Title:
Method and apparatus for generating harmonics
United States Patent 2243600


Abstract:
The present invention relates to methods and apparatus for generating harmonics. A harmonic generator capable of generating substantially any desired harmonic of a given fundamental and without appreciable distortion is useful for many purposes, notably electric musical instruments, laboratory...



Inventors:
Hulst Jr., George D.
Application Number:
US28313039A
Publication Date:
05/27/1941
Filing Date:
07/06/1939
Assignee:
Hulst Jr., George D.
Primary Class:
Other Classes:
250/232, 250/237R, 327/119, 331/66, 331/80
International Classes:
H03B19/00
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Description:

The present invention relates to methods and apparatus for generating harmonics.

A harmonic generator capable of generating substantially any desired harmonic of a given fundamental and without appreciable distortion is useful for many purposes, notably electric musical instruments, laboratory instruments, etc. The object of the present invention is to provide a method and apparatus for generation of harmonics, according to which one or more harmonics of a given fundamental, or any combination of such harmonics, may be obtained with controlled amplitude.

With this object in view, the present invention contemplates the use of a circuit element having a non-linear characteristic of such form that the output is sinusoidal and an integral multiple of the input current or voltage. In its preferred form, the invention comprises a method and apparatus in which the fundamental input operates a sinusoidal scanning mechanism, and the output is obtained from a light-sensitive element whose responsiveness varies from point to point in non-linear fashion in accordance with the harmonic or harmonics to be generated.

A further feature of the invention comprises the use of means whereby a combination of several harmonics, all of controlled amplitude, may be generated.

Still further features of the invention comprise certain novel modes of operation and combinations and arrangement of parts hereinafter described and particularly defined in the claims.

In the accompanying drawings, Fig. 1 is a diagram of a harmonic generator embodying the features of the present invention; Fig. 2 is a diagram illustrating the variation in grain density of the selector; Fig. 3 is a curve illustrating the non-linear characteristic of the device; Fig. 4 illustrates the preferred method of making a selector band; Fig. 5 is a diagram illustrating the use of the invention for combining harmonics; and Fig. 6 is a front elevation of the preferred form of tone plate for the apparatus of Fig. 5.

The apparatus shown in Fig. 1 comprises a tube 4, which may be termed an electrovisual transducer or dissector tube, preferably of the general type employed for television transmission. The tube is provided with a light-sensitive element 6 which is scanned by an electron beam.

The scanning is controlled by a pair of electrostatic deflecting plates 8. For one-dimensional scanning, which is contemplated by the present invention, only a single, pair of deflecting plates is employed. The deflecting plates are connected to an electrical input indicated at 10 of the fundamental frequency, the harmonics of which are to be generated. The tube comprises the usual means for emission -and focusing of the electron beam, further description of which is unnecessary. The light-sensitive element 6 is connected to the usual output circuit 12. The light-sensitive element 6 is illuminated with an image within the range of the scanning beam, the image being of such character as to vary the responsiveness of the light-sensitive element in accordance with the harmonic to be generated. The apparatus will first be described for the generation of a single harmonic, say, the fourth. A source of illumination 14 is projected through an opal glass diffuser screen 16, a selector screen 18 to be presently described, and a focusing system 20 on the light-sensitive surface 6. An image of the screen 18 is projected on the surface 6, as indicated at 21.

The selector screen 18, as shown in Fig. 2, comprises a strip of photographic film, the grain density of which varies along its length in such manner as to affect the sensitivity of the element 6 in accordance with the fourth harmonic of the fundamental frequency impressed on the deflector plates 8. The manner in which the variation of density is determined and the method of constructing the selector screen of the type shown at 18 will be later described. Assuming that the amplitude of the fundamental 10 is such as to scan the length of the image impressed on the element 6, the electrical impulses generated by the tube will be sinusoidal at four times the fundamental frequency, i. e., will comprise the fourth harmonic of the fundamental frequency. The fundamental may be of any desired frequency and the fourth harmonic will be the fourth multiple of that frequency, it being only necessary that the amplitude of the fundamental shall be such as to approximately cover the length of the image. The output may be fed to amplifiers of any suitable form, and the amplitude of the output may be adjusted to any desired value by control of the intensity of the source of illumination 14, or by suitable adjustment of the amplifier.

