EE 230 Lab Lab nf C 2. A. Low-Q low-pass active filters. (a) 10 k! Figure 1. (a) First-order low-pass. (b) Second-order low-pass.

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1 Second-order filter circuits This time, we measure frequency response plots for second-order filters. We start by examining a simple 2nd-order low-pass filter. The we look at the various arrangements of ndorder circuits. Then we build two op-amp based 2-nd order filters. We finish by looking at one of the weirder op-amp that we will come across a mock inductor. This is a busy lab, but if you come prepared, work efficiently, and use Signal Express effectively, you should be able to complete the lab without much trouble. Prior to ab 1. alculate the transfer functions, and the values of ω 0, Q P, and G o, for each of the circuits. 2. eview the theory for the inductor simulation circuit. You may also want to build this one prior to coming to lab, since the wiring for it is a bit fussy. 3. Make sure that you have a flash drive or some other means for saving data. A. ow-q low-pass active filters Figure 1. (a) First-order low-pass. (b) Second-order low-pass. (a) 1 (b) k! k! alculate the expected ω c and G o for first order circuit in Fig. 1(a) and the ω o, Q P, and G o for the second-order circuit of Fig. 1(b). Build the two circuits using M 660 op amps with ± 8-V power supplies. and sinusoidal input voltage (suggested amplitude of 0.5 VMS). Measure the magnitude and phase of each circuit from 10 Hz to 100 khz, with at least 5 measurement points per decade. (Here is a suggested distribution of frequencies: 10, 15,!1

2 25, 40, , 150, 250, 400, 650, etc. This will give a reasonably smooth distribution of points within each decade. But you can use a different distribution if you prefer.) Note: you can use Signal Express to measure the magnitude response, if you d like. However, since you must measure the phase by hand with oscilloscope, using Signal Express to measure magnitudes probably doesn t provide much time savings. Note: What can save you some time is to measure the two circuits simultaneously. Build both circuits on the breadboard and connect the input signal to both circuits. Then, at each frequency, measure the output (magnitude and phase) of each circuit. ecord all the data directly into Excel, and you are ready to make the necessary plots. Graph the magnitude response for each circuit together on one Bode plot. Also, graph the phase response of each circuit together on one plot. The plots should go into your report. B. nd-order filters low Q and high Q. The three circuits shown in Fig. 2 4 use the same components, but with different configurations to give the various types of filter response. For each of the circuits, calculate ω o, Q P, and G o. Then, using Signal Express, measure the frequency response of the magnitude for each. (Ignore the phase this time.) Measure over a range from 10 Hz to 1 MHz with at least 10 points per decade. Measure the magnitude response twice. First use = 150 Ω and then repeat with = 1.5 kω. Save the data from each measurement to Excel. For each of the different circuits, make a Bode plot with the two curves obtained using the different resistances. (So you will end up with 3 plots, each having 2 curves.) These plots go into your report. Figure 2. ow-pass. Figure 3. High-pass Figure 4. Band-pass!2

3 . Active Bi-quads Below are two (out of many possible) active filters that provide second-order responses without the need for inductors. Both are from the category of single-amp biquad (SAB) circuits. The first is a low-pass filter, in a configuration known as Sallen-Key circuit. The second is a band-pass filter. (And it doesn t have a fancy sounding second name.) For each circuit, calculate ω o, Q P, and G o. Then build the circuit with your choice of op amp (M324, M660, or T082) and measure the frequency response from 10 Hz to 100 khz using Signal Express. Include the plots in your report. Notes: Pay attention to power supply limits for your choice of op amp the 324 and 082 can work with ± 15 V supplies while the 660 is limited to ±8 V. The band-pass filter has a fairly high value for Q P, so you may need to increase the number of measurement points per decade in order to obtain a good measurement in the passband. hoose an input signal amplitude that is appropriate for the gain of the circuit. In particular, the bandpass circuit has a fairly high gain, and if the input amplitude is too big the output signal will be clipped. In that case, your measurements will be crap. Before running Signal Express, use the oscilloscope to check that the output is not clipping at the frequency where the output magnitude will be maximum and adjust the input amplitude accordingly. Note: The plots should be Bode plots. (Using decibels on the vertical axis.) Figure 5. Sallen-Key low-pass. Note that you can make a 50 nf capacitor using two 100-nF caps in series. Figure 6. SAB band-pass nf nf 220 k! Vo!3

4 EE 230 ab ab 3 D. Mock inductor circuit We have said several times that bulky, lossy inductors are usually avoided in electronic circuits. Yet, inductance can be very useful in some applications, particularly in filter circuits. The circuit shown in Fig. 7 simulates the impedance of an inductor. The impedance seen at the input terminals increases with frequency, just like an inductor. The equivalent inductance is determined by the resistors and capacitor of the circuit. Figure 7. Z in = jω = k! 22 k! 1 k! nf k! alculate the expected value of the simulated inductance. (It should be close to a familiar value.) Build the inductor simulation circuit using 660 op amps with ±8-V power supplies. heck the connections carefully. eplace the real inductor of the band-pass circuit used in part B with the fake inductor. (emove the real inductor from the circuit of Fig. 4. Then connect the input port of the mock inductor of Fig. 7 in parallel with the capacitor.) Use Signal Express to obtain the frequency response of the magnitude of the transfer function of the circuit with the mock inductor over the frequency range 10 Hz to 1 MHz. Save the data so that you can make a Bode a plot using Excel. Do this for both resistance values used in Part B. Plot the two frequency response measurements real inductor and simulated inductor together on one set of axes. (You should have saved data from the real inductance measurements done in part B.) Note that there will be two separate graphs: one for = 150 Ω using real and simulated inductors and a second for = 1.5 kω using real and simulated inductors.)!4

5 eporting Prepare and submit a report after you have finished the lab a template is available. Each lab group is required to submit a report (i.e. one report for two people). Be sure to include all of the frequency response graphs and answer any questions specified in the template. The report is due in one week at your normal lab time. omment regarding inductor series resistance eal inductors always have some series resistance due to the resistivity of the wire in the coil. For high-quality inductors, the series resistance may be less than 1 Ω and will probably have negligible effect in many applications. For the 15-mH inductors that are being provided, the series resistance should be around 10 Ω. This may have noticeable effects on the measurements. (You should measure the series resistance for your inductor using the ohm-meter.) This higher resistance will show its effect by making the bandpass frequency-response curve asymmetric and by introducing extra loss whenever the inductor is carrying higher currents, like when it is in series with the source. If you see these effects in your measurements, you should make note of them in your report.!5