Bifurkationsanalyse eines LC Tank VCOs unter Berücksichtigung der variablen Kapazität

Bremer, J.-K.; Zorn, Christoph; Mathis, Wolfgang

doi:10.5194/ars-7-169-2009

Cited by 2 publications

(4 citation statements)

References 14 publications

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“…However, details of calculations and the voltage–time waveform are not presented. As part of the bifurcation analysis of differential MOS VCOs, an empirical expression is used, which includes both bias and amplitude dependence of the capacitance . Here, inversion mode MOS diodes are used.…”

Section: Introductionmentioning

confidence: 99%

A study of parallel tuner with voltage‐dependent capacitance

Eskandarian

2011

Circuit Theory & Apps

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SUMMARYA study of varactor tuned LC circuits is presented. Nonlinear time domain circuit differential equation is rewritten in terms of phase plane variables, which can then be solved in closed form. General expressions are derived, which are applicable to any capacitance-voltage relationship. Two types of circuit structures, namely single-ended and balanced, with MOS diodes as the variable capacitance elements, are specifically considered. The nature of the voltage waveforms across the two circuits is determined by phase plane plots. Variation of voltage with time is calculated numerically. It is shown that the voltage waveform for the single-ended circuit is asymmetric, with higher harmonics present. Furthermore, the fundamental resonant frequency is dependent on amplitude of oscillation and could decrease to 94% of its small signal value for large voltage swings. Near 34% control over frequency is calculated, for a bias voltage range of 8 to 1. On the other hand, the balanced structure results in symmetric voltage waveform, with negligible harmonic content. Dependence of frequency on amplitude is weak, only decreasing to 98% of its small signal value, for the largest swings. The tuning range is marginally improved by the balanced structure. The results are compared with those obtained from Fourier-based calculations and experimental data in literature, and good agreement is obtained.

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Section: Introductionmentioning

confidence: 99%

A study of parallel tuner with voltage‐dependent capacitance

Eskandarian

2011

Circuit Theory & Apps

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“…As will become clear shortly, with the exception of the first (second derivative) term, the other three terms on the left side of Equation (10) contribute to form a function that directly corresponds to function h of Equation (6). To make the upcoming relations more manageable, we can eliminate the contribution of the dissipative term on the basis of the following reasoning.…”

Section: Frequency-amplitude Relationsmentioning

confidence: 99%

“…There has been great interest in cross‐coupled voltage‐controlled oscillators (VCOs) in Metal Oxide Semiconductor (MOS) integrated circuits, and various aspects of these circuits have been investigated both theoretically and through experimentation . One important factor in performance of any oscillator is the shift in frequency due to variation of amplitude, which is a result of nonlinearities of circuit elements.…”

Section: Introductionmentioning

confidence: 99%

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Frequency–amplitude relations for cross‐coupled voltage‐controlled oscillator

Eskandarian

2012

Circuit Theory & Apps

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Dependence of frequency on amplitude and control bias is considered for the cross‐coupled voltage‐controlled oscillator. Closed form expressions are derived for frequency of oscillation as a function of amplitude, for positive and negative control bias voltages. Theory of nonlinear ordinary differential equations is utilized to show that the capacitance–voltage relation is the main cause of frequency shift with amplitude. Furthermore, the case of small amplitudes relative to control voltage is analyzed, and a closed form expression is derived for dependence of frequency on amplitude. This relation is then verified using the concept of effective capacitance. The effective capacitance approach is also used to extend the analysis to large voltage swings. Dependence of frequency on tuner control voltage is calculated for both bias polarities. Implications of the aforementioned equations for voltage‐controlled oscillator performance are discussed. Numerical calculations and simulations are used to compare and verify the closed form equations, showing good agreement. Copyright © 2012 John Wiley & Sons, Ltd.

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Bifurkationsanalyse eines LC Tank VCOs unter Berücksichtigung der variablen Kapazität

Cited by 2 publications

References 14 publications

A study of parallel tuner with voltage‐dependent capacitance

A study of parallel tuner with voltage‐dependent capacitance

Frequency–amplitude relations for cross‐coupled voltage‐controlled oscillator

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