## Question

###### Question 1 (35 marks) (a) You are given a black box circuit where the input and...

Question 1 (35 marks) (a) You are given a black box circuit where the input and output voltages are denoted Vin(t) and Vour(t) respectively. You have knowledge of its transfer function H(s), given by: al Vout(t) Vint) (200s) (s + 200)(s + 10)3(s + 200) (1) Using the semi-log graph paper provided in this examination paper (see pages 8-9), sketch the magnitude plot of the frequency response of the circuit. (15 marks) (ii) From your results in (1), what function does this circuit provide? (2 mark) (iii) Determine three frequency domain design parameters that characterises this circuit. (6 marks)

## Answers

iii) the center frequency is

Wo= sqrt(10*200) = 44.7214 rad/ sec

The upper and lower cut off frequencies are 20 and 98 rad/sec

- o Sal? H(s) = 2005 (5+200)*Cs +10°cs+200) The magnitude of His) is given by 1H (5w) l= 2o los r 2003 w3 de . Ljur 200 MJ wt 10 %] The Corner frequencies are w= 10, 200 lad seconds The Slope to a pole is = 20 del dec. The slope for a zero is t2o de Idec. wl lio Asymptotic | H(SW) | |-60.11-9 Actual 2001 - plot plot -9. 91 Actual i ca.15 melden - + 9. 1 odol dec I -60 dBl dec. H(SW) dB / +60 3/+60 doldec. -601 * | (:) 10 200 300 The Circuit is a simple Bond poss dilter with Lower Cut off pequency of w= 10 eodlec and the upper Cut-off frequeny of w=200 sedlec

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