DeVry University

ECET345 Signals and Systems

Name of Student

Class Room Activity #11

*RLC Incitement and Tramp Response*

*Objective of the lab test:*

The extrinsic of this test is to testally estimate the tramp solution of an RLC circumference and assimilate it to the solution 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 give after a while +15 V and -15 V outputs

· Function generator worthy of unresisting unipolar and bipolar clear waves and sinusoids up to 5 KHz

· Oscilloscope

· Three BNC to alligator

· One PC vulgar LabVIEW 2010 or excellent and CodeWarrior 5.9

· MATLAB

· One 2.0 mm flathead screwdriver

**Theory**

The former labs entertain centreed on having a one reactive factor in a circumference to form a depurate. This lab earn centre on what happens if tnear are two opposed reactive factors in the selfselfsame circumference. An RLC circumference after a while two reactive factors (an L and a C) is shown adown. Using the notice gained formerly, the translate administration can abundantly be institute.

Note that all of the factors are conjoined in train and the voltage over the resistor is our output.

Using the voltage divider administration near gives the aftercited conformity:

Now depute numerical esteems of R, L, and C. Then elucidate the countenance to get the translate administration as a ratio of two sensible polynomials in *s* inclosure. Make the coefficient of the highest energy of *s* oneness in twain numerator and denominator. If compulsory, enrich the unimpaired translate administration by a firm reckon.

Now transcribe a MATLAB program that takes in the numerical esteems of R, L, and C; generates the translate administration of the arrangement; and computes its Portend frame, its pole-zero map, and the tramp solution of the arrangement. Use the MATLAB keywords *tf, portend, pzmap,* and *step* to get these results.

Note that on the pole-zero map formd by the *pzmap* direct, poles are verified after a while an *X* and zeroes are verified after a while an* O.*

You should see a Portend frame as shown adown for R = 100, L = 10 mH, and C = 0.1 µF.

Graph done by MATLAB Portend frame direct

Check the pole-zero map to see if it agrees after a while the poles and zeroes of the translate administration that was formd by careful the poles and zeroes manually.This husk of tramp solution you earn see is disclosed as a decaying sinusoid, which can simply repartee in a second-regulate (or excellent regulate) translate administration.

Compare the presumptive tramp solution generated by MATLAB to the express tramp solution estimated after a while the artful circumference.

*Procedure:*

**Step 1 **

Set up the number generator after a while the specifications adown.

V | 5 V |

Frequency | 200 Hz |

Signal Type | Square wave |

**Step 2**

Build the aftercited RLC circumference and remark the tramp solution on the oscilloscope.

The remarkd solution should seem love the aftercited:

Response of the 1Ω circumference as seen on an oscilloscope.

** **

**Step 3**

Input these esteems into MATLAB using the gifted program and remark the presumptive tramp solution.

**Step 4**

Change resistor to 1 kΩ and remark the tramp solution. Then use the MATLAB regulation to remark the presumptive tramp solution.

The remarkd solution should seem love the aftercited:

Response of the 1 kΩ circumference as seen on an oscilloscope

* *

* *

* *

**Step 5**

Change resistor to 100 Ω and remark the tramp solution. Then use the MATLAB regulation to remark the presumptive tramp solution.

The remarkd solution should seem love the aftercited:

Response of the 100 Ω circumference as seen on an oscilloscope

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** **

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**Now repartee the aftercited questions.**

1. Does the tramp solution from the express estimatement contest the presumptive flexion from MATLAB for R = 1 Ω? Note the body of the peak esteem of the tramp solution done by MATLAB and assimilate it to the peak esteem done by the testally estimated flexion. Why is the MATLAB esteem abundant excellent than the testal esteem? (Hint: The inductor is not an conceptional inductor.)

2. What is the mathematical conformity among the incitement and tramp solution of a arrangement?

3. How earn the cast of the tramp solution modify as the esteem of hindrance is increased?

4. Why is it enviable to understand an op-amp buffer to importune the RLC circumference rather than driving the circumference undeviatingly from the administration generator?

5. Why is it that we never see an oscillatory solution in an RC circumference, whose solution is frequently exponential inattentive of hindrance?

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