Mass Transmittance from String to String
Referring to Fig.9.15, the velocity transmittance from string 1 to string 2 may be defined as
![$\displaystyle \hat{\tau}_v(s)
\eqsp \frac{V^{+}_2(s)}{V^{+}_1(s)}.
$](http://www.dsprelated.com/josimages_new/pasp/img2130.png)
![$ \hat{\tau}_v(s) = \frac{V^{-}_1(s)}{V^{-}_2(s)}$](http://www.dsprelated.com/josimages_new/pasp/img2131.png)
![$ V^{-}_2$](http://www.dsprelated.com/josimages_new/pasp/img2132.png)
![$ V^{+}_2=V$](http://www.dsprelated.com/josimages_new/pasp/img2133.png)
![$ \,$](http://www.dsprelated.com/josimages_new/pasp/img196.png)
![$\displaystyle V \eqsp \frac{2R}{ms+2R}V^{+}_1
$](http://www.dsprelated.com/josimages_new/pasp/img2134.png)
![$\displaystyle \zbox {\hat{\tau}_v(s) \eqsp \frac{2R}{ms+2R} \eqsp 1-\hat{\rho}_v(s)}
$](http://www.dsprelated.com/josimages_new/pasp/img2135.png)
![$ m\to\infty$](http://www.dsprelated.com/josimages_new/pasp/img2136.png)
![$ \hat{\tau}_v(s)\to 0$](http://www.dsprelated.com/josimages_new/pasp/img2137.png)
![$ m\to0$](http://www.dsprelated.com/josimages_new/pasp/img2138.png)
We can now refine the picture of our scattering junction Fig.9.17 to obtain the form shown in Fig.9.18.
![]() |
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Simplified Impedance Analysis