ENGINEERING 11, 2004 

                                              ELECTRIC CIRCUIT ANALYSIS                                              

  LABORATORY 4

 Transient Response of Second Order Circuits

 

Objectives:

 To obtain experimental results for the transient response of second order circuits, as well as the impulse response of a first order circuit, and to compare these with analytical predictions.

 

Procedure:

††††† Part 1)Transient response of a second order RLC circuit 

a.Connect the circuit shown with a 1 volt peak-to-peak square wave with a frequency of approximately 100 Hz. Vary the frequency to obtain the best image.Suggested values for R, C, and L are as follows: R = 100 W, C = 0.01 mF, L = 112 mH.

b.  Vary R and C and qualitatively describe the changes in the output.

c.  Print the output for R = 100, 300, 1000, 3000 and 10000 W, and C = 0.01 mF.†† Record frequencies of oscillations and decay rates when appropriate.

 

††††† Part 2)Observing non-idealities in the inductor

a.Replace the resistor with a short circuit.

b.Qualitatively describe how the output varies as C is changed.

c.Print the output with C=0.01 mF.

d.    Measure the DC resistance of the inductor with an ohmmeter.Measure the inductance and resistance of the inductor with the RLC meter.

 

Report:

††††† Part 1)†† Second order circuit

a.Present the derivation of Vo for a value of resistance such that the output is underdamped, overdamped and for the case when the response is critically damped.What value of resistance is needed for critically damped response?There is no need to present the derivation for each of the five resistors used in the lab.

 b.Plot simulated response for Vo for each value of resistance (donít forget to include the internal resistance of the source, if appropriate), and compare with your printouts.Include the equation that goes along with each plot.Note which responses are over-, under- and critically-damped and how one can tell from the plots.Simulations can be done in Matlab or Multisim. 

††††† Part 2)†† Non-ideal nature of the inductor:

From the response determine the internal resistance of the inductor is and compare it to the value measured in lab.

 

††††† Also answer the following questions:

A.      What are the natural frequency and damping ratio of the following systems

i.      

ii.     

B.      Evaluate the system governed by with while varying from 0.5 to 2.  (Note: you can do this in Multisim with the circuit from  part 1) by choosing appropriate values for R, L and C.  The relationship between  and can be determined from equation 2 in the background section).Establish from the data, the peak overshoot; that is the peak amount by which the output exceeds 1, the time at which the peak occurs and an estimate of the time after which the output is always within 5% of 1.  These equations are at the end of the background section.


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