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(i) Simplify the logical expression f = ABC + B \overline{C} D + \overline{A} BC by using Karnaugh map and realise f using NAND gates only. \hfill 10 (ii) The transistor in the following circuit has \beta = 100 and V_A = 90\text{ V}. What value of R_B will give 0 volt d.c. output \hfill 10
What are Brillouin zones ? How are they related to the energy levels of an electron in a metal ? Draw the Brillouin zone for a rectangular lattice of sides \pi and 2\pi. Also compute the energy at the corner and midpoints of the adjacent sides of the first Brillouin zone.
Discuss the motion of an electron in one-dimensional periodic potential and show that it leads to formation of bands of allowed and forbidden states in the electron energy spectrum. How are the insulators, semi-conductors and conductors discriminated on the basis of band structure ?
Define (i) input bias current, (ii) input offset current, (iii) input offset voltage, (iv) output offset voltage, (v) power supply rejection ratio and (vi) slew rate for an OPAMP.
Draw the logic circuit for the following Boolean expression : Y = \overline{A + B} + \overline{C} What are the 'Y' values for the input combinations : (1) 1, 1, 0; (2) 1, 0, 1; (3) 0, 0, 1 ? (ii)
Define \alpha and \beta parameters of a transistor. A germanium transistor with \beta = 45 is biased as shown above. Calculate the value of R_b.
\questiondiagram{} An In As semiconductor sample is cut in the form of a small bar of size 1 \cdot 0 \text{ cm} \times 1 \cdot 0 \text{ cm} \times 2 \cdot 0 \text{ mm}. Its lengthwise resistance is 1 \cdot 25 \ \Omega. A Hall field of 1 \cdot 7 \text{ V/m} develops when a current of 0 \cdot 12 \text{ A} is passed lengthwise and a magnetic field of 0 \cdot 05 \text{ T} is applied normal to its length as shown above. Calculate the carrier density. (iii) Determines the reciprocal lattice vectors of an fcc lattice.
\questiondiagram{} Discuss the functioning of the above oscillator circuit. Obtain the condition for maintenance of oscillations and the expression for the frequency assuming that the resistances of the inductors are negligible.
(i) Discuss briefly the concept of effective mass in semiconductors and explain the significance of negative effective mass. (ii) In isolated atoms, the electrons have discrete and definite energies but in solids they have bands of energies. Explain why. (iii) A proton, deuteron and \alpha-particle accelerated through the same potential difference, on entering a region of uniform magnetic field applied normal to their plane of motion, move in circular orbits. Compare the radii of the orbits described by them.
Give the two forms of the De Morgan's theorem.
Show that the condition of periodicity of lattice leads to the Bloch theorem. What is a Bloch function ?
What is the principle used in 'half-adder' ? Give the truth table for it.
(i) The following information is included on the data sheet for an N-channel JFET : I_{DSS} = 20\text{ mA}, V_p = -8\text{V} and g_{mo} = 5000\text{ }\mu\text{s} Determine the value of drain current and trans-conductance at V_{GS} = -4\text{ V}.
Draw a circuit diagram of an R-C phase shift oscillator. Explain its working. Derive an expression for its frequency.
A transistor with \beta = 50, V_{BE} = 0.7\text{ V}, V_{CC} = 22.5\text{ V} and R_c = 5.6\text{ k}\Omega is used in biasing circuit as shown in the figure. It is designed to establish the quiescent potential at V_{CE} = 12\text{ V}, I_C = 1.5\text{ mA} and stability factor S \le 3. Find the values of resistors R_E, R_1 and R_2, where symbols have their usual meanings.
In the following circuit, Show that the stability factor, S, is given by
S = \frac{1 + \beta}{1 + \frac{\beta R_e}{R_e + R_b}} Where R_b = \frac{R_1 R_2}{R_1 + R_2}
(i) What are high T_c superconductors ? Give two examples indicating their transition temperatures. Differentiate between the conventional and high T_c super conductors. (ii) Explain the principle of feedback in an amplifier. What are the advantages & negate feedback?
What is a Josephson junction ? Discuss dc and ac Josephson effects and obtain the relation. V = \frac{2eV}{h} where the symbols have their usual meaning.
Derive the various current components in a p-n-p transistor when it is actively biased. Using Ebers-Moll model, show that for the common-emitter configuration I_C = -\alpha I_E - I_{CO} \left(E^{V_C/V_T} - 1\right) where the symbols have the usual meaning.
Explain the operation of the following circuit is a gate. Draw the truth table and find the operation carried out by this gate neglecting the source impedance.
junction saturation voltages and diode voltages in forward direction. Find the minimum value of h_{fe}.
Calculate the gain of the following amplifier circuit :
Given that g_m = 10\text{ mV/A}, r_d = 1\ \Omega and Z_L = 10\text{ k}\Omega.