Derive the expression for transfer function

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Reference no: EM13104226

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 (HdB(f)) of H(f).

868_Derive the expression for TRANSFER FUNCTION.png

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

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

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

2481_Derive the expression for TRANSFER FUNCTION1.png


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

1062_Derive the expression for TRANSFER FUNCTION2.png

(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 Vc(0) = -3V.
a) Write an expression for potential across the capacitor.
b) Calculate the steady state capacitor voltage after the opening of the switch.

819_Derive the expression for TRANSFER FUNCTION3.png

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

549_Derive the expression for TRANSFER FUNCTION4.png

7) Consider the analog signal, x(t) = 2 cos (100Πt + 45o)+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.

1339_Derive the expression for TRANSFER FUNCTION5.png

Reference no: EM13104226

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