ELEC 242 Lab

Experiment 6.2

Second Order Systems

Equipment

Components

Part 1: Step Response



Step 1:

 Get an inductor from the cart. With the DMM, measure its resistance.

Step 2:

 Wire the following circuit (this is just the previous circuit with the resistor replaced by an inductor).
\includegraphics[scale=0.650000]{ckt7.3.ps}

Because of the output resistance of the function generator ($R_S$ ) and the internal resistance of the inductor ($R_1$ ) the circuit actually looks like this:

\includegraphics[scale=0.500000]{ckt7.1.ps}


Step 3:

 Set the function generator to produce a 50 Hz, 2 V p-p square wave. Sketch the output waveform, $v_{out}$ .

Step 4:

 We can eliminate the tedium of sketching waveforms by using Labview to capture and print them.

Step 5:

 Disconnect the function generator from the circuit.

Step 6:

 Reconnect the DAQ card inputs and outputs as follows: connect D/A output 1 and A/D input 4 (pins 52 and 46 on the interface board socket strip) to $v_{in}$ and connect A/D input 5 (pin 47) to $v_{out}$ .

Step 7:

 Load the "Step Response" program from the Start menu by following the path Programs -> ELEC 242 -> Step Response.

Step 8:

 Set the Duration to 0.02 sec and the Amplitude to 0.5 V.

Step 9:

 Run the program by pressing the Run button or CTRL-R.

Step 10:

 Print a copy of the step response and put it in your lab notebook.

Step 11:

 Estimate the damped natural frequency ($\omega_d$ ): Count out several cycles of the oscillation (say 10). Measure the length of time taken by this interval. Divide the number of cycles by the total time to get the frequency in Hz. Multiply by $2\pi$ to get $\omega_d$ in radians/sec.

Step 12:

 Estimate the damping coefficient ($\alpha$ ) by finding the time constant of the envelope formed by successive positive peaks of the oscillations.

Question 3:

 Using the values of R, L, and C for your circuit, find the coefficients of the characteristic equation. From these determine the expected values of $\alpha$ and $\omega_d$ . How do these compare with the values you measured?

Part 2: Frequency Response



Step 1:

 Reload the "Frequency Response" Labview program. Set Flo to 200 Hz, Fhi to 2000 Hz, and Amplitude to 0.1 V.

Step 2:

 Run the program and print a copy of the output for your lab notebook.

Step 3:

 Because the peak in the frequency response is so narrow, the small number of frequency samples taken in the previous measurement do not accurately measure its height. Estimate the frequency of the peak from the previous plot. Set Flo to be 100 Hz less and Fhi to be 100 Hz more than your estimated frequency. Run the frequency response program again.

If the peak isn't centered in the display (or if you missed it entirely), choose new frequency limits and try again. When you get a good plot, print a copy for your notebook.

Step 4:

 From this plot, measure the maximum value of the gain and the frequency $f_0$ at which it occurs. Also measure the 3 dB bandwidth, the difference in frequency between the two points on the curve where the gain is 3 dB below its peak value.