Section A
Q1.
(a) Prove that the random process x(t, \phi) = (√(E))/(2T) cos(ω_0 t + \phi) is ergodic, where E, T and ω_0 are constants, and \phi is random and UDF (0, 2π).
(b) Explain the different masking steps required in the fabrication of a simple NMOS transistor starting from a p-type substrate.
(c)
A two-word instruction is stored in memory at an address designated by the symbol A. The address field of the instruction (stored at A + 1) is designated by the symbol B. The operand used during the execution of the instruction is stored at address symbolized by 'C'. An index register contains the value X. State how 'C' is calculated from the other addresses if the addressing mode of the instruction is
(i) Direct
(ii) Indirect
(iii) Relative
(iv) Indexed.
(d) A 75 \Omega resistor is connected to a transmission line of characteristic impedance of 50 \Omega. Compute the VSWR at the termination.
(e) Compute the values of K1 and K2 to obtain a peak time of 1.6 seconds and a settling time of 3.5 seconds for the closed-loop system shown below in response to a step input.
(f) The autocorrelation sequence of a discrete-time stochastic process is R(K) = 1/2)|K|. Determine its Power Spectral Density.
