**ENGINEERING 11****,
2004 **

**
E****LECTRIC CIRCUIT
ANALYSIS****
**

**Transient Response of Second Order Circuits**

**Objectives**:

**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.

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

a. Replace the resistor with a short circuit.

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 V_{o} 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.

_{o} for each value of resistance (don’t
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.