(a) A Butterworth filter is represented in s-domain circuit as shown in Figure Q. 2 (a)....
Q.2 (a) Given a series RL circuit as shown in Figure Q.2(a). 1092 vit) 20mF V.(t) Figure 2.2(a) (i) V.(s) Determine the transfer function, Vi(s) (4 marks) Sketch the magnitude and phase Bode plots for the above transfer function. (4 marks) (iii) Determine the filter type. (2 marks) (b) For a low pass filter application, following signal is channeled through a Butterworth filter; x(t) = 2 sin ( 10Tt - (10nt -) + 3cos (50nt -) + Ssin (100nt +...
Problem 3 (LSM3) (20 pts) Consider a Butterworth filter of order one with a cutoff frequency of we [rad/sec]. (a) Determine the transfer function H(s) of the Butterworth filter so that it is causal and stable (b) Determine the output of the filter in response to the input 1 + cos
Problem 3 (LSM3) (20 pts) Consider a Butterworth filter of order one with a cutoff frequency of we [rad/sec]. (a) Determine the transfer function H(s) of the Butterworth filter...
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c 0.6TT a) b) c) Evaluate the transfer function of the analog filter (10marks) Skecth the block diagram of transfer function (5 marks) Plot the magnitude response of the filters. (5marks)
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c...
Q.6 (a) (4 pts) A Butterworth filter has been designed with 22. = 0.578 and N=3. Draw the locations of the poles of its magnitude squared function H(s)H(-s). (b) (2 pts) What is value of H.(192) at cutoff frequency 2. for a butterworth filter. (c) (3 pts) From the magnitude squared function in part (a) above, find an expression for H(s), the transfer function of the required analog filter. (d) (2 pts) Give the number of poles for the Chebyshev...
53. A 2- order normalized Butterworth filter can be improved by using a so-called Chebeyshev filter The 3dBNLP second order NLP Chebeyshev transfer function is: 0.5012 2 +0.6449s+0.7079 Cheb3dBNLP(s) The Chebeyshev filter has some ripple in the passband but has better roll off, more attenuation in the stop band. If one can tolerate some ripple (sort of like a bouncy car ride) in the passband Chebeyshev filters typically have lower order than Butterworth filters. But, Butterworth filters have NO ripple...
1. Derive the transfer function for the low pass filter shown in Figure 1. The general form is: H(s) w? W. s2 + +w? 2. Determine the component values by equating the derived transfer function to the general transfer function to meet the following specifications: a) fc = 2 kHz, and Q = 0.7071 for a Butterworth response. HH Vi R R C2 HHI Figure 1. Low-Pass Filter
Consider the filter shown in Figure P1 a) Show that the circuit behaves as a band-pass fiter. (Hint: Find the transfer for this circuit and show that it has the same form as the transfer function for a band-pass filter.) b) Find the center frequency, bandwidth and gain for this band-pass filter c) Find the cutoff frequencies and the quality factor for this band-pass filter. 10 u.F 5 k2 50mF 16 400 (2 Figure P1
Explain your process please
1. Design 6th order Butterworth band-pass filter with cut-off frequency is 4KHz and 7KHz and pass- band gain is 20dB Draw the circuit, write the transfer function of the filter, and sketch a frequency spectrum of the filter and show the cutoff frequencies on the spectrum Solution:
Figure 2 shows the circuit of a filter, whose half-power frequency (break frequency) is defined as 1 1 -j 27T fC 27TRC + + Vin V out Figure 2 Find the circuit transfer function, H() (i) [2] Given C 2uF, R= , draw the asymptotic Bode magnitude and phase plots for the (ii) circuit [7]
Figure 2 shows the circuit of a filter, whose half-power frequency (break frequency) is defined as 1 1 -j 27T fC 27TRC + + Vin...
1.
a. Design a bandstop filter with a cutoff
frequency of -3dB at w1 = 20 rad/s and w2 = 100 rad/s
b. Confirm by plotting the magnitude &
phase of the transfer function.
2. Design a 5th order low pass butterworth
filter with wc = 1 rad/s.
Use this equation for both problems.
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