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Journal ArticleDOI

Reduction of spectral distortion in class D amplifiers by an enhanced pulse width modulation sampling process

01 Aug 1991-Vol. 138, Iss: 4, pp 441-448
TL;DR: In this article, an enhanced sampling process was proposed to reduce spectral distortion in the output of digital pulse width modulated class D amplifiers, which can be adjusted such that the spectra produced by the process can take a number of forms for the same signal.
Abstract: An enhanced sampling process which can be used to reduce spectral distortion in the output of digital pulse width modulated class D amplifiers is presented. This process arises from a generalisation of the concepts of natural and uniform sampling and can be adjusted such that the spectra produced by the process can take a number of forms for the same signal. Analytical expressions for the spectra produced by the sampling process are derived for both single and double sided modulation. The performance of the process is assessed by case studies on full bandwidth and bass to midrange audio class D amplifiers. It is shown that at carrier frequencies around 88 kHz in a full bandwidth amplifier and 44 kHz in a bass to midrange amplifier the new sampling process will result in significantly lower distortion when compared with either natural or uniform sampling.
Citations
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Journal ArticleDOI
TL;DR: It is shown that if the maximum magnitude of the derivative of x(t) is smaller than twice the carrier frequency, then a PWM signal consists of a baseband signal y(T) together with y( t) phase-modulated onto each carrier harmonic.

169 citations


Cites background or methods or result from "Reduction of spectral distortion in..."

  • ...More recently, PWM has become important in e=cient energy processing and management in all types of communication systems and audio applications [5,10]....

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  • ...n=1 Jn(k M) jk [{ (f − (kfc − nf1))− (f + (kfc − nf1))} +(−1)n{ (f − (kfc + nf1))− (f + (kfc + nf1))}]; (70) which is exactly the result obtained by the double Fourier series method in [2,10]....

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  • ...This result matches those obtained in [2,10] by the double Fourier series method....

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  • ...Previous studies [3,10], have used a double Fourier series method to obtain the spectrum of the PWM signal when the modulating signal is a pure sinusoid, that is, a single tone....

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Journal ArticleDOI
TL;DR: It is shown that natural PWM does not introduce audible distortion at switching frequencies consistent with power electronics practice, and the experimental full-bridge inverter implementation demonstrates that miniaturization is possible.
Abstract: A complete digital audio amplifier has been developed, implemented and tested. The process is entirely computational, and the output load and filter are the only analog components in the system. The process makes use of digital signal processing and a switching power stage to provide both high fidelity and high efficiency, beginning with a digital audio data stream. The advantages of naturally-sampled pulse-width modulation (PWM) are discussed in depth, including spectral analysis and comparisons to uniformly-sampled PWM. It is shown that natural PWM does not introduce audible distortion at switching frequencies consistent with power electronics practice. Interpolation methods for sample data conversion to natural PWM are discussed, and error analysis is presented based on Lagrange's Expansion Theorem. Noise-shaping processes are used to support high fidelity with practical values of time resolution. A counter conversion process enforces switching dead time in the inverter gate signals. The experimental full-bridge inverter implementation demonstrates that miniaturization is possible. A complete test system delivered more than 50 W into an 8 /spl Omega/ load with an efficiency of 80% and total harmonic distortion plus noise of 0.02%.

130 citations


Cites background from "Reduction of spectral distortion in..."

  • ...Since the square-wave Fourier series and transform are well known, knowledge of the signal-dependent spectrum will lead toPWM SQ ....

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Proceedings ArticleDOI
08 Aug 2000
TL;DR: In this article, a vibration-induced power generator with total volume of /spl sim/1cm/sup 3/ that uses laser-micromachined springs to convert mechanical energy into useful electrical power is presented.
Abstract: Presents the development of a vibration-induced power generator with total volume of /spl sim/1cm/sup 3/ that uses laser-micromachined springs to convert mechanical energy into useful electrical power. The goal of this project is to create a minimally sized electric power generator capable of producing enough voltage to drive low-power ICs and/or micro sensors for applications where mechanical vibrations are present. Thus far, we have developed a generator capable of producing 2V DC with 64Hz to 120Hz input frequency at /spl sim/250/spl mu/m vibration amplitude. We have also demonstrated that this generator has enough power to drive an IR transmitter to send 140ms pulse trains with /spl sim/60sec power generation time.

93 citations

Journal ArticleDOI
TL;DR: In this article, an analytical technique for calculating the harmonic characteristics of the output voltage of an H-bridge inverter with dead time is presented, based on a three-dimensional (3-D) model derived for generating the pulsewidth-modulated (PWM) pulse train.
Abstract: An analytical technique for calculating the harmonic characteristics of the output voltage of an H-bridge inverter with dead time is presented. The analysis is based on a three-dimensional (3-D) model derived for generating the pulsewidth-modulated (PWM) pulse train. By applying double Fourier analysis, a generalized and elegant mathematical function for describing the harmonic components of the output voltage is formulated. The function can be divided into two parts: an ideal part representing the PWM signal without dead time and a correction part representing the dead-time effect. The function provides detailed composition of the fundamental component, signal harmonics, carrier harmonics, and cross-modulated harmonics. The proposed technique has been verified using examples and the theoretical predictions are confirmed with the results obtained from simulations using PSpice.

