Robust Harmonic-Probe Method for the Simulation of Oscillators

Brambilla, A.; Gruosso, Giambattista; Gajani, G. Storti

doi:10.1109/tcsi.2010.2043168

Cited by 12 publications

(6 citation statements)

References 22 publications

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“…Then the steady state solution is found running the harmonic balance simulation together with the optimization routine in a two tier scheme; the outer tier is constituted by the optimization algorithm, usually a gradient optimizer, that iteratively computes the candidate solutions (A 0 , f 0 ) and pass these values to the inner tier represented by the native HB algorithm, that solve for all the other circuital variables; if at a given step, the distance between the goals and the computed solution is neglectable according to a predefined metric the solution is found, otherwise the search for the optimal point continues, until the maximum number of iterations is reached. In this optimization method great care has to be taken, with respect to the probe insertion point (Brambilla et al, 2010) and to the probe amplitude and frequency initial estimate. Usually the linear analysis frequency estimate works well for achieving convergence of the HB analysis with the probe method (Chang et al, 1991), selecting randomly the initial values for the AG amplitude.…”

Section: Probe Methods For Oscillator Analysismentioning

confidence: 99%

Wideband Voltage Controlled Oscillators for Cognitive Radio Systems

Acampora¹,

Georgiadis²

2012

Advances in Cognitive Radio Systems

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Section: Probe Methods For Oscillator Analysismentioning

confidence: 99%

Wideband Voltage Controlled Oscillators for Cognitive Radio Systems

Acampora¹,

Georgiadis²

2012

Advances in Cognitive Radio Systems

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“…A non-constant K vco (v w ) can impact on the loop gain of the linear model of the PLL. The parameter K vco v w ð Þ ¼ do dv w has been computed through a battery of steady-state analyses based on the harmonic balance method, each performed with a different value of v w [41,42]. We then fitted the proposed model to the K vco (v w ) characteristic obtaining K a vco ¼ 4:1082 Â 10 À4 , K b vco ¼ À3:9562 Â 10 À3 and K c vco ¼ 0:045749 , with a = 0.5.…”

Section: Identification Of Model Parametersmentioning

confidence: 99%

Nonlinear behavioural model of charge pump PLLs

Brambilla

Linaro

Storace

2012

Circuit Theory & Apps

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Despite the nonlinear nature of even the simplest versions of phase locked loops (PLLs), linear models are still used during the first phases of the design of modern PLLs. Even though the linear model may represent a crude approach, its use is justified by the fact that accurate numerical simulations often require a too large amount of CPU time, being PLLs by construction stiff circuits, characterised by very different time scales. This aspect has triggered the need for compact models that allow fast and accurate numerical simulations. The scientific literature numbers several models that have been developed with different approaches and tailored to different simulation environments. In this context, we propose a nonlinear model of a type-II PLL, which (1) considers both the switching behaviour of the phase/frequency detector and charge pump and the complex dynamics (including the presence of amplitude and phase noise) of the voltage controlled oscillator, (2) is compact and can be easily implemented in modern mixed analog/digital simulators as a behavioural block, and (3) allows the simulation of spurs owing to the nonlinearities of both the charge pump and the fractional frequency divider

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“…Hence when the discretization is exact this time derivative of the ultimate PSS is in the kernel of A. This has led to study more carefully bordered matrices [1,9] and generalized eigenvalue methods. In [9] the eigentriple (V, W, λ ) is determined such that [λ f C + G]V = 0 and W T [λ f C + G] = 0 for the λ closest to 1.…”

Section: Newton Raphsonmentioning

confidence: 99%

“…In addition, the oscillation frequency (the fundamental HB frequency), is unknown and one needs a gauge equation and an initial estimate. Frequency domain methods to estimate these can be found in [1,3,[6][7][8] (and their references). We present two algorithms for oscillation frequency detection from transient data and improve by (vector) extrapolation [10].…”

Section: Introductionmentioning

confidence: 99%

Initial Conditions and Robust Newton-Raphson for Harmonic Balance Analysis of Free-Running Oscillators

Virtanen

Maten

Honkala

et al. 2012

Mathematics in Industry

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Poor initial conditions for Harmonic Balance (HB) analysis of freerunning oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for the oscillator solution. It also provides an initialization of the probe voltage. Next we describe new techniques from bordered matrices and eigenvalue methods to improve Newton methods for Finite Difference techniques in the time domain as well as for Harmonic Balance. The method gauges the phase shift automatically. No assumption about the range of values of the Periodic Steady State solution is needed.

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Robust Harmonic-Probe Method for the Simulation of Oscillators

Cited by 12 publications

References 22 publications

Wideband Voltage Controlled Oscillators for Cognitive Radio Systems

Wideband Voltage Controlled Oscillators for Cognitive Radio Systems

Nonlinear behavioural model of charge pump PLLs

Initial Conditions and Robust Newton-Raphson for Harmonic Balance Analysis of Free-Running Oscillators

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