GATE EC 2001

Applying KCL,
\begin{aligned} \frac{e_{0}-12}{4}+\frac{e_{0}}{4}+\frac{e_{0}}{4}&=0 \\ \Rightarrow \quad 3 e_{0}&=12 \\ \therefore \quad e_{0}&=4 \mathrm{V} \end{aligned}

\begin{aligned} Z_{\Delta} &=3 Z_{Y} \\ \Rightarrow \quad \sqrt{3} Z_{\Delta} &=3 Z_{Y} \\ Z_{Y} &=\frac{Z_{\Delta}}{\sqrt{3}} \end{aligned}

Impulse response of system is L^{-1}[H(s)]
\frac{1}{s^{2}(s-2)}=\frac{1}{s^{2}} \times \frac{1}{s-2}=\left(t * e^{+2 t}\right) u(t)

\left[\begin{array}{cc} y_{1}+y_{3} & -y_{3} \\ -y_{3} & y_{2}+y_{3} \end{array}\right]=\left[\begin{array}{cc} y_{11} & y_{12} \\ y_{21} & y_{22} \end{array}\right]
y_{12}=-y_{3}

y_{12}=-\frac{1}{20}=-0.05 \mathrm{mho}

\begin{aligned} h(n)&=u(n) \\ H(z)&=\sum_{n=0}^{\infty} 1 . z^{-n} \end{aligned}
For the convergence of H(z)
\sum_{n=0}^{n}\left(z^{-1}\right)^{n}\lt \infty
\therefore ROC is the range of values of z for which
\left|z^{-1}\right| \lt 1\text{ or } |z|\gt |1|

h_{f e}=g_{m} \cdot r_{\pi}

Voltage controlled capacitor.

At the edge of saturation i.e. when drain to source voltage reaches V_{D_{sat}} the inversion layer charge at the drain end becomes zero (ideally). The channel is said to be pinched off at the drain end. If the drain to source voltage V_{DS} is increased even further beyond the saturation edge so that V_{DS} \gt V_{D_{sat}}, an even larger portion of the channel becomes pinched off and effective channel length is reduced.

\begin{aligned} 17 &=010001 \\ -17 &=101111(2 \text { 's complement }) \end{aligned}