0.2 Operational amplifiers and signal conditioning  (Page 5/5)

• Input a 30 Hz square wave into the low-pass filter. Record your observations.
• Measure the time constant from the oscilloscope screen.

Does it correlate with your calculated values based on resistor and capacitor values?

7.3 build a passive low-pass filter

The filter described in step 6.1 is an active filter, meaning it requires an external power source. Since it usesan op-amp, it must have a±12 V power supply. Active filters can have a static gain greater than one. Active filters also have lowoutput impedance, which means that they can pass up to 10 mA of current without any effects on the operation of the filter.

A passive low-pass filter does not require an external power source. A passive filter can be constructed withsimply a resistor and capacitor as shown in Figure 11.

• Build a filter using a 10 k ohm resistor and a 0.1 micro F capacitor.
• Repeat section 6.2 (steps 4-11). Record your results in your lab book. You may use Table 2 to organize your data.

Table 2: Magnitude Ratio Data for First-order Low-pass Filter (Passive)

7.4 build a second-order butterworth filter

Figure 12 below shows a second-order Butterworth low-pass filter. A second-order filter is superior to afirst-order filter in many respects, as we will investigate.

• Build the Butterworth filter circuit using R = 10 k ohm and C = 0.1 micro F.
• Perform the sine wave and square-wave input tests from step 6.2. Record your results in your lab book. You may use Table 3 toorganize your data.

How is the response of this filter different from that of the first-order filter?

Table 3: Magnitude Ratio Data for Second-Order Low-Pass Filter

Part 8: aliasing

Aliasing is a generally undesired phenomenon that results when periodic signals are sampled too slowly. Aliasingcauses high frequency periodic signals to be recorded as signals consisting of lower frequencies, as will be apparent in thefollowing steps.

8.1 non-filtered signal

You will cause a signal to be aliased as it is converted from an analog to a digital signal.

• On the block diagram, create Numeric Indicators to display Frequency and Amplitude.
• Wire the Numeric Indicators to the Tone Measurements icon for the second channel.
• Change the sample rate of the DAQ Assistant to 1000 S/sec (samples per second).
• Calculate the Nyquist Frequency for this sample rate.
• Connect the output of the Function Generator directly to the second input channel on the SCXI.
• Adjust the function generator to create a sine wave with a frequency of 50 Hz and amplitude of 1 V.
• Slowly increase the frequency of the sine wave until you reach 400 Hz. Observe what happens to the sampled version of thesine wave.
• Increase the frequency to 500 Hz. What is the measured frequency and amplitude?
• Why doesn’t LabVIEW display a“true”image of the wave form?
• Continue to increase the frequency of the sine wave to 1000 Hz.
• Describe what happens to the amplitude and the frequency of the sampled signal as the frequency increases.
• Why is the frequency displayed in LabVIEW different from the frequency supplied by the function generator? How are the twofrequencies related?

8.2 anti-aliasing filter

Low pass filters are frequently employed to minimize the portion of a signal that is aliased.

• Input the signal from the function generator to the second-order Butterworth filter from Section 6.2.
• Connect the output of the filter to channel 2 of the SCXI.
• Set the sample rate to 1 kS/sec (as before).
• When used in this way, the filter is called an anti-aliasing filter. Comment on what you observe. How are your observationsdifferent from those in step 10 without the filter?

Bonus

Estimate the damping ratio of the second-order Butterworth filter through experimentation. To do this, you willprobably need to take more measurements near the expected cut-off frequency of the filter (which is near the natural frequency).Support your result with plots and discussion as necessary.

Lab report

For this lab, you will write up the Introduction and Objective sections of a full formal report. Youwill be provided handouts with further instruction regarding what is expected.