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MIT 2 693 - Lectures 1 and 2: Instrument Systems and Limits to Measurement

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6 Lectures 1 and 2: Instrument Systems and Limits to Measurement A system is completely defined by its input and output specifications. For example, an instrument system might measure, record, and display a physical variable. The exact way this is done is unimportant as long as the specifications are met. We often deal with components of an instrument system such as sensors, amplifiers, or recorders but in general these are not complete and their characteristics depend on what they are connected to. The concept of a system being defined by its specification is useful because it frees us from thinking about specific implementations. Instead we may treat the system as a black box and concern ourselves solely with the inputs and outputs. The input to an instrument system is the physical variable to be sensed. Thus the input to a thermometer is temperature, to an acoustic receiver is sound pressure, and to a current meter is velocity field. That the thermometer has self-heating and also may be velocity dependent is a problem to be met inside the system but should not concern us at this stage. For simple measurements, there may be little benefit in thinking of the physical variable independent of the sensor but in more complicated measurements there is an advantage. For example, the physical quantity may be highly variable and require that a long observation be made to obtain the desired statistical significance. This must be recognized immediately and not be masked by the averaging characteristics of some sensor. Furthermore, a clear understanding of the physical variable will aid in sensor design. The sensor in an instrument system converts the physical signal to a more easily manipulated form. The use of the term signal in this context implies a separation of the physical variable into a meaningful part, the physical signal, and a non-meaningful part, noise. This separation often starts in the sensor. Any introduction of false information at the sensor or loss of true information is generally impossible to correct with subsequent processing. So the behavior of the sensor is one of the most critical concerns in an instrument system. The physical signal is composed of direct variations in a physical property such as pressure, concentration, or temperature. The output of the sensor is a voltage, displacement, resistance change, or other easily amplified, averaged, or stored characteristic. After the physical signal is transformed to some other form by the sensor, it can be conditioned by amplifying, filtering, correlating, or sampling. Amplifying can generally be done with little degradation of signal to noise ratio. The term signal to noise ratio defines the ratio of useful information to unwanted information. Extra information added by the amplifier is unwanted. So if it adds information, this is noise. Similarly if in addition to amplifying the signal, it loses a part of it, this reduces the signal to noise ratio. Broadband electrical noise is generated by thermal excitation of electrons in a resistor. Because electronic amplifiers have resistive components, this thermal noise is introduced by amplification. It becomes the limit of the system in those cases where the sensor signal has very low level (as in the case of radio or acoustic receivers) and care must be taken to deal with this noise source and not permit it to become worse than the theoretical limit.7 The thermal noise of a resistor is called Johnson noise. Considered as a current source in series with the resistor, or as a voltage source in parallel with the resistor, two expressions for the noise can be written: in2 = 4KTB/R; en2 = 4KTBR where in2 = mean squared noise current (amps) en2 = mean squared noise voltage (volts) K = Boltzmann's constant - 1.38 * 10-23 J/K T = temperature (K) B = bandwidth (Hz) R = resistance (ohms) From this it can be seen that cooling the amplifier may be required for achieving the best noise figure and this is done for certain space radio receivers and in some photo detectors such as CCD arrays. However for the rest of us, the only reasonable thing to do is lower the bandwidth. Bandwidth is the range in frequency passed by the system. Analog filtering and sampling determine the bandwidth. In a communication system, the bandwidth determines how fast information can be transferred and there is a tradeoff between a fast system and a reliable one. The simplest way to limit bandwidth is with a low pass filter since the bandwidth below a certain frequency is limited to that frequency while the bandwidth above is infinite. In high frequency systems, a narrow band filter is used. When the signal has been filtered, it is often sampled. In modern instruments, it is generally digitized because the signal to noise ratio for digitized data is very high and can be maintained through storage and subsequent processing with little degradation. At this point the problem of aliasing arises. The sampled data contains limited information about signal at frequencies higher than the sampling frequency. In fact, if there is signal at higher frequency than the sampling frequency, it will appear as energy at some lower frequency and thus degrades the data at the lower frequency. This is almost always undesirable. The solution is to filter before sampling and sample at twice the frequency of the high frequency limit of the signal passed by the filter. The high frequency limit may be imposed by the nature of the physical signal, by the response of the sensor, or by a filter in the signal conditioner. A system should have an output that is either directly coupled to a human observer or is indirectly coupled to one through subsequent processing. This defines the output of the system. It might be a display or a data port. But before final presentation, some human engineering is required to match the display to the capabilities of the observer. Modern commercial instruments do this reasonably well but prototype instruments are sometimes incomplete in this area. Recording in temporary form is required in a large class of instruments used in oceanography, those unattended and submerged. Other systems must deal with permanent data storage. Recorders are used to do this storage. They have data limits. However the earlier in the8 processing sequence that the data can be stored, the more chance there is for subsequent processing. This is in conflict with the need to

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