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This paper introduces a theory for fast optimization of the circuit topology and parameters in sinusoidal oscillators. The theory starts from a system model composed of standard active and passive elements. We then include even the output load in the circuit, so that there is no longer any interaction with the outside of the system through the port. This model is thus called *no-input-no-output* (NINO) oscillator. The circuit is cut at an arbitrary branch, and is characterized in terms of the scalar impedance from the cut point. This is called *active impedance* because it is a function of not only the stimulating frequency but also the active device gain. The oscillation frequency and necessary device gain are estimated by solving impedance-domain Barkhausen equilibrium equations. This estimation works for the adjustment of circuit elements to meet the specified oscillation frequency. The estimation of necessary device gain enables us to maximize the oscillation amplitude, thanks to the inherent negative-slope nonlinearity of active devices. The active impedance is also used to derive the oscillation *Q* (quality) factor, which serves as a key criterion for sideband noise minimization i.e. frequency spectrum purification. As an alternative measure to active impedance, we also introduce *branch admittance matrix determinant*. This has the same numerical effect as the scalar impedance but can be used to formulate oscillator characteristics in a more elegant fashion, and provides a lucent picture of the physical behavior of each element in the circuit. Based on the proposed theory, we provide the tabled formulas of oscillation frequency, necessary device gain, active *Q* factor for a variety of typical Colpitts, Hartley, and cross-coupled twin-FET (field-effect transistor) oscillators.

- Publication
- IEICE TRANSACTIONS on Electronics Vol.E91-C No.11 pp.1726-1737

- Publication Date
- 2008/11/01

- Publicized

- Online ISSN
- 1745-1353

- DOI
- 10.1093/ietele/e91-c.11.1726

- Type of Manuscript
- Special Section INVITED PAPER (Special Section on Microwave and Millimeter-wave Technologies)

- Category

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Takashi OHIRA, Tuya WUREN, "Pseudolinear Circuit Theory for Sinusoidal Oscillator Performance Maximization" in IEICE TRANSACTIONS on Electronics,
vol. E91-C, no. 11, pp. 1726-1737, November 2008, doi: 10.1093/ietele/e91-c.11.1726.

Abstract: This paper introduces a theory for fast optimization of the circuit topology and parameters in sinusoidal oscillators. The theory starts from a system model composed of standard active and passive elements. We then include even the output load in the circuit, so that there is no longer any interaction with the outside of the system through the port. This model is thus called *no-input-no-output* (NINO) oscillator. The circuit is cut at an arbitrary branch, and is characterized in terms of the scalar impedance from the cut point. This is called *active impedance* because it is a function of not only the stimulating frequency but also the active device gain. The oscillation frequency and necessary device gain are estimated by solving impedance-domain Barkhausen equilibrium equations. This estimation works for the adjustment of circuit elements to meet the specified oscillation frequency. The estimation of necessary device gain enables us to maximize the oscillation amplitude, thanks to the inherent negative-slope nonlinearity of active devices. The active impedance is also used to derive the oscillation *Q* (quality) factor, which serves as a key criterion for sideband noise minimization i.e. frequency spectrum purification. As an alternative measure to active impedance, we also introduce *branch admittance matrix determinant*. This has the same numerical effect as the scalar impedance but can be used to formulate oscillator characteristics in a more elegant fashion, and provides a lucent picture of the physical behavior of each element in the circuit. Based on the proposed theory, we provide the tabled formulas of oscillation frequency, necessary device gain, active *Q* factor for a variety of typical Colpitts, Hartley, and cross-coupled twin-FET (field-effect transistor) oscillators.

URL: https://global.ieice.org/en_transactions/electronics/10.1093/ietele/e91-c.11.1726/_p

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@ARTICLE{e91-c_11_1726,

author={Takashi OHIRA, Tuya WUREN, },

journal={IEICE TRANSACTIONS on Electronics},

title={Pseudolinear Circuit Theory for Sinusoidal Oscillator Performance Maximization},

year={2008},

volume={E91-C},

number={11},

pages={1726-1737},

abstract={This paper introduces a theory for fast optimization of the circuit topology and parameters in sinusoidal oscillators. The theory starts from a system model composed of standard active and passive elements. We then include even the output load in the circuit, so that there is no longer any interaction with the outside of the system through the port. This model is thus called *no-input-no-output* (NINO) oscillator. The circuit is cut at an arbitrary branch, and is characterized in terms of the scalar impedance from the cut point. This is called *active impedance* because it is a function of not only the stimulating frequency but also the active device gain. The oscillation frequency and necessary device gain are estimated by solving impedance-domain Barkhausen equilibrium equations. This estimation works for the adjustment of circuit elements to meet the specified oscillation frequency. The estimation of necessary device gain enables us to maximize the oscillation amplitude, thanks to the inherent negative-slope nonlinearity of active devices. The active impedance is also used to derive the oscillation *Q* (quality) factor, which serves as a key criterion for sideband noise minimization i.e. frequency spectrum purification. As an alternative measure to active impedance, we also introduce *branch admittance matrix determinant*. This has the same numerical effect as the scalar impedance but can be used to formulate oscillator characteristics in a more elegant fashion, and provides a lucent picture of the physical behavior of each element in the circuit. Based on the proposed theory, we provide the tabled formulas of oscillation frequency, necessary device gain, active *Q* factor for a variety of typical Colpitts, Hartley, and cross-coupled twin-FET (field-effect transistor) oscillators.},

keywords={},

doi={10.1093/ietele/e91-c.11.1726},

ISSN={1745-1353},

month={November},}

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TY - JOUR

TI - Pseudolinear Circuit Theory for Sinusoidal Oscillator Performance Maximization

T2 - IEICE TRANSACTIONS on Electronics

SP - 1726

EP - 1737

AU - Takashi OHIRA

AU - Tuya WUREN

PY - 2008

DO - 10.1093/ietele/e91-c.11.1726

JO - IEICE TRANSACTIONS on Electronics

SN - 1745-1353

VL - E91-C

IS - 11

JA - IEICE TRANSACTIONS on Electronics

Y1 - November 2008

AB - This paper introduces a theory for fast optimization of the circuit topology and parameters in sinusoidal oscillators. The theory starts from a system model composed of standard active and passive elements. We then include even the output load in the circuit, so that there is no longer any interaction with the outside of the system through the port. This model is thus called *no-input-no-output* (NINO) oscillator. The circuit is cut at an arbitrary branch, and is characterized in terms of the scalar impedance from the cut point. This is called *active impedance* because it is a function of not only the stimulating frequency but also the active device gain. The oscillation frequency and necessary device gain are estimated by solving impedance-domain Barkhausen equilibrium equations. This estimation works for the adjustment of circuit elements to meet the specified oscillation frequency. The estimation of necessary device gain enables us to maximize the oscillation amplitude, thanks to the inherent negative-slope nonlinearity of active devices. The active impedance is also used to derive the oscillation *Q* (quality) factor, which serves as a key criterion for sideband noise minimization i.e. frequency spectrum purification. As an alternative measure to active impedance, we also introduce *branch admittance matrix determinant*. This has the same numerical effect as the scalar impedance but can be used to formulate oscillator characteristics in a more elegant fashion, and provides a lucent picture of the physical behavior of each element in the circuit. Based on the proposed theory, we provide the tabled formulas of oscillation frequency, necessary device gain, active *Q* factor for a variety of typical Colpitts, Hartley, and cross-coupled twin-FET (field-effect transistor) oscillators.

ER -