Semester Questions for Analog Electronics_1.

  1. With the help of suitable diagrams/expressions, provide the broad classification of Transistor Amplifiers.
\(2. \;\;For\; physical \;\;OPAMP,\color\red{|A_v|\;\neq\;\infty,R_i\;\neq\;0, \;and\; R_0\neq0,} Show\;that\\ \color\red{\;A_{vf}\;=\;\dfrac{-Y}{Y’-(\dfrac{1}{A_v})-(Y’+Y+Y_i)};} Where, \;symbols\; have\; their\; usual\;meaning\;\\ in\; the\; context\; of\; \; OPAMP,\; and \;the\; Y’s\; are\; the\; admittances\; corresponding \;to \;the\; Z’s.\\ \color\red{Also, A_v\;=\;\dfrac{V_0}{V_i}.}\)

3. Derive the Fourier series and find its coefficients a0,an, and bn​. Define the Dirichlet conditions.

4. Determine the energy and power of the signal \(\color\red{x(t)=cos⁑(t)}\).
5. State whether the signal \(\color\red{π‘₯(𝑑)=cos(2𝑑)+sin(2𝑑)x(t)=cos(2t)+sin(2t)}\) is periodic or not. If periodic, mention its period.
6. Discuss the combined amplitude scaling and amplitude shifting operation with suitable examples. What are the applications of convolution? Find the convolution of \(\color\red{π‘₯_1(𝑛)=\{1,2,0,1\} \;and\; π‘₯_2(𝑛)=\{2,2,1,1\}}\) and show the output by a graphical plot.
7. Find the Fourier transform of: \(\color\red{(i)\;\; π‘₯(𝑑)=𝑒^{βˆ’2𝑑}𝑒(π‘‘βˆ’1)\\ (ii) \;\;π‘₯(𝑑)=𝑑𝑒^{βˆ’3𝑑}𝑒(𝑑)\\ (iii)\;\; π‘₯(𝑑)=𝑒^{βˆ’βˆ£π‘‘βˆ£}u(t) }\) \begin{cases} \text{for } -1 \leq t < 1 \\ = 0, \text{ otherwise} \end{cases}

8. Define the following terms:

a. Static/Dynamic system

b. Causal/Non-Causal systems

c. Time Invariant/Time Variant systems

d. Linear/Non-Linear system

e. Stable/Unstable system

f. Invertibility

g. BIBO stability

h. Additivity, Homogeneity, and Linearity

9. Discuss the combined time scaling and time shifting operation with suitable examples.
10. Discuss and prove any two properties of the Fourier Transform.

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