Phase noise analysis of the connected-sources parallel quadrature oscillator

https://doi.org/10.1016/j.compeleceng.2021.107134Get rights and content

Highlights

  • A novel phase noise analysis of the Connected Sources Parallel Quadrature Oscillator (CSPQO) is proposed.

  • Using a new perspective, closed-form expressions have been derived for its amplitude, ISF, NMF, and phase noise.

  • Based on simulation results, there are less than 2% and 1dB calculation errors for oscillation amplitude and phase noise.

  • The proposed analysis gives circuit designers a deep insight into CSPQO’s performance to achieve the most favorable design.

  • It is shown that a coupling factor of 0.35 is an optimum point for CSPQO to have a better performance compared to DSPQO.

Abstract

In this work, the operation mechanism of the Connected-Sources Parallel Quadrature Oscillator (CSPQO) is investigated meticulously through a novel perspective. It is proven that, unlike Disconnected-Sources Parallel Quadrature Oscillator (DSPQO), conduction angles of the switching and coupling transistors vary versus the coupling factor in CSPQO. This perspective leads to formulating CSPQO's drain currents to derive closed-form expressions for its phase noise for the first time. A comprehensive phase noise analysis for CSPQO is presented using Hajimiri's phase noise theorem. There are less than 2% and 1dB errors for oscillation amplitude and phase noise calculations. Besides, an inclusive comparison is performed between DSPQO and CSPQO, and it is established that CSPQO has a better performance for coupling factors less than 1. It is shown that a coupling factor of 0.35 is an optimum design point for CSPQO to have better phase noise and Figure of Merit (FoM) performances compared to DSPQO.

Introduction

Due to the endlessly shirking size of MOS transistors, satisfying wireless standards’ requirements for high-speed applications has become more challenging. Local oscillators have played a prominent role in transceivers, and their performances directly affect the overall performance of the entire system. Therefore, they should be designed and optimized properly. Phase noise, known as jitter in the time domain, spreads the transmitted signals’ spectrum into nearby frequencies, and, also, it can ruin the received signal, and causes the adjacent interferers to spread over the desired RF signal [1]. As a result, the phase noise of an oscillator is one of the crucial and destructive parameters due to its impact on the overall performance of an RF transceiver in wireline or wireless application. Modeling and analyzing the phase noise have been one of the hardest as well as exhilarating works that have been performed by RFIC designers. In general, analyzing noise sources and discovering and understanding how a system responses to them has always been crucial in the field of electronics [2], [3], [4], [5], [6].

Analysis of the oscillator's phase noise was started by Leeson [7] in 1966, which does not provide general formulas for phase noise calculation. In 1998, Hajimiri provided a general theory for the oscillator's phase noise, which can give an excellent insight into what it depends on, and closed-form expressions are provided for accurate calculation of the phase noise [8], [9], [10]. Others like Andreani [11,12], and Mirzaei [13] extended Hajimiri's and Leeson's models to quadrature oscillators, especially Parallel Quadrature Oscillator (PQO), which was introduced by Rofugaran in 1996 [14]. This quadrature oscillator was the first one to provide quadrature outputs that uses coupling transistors in order to lock two single LC cross-coupled oscillator cores. It is one of the best quadrature oscillators that has remarkable stability in terms of phase noise and phase error against PVT variations. Therefore, PQO is one of the most widely used in the industrial and academic fields. It has been used in many wireless and wireline transceivers, proximal-field sensing [15], and frequency multiplier and divider circuits [16,17].

Although numerous effective and compelling analyses for phase noise understanding have been published [[12], [13], [14],[18], [19], [20], [21], [22], [23], [24]], there are cases that phase noise performance of an oscillator is still unclear. In [12], the phase noise of Disconnected-Sources (DS)PQO is thoroughly analyzed, and closed-form expressions are proposed; however, there are no such expressions for the Connected-Sources (CS)PQO. In all works presented in [[12], [13], [14],[18], [19], [20], [21], [22], [23], [24]] no phase noise analysis has been performed for CSPQO; they all focus more on DSPQO. Only in [12], it is claimed that the phase noise of CSPQO is analyzed numerically, and only a limited number of numerical results are provided to compare theory and simulation results.

Therefore, no mathematical analysis has been provided for CSPQO's phase noise performance, and this gap remains unfilled so far, and those who are interested in this field have no insight into the performance of its phase noise, while it is one of the most used PQO in industrial and academic fields. This is the main motivation behind this work to fill this gap in order to give a deep understanding of CSPQO's phase noise performance. The proposed analysis is a pioneer in formulating CSPQO's phase noise, and we believe that it is a starting point to be developed by other researchers. It should be noted that phase noise analysis is essential for a particular oscillator, because it strongly depends on the structure, and it can provide readers with new ways and ideas. This is why the focus of this work is on the phase noise analysis of CSPQO and comparison with DSPQO's performance.

