A Novel Phase-Noise Module for the QUCS Circuit Simulator. Part I : the Periodic Steady-State

TL;DR

The paper presents the first implementation of a time-domain periodic steady-state (PSS) analysis module for autonomous circuits within QUCS, addressing a gap left by the existing harmonic-balance option. The QUCS-COPEN PSS engine leverages a single-shooting/Newton framework, augmented for autonomous operation, and integrates with the QUCS-S GUI to deliver stabilization transients, PSS waveforms, and PSS spectra. Validation against Keysight-ADS demonstrates accurate oscillator frequencies and convergence behavior, while convergence-zone analysis reveals a robust, though not quadratic, convergence with an estimated order around 1.5 inside the convergence region. The work lays the groundwork for future enhancements (multiple-shooting, damping, Krylov solvers) and outlines plans for Part II to extend the tool to coupled-oscillator phase-noise analysis.

Abstract

The paper discusses work done to expand and extend the capabilities of the open-source QUCS circuit simulator through the implementation of a computationally efficient time-domain steady-state analysis module, supporting simulation of autonomous circuits. To our knowledge, this represents the first time such an analysis module has been implemented in the QUCS environment. Hitherto, the only available option was a harmonic-balance module which was strictly limited to non-autonomous (driven) circuits. The research has several important scientific and industrial applications in the area of large-signal steady-state analysis of autonomous circuits e.g. free-running and coupled oscillator circuit networks. The reported results will have great impact w.r.t. analyzing, synthesizing and optimizing oscillatory behavior of various important industrial circuits and systems. The developed tool, furthermore, introduces support for simulating noise performance of circuits operating under large-signal conditions. This paper is the first part of a two-part series documenting the implementation of a novel (coupled)-oscillator phase-noise simulator engine in the QUCS environment. The goal of this undertaking is the advancement of the open-source QUCS project towards becoming a viable competitor to the commercial simulators currently on the market.

Figures (5)

• Figure 1: The figure shows the QUCS-COPEN PSS simulation unit integrated into the QUCS-S GUI environment. The analysis module is chosen from the main-dock and then placed on the schematic. The unit has two main parameters : Tper and Tstab, and the PSS precision is fixed in all experiments at EpsMax=$10^{-12}$ (see \ref{['sec1:alg1']}) The 3 plotted graphs represent the 3 types of output datasets generated by the PSS simulator (unspecified oscillator circuit & output node). These are (w/ file extensions), purple graph : initial/stabilization transient, (.Vt, .It), blue graph : PSS time-domain solution, (.Vp, .Ip) and red graph : PSS solution, frequency-domain spectrum, absolute value, (.Vpa, .Ipa). which is plotted in dBm
• Figure 2: The figure shows the QUCS-COPEN PSS calculator applied to a simple Van-der-Pol(VDP)-type oscillator first proposed in djurhuus22. This circuit is referred to below as OSC.#1. All parameters are as in djurhuus22 (primary osc. parameter set). Two of the three available PSS datasets are plotted for the voltage node, vout, (stabilization transient data is not shown). Refer to \ref{['sec1:fig1']} caption for details.
• Figure 3: The simulator is applied to a BJT Colpitts oscillator taken from Kaertner1990. All circuit parameters as in Kaertner1990, w/ the following exceptions : resonator resistor $r_0 = 1.65 \mathrm{Ohm}$ (was $0.65 \mathrm{Ohm}$ in the paper) and the BJT nonlinear base resistor is set to zero due to an internal qucsator BJT model issue (see \ref{['sec2:foot1']}). This circuit is referred to below as OSC.#2. The figures plot the PSS output datasets for the external BJT emitter node, referred to as, Vemit, in the schematic. See the captions of \ref{['sec1:fig1', 'sec2:fig1']} for details.
• Figure 4: Figure shows the QUCS-COPEN PSS simulation tool applied to a MOSFET cross-coupled LC-tank oscillator. The circuit is similar to the oscillator proposed in Maffezzoni2013 with minor variations (see text). This circuit is referred to below as OSC.#3. The figures plot the PSS output datasets for the right-hand MOSFET device drain-node, referred to as, Vm, in the schematic. See also \ref{['sec1:fig1', 'sec2:fig1']} for details.
• Figure 5: Convergence measures, $\epsilon$ (solid line left y-axis), and $\Delta_f$ (dashed line, right y-axis), defined in \ref{['sec2:eq1', 'sec2:eq2']}, plotted as a function of the PSS iteration index $l$ (see \ref{['sec1:sub1', 'sec1:sub2', 'sec1:alg1']}) for different circuits and parameter configurations. Dotted curves represent sequences of varying convergence order $\sigma$ (see \ref{['app1:sec1']}) : $\sigma=2$ (brown $\cdots$), $\sigma=1.5$ (cyan $\cdots$), $\sigma=1$ (purple $\cdots$) w/ linear convergence rate $\mu_L = 2$. (a) : PSS measures, $\epsilon,\Delta_f$, are plotted for each of the oscillators OSC.#1-3 (see \ref{['sec2:tab1']} caption & sec2:fig1sec2:fig3) w/ initial conditions, $\Delta_f^{\text{\tiny init}} \sim 6\%$ and $K_{\text{\tiny STAB}} \sim 30{-}35$ (see \ref{['sec2:eq3', 'sec2:eq4']}). (b) : figure plots the PSS measures for circuit OSC.#3, for 3 different initial conditions as specified by the parameter $\Delta_f^{\text{\tiny init}}$ and w/ $K_{\text{\tiny STAB}} \sim 30{-}35$.