Analog & Digital Electronics
LAB 4: LCR filters: March 7
Equipment
You will need an oscilloscope, breadboard, function generator, inductor (≈10 mH), resistor (470 ) and capacitor (≈2.2 nF).
Purpose
This lab will provide a brief introduction to LCR circuits (2nd order filters) and the terminology of filters.
Note:I recommend that you use the ×10 probes to measure the signal across the resistor. They will disturb the circuit less.
Experiment
Part I: BandPass
Make a series LCR circuit and look at the voltage across the resistor. I suggest that you try L=10mH, C = 2.2 nF and R= 470. (Measure all the component values.) The output resistance of the generator is 50, so the 470 resistor will load it down a littlenear resonance. The inductor is not ideal, having a small series resistance and a parallel capacitance. Measure the inductor’s resistance. Calculate the expected resonant frequency, f = 1/[2(LC)1/2], and the expected Q, (1/R)(L/C)1/2 . /Let the input be a sine wave of between 5 to 10 Vp-p. Find the resonant frequency by looking at the output over a range of frequencies from about 100 Hz to 1 MHZ. Quickly scan this range. (Display both the “input” and the output on the scope.) I want to see what you are doing at this point. Where is the output a maximum (what frequency)? Is this the expected resonant frequency? Estimate the Q of the filter (measure the -3dB frequencies, i.e. where |H| is down by -3dB from its maximum. Doing it this way should eliminate the effect of the resistance of the generator on Q. However the 50 in the generator will make the input voltage change. It’s an inconvenience, but it’s not too bad.) If the inductor was ideal, the input and the output would be the same at resonance, but they won’t quite be equal. Measure the output at enough frequencies to be able to sketch a “Bode” plot, i.e. |H| in dB vs. log(f). Don't do too many points; just enough for a quick plot. However, you should measure both the input and output amplitudes and take the ratio when finding |H|. I recommend you try the following values where fo is the measured resonant frequency, 0.3fo, 0.6 fo, fo, 1.5fo, and 3fo in addition to the -3dB points.
Part II: LowPass
Try looking at the voltage across the capacitor as a function of frequency. (You will have to interchange the capacitor and resistor in the circuit above so that one of the scope leads can be grounded.) Sweep through the frequencies so you can get a feel for what happens. Is the output voltage ever larger than the input voltage? The ratio of Vo/Vin at the resonant frequency should equal Q. Does it match the Q you measured in Part I? Let me see your circuit at this time.
Now change R so the damping factor is about 0.7. (Calculate what R to use.) Quickly make a Bode plot for this case. If fo is the resonant frequency, make measurements at 0.03fo, 0.1fo, 0.3fo, 0.8fo, fo, 1.2fo, 3fo, and 10fo.