In this paper, using a novel perspective of CSPQO's operation mechanism, closed-form expressions are derived for its currents, oscillation amplitude, ISFs, NMFs, phase noise, and FoM. The results are compared with DSPQO, which brings about a definite comparative conclusion. It shows that the phase noise performance of DSPQO is better than that of CSPQO in the same settings, regardless of their coupling factors. However, in terms of the Figure of Merit (FoM), CSPQO has a better outcome for the coupling factors less than 1. This comprehensive comparison between CSPQO and DSPQO gives rise to achieving an optimum design point for CSPQO to have the lowest possible phase noise, best FoM, and a reasonable phase error. Therefore, it incontrovertibly gives designers unprecedented insight into their operations and performances to achieve a low phase noise quadrature oscillator.

We observed that the operation mechanism of CSPQO is entirely different from that of DSPQO. It is established that increasing the coupling factor does not affect the injection current amplitude, and it only causes changes in transistors' conduction angles with a constant amplitude. Using the fact that the conduction angles can be the main key to derive the current equations of transistors, we were able to obtain closed-form expressions.

The rest of this paper is organized as follows. In Section II, Andreani's analysis for DSPQO is reviewed to provide some basic concepts using [12]. The proposed analysis of the CSPQO's phase noise and a comprehensive comparison between CSPQO and DSPQO performances are introduced in Section III. Section IV includes simulation results to authenticate proposed closed-form expressions. Finally, Section V gives the conclusions of the paper.

Section snippets

Phase noise analysis of DSPQO

Fig. 1(a) demonstrates the circuit schematic of DSPQO, in which two I and Q oscillators are coupled in their first harmonic via cross-connecting their outputs through four coupling transistors (MC1-MC4), which inject coupling currents to the second oscillator to generate quadrature outputs. According to Fig. 1(b), which shows outputs and drain currents of switching (MS1-MS4) and coupling (MC1-MC4) transistors for two cases of weak and strong coupling factors, drain currents of all switching and

Phase noise analysis of CSPQO

Fig. 4(a) shows the circuit schematic of CSPQO. The difference between CSPQO and DSPQO is that in CSPQO, all the coupling and switching transistors’ source terminals are connected to each other and derived by the same tail current (Ibias). At first glance, there may not be much difference between the two PQOs, but their performances and operation mechanisms are completely different. This difference results in different shapes of their currents, ISFs, and NMFs, which end up in completely

Certify by simulation

To verify the proposed analysis and expressions, CSPQO is simulated by Level-3 MOS transistors with the same settings of 0.18μm CMOS technology in ADS. In the simulation, the quality factor of 15, voltage supply of 2 V, the bias current of 2mA, and the oscillation frequency of 3.5 GHz are selected.

Simulation results for switching and coupling transistors conduction angles, oscillation amplitude, and phase noise are reported and compared with their relative equations in Fig. 11(a)–(c),

Conclusions

The operation of the Connected-Sources Parallel Quadrature Oscillator (CSPQO) is explored using a novel viewpoint. It was proven that the conduction angles of switching and coupling transistors in CSPQO, unlike DSPQO, are not constant and vary by changing the coupling factor. It was established that the conduction angles of the switching and coupling transistors are decreased and increased by increasing the coupling factor, respectively. A novel and comprehensive analysis of CSPQO's phase noise

Author statement

All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work.

The specific contributions made by each author have been listed below.

Bahram Jafari (first author): Conceptualization, Methodology, Software, Formal analysis, Validation, Writing - Original Draft, Writing - Review & Editing.

Samad Sheikhaei (second author): Methodology, Formal analysis, Supervision, Writing - Review & Editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Bahram Jafari received the B.Sc. and M.Sc. degrees in Electrical Engineering from Tabriz University, Tabriz, Iran, in 2015, and University of Tehran, Iran, in 2018, respectively. He was involved with IC design projects at the Advancom Laboratory, University of Tehran, at which he is now a research assistant. His research areas are analog, RF, and mixed-signal integrated circuit design.

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    Bahram Jafari received the B.Sc. and M.Sc. degrees in Electrical Engineering from Tabriz University, Tabriz, Iran, in 2015, and University of Tehran, Iran, in 2018, respectively. He was involved with IC design projects at the Advancom Laboratory, University of Tehran, at which he is now a research assistant. His research areas are analog, RF, and mixed-signal integrated circuit design.

    Samad Sheikhaei received his Ph.D. degree in Electrical Engineering from the University of British Columbia, Canada, in 2008. Then, he joined the School of Electrical and Computer Engineering at the University of Tehran, Iran, where he is currently an Associate Professor. His research interests are analog, mixed-signal, and RF integrated circuits design.

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