Theory

The previous labs have focused on having a single reactive component in a circuit to create a filter. This lab will focus on what happens if there are two different reactive components in the same circuit. An RLC circuit with two reactive components (an L and a C) is shown below. Using the knowledge gained previously, the transfer function can easily be found.

Note that all of the components are connected in series and the voltage across the resistor is our output.

Using the voltage divider rule here gives the following relationship:

Now substitute numerical values of R, L, and C. Then simplify the expression to get the transfer function as a ratio of two rational polynomials in s domain. Make the coefficient of the highest power of s unity in both numerator and denominator. If necessary, multiply the whole transfer function by a constant number.

Procedure

1) Write a MATLAB program that takes in the numerical values of R, L, and C; generates the transfer function of the system; and

2) computes its Bode plot,

3) its pole-zero map, and

4) the step response of the system.

5) Check the pole-zero map to see if it agrees with the poles and zeroes of the transfer function that was created by calculating the poles and zeroes manually.

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