1 for the circuit below given r1100omega

Question

1) For the circuit below, given R₁=100Ω, R₂=100Ω and L=5μH.
a) Derive the expression for TRANSFER FUNCTION (H(f)).

b) Write the expression for magnitude and phase of H(f).

c) Write the expression for decibel magnitude (H_dB(f)) of H(f).

2) The Transfer Function (H(f)) of a filter is shown in the figure below. For the input signal :

v_in(t)=3 + 5 cos (8000Πt + 10^o) - 6 cos (5000Πt)

find the expression for the output signal (in time domain).

3) Consider the digital filter equation : y(n)=0.95y(n-1)+0.05x(n)

Calculate the first 3 terms of the response (y(n)), for the input

(the filter is reset, y(n)=0 n<0)

4) a) Convert the following binary number to decimal: 101.011
b) Convert the following decimal number to binary: 21.14

5) For the circuit below, at t=0, the switch is opened and V_c(0) = -3V.
a) Write an expression for potential across the capacitor.
b) Calculate the steady state capacitor voltage after the opening of the switch.

6) For the circuit below, calculate the equivalent resistance (Rab) between terminals a and b.

7) Consider the analog signal, x(t) = 2 cos (100Πt + 45^o)+3 sin (60Πt) as an input to a AD converter;

a) What is the minimum sampling frequency for x(t)?

b) If this AD converter has 42 levels of quantization, how many bits are required for coding?

8) For the circuit below, calculate the current values (i₁,i₂) and potential v.