Electronic Signal: draw a labelled phasor diagram for a capacitive low-pass first-order filter. Include in your diagram the angle labelled α which represents the magnitude of the phase difference between output voltage and input voltage.

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Electronic Signal

Question 5 (4 marks)

a. Draw a labelled phasor diagram for a capacitive low-pass first-order filter. Include in your diagram the
angle labelled α which represents the magnitude of the phase difference between output voltage and
input voltage.(2 marks)

b. Using your diagram, show that gain G = cos α.
(1 mark)

c. What is the gain when magnitude of the phase difference between output and input is 60 degrees?
(1 mark)

Question 6 (4 marks)

The equation in Question 5(b) for the relationship of gain G to phase angle α for a low-pass filter allows the
variation of phase angle with frequency to be deduced directly from the behaviour of gain with frequency.
Note: neither question 6(a) nor 6(b) requires significant calculation.

a. For a low-pass filter, describe how the phase difference between output and input varies as frequency
falls towards zero.
(2 marks)

b. For a low-pass filter, describe how the phase difference between output and input varies as frequency
increases.
(2 marks)

Question 7 (4 marks)

a. Express (5 – 7j)j in the form a + bj.(1 mark)

b. Express the following complex fraction in the form a + bj.(1 mark)

c. What is the value of r when 5 – 7j is expressed in polar coordinates? Give your answer to 3 significant
figures.(1 mark)

d. What is the value of θ when 5 – 7j is expressed in polar coordinates? Give your answer to 3 significant
figures.(1 mark)