Introduction to CMOS Resonant Oscillators

Introduction

Resonant oscillators remain one of the few fields in analog electronics that maintain their crucial role. These circuits generate time-varying periodic signals from a constant power supply. While generating basic oscillation is relatively straightforward, achieving high-quality oscillation under modern design constraints poses significant challenges. These constraints include low supply voltage, limited power consumption, a wide frequency tuning range, and compatibility with digital CMOS processes [1].

Figure 1: LC resonator with loss and its equivalent parallel model, showing the fundamental building block of a resonant oscillator.

Basic Operating Principle

The foundation of a resonant oscillator is an LC resonator composed of a parallel inductor (L) and capacitor (C), often referred to as an LC oscillator. This configuration serves as an energy storage unit, resonating at an angular frequency of ω₀ = 1/√LC, where the impedances of the inductor and capacitor cancel each other out.

Figure 2: Simplified diagram of a Colpitts oscillator, illustrating the basic architecture using a single-ended common-gate implementation.

The Colpitts oscillator, invented by E. Colpitts in 1918, represents an elegant implementation of a negative resistance oscillator. The required negative resistance is generated via positive feedback from the nMOS drain to source through the voltage-divider capacitors (C1-C2). This design requires only a single active device, as the current source can be implemented with a simple resistor.

Figure 3: Small-signal equivalent circuit of the Colpitts oscillator, demonstrating the analytical setup for determining oscillation conditions.

Phase Noise Characteristics

Phase noise is a key performance metric for resonant oscillators. Due to various noise sources, the uncertainty in the oscillation phase grows indefinitely over time. In the time domain, this uncertainty manifests as jitter, while in the frequency domain, it appears as phase noise, expressed in dBc/Hz.

Figure 4: Oscillation affected by strong white noise sources, illustrating the impact of noise on signal quality.

Figure 5: Spectrum of a noisy oscillator, showing characteristic phase noise sidebands.

Advanced Oscillator Architecture

Modern CMOS implementations commonly use cross-coupled differential pair oscillator designs. This architecture provides differential phase outputs, which are essential for most modern applications. Negative resistance is achieved by cross-coupling the differential resonator outputs to the inputs of a differential nMOS pair.

Figure 6: Simplified diagram of a Class-B oscillator with a single cross-coupled differential pair, illustrating a popular modern implementation.

Frequency Tuning Mechanisms

Practical oscillators require frequency tuning capability to compensate for component value uncertainties and process variations. The most common approach is to replace part of the resonator capacitance with a voltage-controlled capacitor (varactor).

Figure 7: Cross-sectional diagram of an AMOS varactor, illustrating the structure of a voltage-controlled capacitance element.

Figure 8: Comparison of C-V curves between an AMOS varactor and a pMOS device, showing capacitance variations under control voltage.

Multi-Core and Advanced Implementation

To achieve better phase noise performance, multiple identical oscillators can be coupled and operated synchronously. This method can proportionally reduce phase noise power according to the number of cores but increases power consumption and silicon area.

Figure 9: Reconfigurable coupled oscillator array, demonstrating the implementation of a multi-core oscillator array system.

Techniques based on transformers and mode-switching have attracted extensive research interest. These advanced architectures aim to break traditional trade-offs between phase noise, power consumption, and tuning range while enhancing overall performance metrics.

Conclusion

Resonant oscillators continue to play a fundamental role in modern communication systems, especially in applications requiring high-frequency purity. While the basic principles remain relatively stable, modern implementations continue to evolve to meet increasingly stringent specifications. Ongoing innovation in new architectures and technologies, particularly in transformer-based designs and multi-core implementations, highlights the dynamic nature of this field.

References

[1] P. Andreani and A. Bevilacqua, "Harmonic Oscillators in CMOS—A Tutorial Overview," IEEE Open Journal of the Solid-State Circuits Society, vol. 1, pp. 2-17, Sept. 2021, doi: 10.1109/OJSSCS.2021.3109854.