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Engineering and Comp Sci Homework Help
Understanding Impedance: How to Find Poles and Zeros of a Network
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[QUOTE="roam, post: 4687708, member: 120460"] [h2]Homework Statement [/h2] I have some trouble understanding the worked examples below: Considering the input impedance of the network below: [CENTER][ATTACH=full]168073[/ATTACH][/CENTER] ##z_{in} = R+ \frac{sL/sC}{sL+(1/sC)}## ##z_{in} = R \left[ \frac{s^2+s/(RC)+1/(LC)}{s^2+1/(LC)} \right]## Where ##s=j\omega##. How did they get from the first expression to the second expression? [h2]The Attempt at a Solution[/h2] Clearly looking into the network R is in series with the parallel combination of L and C, so we have ##R + L \parallel C## which is the first expression: ##z_{in} = R+ \frac{sL/sC}{sL+(1/sC)}## We can further write this as: ##z_{in} = R+ \frac{sRL + (R/sC)+(sL/sC)}{sL+(1/sC)}## I'm really confused. Where does the second expression given above come from? :confused: Any help is greatly appreciated. P.S. This is part of a problem about finding poles and zeros of the network. The quadratics in the numerator and denominator of the 2nd expression can be factorized to give the poles and zeros. [/QUOTE]
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Understanding Impedance: How to Find Poles and Zeros of a Network
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