ECE homework

ECE 2054 Homework 9 Submit your work as a pdf to Canvas. Filename should be HW9_yourPID.pdf. Make sure your work is neat and legible; if I can’t read it or understand it, it will be marked wrong. Please box all your answers. Problem #1 For the high pass filter transfer function H(f) = Vout/Vin (where frequency is in Hz) given by

   21000/1

)1000/(3

f

f fH

    



  

 

1000 arctan90

f fH

find an expression for vout(t) as a function of time with an input signal that can be broken into frequency components given by: vin(t) = 1 + 2cos(1000πt + 30

o) + 5cos(2000πt – 30o) + 4cos(15000πt) Problem #2 You have input voltage signal to a circuit and you measure both the input and output voltage functions with an oscilloscope. The input voltage has a peak-to-peak amplitude of 4V and a period of 4ms, with the first positive peak at 1ms. The output voltage has a peak-to-peak amplitude of 12V, a period of 4ms, and the first positive peak at 1.5ms.

a. Find the frequency of the signals b. Find the gain of the transfer function of the circuit c. Find the phase shift of the transfer function of the circuit (Hint: recall that -(td/T) x 360o) d. Write and expression for the transfer function in terms of a phasor.

Problem #3 You are designing a first order low pass filter with a simple RC circuit that will reduce 50kHz frequencies by 46 dB, as shown below:

Recall that

   21

1

B ff

fH 



   

   

 

B f

f fH arctan

a. What is the linear factor will a 50 kHz frequency attenuated? b. What is the half power frequency of the filter? c. By what linear factor would a 2 kHz signal be attenuated?

d. By how many decibels is a 2 kHz signal lowered? e. What is the phase shift of a 2 kHz signal? f. If you pick a capacitor value of 22nF for this filter, what will the value of the resistance R be?

Problem #4 Find the following:

a. A frequency that is 2 octaves higher than 4 kHz. b. A frequency that is 1 octave lower than 4 kHz. c. A frequency that is 2 decades higher than 4 kHz. d. A frequency that is 3 decades lower than 4 kHz.

Problem #5 For the circuit shown, find the following:

a. The resonant frequency, fo, of the circuit in Hz b. The quality factor Qs of the series resonant circuit c. The bandwidth of the circuit in Hz d. The half-power frequencies fH and fL of the circuit in Hz e. If Vs has a phase angle of 0

o, find the phasor for the current Is in the circuit at the resonant frequency in Hz.

f. Find the phasor voltages across C1, L1, and R1 at the resonant frequency. g. If we take Vout to be the voltage across R1, what type of filter does this circuit function as?

Problem #6 If you have an RLC parallel circuit with a resonant frequency fo = 5MHz, a bandwidth B = 100 kHz, and a maximum impedance Zmax = 25 kΩ, find the values for R, L, and C in terms of ohms, Henries, and Farads.