Introduction The lab introduces the “Butterworth” second order low-pass active filter design. A sine wave will be produced by a signal generator and filtered through the circuit. The frequencies tested will range from 100 Hz to 1 kHz incremented by 100 Hz and 1 kHz to 10 kHz incremented by 1 kHz. The frequency calculations will be verified by MATLAB. The circuit will then be built virtually in the Pspice/OrCad software environment. Next, the circuit will be built on a solder less breadboard. The filter is tested and measured using a function generator, power supply, and oscilloscope.

All of the results will be compiled and recorded on a table and then plotted onto a graph using Matlab. Finally, myDAQ will be used to measure the frequency response.

Results and Discussions The “Butterworth” filter is designed to pass all frequencies below its cutoff range. This particular design maintains unity or has 0 dB maximum voltage gain below the cutoff range. The attenuation is -12 dB/octave or -40 dB/decade. As the frequency approaches the 3 dB cutoff range the frequency phase will begin to slightly increase negatively or lag behind the initial sine wave and the voltage will drop by scale discussed above.

First, a Matlab code is used to predict the values of the 3dB cutoff frequency and the voltage gain in decibels of the active low-pass filter for the frequencies discussed in the introduction.

The Matlab code calculates the gain in decibels and the phase shift in degrees. It also produces a plot of the data to predict the cutoff frequency. This will also be used later in the text to complete the graphing portion of the report.

Your critical frequency is:

478.8917

Your continuous-time frequency response for 100 Magnitude (dB) -0.0007 Phase (degrees) -16.9968

Your discrete-time frequency response for 100 Magnitude (dB) -0.0007 Phase (degrees) -16.9969

Your continuous-time frequency response for 400 Magnitude (dB) -1.6400 Phase (degrees) -75.5037

Your discrete-time frequency response for 400 Magnitude (dB) 1.0287 Phase (degrees) -75.5078

Your continuous-time frequency response for 500 Magnitude (dB) -3.313 Phase (degrees) -93.5272

Your discrete-time frequency response for 500 Magnitude (dB) -3.3145 Phase (degrees) -93.5339

Your continuous-time frequency response for 1000 Magnitude (dB) -12.9751------ -12dB/octave from 500 Hz Phase (degrees) -138.9779------steep decline from 500 Hz

Your discrete-time frequency response for 1000 Magnitude (dB) -12.9805 Phase (degrees) -138.9928

Your continuous-time frequency response for 5000 Magnitude (dB) -40.7481------ -40dB/decade from 500 Hz Phase (degrees) -172.2929------gradual decline from 1 kHz

Your discrete-time frequency response for 5000 Magnitude (dB) -40.8912 Phase (degrees) -172.3566

Your continuous-time frequency response for 10000 Magnitude (dB) -52.7901----- -12dB/octave from 5 kHz Phase (degrees) -176.1556----2.8 degree climb from 5 kHz

Your discrete-time frequency response for 10000 Magnitude (dB) -53.3728 Phase (degrees) -176.2826

Figure 1 Matlab Sample of Results

Next, the circuit will be simulated virtually in the Pspice/OrCad software environment.

Figure 2 Pspice Circuit

Here is the magnitude of the voltage in dB vs. the frequency range in Hz.

Figure 3 Pspice Simulation (3dB cutoff)

Here is the phase of the voltage vs. the frequency range in Hz.

Figure 4 Pspice Simulation (3dB cutoff)

Next, the circuit is built on the breadboard and the oscilloscope is used to visualize the results.

Figure 1 Oscilloscope Measurement of Breadboard Circuit

This table compares all the values calculated in the lab experiment.

Table 1 Comparison of Values

Frequency (Hz)

Theoretical (dB) (MATLAB)

Simulated (dB) (PSpice)

Measured (dB) (Oscilloscope)

100 -0.0007 0 +(.0007) -0.30 -(.2993) 200 -0.1006 -0.25 + (.15) -1.04 -(.9394) 300 -0.5626 -0.65 +(.0874) -1.5 -(.9374) 400 -1.6400 -1.60 + (.04) -3.08 -(1.44) 500 -3.3137 -3.40 -(.0863) -4.00 -(.6863) 600 -5.3164 -5.60 -(.2836) -5.03 +(.2864) 700 -7.3875 -7.60 -(.2125) -6.88 +(.5075) 800 -9.3832 -9.70 -(.3168) -10.3 -(.9168) 900 -11.2493 -11.80 -(.5507) -12.04 -(.7907) 1000 -12.9751 -13.00 -(.0249) -12.32 +(.6551)

2000 -24.8360 -22.00 +(2.836) -23.106 +(1.73) 3000 -31.8738 -32.00 -(.1262) -33.435 -

(1.5612) 4000 -36.8713 -36.00 +(.8713) -34.84 +(2.03) 5000 -40.7481 -41.00 -(.2519) -41.17 -(.4219) 6000 -43.9156 -44.00 -(.0844) -41.2

+(2.716) 7000 -46.5937 -47.00 - (.4063) -46.48

+(.1137) 8000 -48.9135 -49.00 -(.0865) -48.87

+(.0435) 9000 -50.9598 -51.00 -(.0402) -50.54

+(.4198) 10000 -52.7901 -53.00 -(.2099) -50.7 +(2.09)

Figure 2 Bode Plot and Scaled Bode Plot

The oscilloscope is used to measure the input sine wave (yellow) against the filtered output signal (blue). Notice that it starts to lag behind and is scaled down.

Figure 3 Original Input vs Filtered Input

Figure 4 Labview Frequency Response

Summary and Conclusions The results are conclusive that the filter works properly.

References Author, A. A. (Year of publication). Title of work: Capital letter also for subtitle. Location: Publisher.