Inductor Energy Storage
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1 School of Compuer Science and Elecrical Engineering 5/5/ nducor Energy Sorage Boh capaciors and inducors are energy sorage devices They do no dissipae energy like a resisor, bu sore and reurn i o he circui depending on applied currens and volages n he capacior, energy is sored in he elecric field beween he plaes n he inducor, energy is sored in he magneic field around he inducor ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs
2 School of Compuer Science and Elecrical Engineering 5/5/ We wrie Energy Sorage Formula P and since energy E E and, assuming he iniial curren and he final curren, we have d d Pd d d d d Compare wih capacior E C E ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs
3 School of Compuer Science and Elecrical Engineering 5/5/ Series nducors N N Equiv d d d d d ( N ) d N N d d Equiv d d Equiv N So inducors in series add like resisors in series ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs 3
4 School of Compuer Science and Elecrical Engineering 5/5/ Parallel nducors N N Equiv For any inducor r on he lef r d d r r r d [ + r () assumed] Equiv d N d r r r r N d N Equiv i i So inducors in parallel add like resisors in parallel ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs 4
5 School of Compuer Science and Elecrical Engineering 5/5/ Behaviour of Simple R Circuis Consider ha he swich has been in he posiion shown for a long ime so ha no curren is flowing. The swich moves o he oher posiion a ime. Wha is he behaviour of he volage, v, across he inducor? R s i v ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs 5
6 School of Compuer Science and Elecrical Engineering 5/5/ Simple R Circui niially, here will be no curren hrough he inducor because he inducor will creae a volage o oppose a sep change in curren. Hence a volage of s will iniially appear across he inducor. As he curren increases, he volage across he inducor will decrease. Evenually, a seady curren of s /R will be reached and v will fall o zero. R s i v ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs 6
7 School of Compuer Science and Elecrical Engineering 5/5/ Analysis of R Circui ecure 8 Assume he inducor is no soring energy a (no curren) K for his circui yields s Ri + We know he soluion has he form i( ) di d τ niial and final boundary values yields s iniial A + B ; final A R ENG3 Elecrical Physics and Elecronics A + B e s s τ i( ) e (*) R R B.ovell/T.Downs 7
8 School of Compuer Science and Elecrical Engineering 5/5/ Final Soluion Now we jus need o deermine he ime consan τ Differeniaing (*) yields di d s τ R e τ τ s R i Backsubsiuion ino he K equaion yields τ s s s Ri + τ R Ri Rτ R i ( Ri) s s i( ) R R e ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs 8
9 School of Compuer Science and Elecrical Engineering 5/5/ Curren Characerisics f we plo normalised curren (fracion of final curren s /R) hrough he inducor agains ime expressed in muliples of he ime consans, τ /R, we obain he following graph. Curren τ 63.% 98.% 86.5% 95.% 99.3% Time Afer τ we obain 63.% of he final curren. Afer 5τ, we obain 99.3% of he final curren niial slope is /τ. This is a quick way o esimae τ on an oscilloscope. ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs 9
10 School of Compuer Science and Elecrical Engineering 5/5/ olage Characerisics Similarly, f we plo normalised volage (fracion of supply volage, s ) across he inducor agains ime expressed in muliples of he ime consan, τ /R, we obain he following graph. olage % 3.5% 4.98%.83% τ Time.6% Afer τ we obain 36.8% of supply volage. Afer 5τ, we obain.6% of he supply volage niial slope is s /τ. This is a quick way o esimae τ on an oscilloscope. ecure 8 ENG3 Elecrical Physics and Elecronics B.ovell/T.Downs
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