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A Novel Phase-Noise Module for the QUCS Circuit Simulator. Part II : Noise Analysis

Torsten Djurhuus, Viktor Krozer

Abstract

The paper documents the implementation of a novel phase-noise analysis module within the open-source QUCS circuit simulator environment. The underlying algorithm is based on a rigorous, unified time-domain methodology of (coupled) oscillator noise-response, recently proposed by the authors. The theoretical approach used to develop this model is entirely unconstrained by any empirical and/or phenomenological modelling techniques, such as e.g. LTI and LTV theory, and this differentiates it from all prior proposals on this topic. The paper introduces important, and previously unpublished, extensions to this framework, in the form of novel unified closed-form expressions for both the amplitude and phase-amplitude correlation response of a general coupled oscillating circuit perturbed by noise. The research discussed herein has many important scientific and industrial applications w.r.t. predicting, synthesizing and optimizing the performance of noise-perturbed free-running and coupled autonomous circuits operating under large-signal steady-state conditions. These timing circuits are ubiquitous in all modern communication and remote-sensing systems and the developed simulation tools will prove to have great impact in various areas of industrial circuit design. This paper represents second part of a two-part series with the first part discussing the implementation of the underlying steady-state analysis module. The open-source simulator, discussed and developed herein, applies advanced state-of-the-art stochastic modelling techniques, in-order to produce noise simulation tools with capabilities and scope which, in many areas, exceed what is found in the commercial EDAs currently on the market.

A Novel Phase-Noise Module for the QUCS Circuit Simulator. Part II : Noise Analysis

Abstract

The paper documents the implementation of a novel phase-noise analysis module within the open-source QUCS circuit simulator environment. The underlying algorithm is based on a rigorous, unified time-domain methodology of (coupled) oscillator noise-response, recently proposed by the authors. The theoretical approach used to develop this model is entirely unconstrained by any empirical and/or phenomenological modelling techniques, such as e.g. LTI and LTV theory, and this differentiates it from all prior proposals on this topic. The paper introduces important, and previously unpublished, extensions to this framework, in the form of novel unified closed-form expressions for both the amplitude and phase-amplitude correlation response of a general coupled oscillating circuit perturbed by noise. The research discussed herein has many important scientific and industrial applications w.r.t. predicting, synthesizing and optimizing the performance of noise-perturbed free-running and coupled autonomous circuits operating under large-signal steady-state conditions. These timing circuits are ubiquitous in all modern communication and remote-sensing systems and the developed simulation tools will prove to have great impact in various areas of industrial circuit design. This paper represents second part of a two-part series with the first part discussing the implementation of the underlying steady-state analysis module. The open-source simulator, discussed and developed herein, applies advanced state-of-the-art stochastic modelling techniques, in-order to produce noise simulation tools with capabilities and scope which, in many areas, exceed what is found in the commercial EDAs currently on the market.
Paper Structure (20 sections, 26 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 26 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. A Note on Alternative Open-Source Engines : qucsatorRF, GnuCap, ngspice & Xyce.
  3. Outline of paper
  4. Background Theory & PNOISE Module Implementation.
  5. Deriving the Floquet Decomposition.
  6. The Concept of a Floquet Mode & Floquet Mode Response.
  7. The Special PSS Floquet Mode.
  8. The Novel COSC-PMM Modelling Framework.
  9. Expanding the COSC-PMM Framework : Adding Amplitude and Correlation Contributions.
  10. The COSC-PMM Amplitude Noise Spectrum.
  11. The COSC-PMM Cross-Correlation Noise Spectrum
  12. The Reduced Single Oscillator Expressions.
  13. Implementing the QUCS-COPEN PNOISE Module.
  14. SubProc. I : the Floquet Decomposition.
  15. SubProc. II + III : Calculate Noise Operators & Output Spectra.
  16. ...and 5 more sections

Figures (6)

  • Figure 1: The figure shows the QUCS-COPEN PSS+PNOISE simulation units integrated into the QUCS-S GUI environment. Both the PNOISE and PSS reference modules are chosen from the main-dock and then placed on the schematic. The PNOISE & PSS modules are linked through the PNOISE parameter PssSim (see \ref{['sec1:alg1']}). PSS & PNOISE datasets (unspecified circuit & output node), with file extensions, blue graph : PSS time-domain solution, (.Vp, .Ip), red graph : PSS spectrum, absolute value, (.Vpa, .Ipa), which is plotted in $\mathrm{dBm}$, orange graph : Phase noise spectrum, in $\mathrm{dBc}$, (.Vpn, .Ipn) and brown graph : Amplitude noise spectrum, in $\mathrm{dBc}$ (.Van, .Ian).
  • Figure 2: The QUCS-COPEN PNOISE calculator module applied to a simple Van-der-Pol(VDP)-type oscillator, proposed in Djurhuus2022. This circuit is referred to below as OSC.#1. All parameters (including the external noise source) are as in Djurhuus2022 (primary osc. parameter set). The datasets introduced in \ref{['sec1:fig1']} are plotted for the voltage node, vout. Refer to \ref{['sec1:fig1']} caption for further details.
  • Figure 3: The QUCS-COPEN PNOISE module is applied to a BJT Colpitts oscillator taken from Kaertner1990, referred to below as OSC.#2. All circuit parameters as in Kaertner1990, with a few minor exceptions (see Djurhuus2025 for details). In this simulation the BJT device is noiseless except for internal resistor contributions. The PSS+PNOISE datasets, introduced in \ref{['sec1:fig1']}, are plotted for the BJT emitter node (called Vemit in schematic). See \ref{['sec1:fig1']} for further details.
  • Figure 4: The QUCS-COPEN PNOISE simulation tool applied to a MOSFET cross-coupled LC-tank oscillator, referred to below as OSC.#3, similar to the oscillator proposed in Maffezzoni2013 with minor modifications(see Djurhuus2025 for details). All parameters (including the external noise source) are as in Djurhuus2022. The PSS & PNOISE datasets, introduced in \ref{['sec1:fig1']}, are plotted for the right MOSFET right drain node Vm. See also \ref{['sec1:fig1']} for further details.
  • Figure 5: The QUCS-COPEN PNOISE module is applied to an injection-locked circuit (ILO) configuration referred to as COSC.#1 (see text for details). Relevant datasets (see \ref{['sec1:fig1']}) are plotted for the output nodes of both the primary (dashed line plots) and secondary (solid line plots) oscillator nodes. In the schematic these nodes are referred to as $\text{V}_{\text{prm}}$ and $\text{V}_{\text{ref}}$, respectively. It is immediately observed that the calculated secondary oscillator ($\text{V}_{\text{ref}}$) PNOISE spectrum (orange solid line plot) does not follow the standard Lorentzian profile (see \ref{['sec1:foot5']}).
  • ...and 1 more figures