91 citations


Cites methods from "Reduction of spectral distortion in..."

  • ...Similar approaches have been used in [ 8 ] and [9] to analyze the harmonic characteristics of an H-bridge converter....

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Journal ArticleDOI
TL;DR: This paper simplifies the time-domain expression for the algorithmic PWM linear interpolation (LI) sampling process and analytically derive its double Fourier series expression and shows the attractive attributes of a Class-D amplifier embodying the simplified LI sampling expression and reduced clock rate pulse generator.
Abstract: A digital Class-D amplifier comprises a pulsewidth modulator (PWM) and an output stage. In this paper, we simplify the time-domain expression for the algorithmic PWM linear interpolation (LI) sampling process and analytically derive its double Fourier series expression. By means of our derivation, we show that the nonlinearities of the LI process are very low, especially given its modest computation complexity and low sampling frequency. In particular, the total-harmonic distortion (THD) /spl ap/0.02% and foldback distortion is -98.4 dB (averaged from modulation indexes M=0.1 to 0.9) for the 4-kHz voiceband bandwidth @1-kHz input, 48-kHz sampling. We also describe a simple hardware for realizing the LI process. We propose a frequency doubler (with small overheads) for the pulse generator for the PWM, thereby reducing the counter clock rate by 2, leading to a substantial /spl sim/47% power dissipation reduction for the Class-D amplifier. By means of computer simulations and on the basis of experimental measurements, we verify our double Fourier series derivation and show the attractive attributes of a Class-D amplifier embodying our simplified LI sampling expression and reduced clock rate pulse generator. We show that our Class-D amplifier design is micropower (/spl sim/60 /spl mu/W @1.1 V and 48-kHz sampling rate, and THD /spl ap/0.03%) and is suitable for practical power-critical portable audio devices, including digital hearing aids.

64 citations


Cites background from "Reduction of spectral distortion in..."

  • ...Note that we have not included the double Fourier series expression for the LI given in reference [4] due to its imprecision....

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  • ...The reported sampling processes for the algorithmic PWM methods include the linear interpolation (LI) [4], [5], pseudonatural PWM [5], static-filter PWM [8], weighted PWM and its variants [9], derivative PWM [10], parabolic correction PWM [23], prediction correction PWM [28], [29] and more recently, our earlier proposed Delta compensation ( C) PWM [11] sampling processes....

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  • ...LI is arguably first reported in [4] but inadvertently for and in [22] instead of ; we can show that and are poorly optimized, resulting in high nonlinearities....

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  • ...The time-domain pulsewidth expressions reported in [4] [see (2a)] and in [5] [see (2b)] are somewhat different due to the different normalizations (equivalent to the bounded range) assumed for...

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  • ...It is interesting to note that reported work on the LI process [4], [5], [22], the mechanisms for the nonlinearities of the LI process, in particular the harmonic distortion and foldback distortion, are not well understood; the reported double Fourier series expression [4] for the LI process is imprecise....

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References
More filters
Journal ArticleDOI
TL;DR: In this paper, a new method of computing modulation products by means of multiple Fourier series is described, which is used to obtain for the problem of modulation of a two-frequency wave by a rectifier a solution which is considerably simpler than any hitherto known.
Abstract: A new method of computing modulation products by means of multiple Fourier series is described. The method is used to obtain for the problem of modulation of a two-frequency wave by a rectifier a solution which is considerably simpler than any hitherto known.

141 citations

Journal ArticleDOI
E. Fitch1
TL;DR: In this paper, the spectrum of a train of rectangular pulses sinusoidally modulated in any one of these ways is derived, and it is shown that in none of these methods is there any harmonic distortion or audio crosstalk.
Abstract: Some methods proposed for evaluating the spectra of modulated pulse trains are discussed. The basic pulse-frequency, -phase, -length and -amplitude modulation systems are defined and the spectrum of a train of rectangular pulses sinusoidally modulated in any one of these ways is derived. Modulation by more than one tone is also considered. It is shown that in none of these methods is there any harmonic distortion or audio crosstalk. Anharmonic distortion arises from sidebands of harmonics of the pulse repetition frequency, and graphs are given to illustrate its magnitude. The formulae are extended to cover non-rectangular pulses, and it is shown that the distortions to be expected are practically the same as for rectangular pulses. The reproduction of transients is briefly examined. It seems that they suffer little distortion in form but that their timing is modified by the pulse modulation, the maximum time-shift being half the pulse repetition period.

32 citations

Journal ArticleDOI
J.D. Martin1
01 Jun 1970
TL;DR: In this article, the theoretical efficiencies of class-D amplifiers are compared with those of conventional amplifiers by means of a power balance, and it is suggested that class-AD and class-BD modes of operation should be defined.
Abstract: The theoretical efficiencies of class-D amplifiers are compared with those of conventional amplifiers by means of a power balance. As a result of certain similarities, it is suggested that class-AD and class-BD modes of operation should be defined. The class-D amplifier converts the collector dissipation of a conventional amplifier into load power components at a large number of modulation frequencies. When these are removed by filtering, a high overall efficiency results. The analysis presented includes an idealised treatment of the class-D amplifier with an inductive load, and enables constructive comparisons to be made.

22 citations