Triangle wave

Abstract: A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.

Abstract: A general BIST architecture for A-to-D converters involves the integration of both an analog test signal generator and a digital output response analyzer. This paper presents a structure for the internal generation of a linear signal used with the histogram-based test technique. The structure is based on two highly linear ramp generators together with a feedback control circuitry. Results show that the proposed structure preserves the linearity of the ramp generators while accuracy of the triangle-wave is provided by means of a calibration scheme.

Abstract: Piezoelectric tube scanners are the actuators of choice in scanning probe microscopy. These nanopositioners exhibit a dominant first resonant mode that is excited due to harmonics of the input scan signal. This introduces errors in the scan obtained. The presence of this resonant mode limits the upper bound of a triangular scan rate to around 1/100th of the first mechanical resonance frequency. Passive and active shunts have shown to damp this resonant mode substan- tially and improve scan performance. Sensorless active shunts optimised using H2 and H1 tech- niques, is designed. These shunts reduce the amplitude of the first resonant peak of a prototype tube nanopositioner by 24 dB. A triangle wave input is used to test the improvement in scan per- formance due to the damping achieved by these active shunts. Analysis shows that damping the resonant mode in such fashion reduces the scan error by five times.

Abstract: A variable differential transformer system (10), both linear and rotary (L/RVDT) includes a primary coil (12) drive by a primary drive (20) having a triangle wave generator whose frequency is set by an external frequency control (R osc and C osc ) which includes compensation for gain temperature error. Secondary coils (14, 16) have a common connection for balanced loading with an input stage arrangement (R7, R8, R9, R10) providing low common mode range and a way to differentiate between normal operation and coil faults detected by a fault detection network (28). Synchronous demodulation (22) extracts both magnitude and direction from the secondary coil signals. Electronic calibration (24) is shown which compensates for sensor offset and gain. Sensor offset calibration is accomplished by adding a percentage of the synchronous demodulation reference wave form to the differential secondary signal. A filter network (26) averages the synchronous demodulated signal in order to extract the DC component of the wave form. A dual function output amplifier (30) provides a means of reporting the analog sensor output and the occurrence of a sensing element fault with sufficient drive current to interface with external loads. A variable rotary core assembly (18) and a variable linear core assembly (18') are shown which allow axial adjustment of the core relative to the coils to provide offset temperature error compensation.