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The design of MOS multipliers with CAD was studied. In particular the Fourier analysis capability of the CAD program was used to analyze the harmonic distortion rejection, DR, of the multiplier.
An open loop digital frequency multiplier is described which has a multiplied output synchronized to low frequency clock pulse. The system includes a multistage digital counter which provides a pulse output as a function of an integer divisor. The integer divisor and the timing or counting cycle of the counter are interrelated to the frequency of a clock input. The counting cycle is controlled by a one shot multivibrator which, in turn, is driven by a reference frequency input.
The absolute counting efficiency and pulse height distributions of a continuous-channel electron multiplier used in the detection of hydrogen, argon and xenon ions are assessed. The assessment technique, which involves the post-acceleration of 8-eV ion beams to energies from 100 to 4000 eV, provides information on counting efficiency versus post-acceleration voltage characteristics over a wide range of ion mass. The charge pulse height distributions for H2 (+), A (+) and Xe (+) were measured by operating the experimental apparatus in a marginally gain-saturated mode. It was found that gain saturation occurs at lower channel multiplier operating voltages for light ions such as H2 (+) than for the heavier ions A (+) and Xe (+), suggesting that the technique may be used to discriminate between these two classes of ions in electrostatic analyzers.
A power conditioner was developed which used a capacitor diode voltage multiplier to provide a high voltage without the use of a step-up transformer. The power conditioner delivered 1200 Vdc at 100 watts and was operated from a 120 Vdc line. The efficiency was in excess of 90 percent. The component weight was 197 grams. A modified boost-add circuit was used for the regulation. A short circuit protection circuit was used which turns off the drive circuit upon a fault condition, and recovers within 5 ms after removal of the short. High energy density polysulfone capacitors and high speed diodes were used in the multiplier circuit.
Hard X-ray and microwave observations of multiply-impulsive solar bursts, identified in the OSO-5 data were analyzed. Spectra in both frequency ranges were used to determine whether or not the source properties change from peak to peak within individual bursts. Two categories of microwave spectral behavior were identified: those events during which the microwave turnover frequency and spectral shape remain the same from peak to peak, and those during which the turnover frequency and spectral shape change significantly. These categories correspond to two classes of multiply-impulsive bursts: those for which the emission can be characterized by a constant magnetic field and therefore a single source region, in which case the multiplicity may be due to modulation of the emission process; and those in which groups of component spikes appear to originate in regions of different magnetic-field strengths, corresponding to separate source regions which flare sequentially. Examples of the latter type of events are presented. The discrete flaring regions are analyzed and their spatial separations estimated.
Some results from the analysis of a set of multiply impulsive hard X-ray and microwave solar bursts are presented, showing that some bursts can exhibit widely different magnetic-field strengths at different times. Two categories of microwave spectral behavior are identified: those events during which the microwave turnover frequency (MTF) and spectral shape (SS) remain the same from peak to peak, and those during which the MTF and SS change significantly. These categories correspond to two classes of multiply impulsive bursts: those for which the emission can be characterized by a constant magnetic field and therefore a single source region, and those in which groups of component spikes appear to originate in regions of different magnetic-field strengths, corresponding to separate source regions which flare sequentially. With regard to the latter type, examples are presented, the discrete flaring regions are examined, and their spatial separations are estimated.
An MC68000 based microcomputer including a hardware multiplier processor has been designed and prototyped for a reentry vehicle navigation and control application. In this paper, the microcomputer is discussed with emphasis on the multiplier processor architecture, software control and theory of operation.
The influence of the choice of the Lagrange multiplier on constrained linear inversions is explored, with reference made to applications in inferring the columnar aerosol size distributions from spectral aerosol optical depth measurements. A range of the Lagrange multiplier is examined to find all positive solutions for the solution vector, which represents modifying factors to the assumed form of the size distribution. An iterative method is devised to constrain the calculations to consideration of only positive quantities and a requirement that the regression fit to data be consistent with measurement errors. The determination of the variances and covariances is formulated and applied to existing data sets for optical depth. Variances in the solution are found to be large for particle radii when the information content of the data is small.
Pressure multipliers, which were originally intended to continuously sample an unknown pressure and increase it by a known factor, so that measurements could be conducted at low pressures with liquid-in-gas gauges, may be usefully applied to the increasing number of components available for use in molecular flow networks. An intriguing possibility involves the electric control of pressure multiplier gain by means of a piezoelectric valve.
Multipliers based on new algorithm for Galois-field (GF) arithmetic regular and expandable. Pipeline structures used for computing both multiplications and inverses. Designs suitable for implementation in very-large-scale integrated (VLSI) circuits. This general type of inverter and multiplier architecture especially useful in performing finite-field arithmetic of Reed-Solomon error-correcting codes and of some cryptographic algorithms.
A Very Large Scale Integration (VLSI) architecture and layout for an 8-bit finite field multiplier is described. The algorithm used in this design was developed by Massey and Omura. A normal basis representation of finite field elements is used to reduce the multiplication complexity. It is shown that a drastic improvement was achieved in this design. This multiplier will be used intensively in the implementation of an 8-bit Reed-Solomon decoder and in many other related projects.
A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-pw technology.
Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.
Finite field multiplication is central in the implementation of some error-correcting coders. Massey and Omura have presented a revolutionary design for multiplication in a finite field. In their design, a normal base is utilized to represent the elements of the field. The concept of using a self-dual normal basis to design the Massey-Omura finite field multiplier is presented. Presented first is an algorithm to locate a self-dual normal basis for GF(2 sup m) for odd m. Then a method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function base on a self-dual basis is simpler than that based on an arbitrary normal base.
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.
A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.
A focused-mesh electron multiplier (FMEM) has been combined with a wedge and strip position-sensitive anode to create a novel detector that is considered likely to have a number of applications in space astronomy and laboratory image sensing. Results from the first application of a wedge and strip anode to an FMEM are presented including spatial resolution, spatial linearity, background rate, and pulse risetime. The converted multiplier retains the attributes of an FMEM that made it attractive in the first place, such as low background, high speed, and high dynamic range.
Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.