Determine an expression for the transfer function, MATLAB Programming

The circuit diagram of an active filter is shown below.

(a) Determine an expression for the transfer function of the filter.

(b) Hence find an expression for the frequency response of the filter.

(c) Calculate the ratio R1/R2 when low-frequency gain of the filter is 40 dB.

(d) Calculate R and C such that the break frequency on the Bode plot occurs at w0 = 500rad/s, (suggest commercially available values).

(e) For the values of the components obtained in parts (c) and (d) simplify the transfer function of the filter.

(f) Hence, using inverse Laplace transform, find h(t), the unit impulse response of the system.

(g) If the input to the filter is vi(t)=10e-100t find an expression for the output of the system.

(h) For the input vi(t)=1/√2 cosθ, obtain an expression for the steady-state sinusoidal response of the filter. 

1176_steady-state.png

Practical work

1.  Invoke MATLAB.

2.  The enclosed m-file is a MATLAB program that simulates the above problem.  In a new m-file type in the entire commands in the m-file

3.  Save the m-file, giving it a suitable file name.

4.  In MATLAB command window execute the program by typing its file name.

5.  If you have made no typing error(s), you should obtain a plot of the Magnitude and the Phase of the Frequency Response of the filter.

6.  Use the Bode plot for the magnitude and phase of the frequency response and measure and calculate the gain and phase for the input signal vi(t) = 1/√2 cos(500t), hence (i.e. using these measured values) write down an expression for the output of the filter.

7.  Verify that your measurements from the plots are in agreement with what you have found theoretically.  Comment with reason(s) if they do not agree.

8.  If the input to the filter is vi(t) =3 sin(2000 t), then what is an estimated expression for the output of the filter?  Write it down and explain how you came up with this answer.

Posted Date: 3/12/2013 1:05:07 AM | Location : United States







Related Discussions:- Determine an expression for the transfer function, Assignment Help, Ask Question on Determine an expression for the transfer function, Get Answer, Expert's Help, Determine an expression for the transfer function Discussions

Write discussion on Determine an expression for the transfer function
Your posts are moderated
Related Questions
Input in a for Loop: The script below repeats the process of prompting the user for a number, and echo printing the number (that means simply printing it back out). A for loop

wite a function that will take In a simplex an an associated and return the nitial feasible solution of the tableau x as a column vector as well as the objective the objective fun

Objectives In the following exercises, students are required ?rstly to implement code to determine the frequency components present in a signal, and then to extract a desired si

kind in geometric calculity in space AREA. >

The fundamental theorem of calculus states that the de?nite integral of a function may be found from the antiderivative of the function. However, for many functions, it is much eas

The game of Simpli ed Poker is a simple game by today''s standards. You start o with a standard deck of cards, shue the cards, and then give each player 3 cards. Each card has a

User-Defined Functions which return a Single Value: We have seen the use of many functions in the MATLAB. We have used many built-in functions like fix, sin, abs, double, and

Your functions will allow you to create the following graph, which contains a piecewise function where a line exists in the first interval, a parabola in the second interval, and t

Your Task: Write an M-function that computes simple returns as formula (1). Use this function to calculate the daily returns for each index. Using MATLAB build-in functions estimat

Error in variables statements: Error: The expression in the left of equals sign is not a valid target for an assignment. >>  By placing a semicolon at the end of the sta