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sensitivityThe minimum signal power that can be distinguished from the random fluctuations in the output of a measuring system caused by noise inherent in the system. In a radio telescope contributions to the system noise include noise generated in the first stage of the receiver, thermal noise due to loss in the antenna/feeder system, synchrotron emission received by the antenna from the Galaxy (see radio source), and thermal emission from the atmosphere and from the ground. If the system noise has a power P watts, then an equivalent system temperature, or noise temperature, can be ascribed to it given by
The signal/noise ratio of a radio telescope is the ratio of the power in the output that is due to the radio source under observation to that caused by the system noise. The sensitivity is usually defined as the flux density of a source that would produce the same signal power as the noise power, i.e. a signal/noise ratio of one. If the signal changes only slowly with time, the sensitivity may be improved by increasing the integration time used in the measuring system. See also confusion.
of an automatic control system, the dependence of the dynamic properties of an automatic control system on a variation of the system’s parameters or characteristics. A variation of a system’s parameters is taken to mean any deviations of the system’s parameters from the values adopted as the initial values. Such deviations may be completely known and described by certain functions of time or may be known only to the extent of belonging to a specified class, for example, limited in magnitude. The variations of a system’s parameters may be finite or infinitesimal. Hence, the order of the differential equations that describe the variations may remain unchanged or may vary.
Sensitivity functions are used for the direct evaluation of sensitivity. Such functions play a major role in the quantitative evaluation of the extent to which variations of a system’s parameters affect the dynamic properties of the system.
Sensitivity functions contain extremely valuable information, for example, for solving problems of the synthesis of automatic control systems. A very important problem is the synthesis of systems that have a minimum sensitivity to variations of their parameters. The problem of sensitivity may be considered a problem of the theory of games for automatic control, if we assume that a disturbance caused by a variation of a system’s parameters is in conflict with both the dynamic properties of an object and a control action. Such an application of the methods of the theory of games in sensitivity theory is promising, especially for the synthesis of optimal control systems, which are insensitive to variations of the parameters of a controlled object and have minimax properties.
Of great practical importance is the inverse problem, which consists in the estimation of a variation of a system’s parameters by observing the disturbance of an output signal that is caused by the variation. Parameter variations computed on the basis of a deviation of an output signal may be used to modify the parameters of a control system in order to improve the quality of the operation of the system as a whole.
REFERENCESMetody teorii chuvstvitel’nosti v avtomaticheskom upravlenii. Leningrad, 1971.
Tomović, R., and M. Vukobratović. Obshchaia teorii achuvstvitel’nosti. Moscow, 1972. (Translated from Serbian and English.)
a property of a measuring instrument that is expressed by the ratio of the linear displacement (Δl) or the angular displacement (Δα) of the pointer on the scale of the instrument—that is, the signal at the output of the instrument—and the change in a measured quantity that causes the displacement. A distinction is made between absolute sensitivity and relative sensitivity. Absolute sensitivity S = Δl/Δx or Δα/Δx, where Δx is the change in a measured quantity x and is expressed in the same units as the quantity. Relative sensitivity S0 = Δl/(Δx/x) or Δα/(Δx/x).
A property of a system, or part of a system, that indicates how the system reacts to stimuli. The stimuli can be external (that is, an input signal) or a change in an element in the system. Thus, sensitivity can be interpreted as a measure of the variation in some behavior characteristic of the system that is caused by some change in the original value of one or more of the elements of the system.
Sensitivity is commonly used as a figure of merit for characterizing system performance. As a figure of merit, the sensitivity is a numerical indicator of system performance that is useful for predicting system performance in the presence of elemental variations or comparing the relative performance of two or more systems that ideally have the same performance. In the latter case, the performance of the systems relative to some parameter of interest is rank-ordered by the numerical value of the corresponding sensitivity functions. If T is the performance characteristic and X is the element or a specified input level, then mathematically sensitivity is expressed as a normalized derivative of T with respect to X.
A limiting factor in using the sensitivity of a system to characterize performance at low signal levels is the noise. Noise is a statistical description of a random process inherent in all elements in a physical system. The noise is related to the minimum signal that can be processed in a system as a function of physical variables such as pressure, visual brightness, audible tones, and temperature.
There exist many situations where the sensitivity measure indicates the ability of a system to meet certain design specifications. For example, in an electronic system the sensitivity of the output current with respect to the variation of the power-supply voltage can be very critical. In that case, a system with a minimum sensitivity of the output current with respect to the power-supply voltage must be designed. Another example is a high-fidelity audio amplifier whose sensitivity can be interpreted as the capacity of the amplifier to detect the minimum amplifiable signal.