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Simulation of the Ondes Martenot Ribbon-Controlled Oscillator Using Energy-Balanced Modeling of Nonlinear Time-Varying Electronic Components

Judy Najnudel 1 Thomas Hélie 1 David Roze 1
1 S3AM - Systèmes et Signaux Sonores : Audio/Acoustique, instruMents
STMS - Sciences et Technologies de la Musique et du Son
Abstract : The Onde Martenot is a classic electronic musical instrument. This paper focuses on the power-balanced simulation of its ribbon-controlled oscillator, composed of linear and non-linear as well as time-varying components. To this end, the proposed approach consists of formulating the circuit as a Port-Hamiltonian System for which power-balanced numerical methods are available. A specificity of the Martenot oscillator is to involve parallel capacitors, one of them having a capacitance that non-linearly depends on the time-varying ribbon position state. In the case of linear time-invariant (LTI) capacitors in parallel, an equivalent component can be deduced using the classic impedance approach. Such a reformulation into a single equivalent component is required to derive a state-space Port-Hamiltonian representation of a circuit. One technical result of this paper is to propose a method to determine such an equivalent component in the non-LTI case. This method is applied to the present Martenot oscillator. Then, power-balanced numerical experiments are presented for several configurations: fixed ribbon position, realistic, and over-speed movements. These results are examined and interpreted from both the electronic and mechanical points of view.
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https://hal.archives-ouvertes.fr/hal-02425249
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Submitted on : Wednesday, September 2, 2020 - 2:58:54 PM
Last modification on : Friday, October 1, 2021 - 6:00:20 PM
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Judy Najnudel, Thomas Hélie, David Roze. Simulation of the Ondes Martenot Ribbon-Controlled Oscillator Using Energy-Balanced Modeling of Nonlinear Time-Varying Electronic Components. AES - Journal of the Audio Engineering Society Audio-Accoustics-Application, Audio Engineering Society Inc, 2019, 67 (12), pp.961-971. ⟨10.17743/jaes.2019.0040⟩. ⟨hal-02425249⟩

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