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 Ω resistor

· One 100 Ω resistor

· One 1 kΩ 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.

V |
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 1Ω 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 kΩ 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 Ω circuit as seen on an oscilloscope

** **

** **

** **

** **

**Now answer the following questions.**

1. Does the step response from the actual measurement match the theoretical curve from MATLAB for R = 1 Ω? 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?

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

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

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

Assignment Help has assembled a team of highly skilled writers with diverse experience in the online writing circles. Our aim is to become a one stop shop for all your Academic/ online writing. Check out below our amazing service!

Essays

At Assignment Help, we prioritize on all aspects that creates a good grade such as impeccable grammar, proper structure, zero-plagiarism, and conformance to guidelines. The principal purpose of essay writing is to present the author's evaluation concerning a singular subject about which they have made. Since Professionalism is the mother of every success, try our team of experienced writers in helping you complete your essays and other assignments.

Admissions

Admission Papers

You have been trying to join that prestigious institution you long yearned for, but the hurdle of an admission essay has become a stumbling block. We have your back, with our proven team that has gained invaluable experience over time, your chance of joining that institution is now! Just let us work on that essay.How do you write an admission essay? How do you begin the essay? For answers, try Quality Custom Writers Now!

Editing

Editing and Proofreading

Regardless of whether you're pleased with your composing abilities, it's never an impractical notion to have a second eye go through your work. The best editing services leaves no mistake untouched. We recognize the stuff needed to polish up a writing; as a component of our editing and proofreading, we'll change and refine your write up to guarantee it's amazing, and blunder free. Our group of expert editors will examine your work, giving an impeccable touch of English while ensuring your punctuation and sentence structures are top-notch.

Coursework

Technical papers

We pride ourselves in having a team of clinical writers. The stringent and rigorous vetting process ensures that only the best persons for job. We hire qualified PhD and MA writers only. We equally offer our team of writers bonuses and incentives to motivate their working spirit in terms of delivering original, unique, and informative content. They are our resources drawn from diverse fields. Therefore your technical paper is in the right hands. Every paper is assessed and only the writers with the technical know-how in that field get to work on it.

Coursework

College Essay Writing

If all along you have been looking for a trustworthy college essay service provider that provides superb academic papers at reasonable prices, then be glad that you search has ended with us. We are your best choice! Get high-quality college essay writing from our magnificent team of knowledgeable and dedicated writers right now!

Coursework

Quality Assignment/Homework Help

We give the students premium quality assignments, without alarming them with plagiarism and referencing issues. We ensure that the assignments stick to the rules given by the tutors. We are specific about the deadlines you give us. We assure you that you will get your papers well in advance, knowing that you will review and return it if there are any changes, which should be incorporated.