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Technical Analysis |
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Simple Analysis
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More Complex Analysis On 11 Dec 1999 12:17:39 GMT, Sverre Brubaek <sverre.brubak@fi.uib.no> wrote on rec.audio.high-end: Notation: Speaker terminals=T Amp terminals=A We indicate impedance by Zx where x is w for wire, a for amp or s for speaker We start by showing wiring diagrams of the two connection types. Single Wire: T-+ T-+----Zw----A Biwire: T----Zw----+ T----Zw----+-A So far so good, now lets look into the amp and speakers: Single Wire: ...-Zs1---T-+ ...-Zs2---T-+----Zw----A---Za---... Biwire: ...-Zs1---T----Zw----+ ...-Zs2---T----Zw----+-A---Za---... Let's find total impedance (|| is the symbol for a parallel connection): Single Wire: Zsw=Za+Zw+(Zs1||Zs2) Biwire: Zbw=Za+((Zw+Zs1)||(Zw+Zs2)) Let's resolve the parallel connections. This is done by: Ztotal=(Z1||Z2) => Ztotal^-1=Z1^-1+Z2^-1 => Ztotal = 1/(1/Z1 + 1/Z2) Single wire: Zsw=Za+Zw+1/(1/Zs1 + 1/Zs2)=Za+Zw+Zs1Zs2/(Zs1+Zs2) Biwire: Zbw=Za+1/(1/(Zw+Zs1)+1/((Zw+Zs2)) =Za+((Zw+Zs1)(Zw+Zs2))/(2Zw+Zs1+Zs2) We know that Zw << Zs, this implies that (Zw+Zs) ~~ Zs. We simplify with that assumption: Zbw=Za+((Zs1)(Zs2))/(Zs1+Zs2)=Za+Zs1Zs2/(Zs1+Zs2) ^^^^^^^^^^^^^^^^^^^ Single wire: Zw is almost zero. We let Zw -> 0: lim(Zw->0)(Zsw)=lim(Zw->0)(Za+Zw+Zs1Zs2/(Zs1+Zs2))=Za+Zs1Zs2/(Zs1+Zs 2)=Zbw ^^^^^^^^^^^^^^^^^^^ Note that the two underlined expressions are the same (Conclusion) We have shown that Biwiring (electrically is the same) Single wiring if Zw ~~ 0 and Zw << Zs (IOW, Biwiring has no electrical effect if the speaker wire is properly designed for the speaker and the length of the wire, and the wire has lower series impedance than the source impedance of the power amp - both these conditions are commonly satisfied) More complex analysis |
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