Books by Fernando Chierchie
In this thesis a study of the stages comprising a class D or switching amplifier is made. The app... more In this thesis a study of the stages comprising a class D or switching amplifier is made. The approach ranges from the signal conditioning and digital signal processing stages up to the transducer, also covering the power stage.
The research focuses on the analysis and compensation of the distortion generated in the different stages through which signal passes.
The development is theoretical/practical. Various pulse width modulation (PWM) schemes are studied in the frequency domain. The effects on the spectral content of the PWM signal with dead times, necessary between the on and off states of the power semiconductor devices, are analysed. A bound in the total harmonic distortion, that can not be reduced increasing the carrier frequency or changing the modulation technique, is shown.
Some digital signal processing algorithms for the reduction of distortion, generated by the modulation and the digital stage due to the use of a fixed point processor, are studied. Oversampling, decimation, interpolation, cuantization noise shaping and digital pulse width modulation schemes are investigated and experimental results obtained with a dynamic signal analizer
are reported.
These tools are applied to the design of a closed loop switching amplifier that holds the acoustic pressure constant in a determined frequency range.
Different models of the loudspeaker which link the electric and acoustic variables are discussed. Finally a linear, digital control, feedback loop that uses the acceleration of the speaker cone as ouput is designed.
Papers by Fernando Chierchie
—Accurate models for PWM modulators composed by the parallel connection of p-th order powers foll... more —Accurate models for PWM modulators composed by the parallel connection of p-th order powers followed by a linear filter have been recently presented in the literature. In this paper we derive closed-form expressions for the impulse responses and frequency responses of those filters. This allows to predict the amplitudes and frequencies of the spurious components appearing in the baseband when using sinusoidal inputs and also to obtain a closed-form expression for the THD. Resumen— Recientemente se han presentado en la literatura modelos precisos para moduladores PWM compuestos por la conexión en paralelo de potencias de orden p seguido de un filtro lineal. En este trabajo se derivan expresiones cerradas para las respuestas impulsivas y respuestas en frecuencia de los filtros. Esto permite predecir las amplitudes y frecuencias de las componentes espurias que aparecen en la banda base cuando se utilizan entradas sinusoidales y también obtener una expresión cerrada para la distorsión armónica total.
Resumen: En este trabajo se presenta el modelo de un altavoz de doble bobinado. Se revisa el mode... more Resumen: En este trabajo se presenta el modelo de un altavoz de doble bobinado. Se revisa el modelo clásico basado en las propiedades físicas de la parte mecánica y eléctrica del parlante, y para salvar las discrepancias observadas entre las mediciones y el modelo matemático se incluye el efecto semi-inductivo causado por las corrientes parásitas, que da lugar a un modelo de orden fraccionario. El principal aporte del trabajo es considerar el efecto semi-inductivo también sobre el acoplamiento mutuo entre los bobinados, efecto que no ha sido observado en la literatura consultada. El modelo teórico se valida mediante resultados experimentales.
IEEE Transactions on Circuits and Systems I: Regular Papers, 2015
IEEE Transactions on Power Electronics, 2000
ABSTRACT The effect of dead-time on the spectrum of pulse-width modulated signals is analyzed in ... more ABSTRACT The effect of dead-time on the spectrum of pulse-width modulated signals is analyzed in this paper. The study is valid for arbitrary, band-limited modulating signals, extending previous results in the literature. A simple distortion index is developed that can be used at the design stage to select dead-time or switching frequency based on maximum allowed distortion. Experimental results with various band-limited signals reveal a very good agreement between the theoretical results and the experiments.
IEEE Transactions on Industrial Electronics, 2000
ABSTRACT A real-time, digital algorithm for pulse width modulation (PWM) with distortion-free bas... more ABSTRACT A real-time, digital algorithm for pulse width modulation (PWM) with distortion-free baseband is developed in this paper. The algorithm not only eliminates the intrinsic baseband distortion of digital PWM but also avoids the appearance of side-band components of the carrier in the baseband even for low switching frequencies. Previous attempts to implement digital PWM with these spectral properties required several processors due to their complexity; the proposed algorithm uses only several FIR filters and a few multiplications and additions and therefore is implemented in real time on a standard DSP. The performance of the algorithm is compared with that of uniform, double-edge PWM modulator via experimental measurements for several bandlimited modulating signals.
IEEE Transactions on Industrial Electronics, 2000
ABSTRACT An all-digital Class-D amplifier based on a discrete-time implementation of the click mo... more ABSTRACT An all-digital Class-D amplifier based on a discrete-time implementation of the click modulator is presented. The algorithm is able to generate binary signals with separated baseband, displacing the harmonic content produced by the modulation process above certain frequency chosen by the designer. Perfect demodulation can be achieved by a simple low-pass filter. Previous implementations of the discrete-time click modulator reported in the literature suffer from aliasing in the frequency domain. The approach proposed here avoids aliasing, without the necessity to increase (interpolate) the sampling frequency of the signals. Following a brief theoretical introduction, the performance of the proposed architecture is demonstrated by experimental measurements performed on an H-bridge amplifier. An 88 dB signal-to-noise ratio (SNR) and a total harmonic distortion (THD) $+$ N less than 0.04% is attainable over the entire audio band, extending from 20 Hz up to 20 kHz; on the other hand, no traces of IMD appear above the predicted noise floor. These performance indices are obtained for switching rates as low as 40 kHz. The reduction of the switching frequency provides more flexibility for the design of the demodulation stage allowing to trade off between the complexity of the demodulation filter and the achievable efficiency of the switching stage.
