The Biased Ideal Rectifier

Bennett, W. R.

doi:10.1002/j.1538-7305.1947.tb01313.x

Cited by 20 publications

(16 citation statements)

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“…Except for minor notational changes relations (2.2) are equivalent to the original results of Bennett [1], [2]. All of the properties of the functions Amn(h, k) given in Parts I and II apply.…”

mentioning

confidence: 86%

A General Solution of the Two‐Frequency Modulation Product Problem III. Rectifiers and Limiters

Sternberg

1954

Journal of Mathematics and Physics

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mentioning

confidence: 86%

A General Solution of the Two‐Frequency Modulation Product Problem III. Rectifiers and Limiters

Sternberg

1954

Journal of Mathematics and Physics

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“…in the second line of (23) is more complicated; for this we use the method of Bennett [21], [22]. The detailed derivation is given in the Appendix, with the final expression for g a (t) being…”

Section: B Intermodulation Distortionmentioning

confidence: 99%

Intrinsic Distortion of a Fully Differential BD-Modulated Class-D Amplifier With Analog Feedback

Cox

Goh

et al. 2013

IEEE Trans. Circuits Syst. I

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Abstract-This paper presents a mathematical analysis of a fully differential BD-modulated Class-D amplifier with analog feedback, i.e., one having a bridge-tied-load output configuration with negative feedback and ternary PWM signal. Notwithstanding the highly nonlinear nature of the amplifier's operation, an extremely accurate closed-form expression for the audible output signal is derived and verified based on computer simulations. This expression demonstrates that there exist larger high-order intrinsic distortions (e.g., 5th-order harmonic distortion and intermodulation distortion) for BD-modulation, compared to that for AD-modulation (binary PWM signal). Furthermore, the 3rd-order harmonic distortion has a roughly parabolic response as a function of the magnitude of the input signal and reaches its peak when the modulation index of the input signal is around 0.7. Overall, the BD-modulated Class-D amplifier has a larger intrinsic distortion for small input signal but a smaller intrinsic distortion for large input signal, compared to AD-modulated designs.

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“…by the method of Bennett [2] and denving in §5 power series expansions for the lower order coefficients mentioned.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

A General Solution of the Two‐Frequency Modulation Product Problem. I.

Sternberg

Kaufman

1953

Journal of Mathematics and Physics

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1. Introduction. The purpose of thIS paper IS to present a general method for readIly obtammg apprOXImate numencal values of the amplItudes of the modulatIOn products which occur m the output when a two-frequency mput IS applied to an arbItrary modulator havmg a contmuous output versus input characteriStIC. a partial analytical solutIOn of the problem is also indIcated In solvmg the problem It is shown, m particular, that apprOXImate values of the modulation product amplitudes always can be determmed as simple lmear combmatIOns of the values of four new functions introduced by W. R. Bennett [1,2] and that the output can be approxImated umformly for all tIme by the convergent double FourIer senes havmg these apprOXImate values as coefficients. The approximate values of the modulation product amplItudes determined by the method gIven are shown to be capable of an arbItrmy degree of refinement, subject only to lImits of accuracy of determmatIOn of the four new functions mentioned, tables of which are to be given in Part II of the present paper, and an estimate of error is mdicated. The method yields exact values of the modulatIOn product amplitudes in the case of such modulators as the bIased Ideal rectifier or Ideal hmIter, whose output versus input characteristIC is a continuous polygonal functIOn, and IS an extension of the method employed by Bennett [2] in connection with those two devices Finally, the method will be applied in Part III to study in some detail a number of examples mcludmg among others the two partIcular modulators Just mentIOned.The problem IS formulated in §2 In §3 an apprOXImate solution IS derived. The coefficients in that solutIOn are reduced m §4 by the method of Bennett and are thus found to be expresslble m terms of the four new functIOns mentioned; several properties of these functions are noted and power senes expansions for them are obtamed in §5.

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The Biased Ideal Rectifier

Cited by 20 publications

References 0 publications

A General Solution of the Two‐Frequency Modulation Product Problem III. Rectifiers and Limiters

A General Solution of the Two‐Frequency Modulation Product Problem III. Rectifiers and Limiters

Intrinsic Distortion of a Fully Differential BD-Modulated Class-D Amplifier With Analog Feedback

A General Solution of the Two‐Frequency Modulation Product Problem. I.

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