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EE 210 Lab Exercise #10: RC Filters

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EE 210 Lab Exercise #10: RC Filters EE 210 Lab Exercise #10: RC Filters EE210 crate, 0.01uF capacitor, ITEMS REQUIRED Breadboard Submit questions and plots at the ASSIGNMENT beginning of the next lab period Introduction An electronic filter is basically a circuit that only lets a specified range of frequencies “pass” to the output, while blocking all of the other undesired frequencies. Typically the signal to be blocked is considered “noise”, or an unwanted signal interfering with the desired signal. This undesired signal doesn’t have to be “noise” per say, it can also be any another signals that are combined with the desired signal, as in the case of communication systems. A filter can be considered a two-port network as shown below: Iin Iout + + Vin Filter Vout - - output The transfer function of the network is defined as H = , where the inputs and outputs may input be either voltage or current. The range of frequencies that a filter will pass is the “pass-band”, and the range of frequencies that the filter will reject is the “stop-band”. The cut-off frequency is defined as the frequency at which the transition between the pass-band and stop-band occurs. The four basic types of ideal filters are shown below in Figure 1. As will be seen in the exercise, a practical filter will not have the sharp transitions between the pass-band and stop-band. Figure 1: Transfer functions of 4 ideal filters 1 Passive RC Filters Passive RC filters are the most basic type of electric filter, consisting of a single resistor and capacitor in series as shown in Figure 2. Notice the similarity between the transfer function expressions of the filters and those of the voltage divider circuit studied in Lab #3. Note that the cut-off frequency for a non-ideal filter is not well defined like the ideal filter. For this case, the cut-off frequency is generally chosen to satisfy: Hmax Hj()ωc ==0 . 707 Hmax 2 Figure 2: Passive RC Filters 1 Z jCω Z R Hj()ω = C = Hj()ω = R = ZZ+ 1 ZZ+ 1 cR + R cR + R jCω jCω 1 jRCω = = 1+ jRCω 1+ jRCω 11 ω =→=f ccRC 2πRC 2 Examining the Frequency Response a Filter using AC Sweep Procedure: 1. Using C=0.01uF, create a passive low-pass circuit in PSpice with fc ≈4kHz. Use the part labeled VAC in the SOURCE library as the input and set Vac=3V. 2. Create a new simulation profile. Under the Analysis tab, set the Analysis type to AC Sweep/Noise. Enable a logarithmic plot, set the Start Freq. to 10Hz, the End Freq. to 1MHz (use Meg), and the Total points to 200. This will generate a frequency response plot for the circuit. 3. Simulate the circuit. Plot the magnitude response of the output voltage and label the cut- off frequency on the plot with a marker. Print the magnitude response plot. 4. Add a plot to the window to view the phase response of the output. Add a trace to the new plot and select “P( )” from the functions menu to the right of the window. Insert the output voltage between the parentheses of “P( )” trace expression and click OK. Print the phase response plot. 5. Construct the circuit on your breadboard and monitor the input and output of the circuit using the oscilloscope. 6. Vary the input frequency using the waveform generator from 10Hz to 1MHz. Record the experimental magnitude and phase of the output voltage as a function of frequency on the PSpice plots created earlier at the following frequencies in Hertz: 10, 31.6, 100, 316, 1k, 3.16k, 10k, 31.6k, 100k, 316k, 1M. To make it easer to plot, the 3.16 x 10N values are approximately the midpoints between the 10N values on the logarithmic plot. Remember that the phase response indicates the difference in phase between the input and output signals. Connect the points and indicate the experimental cut-off frequencies on the plots. 7. Repeat steps 1-6 for a passive high-pass filter with the same values for R and C. 3 EE210 Lab #10 – Questions (to be completed after lab) 1) What type of filter does a negative feedback op-amp configuration behave as? 2) a) What type of filter would be used to remove only the 60Hz noise generated by the florescent lights? b) What type of filter would be used to remove any undesired high frequency noise from an audio circuit, such as the design project? 3) a) Based on the passive circuits from in Figure 2, sketch a band-pass filter that passes frequencies between 800Hz and 6kHz. Include calculations and values selected. b) Sketch an equivalent circuit using only inductors and resistors. Include cutoff frequency relations, no values are required. 4 4) a) Comment on the simulated and experimental frequency/phase response curves and cut- off frequencies for the passive low-pass and high-pass filters. Explain any discrepancies. b) Are these filters ideal? Can an ideal filter be implemented practically with discrete components? Explain. 5 c) What is the significance of the phase response? What would be considered an ideal phase response? Explain. 5) a) What is the magnitude of Vout for the low-pass filter if Vin is 3V DC? b) For the high-pass filter? c) How will these values differ with a very high frequency Vin? 6 .
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