Agilent Uncertainty Propagation Uncertainty Propagation for Measurements with Multiple Output Quantities c20 free download

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Uncertainty Propagation for Measurements with Multiple Output Quantities Michael Dobbert [email protected] Bart Schrijver [email protected] Keysight Technologies 1400 Fountaingrove Parkway Santa Rosa, CA, 95403 Abstract: The ISO Guide to the Expression of Uncertainty in Measurement (GUM) [1] limits the description of the law of propagation of uncertainty to real input quantities and a single real output quantity. The GUM provides little guidance for uncertainty analysis of measurements with multiple output quantities, such as complex valued S-Parameter measurements that have both real and imaginary components. Complex measurement quantities are common in RF and microwave measurements. Likewise, measurements with multiple output quantities exist in many disciplines. Supplement 2 [2] to the GUM extends the law of propagation of uncertainty to an arbitrary number of output quantities, which is a more general solution. This paper discusses this more general solution clearly and concisely using matrix notation. It demonstrates that the GUM expressions for uncertainty propagation are a specific case of this more general solution. This method is then applied to a practical measurement uncertainty example involving complex quantities. 1. Introduction The GUM [1] assumes that a measurement system is modeled as a function of multiple real input quantities and a single real output quantity. This is represented as ( ). (1) In this case, the measurand, , is a scalar quantity as are each . There exist, however, measurement problems where the measurand must be represented by more than one quantity. To demonstrate this, consider the following example from electrical metrology. A common task in electrical metrology is the measurement of sine waves. Sine waves, of course, are represented by the sine function ( ) ( ), (2) where