IEEE Transactions on Circuits and Systems I: Regular Papers
A discrete-time pulse width modulator (PWM) with zero baseband distortion for arbitrary band-limi... more A discrete-time pulse width modulator (PWM) with zero baseband distortion for arbitrary band-limited modulating signals is developed in this paper. It is based on adjusting the duty-cycles of the PWM such that the samples of an ideal low-pass filtered version of the PWM signal coincide with the discrete-time samples of the modulating signal. Elaborating on previous approaches in the literature, it is shown that this problem can be stated as a multidimensional inverse function approach, and therefore it can be solved using iterative methods. Starting with the duty-cycle values of a uniform PWM, the successive iterations provide slight duty-cycle corrections that, in the limit, result in zero baseband distortion even for low carrier-to-modulating frequency ratios. Aiming at a practical, real-time implementation two new results are provided. First, explicit bounds on the improvement achievable after each duty-cycle correction are derived. Second, a block processing architecture suitable for real-time implementation is proposed, and the increase of distortion caused by its use is quantified. Several examples with typical band-limited signals demonstrate the performance of the algorithm.
En este trabajo se presenta la utilización de una Red Neuronal Artificial (RNA) para la reducción... more En este trabajo se presenta la utilización de una Red Neuronal Artificial (RNA) para la reducción de la distorsión en un modulador PWM Uniforme (UPWM). La técnica propuesta se basa en un método de análisis de señales PWM que es válido para moduladoras arbitrarias, de ancho de banda limitado, y no solamente para señales sinusoidales, como es frecuente en la literatura especializada. El entrenamiento de la RNA emplea una señal chirp, cuyo contenido espectral puede ser ajustado a un rango de frecuencias adecuado para una aplicación específica. El modulador basado en la RNA y el modulador UPWM son implementados en un lenguaje de descripción de hardware (VHDL). Los resultados de la simulación muestran una reducción significativa de la distorsión.
The analytical spectrum of pulse width modulated (PWM) signals with dead-time is derived in this ... more The analytical spectrum of pulse width modulated (PWM) signals with dead-time is derived in this paper. Previous results were based on the double Fourier series expansion and therefore they are only valid for a single tone modulating signal. In this work analytical expressions for finite bandwidth input signals are presented. Some simplifying assumptions are considered to derive manageable expressions; however, extensions to more general cases are straightforward. Theoretical results are compared with computer simulations.
In this paper the discrete-time model of a synchronous buck converter is discussed. Although this... more In this paper the discrete-time model of a synchronous buck converter is discussed. Although this topic has been reviewed many times in the literature, very few articles address the nonlinear nature of the model, and frequently use certain kind of linear approximation. We show in this note that nonlinearity appears as a input-dependent gain, and for parameter values resulting from typical design rules, the discrete time model is only mildly nonlinear. Therefore, good performance can be achieved using linear controllers. This fact is shown by designing a cascade proportional-plus-integral linear control that allows for a fast settling time of output voltage under reference and load changes. Simulation and experimental results demonstrate the good performance of the proposed controller.
The analytical spectrum of a pulse width modulated signal with dead-times is derived in this pape... more The analytical spectrum of a pulse width modulated signal with dead-times is derived in this paper. The results are valid for any bounded, bandlimited signal. The harmonic content of the output voltage is computed by dividing the PWM signal in three components: a 50% duty cycle square-wave, a symetrical, time-varying duty cycle square wave, and a pulse train that accounts for the dead-time. Specific expressions are obtained for simple modulating signals. Some numerical examples are included for comparison with theoretical results.
En este trabajo se presenta una primera aproximación al control por realimentación de un parlante... more En este trabajo se presenta una primera aproximación al control por realimentación de un parlante reproductor de bajas frecuencias (“woofer”) sensando la aceleración del cono, usando controladores discretos. La técnica de diseño se basa en un método lineal algebraico que permite especificar de manera sencilla la respuesta en frecuencia del sistema de lazo cerrado. El diseño se ensaya sobre un procesador digital de señales de punto fijo, y se incluyen resultados de simulación y experimentales. Aunque el enfoque es simple, los resultados obtenidos en el laboratorio son similares a los presentados en la literatura con controladores mucho más complejos.
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In this paper a first approach to feedback control of a low frequency speaker ("woofer") sensing the acceleration of the cone, using discrete controllers is presented. The design technique is based on a linear algebraic method which allows to easily specify the frequency response of the closed loop system. The design is tested on a fixed point digital signal processor. Although the approach is simple, the results obtained in the laboratory are similar to those presented in the literature with more complex controllers. Simulations and experimental results are included.
