Type of Document	Thesis
Author	Smith, Ronald Joseph
Author's Email Address	joe.smith@ieee.org
URN	etd-03162007-235641
Title	Microwave Noise Temperature Measurement Uncertainty Analysis Utilizing Monte Carlo Simulations
Degree	Master of Science
Department	Electrical and Computer Engineering, Department of
Advisory Committee	Advisor Name Title Mark H. Weatherspoon Committee Chair Rajendra K. Arora Committee Member Rodney G. Roberts Committee Member
Keywords	thermal noise shot noise flicker noise hot-electron noise one-port two-port probability median uncertainty classification data simulation optimization hot load system uncertainty noise power percent uncertainty transducer gain reflection coefficient noise resistance noise conductance noise resistance equivalent temperature optimal reflection coefficient optimum reflection coefficient noise figure effective noise temperature fractional uncertainty standard uncertainty expanded uncertainty c-band cold load ambient load noise parameters monte carlo method
Date of Defense	2007-01-05
Availability	unrestricted
Abstract The ability to quantify device performance characteristics is a concern shared by developers, manufacturers, and consumers alike. From a subatomic perspective, the fluctuations found in repeated measurements can be attributed to the random nature of the charge carriers – the electrons. This limitation is also present in any receiver noise measurement set-up. The uncertainty of a noise measurement should be reported with the measurement, but assessing it can be problematic. The receiver system noise equation, which describes a measurement system, possesses non-linear parameter dependencies. Because of this, an intuitive or quantitative assessment of the measurement uncertainties would be very difficult, if not impossible, to obtain. This research work analyzes the measurement uncertainty inherent to a receiver noise measurement set-up utilizing Monte Carlo simulations. The algorithm used to assess the uncertainty incorporates a random number generator, a non-linear least squares fitting routine, and an uncertainty extraction routine. The random number generation depends on the behavior of noise sources; consequently, it produces either a normal or uniform distribution of data. Normalizing the generator allows the spread to be centered about a desired mean with a desired variance. The variance is a function of the underlying uncertainties associated with the test equipment employed. These values are given in the equipment specification sheets. The spread of real measurement data taken in a testing environment arises from perfectly uncorrelated, partially correlated, and perfectly correlated noise sources. The extreme cases (perfectly uncorrelated and perfectly correlated) are utilized to determine the effect of the erratic behavior of the charge carriers at the extremes. To simulate correlated noise sources, the random numbers are generated with the same random number generator. For the uncorrelated noise sources, the random numbers are generated by separate random processes. Once the random numbers are created, they are used to generate a spread of noise parameter simulated data. Due to the non-linear dependencies of these noise parameters, the effects of the random deviants on measurement uncertainty can not be predicted. An over-determined system of equations allows the receiver parameters of interest to be solved for. The over-determined system of equations can be created because one of the underlying noise parameters has multiple states. Over-determining the system allows for statistical smoothing of the data points. As mentioned previously, the noise parameters have non-linear dependencies and the system noise equation can not easily be transformed into a linear form. Consequently, a non-linear fitting routine is employed. The number of solutions the routine could find for one over-determined set of equations is endless, therefore the acceptable solutions are confined to values close to the true values – “true values” being a set of values actually measured in the testing environment. This confinement simply entails setting the value used as the initial guess for the fitting routine to that of the true value. Once a set of values is found for the receiver parameters, the process is repeated N times (N being the number of simulated data points desired). For each receiver parameter, there are N values that deviate about some mean value. The spread in values is a function of the underlying random process, but the behavior can not be predicted due to the non-linear dependencies. The only assumption that can be made is that the spread should exhibit a Gaussian distribution since all of the random data (except ambient temperature) is created based on this normal distribution. The overall uncertainty in the noise temperature for several devices is determined and compared with the value estimated for a simulated system. Several frequencies are selected for the analysis. The results show good agreement for calculations performed within either 1 or 2 standard deviations of the mean value for the hot and ambient loads. The estimated uncertainty for the simulated receiver system offers explanation as to why the cold load noise temperature measurement uncertainty diverges from the values found for the other DUTs.
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