Todai Entrance Exam: Subject 2010 – Problem 1
(1)
![\[ V_{T} = -Z_{F}\sum_{i=1}^{n} \frac{V_{i}}{Z_{i}} \]](http://www.vynguyen.net/wp-content/ql-cache/quicklatex.com-c79807db1be85b617b096c36d7425e3b_l3.png "Rendered by QuickLaTeX.com")
![\[ V_{T} = -Z_{F}\frac{V_{1}}{Z_{1}} \]](http://www.vynguyen.net/wp-content/ql-cache/quicklatex.com-a59bdbc90d4d810df0fef3f138984fe6_l3.png "Rendered by QuickLaTeX.com")
(2)
We see that:
![\[ \frac{1}{s+\sqrt{3}} = \frac{1}{\sqrt{3}s}\frac{1}{\frac{\sqrt{3}}{3} + \frac{1}{s}} \]](http://www.vynguyen.net/wp-content/ql-cache/quicklatex.com-8d00a6a52a39552e5ed58572e9e07d32_l3.png "Rendered by QuickLaTeX.com")
So:
(3)
(4)
When the input signal is amplified into a wider range, its overall shape is less likely heavily distorted by the noise. It makes the input signal to be more tolerant against noise in communication. Reference: see slide 12-14.