En este trabajo se presenta el modelo de un altavoz de doble bobinado. Se revisa el modelo clásic... more En este trabajo se presenta el modelo de un altavoz de doble bobinado. Se revisa el modelo clásico basado en las propiedades físicas de la parte mecánica y eléctrica del parlante, y para salvar las discrepancias observadas entre las mediciones y el modelo matemático se incluye el efecto semi-inductivo causado por las corrientes parásitas, que da lugar a un modelo de orden fraccionario. El principal aporte del trabajo es considerar el efecto semi-inductivo también sobre el acoplamiento mutuo entre los bobinados, efecto que no ha sido observado en la literatura consultada. El modelo teórico se valida mediante resultados experimentales.
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This paper presents a model for a dual voice coil loudspeaker. The classical model is reviewed based on the physical properties of the mechanical and electrical parts of the speaker. To bridge differences between the measurements and the mathematical model, the semi-inductive effect caused by eddy currents is included. This results in a fractional-order model. The main contribution of this paper is to consider the semi-inductive effect also on the mutual coupling between the windings, an effect that has not been reported in the literature. The theoretical model is validated by experimental results.
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Books by Fernando Chierchie
The research focuses on the analysis and compensation of the distortion generated in the different stages through which signal passes.
The development is theoretical/practical. Various pulse width modulation (PWM) schemes are studied in the frequency domain. The effects on the spectral content of the PWM signal with dead times, necessary between the on and off states of the power semiconductor devices, are analysed. A bound in the total harmonic distortion, that can not be reduced increasing the carrier frequency or changing the modulation technique, is shown.
Some digital signal processing algorithms for the reduction of distortion, generated by the modulation and the digital stage due to the use of a fixed point processor, are studied. Oversampling, decimation, interpolation, cuantization noise shaping and digital pulse width modulation schemes are investigated and experimental results obtained with a dynamic signal analizer
are reported.
These tools are applied to the design of a closed loop switching amplifier that holds the acoustic pressure constant in a determined frequency range.
Different models of the loudspeaker which link the electric and acoustic variables are discussed. Finally a linear, digital control, feedback loop that uses the acceleration of the speaker cone as ouput is designed.
Papers by Fernando Chierchie
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In this paper a first approach to feedback control of a low frequency speaker ("woofer") sensing the acceleration of the cone, using discrete controllers is presented. The design technique is based on a linear algebraic method which allows to easily specify the frequency response of the closed loop system. The design is tested on a fixed point digital signal processor. Although the approach is simple, the results obtained in the laboratory are similar to those presented in the literature with more complex controllers. Simulations and experimental results are included.
//
This paper presents a model for a dual voice coil loudspeaker. The classical model is reviewed based on the physical properties of the mechanical and electrical parts of the speaker. To bridge differences between the measurements and the mathematical model, the semi-inductive effect caused by eddy currents is included. This results in a fractional-order model. The main contribution of this paper is to consider the semi-inductive effect also on the mutual coupling between the windings, an effect that has not been reported in the literature. The theoretical model is validated by experimental results.
The research focuses on the analysis and compensation of the distortion generated in the different stages through which signal passes.
The development is theoretical/practical. Various pulse width modulation (PWM) schemes are studied in the frequency domain. The effects on the spectral content of the PWM signal with dead times, necessary between the on and off states of the power semiconductor devices, are analysed. A bound in the total harmonic distortion, that can not be reduced increasing the carrier frequency or changing the modulation technique, is shown.
Some digital signal processing algorithms for the reduction of distortion, generated by the modulation and the digital stage due to the use of a fixed point processor, are studied. Oversampling, decimation, interpolation, cuantization noise shaping and digital pulse width modulation schemes are investigated and experimental results obtained with a dynamic signal analizer
are reported.
These tools are applied to the design of a closed loop switching amplifier that holds the acoustic pressure constant in a determined frequency range.
Different models of the loudspeaker which link the electric and acoustic variables are discussed. Finally a linear, digital control, feedback loop that uses the acceleration of the speaker cone as ouput is designed.
//
In this paper a first approach to feedback control of a low frequency speaker ("woofer") sensing the acceleration of the cone, using discrete controllers is presented. The design technique is based on a linear algebraic method which allows to easily specify the frequency response of the closed loop system. The design is tested on a fixed point digital signal processor. Although the approach is simple, the results obtained in the laboratory are similar to those presented in the literature with more complex controllers. Simulations and experimental results are included.
//
This paper presents a model for a dual voice coil loudspeaker. The classical model is reviewed based on the physical properties of the mechanical and electrical parts of the speaker. To bridge differences between the measurements and the mathematical model, the semi-inductive effect caused by eddy currents is included. This results in a fractional-order model. The main contribution of this paper is to consider the semi-inductive effect also on the mutual coupling between the windings, an effect that has not been reported in the literature. The theoretical model is validated by experimental results.