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2019, vol. 47, br. 3, str. 624-633
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Probabilistička analiza uređaja za razdvajanje odnosa naponskog razdelnika
Probabilistic analysis of voltage divider ratios
aPublic Company Nuclear Facilities of Serbia, Belgrade bUniverzitet u Beogradu, Mašinski fakultet, Srbija
e-adresa: avasic@mas.bg.ac.rs
Projekat: Fizički i funkcionalni efekti interakcije zračenja sa elektrotehničkim i biološkim sistemima (MPNTR - 171007)
Sažetak
Tolerancija modernih otpornika obično varira od 0.1% do 1 %. Sa probabilističke tačke gledišta to znači da se odgovarajući otpor može posmatrati kao slučajna promenljiva sa odgovarajućom funkcijom gustine raspodele verovatnoće (PDF). Dobijen je izraz za PDF za odnos prenosa dvo-otporničkog razdelničkog napona, kada je otporima u razdelniku dodeljena uniformna raspodela. Grafikoni dobijeni analitičkim izrazima, za različite kombinacije nominalnih otpora i tolerancije dvaju otpornika, upoređeni su sa onima dobijenim numeričkim simulacijama. Asimetrični karakter dobijenog rezultantnog PDF-a, uzrokovan nelinearnošću funkcije razdelničkog kola, implicira da se nominalna, srednja i najverovatnija vrednost razdelničkog odnosa mogu razlikovati. Za normalnu raspodelu otpora u dvootporničkom razdelniku, analitički pristup postaje složen, dok Monte Karlo simulacije lako daju grafikone naponskih odnosa PDF-a i izračunavaju vrednosti njihovih parametara.
Abstract
Tolerance of modern resistors typically ranges from 0.1% to 1%. From the probabilistic viewpoint, this is taken to mean that the corresponding resistance can be treated as a random variable, with an appropriate probability density function (PDF). We derive an expression for the PDF of a two-resistor voltage divider's transfer ratio, when the resistances in the divider are assigned uniform distributions. Plots of the obtained analytical expression, for various combinations of nominal resistances and tolerances of the two resistors, are compared to those produced by numerical (Monte Carlo) simulations. The asymmetrical character of the obtained resultant PDF, caused by non-linearity of the divider's circuit function, implies that the nominal, the mean and the most probable value of the divider's ratio can all differ. For normally distributed resistances in the two-resistor divider, analytical approach becomes complex, while Monte Carlo simulations readily provide the plots of voltage ratio PDFs and calculate the values of their parameters.
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