The manner in which the variation of grain density of the selector screen is determined is illustrated in Fig. 2. The distance A represents one-half of the length of the image imposed on the light-sensitive element. The instantaneous deflection of the scanning spot from the center of the image, assuming a sinusoidal fundamental, is given by the equation x=A cos wt (1) where w=27r times the frequency of the input. 5 The density of the screen at different points is determined by the formula D=Do cos nwt+constant (2) where n is the number of the harmonic, the i fourth in the case above assumed.

From these equations, the required variation in density of the selector screen may be solved. It will be observed that ct may be eliminated from the equations to express for density explicitly in i terms of deflection. Omitting constant terms, the explicit solutions for density as a function of deflection are as follows, for the first few harmonics: (n=2) 22--1 (n=3) 4X3-3x (3) (n=4) 8x4-8x_+1 These expressions will be recognized as series, the coefficients of which are the coefficients of the terms in the familiar expansions of trigonometric functions of multiple angles. The solution may be carried out for a harmonic of any number.

In Fig. 3 is plotted a characteristic of the tube, as affected by the fourth harmonic image projected on the light-sensitive element. This is a 3 plot illustrating the functional relationship between any input voltage e impressed on the input circuit and the output voltage E obtained from the tube. For the fourth harmonic, E=k(8e4-8e2+1) where k is a factor depending on the inherent properties of the tube. If e is a sinusoidal function of time, and of an amplitude such that the scanning spot substantially covers the width of the image of Fig. 2, then E is also a sinusoidal function of time, but at four times the frequency of the impressed voltage. The tube is thus given at will a non-linear characteristic such that the desired harmonic, and only the desired harmonic, is generated. The present invention thus differs from the usual frequency multipliers, in that no unwanted frequencies are present in the output.

A method of making the individual selector screens for the different harmonics by a photographic process is described as follows: A template, as illustrated at 22 in Fig. 4, is cut to a shape such that the ordinates are proportional to the desired one of the expressions (3). For example, for the fourth harmonic, the ordinates are determined as a function of x in accordance with the last-expression above written. The image of the template is then projected through a cylindrical lens 24 on a photographic plate or film, the cylindrical lens acting to focus the image horizontally without focusing it vertically, thereby producing a distorted image from which, after development of the film, a band 26 may be cut. Although the original template 22 corresponds to the expression in the variation of its ordinates, the band 26 has variations in density corresponding to Equations 1 and 2. Thus the variable-ordinate template in converted to a variable-density screen suitable for harmonic generation. A complete set of such bands made up from suitable templates may be used for all frequencies from the fundamental up to any desired harmonic.

It will be understood that the foregoing formulas apply only to the case of a pure sine wave impressed on the deflecting plates 8. The input may, however, be of wave form other than sinusoidal, in which case Equation 1 would be expressed as Fourier's series in accordance with Sthe known wave form of the impressed input.

An input of complex wave form would make a mathematical solution very difficult, but a graphical solution for the form of the templates could be readily obtained. For reasons of simplicity, 0 it is preferred to utilize a pure sine wave for the input.

The apparatus illustrated in Fig. 5 permits the combination of harmonics of any number and of any desired relative amplitude. A tone plate 30, of the type shown in Fig. 6, composed of a series 'of selector bands for the individual harmonics, is mounted in front of a source of illumination 31 and a diffusing plate 32. Between the diffusing plate and the tone plate a series of rotary inter0 ceptor blades 34 is mounted, one for each of the bands of the tone plate. By rotating the blades to different positions, the relative amplitudes of the several harmonics may be adjusted. Between the tone plate and the light-sensitive ele.5 ment is mounted a cylindrical lens 36 which focuses the image in a horizontal direction without focusing it in a vertical direction. The effect of the cylindrical lens is thus to superpose the images of all the selector bands, and thus to im3 pose on the light-sensitive element a variable degree of illumination corresponding to the combined effects of the several selector bands. In Fig. 5, the elements of the tube 4, with the exception of the light-sensitive surface 6, are omit" ted for simplicity.

