Minimum detectable signal

Abstract: The design, modeling, and simulation of a novel micromachined magnetic field sensor are discussed. The sensor uses an electrostatic resonator whose fundamental resonant frequency is modified by a Lorentz force generated from the interaction of the sensor structure and the present magnetic field. The sensor was fabricated in a standard bulk micromachining process without the need for any additional processing steps. Since the sensor does not employ any magnetic materials, it does not exhibit hysteresis. A comprehensive model of the sensor behavior is derived which encompasses the interactions of the involved physical domains. Validity of the modeling results was verified by finite-element simulations, and later, through experiments. The sensitivities of the fabricated sensors are in the range of 48-87 Hz/T, depending on sensor structure and dimensions. The design of the sensor allows for its fabrication in many standard microelectromechanical system processes and is compatible with CMOS processes. The theoretical minimum detectable signal with current devices is on the order of 217 nT. Methods to improve the sensitivity of the current sensors are suggested. A linear response to a wide range of magnetic fields makes this design suitable for applications where large fields need to be measured with high resolution.

Abstract: The present paper examines theoretically the relative sensitivity of the detection of signal pulses in the presence of noise, (a) by observation of an oscilloscope, (b) by aural perception, in which one listens to the fundamental or a low harmonic of the pulse repetition frequency (PRF), (c) and by a meter. The metering scheme may be either aperiodic, where the rectified current is fed directly to a meter with a long time‐constant, or periodic, where the rectified current is sent through an audio‐filter tuned to the PRF, given a supplementary rectification, and then passed through the meter. The dependence of the sensitivities of the different methods on various relevant parameters is studied in some detail. These parameters include the width and the shape of the IF response, the pulse length, the PRF, and in aural or meter reception, the duration of the gate, the width of the audio‐filter, and/or the time constant of the meter. The descriptive survey of the results is given in Part I and the mathematical analysis in Part II. Among the more important results are (I): The optimum IF filter is the conjugate of the Fourier transform of the pulse, not merely for visual reception, as was previously known, but also for aural or meter reception as well. (II): For very weak signals the linear detector requires only about 5 percent more input signal power than does the quadratic to achieve the same minimum detectable signal (same final signal‐to‐noise ratio). (III): The aperiodic meter has the advantage of not requiring knowledge of the PRF, and has potentially great sensitivity if spurious fluctuations in gain can be balanced out. (IV): Meter methods can be made more sensitive than the oscilloscope if long time‐constants are available. Gating is also necessary. (V): Although the best IF filter is the Fourier transform of the pulse, the best pulse is not the Fourier transform of the filter in aural reception (though it is in visual), for the best results in meter or audio‐detection are obtained by using long pulses. In visual work, the pulse length is immaterial, to a first approximation. Curves are given showing the power required to achieve a given signal‐to‐noise ratio as a function of pulse length, IF filter width, the PRF, gating time, and audio‐filter width, in some cases when the pulse and filter are not matched (i.e., are not related as Fourier transforms). Some numerical estimates of aural and meter performance relative to visual are also essayed.

Abstract: An integrated receiver that includes both the time-to-digital converter (TDC) and the receiver channel and is intended for a pulsed time-of-flight laser rangefinder with a measurement range of approximately 10 m has been designed and fabricated in a standard 0.13 mum CMOS process. The receiver operates by detecting the current pulse of an optical detector and producing a stop timing mark for the TDC by means of a leading edge timing discriminator. The TDC is used to measure the actual time interval between the start and stop pulses and the slew-rate of the stop pulse, to compensate for a walk error produced in the discriminator. The single-shot precision of the whole receiver is 250 ps for a minimum detectable signal, and its accuracy and power consumption are plusmn 37 ps with compensation within a dynamic range of at least 1:10,000 and less than 45 mW, respectively. The size of the die is 1300 mum times1300 mum including pads.

Abstract: A device which performs a sequential test on a mixture of signal and noise is called a Sequential Detector. With such a device, two thresholds are introduced, each of which is associated with a terminal decision. The length of the detection process (integration time) is not fixed in advance of the experiment but is a random variable, depending on the progress of the test. An optimum form of such a test exists and is characterized by the fact that detection is performed on the average faster than with conventional; i.e., fixed sample size (optimum or non-optimum), devices. The sequential analysis developed by A. Wald is fully applied in this paper, but an important new feature is the treatment of correlated samples and its application to continuous sampling processes. In the introduction, the problem is presented within the framework of Wald's Statistical Decision Theory, and the optimum properties of sequential detectors are discussed accordingly. It is pointed out that a sequential detector is defined in terms of conditional probabilities and hence its operation is essentially independent of a priori information, although the average risk or cost of detection necessarily depends on the a priori signal data. The general theory is illustrated with some cases of special interest. The simplest example of detection involves independent, discrete observations; e.g., the case of a pulsed carrier in normal noise. Here the optimum detector still has the well-known \log I_0 structure, but it is shown that the square law approximation for weak signals requires a bias correction due to the fourth order term. Coherent sequential detection of causal signals in normal noise provides another illustration of the theory. An interesting result is that the probabilities of error do not depend on the shape of the filter, provided the proper computer is used. The use of RC-filtered noise illustrates the treatment of continuous detection processes. Finally, the reduction in minimum detectable signal level resulting from the use of a sequential detector is computed. A third example is the sequential detection of random signals in normal noise. It is shown that, although the optimum computer involves the knowledge of the inverted correlation matrix, the average length of the test does not. Hence a curious result is obtained that in this instance detection can be performed in an arbitrarily short time. The paper concludes with a discussion of the practical necessity of truncating the detection process and exact expressions for the error probabilities of such truncated tests are derived and compared with Wald's original approximations.