Todai Entrance Exam: Subject 2010 – Problem 1

(1)

    \[ V_{T} = -Z_{F}\sum_{i=1}^{n} \frac{V_{i}}{Z_{i}} \]

    \[ V_{T} = -Z_{F}\frac{V_{1}}{Z_{1}} \]

(2)

We see that:

    \[ \frac{1}{s+\sqrt{3}} = \frac{1}{\sqrt{3}s}\frac{1}{\frac{\sqrt{3}}{3} + \frac{1}{s}} \]

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.


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