In its broader aspects, the invention contemplates the use of a circuit element having a nonlinear characteristic such that the output is ex0 pressed as a function of the input according to a series in which the coefficients of the terms are given by the expressions for trigonometric functions of multiple angles. In the preferred form of the invention, the non-linear characteristic is Sobtained in any desired form by optically imposing an image of the desired density on a lightsensitive element and scanning the image at the fundamental frequency. However, the invention is not to be considered as limited to the particu50 lar embodiments shown and described but may be varied within the broader concept above mentioned.

Having thus described the invention, I claim: 1. A method of generating harmonics which 5 consists in impressing on a light-sensitive element a scanning beam moving at a fundamental frequency, and imposing on the light-sensitive element a variable-density optical image to vary the responsiveness of said element from point to 0 point at a frequency which is a multiple of the scanning frequency.

2. A method of generating harmonics which consists in impressing on a light-sensitive element a scanning beam moving at a fundamental 35 frequency, and imposing on the light-sensitive element a variable density optical image the illumination of which varies from point to point to vary the responsiveness of said element at a multiple of the scanning frequency.

70 3. A method of generating harmonics which consists in impressing on a light-sensitive element a scanning beam moving at a fundamental frequency, and imposing on the light-sensitive element within the range of the scanning beam 75 a variable density optical image the illumination of which varies in accordance with a multiple of the scanning frequency.

4. A method of generating harmonics which consists in impressing on a light-sensitive element a scanning beam moving at a fundamental frequency, and imposing on the light-sensitive element within the range of the scanning beam a variable density optical image the illumination of which varies in accordance with selected multiples of the scanning frequency.

5. Apparatus for generating a harmonic of a given frequency comprising a light-sensitive element, means for imposing on the light-sensitive element a variable density optical image the illumination of which varies in accordance with the desired harmonic, and means for scanning the image with an electron beam at the given frequency.

6. Apparatus for generating a harmonic of a given frequency comprising a light-sensitive element, an optical selector screen the density of which varies in accordance with the desired harmonic, means for imposing an image of the screen on the light-sensitive element, and means for scanning the image with an electron beam at the given frequency.

7. Apparatus for generating harmonics of a given frequency comprising a light-sensitive element, an optical screen having bands the density of which varies in accordance with selected harmonics, means for imposing on the light-sensitive element a superposed image of selected bands, and means for scanning the image with an electron beam at the given frequency.

8. A method of generating harmonics which consists in impressing on a light-sensitive element a scanning beam moving at a fundamental frequency, and optically projecting on the lightsensitive element within the range of the scanning beam a variable density image, the illumination of which varies in accordance with a multiple of the scanning frequency.

9. A method of generating harmonics which consists in impressing on a light-sensitive element a scanning beam moving at a fundamental frequency, and optically projecting on the lightsensitive element a plurality of superposed variable-density images, the density of each image varying in accordance with a selected multiple of the given frequency.

10. Apparatus for generating a harmonic of a given frequency comprising a light-sensitive element, an optical selector screen the density of which varies in accordance with the desired harmonic, an optical projector for imposing an image of the screen on the light-sensitive element, and means for scanning the image with an electron beam at the given frequency.

11. Apparatus for generating harmonics of a given frequency comprising a light-sensitive element, an optical screen having bands the density of which varies in accordance with selected harmonics, optical projection means for imposing on the light-sensitive element a superposed image of selected bands, and means for scanning the image with an electron beam at the given frequency.

12. Apparatus for generating harmonics of a given frequency comprising a light-sensitive element, an optical screen having bands the density of which varies in accordance with selected harmonics, optical projection means including a cylindrical lens for imposing on the light-sensitive element a superposed image of selected bands, and means for scanning the image with an electron beam at the given frequency.

GEORGE D. HULST, Ja,