Lee and Hajimiri 2000 - Squeezing the Best Out of Your Oscillator

To design low-phase-noise oscillators, maximize signal amplitude and resonator Q, minimize sensitivity to noise injection timing, and exploit waveform symmetry. Classical models fall short—linear time-varying (LTV) theory offers actionable guidance.

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🔹 1. LTV Model > LTI Model for Predictive Accuracy

• Traditional linear time-invariant (LTI) models like Leeson's equation offer qualitative insights but fail to predict measured phase noise.

• Oscillators are inherently linear but time-varying (LTV) systems—impulse response varies with time due to periodicity.

• The Impulse Sensitivity Function (ISF) quantifies how susceptible the oscillator phase is to noise at each point in time.

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🔹 2. Symmetry Suppresses 1/f Noise Upconversion

• Close-in phase noise is worsened by upconversion of 1/f noise; this can be greatly reduced by minimizing the ISF’s DC value. This requires symmetry - ensure rise/fall times are matched.

• Oscillators like the Colpitts and symmetrical negative-resistance LC oscillators naturally suppress noise at sensitive points in the waveform cycle.

• Proper timing and symmetry ensure energy injection occurs when phase disturbance is minimal.

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🔹 3. Practical Circuit Design Guidelines

• Deliver energy impulsively during ISF minimum (voltage peaks) instead of continuously across the cycle.

• In CMOS, use layout symmetry and matched devices to mitigate substrate/supply noise.

• Ring oscillators have poor phase noise due to bad resonator quality but can be made resilient to common-mode noise with proper correlation across stages.

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🔹 4. Simulation and Amplitude Considerations

• Use direct impulse simulation to extract accurate ISFs.

• Amplitude noise dominates far from the carrier and must be handled with separate decay dynamics (especially in high-Q oscillators).