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58 The PCB Design Magazine • October 2017 Numbers are fascinating things and the way they are presented can influence our thinking far more than we would like to admit, with $15.99 seeming like a much better deal than $16.00 (though it depends which side of the trans- action you sit on!) When looking for a new job, you may prefer to round your existing salary up to the nearest thousand dollars, not down, when speaking with a poten- tial employer. Likewise, a salary of $60,000 sounds better than one of $0.061 mil- lion, even t h o u g h the latter is a larger num- ber. Our brain has been programmed to suppress the importance of numbers to the right of the decimal point. Such is the case with the loss tangent of materials. It is a tiny num- ber and so to our minds looks insignifi- cant, but it has a directly proportional effect on the energy loss suffered by a dielectric. I am always curious that engineers seem to obsess over dielectric constant [1] , the ability of a sub- strate to store energy and its effect on imped- ance, which is a one over root effect i.e., – so this is a second order impact on Z 0 . Yet engineers go to great lengths to attempt to find the exact value of Er despite its sec- ond-order effect on the circuit charac- teristic impedance. But the loss tan- gent? Well, it's a small number, isn't it? So, why not round it off to a few decimal plac- es? Logical thought is suspended just be- cause it is a small number, but when you are model- ing insertion loss, the loss is directly proportional to the loss tangent [2] . A Practical Example Because loss tangent is a small number, it is perhaps easy to forgive people who round it off to fewer decimal places. Our minds are wired to dis- miss numbers far to the right of the decimal point. However, this can lead to unintended miscalculations when rounding small value by Martyn Gaudion POLAR INSTRUMENTS FEATURE COLUMN: THE PULSE

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