analogy analogy method representing mechanical system analogous electrical system advantage large body theory analysis techniques concerning complex electrical systems especially field filters converting electrical representation tools electrical domain directly applied mechanical system modification advantage occurs systems converting mechanical system electrical domain allows entire system analysed unified mathematical behaviour simulated electrical system identical mathematical behaviour represented mechanical system element electrical domain corresponding element mechanical domain analogous equation law circuit analysis laws apply electrical domain applies mechanical analogy analogy main mechanical electrical representing mechanical systems electrical domain mobility analogy roles voltage current reversed methods electrical representations produced dual circuits analogy preserves analogy electrical mechanical mobility analogy hand mobility analogy preserves mechanical system transferred electrical domain analogy applications analogy widely model behaviour mechanical filters filters intended use electronic circuit work entirely mechanical waves provided input output filter convert electrical mechanical domains common use field audio equipment consist mechanical moving parts acoustic waves waves mechanical motion air molecules fluid medium early application type significant improvements audio performance designed mechanical parts behave flat filter anticipating electronic filter elements electrical analogy developed mechanical system described abstract mechanical network mechanical system broken number ideal elements paired electrical symbols mechanical elements network shown following sections individual element mechanical electrical elements elements assumed mechanical component possessing element small time taken mechanical waves end component neglected developed distributed elements transmission lines greatest benefits element circuits mechanical required passive electrical elements resistance determined mechanical property chosen represent effort analogy voltage property chosen represent flow analogy current analogy effort variable force flow variable velocity resistance mechanical analogy electrical resistance loss energy moving system processes friction mechanical component analogous shock property analogous resistance governed equation law formula analogous equation mechanical domain formula resistance voltage current mechanical resistance force velocity induced force electrical resistance represents real electrical likewise mechanical resistance real mechanical mechanical analogy analogy mass mechanical component analogous large rigid weight governed equation formula analogous equation mechanical domain newton second law motion formula time mass purely imaginary given formula analogous mechanical given formula electrical imaginary unit angular frequency mechanical mechanical analogy analogy compliance common mechanics discuss compliance analogy electrical domain commonly mechanical component analogous spring governed equation formula analogous equation mechanical domain form law formula purely imaginary given formula analogous mechanical given formula alternatively write formula mechanical compliance directly analogous electrical expression mechanical consists mass element compliance element mechanical analogous electrical circuits consisting real mechanical components mass compliance practical proposition single component fact difficult pure mass pure compliance single component spring certain compliance mass mass compliance eliminated altogether mechanical key component mechanical filters generators exist active electrical elements voltage source current source generators mechanical analogy constant voltage generator constant force generator mechanical constant current generator constant velocity generator example constant force generator constant force spring analogous real voltage source battery remains near constant voltage load provided load resistance higher battery internal resistance example practical constant velocity generator lightly loaded powerful machine motor driving belt systems require convert electrical mechanical domains analogous port networks like described pair simultaneous arbitrary parameters numerous possible representations form applicable analogy arbitrary parameters units matrix form electrical taken port representation formula element formula open circuit mechanical presented mechanical current open circuit entering electrical element formula conversely electrical presented electrical mechanical prevented moving velocity zero remaining elements formula formula describe forward reverse transfer functions respectively analogous transfer hybrid electrical mechanical quantity mechanical analogy simple machine force applied load greater input force depending mechanical advantage machine greater unity respectively mechanical advantage analogous turns ratio analogy mechanical advantage greater unity analogous step unity analogous step power energy examples simple circuit figure shows mechanical arrangement platform mass suspended substrate spring resistance analogy equivalent circuit shown right arrangement consists series circuit system frequency natural frequency heavily model human ear circuit shows analogy model human ear ear canal section followed representing acoustic waves air ear canal mechanical vibrations bones middle ear change medium mechanical vibrations fluid filling example demonstrates power electrical bringing domains acoustic mechanical fluid flow single unified nerve flowing brain included model electrical domain domains encompassed model portion circuit uses finite element analysis continuous transmission line ideal representation structure use elements infinite number model divided sections section modelled small number elements advantages principal advantage analogy alternative mobility analogy maintains analogy electrical mechanical mechanical represented electrical mechanical resistance represented electrical resistance electrical equivalent circuit natural think force analogous voltage generator called force velocity analogous current basic analogy leads analogy electrical mechanical principal disadvantage analogy preserve mechanical system elements series mechanical system parallel electrical equivalent circuit vice versa matrix representation transforms force mechanical domain current electrical domain likewise velocity mechanical domain transformed voltage electrical domain port device transforms voltage analogous quantity represented simple device transforms voltage dual property voltage current velocity represented force analogous voltage current like disadvantage face practical especially audio frequencies work electromagnetic induction governed relationship instance force current carrying conductor given formula magnetic density length conductor history analogy called analogy mechanical explain ideas electromagnetic fields term coined idea complex introduced concept extended mechanical domain describe pair linear relating electrical voltage current mechanical force velocity express terms mechanical electrical
Impedance analogy