前，會先經由頻率校準電路將振盪器自振頻率校準到接近參考頻率，使得接下來的注入鎖定可以達到更佳的效果。負責校準的數位電路以及其所面臨的實際問題，也會在論文中探討。 接著本論文從動態系統的角度出發，探討適用於任何非線性自治系統的注入鎖定振盪器之相位雜訊、鎖定範圍和相位誤差，由此解釋本文電路中的實際物理現象。以龐加萊映射(Poincare' Map)對應的離散時間動態之特徵向量作為基底，將隨機向量投影在耦合振盪器之狀態空間中的二維流形上，透過求解隨機微分方程沿著兩個主導方向上的隨機程序之自相關函數，推導受注入之振盪器的極限環上(來自解耦合極限環經過分岔)的相位調變在低偏移頻率內如何受到軌道穩定性(orbital stability)和李亞普諾夫指數(Lyapunov exponent)抑制，以及注入訊號源如何主宰整個耦合振盪器相位擴散的維納過程之統計特徵。最後探討受注入振盪器與注入相位之間的相位差之一維動態，以了解在注入過程中，振盪器是如何對齊到注入相位，並由是否存在穩定平衡點來得到鎖定範圍。接著將該分析方式延伸到注入鎖定多相位耦合振盪器，得到多個子振盪器的相位差之多維動態，透過求解其穩定平衡點，得到最終的多相位分佈，以了解注入鎖定對相位誤差的影響。 最後晶片採用TSMC 180-nm CMOS製成實現，操作電壓為1.8V，參考頻率為400 MHz，並產生400 MHz ~ 1.6 GHz的輸出範圍。在4倍頻的1.6 GHz輸出當中，在1-MHz偏移頻率的相位雜訊為-123 dBc/Hz，峰對峰抖動為14.9 ps，功耗為7.5 mW。

The objective of this thesis is to realize an open-loop programmable frequency multiplier. In order to achieve open-loop frequency-locking, this work adopts the injection-locking approach. However, the use of injection locking first faces the problem that the locking range of subharmonic injection locking is too narrow, making it unable to cope with variations in the free-running frequency by itself. In addition, when the injection strength is too large, the oscillator waveform will be strongly disturbed, such that even a slight mismatch between the free-running frequency and the injection frequency may lead to severe subsequent problems. Therefore, in this thesis, same-frequency injection locking is first used to generate multiple phases, and these multiple phases are then combined to synthesize a signal whose multiplication factors correspond to the divisors of the number of phases. In this manner, the narrow-locking-range problem of subharmonic injection locking is avoided. In addition, several circuit mechanisms employed in this work overcome the trade-off between phase noise and phase error, enabling the system to maintain strong phase-noise suppression under large injection strength while avoiding excessive distortion of the oscillator waveform, which would otherwise result in severe deterministic jitter and spurs in the subsequently synthesized frequency-multiplied output signal. Furthermore, compared with delay-locked-loop-based multi-phase generation, the multi-phase generation method used in this work can save a significant amount of power consumption, and this architecture can produce more phases without incurring excessive additional power. Before the overall system begins operation, a frequency-calibration circuit is used to calibrate the free-running frequency of the oscillator to be close to the reference frequency, so that the subsequent injection locking can achieve better performance. The digital circuit responsible for calibration, as well as the practical issues it encounters, are also discussed in this thesis. Next, this thesis investigates the phase noise, locking range, and phase error of injection-locked oscillators from the perspective of dynamical systems, in a manner applicable to any nonlinear autonomous system, thereby explaining the actual physical phenomena in the implemented circuit. Using the eigenvectors of the discrete-time dynamics associated with the Poincaré map as the basis, the random vector is projected onto a two-dimensional manifold in the state space of the coupled oscillator. By solving the autocorrelations of stochastic processes along two dominant directions via stochastic differential equations, this work derives how the phase modulation on the limit cycle of an injected oscillator (after bifurcation from the uncoupled limit cycle) is suppressed at low offset frequency by orbital stability and the Lyapunov exponent, and how the injection source governs the statistical characteristics of the Wiener process associated with the overall phase diffusion of the coupled oscillator. Finally, the one-dimensional dynamics of the phase difference between the injected oscillator and the injection phase are analyzed in order to understand how the oscillator aligns to the injection phase during the injection process, and to obtain the locking range from the existence of a stable equilibrium point. This analysis is then extended to an injection-locked multi-phase coupled oscillator, yielding the multi-dimensional dynamics of the phase differences among multiple sub-oscillators. By solving for their stable equilibrium points, the final multi-phase distribution is obtained, enabling investigation of the impact of injection locking on phase error. Finally, the chip is implemented in TSMC 180-nm CMOS technology, operating at a supply voltage of 1.8 V, with a reference frequency of 400 MHz, and produces an output frequency range of 400 MHz to 1.6 GHz. At the 4× multiplied 1.6-GHz output, the phase noise is −123 dBc/Hz at a 1-MHz offset, the peak-to-peak jitter is 14.9 ps, and the power consumption is 7.5 mW.