Quadrature Condition Research Articles

Computational Aspects Of Numerical Integration Based On Optimal Nodal Splines

The numerical construction of nodal spline integration rules is considered for the evaluation both of weakly singular integrals and of certain integrals defined in the Hadamard finite part sense. A bound for the quadrature sum condition number is also given.

AM noise impact on low level phase noise measurements.

The influence of the source AM noise in microwave residual phase noise experiments is investigated. The noise floor degradation problem, caused by the parasitic detection of this type of noise by an unperfectly balanced mixer, is solved thanks to a refinement of the quadrature condition. The parasitic noise contribution attributable to the AM to PM (phase modulation) conversion occurring in the device under test is minimized through the development of a dedicated microwave source featuring an AM noise level as low as -170 dBc/Hz at 10 kHz offset from a 3.5 GHz carrier.

Microcontroller based LCR meter

A microcontroller based scheme for LCR measurement is described. The unknown element (an inductor or a capacitor or a resistor) is measured employing a non conventional ac bridge. The element to be measured forms one arm (side) of the bridge and the second (series) arm is made up of a simple resistor. A Multiplier type Digital to Analog Converter (MDAC), controlled by a microcontroller, serves as the other two arms. The microcontroller, after obtaining quadrature condition between the bridge output and one of the designated bridge voltages, acquires the current through and voltage across the series connected resistor. With these values and the value of digital input to the MDAC, the parameters of L or C or R values are evaluated by the microcontroller and displayed in appropriate display fields. The scheme was implemented using an Intel 8751 microcontroller. An overall accuracy of the order of ± 1.0% was achieved for the prototype with a 12-bit MDAC having an accuracy of ± 0.2%.

A photoelastic fiber-optic strain gage

This paper reports on the development of a photoelastic fiber-optic strain gage sensitive to transverse strain. The sensing element is made from an epoxy resin which is stress frozen to passively achieve the quadrature condition. Light, emitted from an LED operating at 820 nm, is transmitted to and from the sensing element via multi-mode fibers and the signal is detected using a dual-channel operational photodiode/amplifier.

Surface topography using diffuse point differential interferometry

A high sensitivity non-contact optical profilometer based on diffuse point differential interferometry has been developed and used to measure the surface profile of camshafts. The high sensitivity of the system is achieved through differential detection of the interference patterns of the scattered light. An electronic phase-lock feedback loop is used to control the quadrature condition and determine the surface height. Preliminary measurements show that the interferometer system is sensitive to surface height variations in the order of 0·002 μm. The influence of the surface speckles on the interference pattern is analyzed, and the performance of the diffuse point differential interferometer is evaluated. The system has the advantage of not having any moving mechanical parts which leads to fast and more accurate measurements of the surface contours.

Optical-fiber thermal modulator

This paper describes a new device which utilizes the thermal sensitivity of optical fibers to modulate the phase of the light in an interferometric sensor. The purpose of the optical-fiber thermal modulator is to maintain the interferometer in its most sensitive (quadrature) condition, and it thus represents a potential replacement for the comparatively bulky piezoelectric transducers (PZT) customarily used. Shorter lengths of fiber and considerably lower voltages than are required for the piezoelectric devices produce phase shifts of many wavelengths in the optical-fiber thermal modulator.

Instrument for Continuous High Resolution Measurement of Changes in the Velocity of Ultrasound

The frequency of the ``reference'' oscillator in a coherent pulse echo apparatus is phase-locked to the spacing in time of the acoustic echoes. A change in echo spacing is thereby converted to the same fractional change of oscillator frequency, which is measured continuously. Echo spacing changes of 2 to 3 parts in 108 have been resolved at 12 Mc. The gated AFC circuit which controls the reference oscillator derives its error voltage from a phase-detected echo. The error voltage is zero when the echo is in quadrature with the reference. When the echo spacing changes, the AFC shifts the reference frequency to preserve the quadrature condition. The system is largely insensitive to changes of echo amplitude because such changes do not affect the quadrature condition. The attainable accuracy is set mainly by the temperature stability of the sample. There is a detailed discussion of circuitry, performance, and suggested refinements.