# Ecet345 signals and systems class class room activity #11 rlc

DeVry University

ECET345 Signals and Systems

Name of Student

Class Room Activity #11

RLC Impulse and Step Response

Objective of the lab experiment:

The objective of this experiment is to experimentally measure the step response of an RLC circuit and compare it to the response predicted using MATLAB.

Equipment list:

·         One LM741 op amp

·         One 1 resistor

·         One 100 resistor

·         One 1 k resistor

·         One 0.1 µF capacitor

·         One 10 mH inductor

·         One1 NI Elvis II board

·         Power supply with +15 V and -15 V outputs

·         Function generator capable of producing unipolar and bipolar square waves and sinusoids up to 5 KHz

·         Oscilloscope

·         Three BNC to alligator

·         One PC running LabVIEW 2010 or higher and CodeWarrior 5.9

·         MATLAB

·         One 2.0 mm flathead screwdriver

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.

Now write a MATLAB program that takes in the numerical values of R, L, and C; generates the transfer function of the system; and computes its Bode plot, its pole-zero map, and the step response of the system. Use the MATLAB keywords tf, bode, pzmap, and step to get these results.

Note that on the pole-zero map created by the pzmap command, poles are identified with an X and zeroes are identified with an O.

You should see a Bode plot as shown below for R = 100, L = 10 mH, and C = 0.1 µF.

Graph produced by MATLAB Bode plot command

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.This kind of step response you will see is known as a decaying sinusoid, which can only appear in a second-order (or higher order) transfer function.

Compare the theoretical step response generated by MATLAB to the actual step response measured with the constructed circuit.

Procedure:

Step 1

Set up the frequency generator with the specifications below.

 VPP 5 V Frequency 200 Hz Signal Type Square wave

Step 2

Build the following RLC circuit and observe the step response on the oscilloscope.

The observed response should look like the following:

Response of the 1 circuit as seen on an oscilloscope.

Step 3

Input these values into MATLAB using the supplied program and observe the theoretical step response.

Step 4

Change resistor to 1 kΩ and observe the step response. Then use the MATLAB code to observe the theoretical step response.

The observed response should look like the following:

Response of the 1 k circuit as seen on an oscilloscope

Step 5

Change resistor to 100 Ω and observe the step response. Then use the MATLAB code to observe the theoretical step response.

The observed response should look like the following:

Response of the 100 circuit as seen on an oscilloscope

1.       Does the step response from the actual measurement match the theoretical curve from MATLAB for R = 1 ? Note the magnitude of the peak value of the step response produced by MATLAB and compare it to the peak value produced by the experimentally measured curve. Why is the MATLAB value much higher than the experimental value? (Hint: The inductor is not an ideal inductor.)

2.       What is the mathematical relationship between the impulse and step response of a system?

3.       How will the shape of the step response change as the value of resistance is increased?

4.       Why is it desirable to include an op-amp buffer to drive the RLC circuit rather than driving the circuit directly from the function generator?

5.       Why is it that we never see an oscillatory response in an RC circuit, whose response is always exponential regardless of resistance?

Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.