Minimum achievable phase noise of RC oscillators

Navid, Reza; Lee, T.H.; Dutton, R.W.

doi:10.1109/jssc.2005.843591

Cited by 112 publications

(111 citation statements)

References 13 publications

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“…In order to simplify (9), we first take note of the fact that, according to the fluctuation-dissipation theorem of thermodynamic, during the equilibrium time , the noise PSD in the NMOS and PMOS devices are given by and , respectively. If we further assume that the current flow in NMOS and PMOS transistors are nearly equal and equal to ( through proper device sizing), (9) can be simplified to (11) which after solving for gives (12) In order to find the total noise PSD we use (12) along with the value of from simulation results (Spice models at Typical corner) and the values of and from the measurements. For a supply voltage of 1.8 V , in this 0.18 CMOS process, total drain current noise PSD (NMOS+PMOS) is , , and at 0.18 , 0.38 , and 0.54 channel length, respectively.…”

Section: B Measurement Results and Discussionmentioning

confidence: 99%

“…To calculate phase noise, we use the approach presented in [11]: first we calculate jitter in the time domain and then convert that to the frequency domain to find phase noise. To calculate jitter, we first calculate the variance of each switching instance.…”

Section: B Analytical Formulation Of Phase Noisementioning

confidence: 99%

“…In order to calculate the variance of the switching instance , we first need to calculate the variance of at that time. It can be shown that the variance of the voltage across a capacitor ( for brevity) connected in parallel with a resistor and a current noise source with a PSD of after time is given by [11] (1) where is the variance of at time , is Boltzmann constant and is the absolute temperature. To calculate the variance of at , we can break the time interval between and into three regions: the second half of (charging state), (equilibrium state) and the first half of (discharging state).…”

Section: B Analytical Formulation Of Phase Noisementioning

confidence: 99%

“…Section IV concludes this paper by presenting device noise data for a commercial 0.18 m CMOS process. Although some parts of the work have been briefly reported in [10] and [11], our work on the analytical formulation of phase noise, simulation results and interpretation of the experimental data are presented here in greater detail.…”

Section: Introductionmentioning

confidence: 99%

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Circuit-Based Characterization of Device Noise Using Phase Noise Data

Navid

Lee

Dutton

2010

IEEE Trans. Circuits Syst. I

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Abstract-A circuit-based device noise characterization technique is introduced which uses phase noise data to estimate the power spectral density (PSD) of high-frequency noise in MOSFETs. To apply this technique to a typical CMOS process, an oscillator structure is introduced which provides a predictable phase noise level for a given device noise PSD. The analytical equations governing the phase noise of this oscillator are presented and subsequently verified using circuit simulations. Three oscillators, using transistors of various channel lengths, are fabricated in a commercial 0.18 m CMOS process technology to study short-channel excess noise. It is shown that, at equal current levels, the noise PSD in minimum-channel-length transistors is 8.7 dB larger than that in 3 -minimum-channel-length devices. The proposed method is especially suitable for applying to a state-of-the-art CMOS process to provide a quantitative analysis of various noise tradeoffs which are sometimes missing in foundry-provided models.

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Section: B Measurement Results and Discussionmentioning

confidence: 99%

Section: B Analytical Formulation Of Phase Noisementioning

confidence: 99%

Section: B Analytical Formulation Of Phase Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Circuit-Based Characterization of Device Noise Using Phase Noise Data

Navid

Lee

Dutton

2010

IEEE Trans. Circuits Syst. I

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“…Such relaxation oscillators have two advantages with respect to ring oscillators: 1) they have a constant frequency tuning gain; and 2) their phase can be read out continuously due to their triangular (or sawtooth) waveform. A major disadvantage of practical relaxation oscillators is their poor phase-noise compared to ring oscillators [1,2,4].The 1/f 2 phase-noise performance of oscillators can be compared using the FoM definition given in Fig. 19.5.3 [1].…”

mentioning

confidence: 99%

A 90μW 12MHz Relaxation Oscillator with a -162dB FOM

Geraedts

Tuijl

Klumperink

et al. 2008

2008 IEEE International Solid-State Circuits Conference - Digest of Technical Papers

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Both ring oscillators and relaxation oscillators are subsets of RC oscillators featuring large tuning ranges and small areas. Figure 19.5.1 shows a typical relaxation oscillator with a capacitor and two switched current sources. Such relaxation oscillators have two advantages with respect to ring oscillators: 1) they have a constant frequency tuning gain; and 2) their phase can be read out continuously due to their triangular (or sawtooth) waveform. A major disadvantage of practical relaxation oscillators is their poor phase-noise compared to ring oscillators [1,2,4].The 1/f 2 phase-noise performance of oscillators can be compared using the FoM definition given in Fig. 19.5.3 [1]. Navid et al. have shown that at 290K thermodynamics limits the FoM of ring oscillators and relaxation oscillators to -165.3dB and -169.1dB, respectively [2]. Interestingly, they have also shown that the FoM of practical ring oscillators is generally better than about -160dB, while the FoM of practical relaxation oscillators is about 10dB worse. So in theory relaxation oscillators can be better, but in practice they are not. Part of the explanation is given in [2]; the noise added by the comparator, which is present in relaxation oscillators (cmp osc in Fig. 19.5.1) but not in ring oscillators, increases the phase-noise. We will show below that filtering this noise by exploiting a switched-capacitor discharge mechanism, the FoM of a practical relaxation oscillator can be as good as the FoM of ring oscillators. Fig. 19.5.1, I 1 charges capacitor C 1 . However, C 1 is not grounded, but connected across an OTA, and the discharge process exploits a switched capacitor, C 2 , which is reversed periodically. The operation of the circuit is described in the next sentences. has been subtracted from C 1 . V 3 = V + -V -is a sawtooth waveform. Subtracting this fixed charge packet filters out the noise of the oscillator comparator. The operation is illustrated in Fig. 19.5.3, which shows the control signal X, V 3 and the output of the comparator cmp out , V out , is also shown, which produces an edge whenever voltage V 3 reverses polarity. Suppose now that cmp osc is noisy and C 2 is reversed at t 4 instead of at t 3 . Although the duty cycle of V out is changed (at t 5 ), the active edge of V out at t 6 is unaffected and so is the phase-noise. This filter technique is similar to the anti-jitter circuit (AJC) technique used in open-loop jitter filters [3]; note that we apply a switched-capacitor circuit to subtract the charge packet, which is very power-efficient.Filtering out the noise of the oscillator comparator has two consequences: 1) the power dissipated by the oscillator comparator and its reference can be reduced without deteriorating the phasenoise; and 2) the two remaining contributions to the 1/f 2 phasenoise are the white noise of the charging and discharging mechanisms. It can be shown that the resulting FoM of such a relaxation oscillator is given by the equation in Fig. 19.5.3, where k is the Boltzmann constant, T the absolute tem...

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Noise Properties of Practical Oscillators

Kroupa

2012

Frequency Stability

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Minimum achievable phase noise of RC oscillators

Cited by 112 publications

References 13 publications

Circuit-Based Characterization of Device Noise Using Phase Noise Data

Circuit-Based Characterization of Device Noise Using Phase Noise Data

A 90μW 12MHz Relaxation Oscillator with a -162dB FOM

Noise Properties of Practical Oscillators

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