Daniel Choi 904169062 Laboratory 2 Section 2A a We got an LCR meter and two 0 01 F capacitors Using the vice clips we connected our capacitor to the LCR meter We turned it on and switched it over to the 20nF scaling For our first capacitor we had a reading of 9 76nF and 9 47nF for the second one We then grabbed a breadboard and put the capacitors in parallel and in series In parallel we got a reading of 19 32nF In series we got a reading of 4 77nF b We build our circuit using our function generator oscilloscope 10k resistor and 0 01 F capacitor in the following manner We run the function generator with a 500 Hz signal with the square function We measure the time constant where the output drops by 37 By using the cursor function of our scope we see the peak occurs at 5 84V and 37 of that is 3 68V The cursor is useful because in the amplitude mode we can create horizontal lines to see where the peak lies on our graph We can also use the cursor in time mode to create vertical lines to precisely see the times that we want to measure We see that it drops from 100 to 37 of its output in 125 s We then measure the time for the wave to climb from 063 which we find to be 125 s as well We must use the AC coupling on tour scope because on the AC coupling it puts a capacitor in series to terminate low frequencies These low frequencies carry an offset and the AC coupling will not read it and DC information will be lost In short the AC coupling will hide DC information The rise time is found to be 246 s using our scope The fall time is 246 s as well We see that they are different because the scope measures the fall time and rise time from 0 to 100 while we made measurements from 37 to 100 and 0 to 63 c Building the circuit as following We drive the function generator with a square wave at 100kHz The differentiator will give us the derivative of the function we input We see for the square wave the output is For the sine wave For the triangle wave 1 thus the combined impedance is infinite 0 The impendence at f infinity Z R 100 Z c 0 thus the combined impedance is 100 The impedance at f 0 Z R 100 Z c d Building the circuit as following The input impedance at DC 100Hz Z R 10 k Z c Z tot Z R Z c 20 000 At infinite frequency Z R 10 000 Z c Z tot 10 000 1 10 k 0 01 F 1 10 k When we drive the function generator with a triangle wave the output waveform looks like a negative cosine function but it is actually parabolas that are alternating signs When we dropped the input frequency to 10Hz we saw that the integrating properties disappeared and the input function was the same as the output function 2 4 e 1 2 Power 3dB P out P P dB 10 log 10 out P 1 10 log 10 3 2 1 1 Power 3 dB 0 707 2 2 Be l log 10 f We will build a low pass filter using a 15k resistor a 0 01 F capacitor a function generator and oscilloscope in the following manner Using the values of our resistor and capacitor we can calculate the filter s 3dB frequency When w w o w c 1 the ratio of the amplitudes is RC 1 RC f 3 dB 1 0 707 2 1 6666 67 1060 Hz 2 15 000 0 01 F We will drive the circuit with a sine wave and we will sweep from 1kHz to 10kHz to observe its low pass property We gathered multiple data points to create a graph to find the filter s 3dB frequency experimentally We do this by varying the frequency of our function generator from 1kHz to 10kHz We will use the measure option on the scope to find the peak to peaks pk pk of our graphs Our input voltage was 10 6V and we find that the 3dB frequency corresponds to 70 7 of the input voltage We find that to be 7 49V Using the data points below we can see about where this point lies f kHz V out V 1 7 84 1 2 7 12 1 5 6 24 1 7 5 76 2 5 12 2 2 4 80 2 6 4 24 3 3 76 3 5 3 28 4 2 96 5 2 40 6 2 08 7 1 84 8 1 60 9 1 52 10 1 36 9 8 7 Voltage v 6 5 4 3 2 1 0 0 2 4 6 Frequency kHz 8 10 12 We find that the 3dB frequency lies in between the 1kHz and 1 2kHz on our graph This is accurate because the calculated frequency was 1 06kHz For low frequencies as the 1kHz case t 136 s 1 t 7 353 kHz V 180mV The phase shift is seen to be about 45 For high frequencies as the 10kHz case t 23 s 1 t 43 38 kHz V 160mV The phase shift is about 90 Next we wanted to if the low pass filter would attenuate at the 6dB octave for frequencies well above the 3dB point We measured the output at 10 times and 20 times the frequency at 3dB Input kHz 10 20 Output V 3 92 2 08 We see that the output voltage dropped by a factor of 2 We then want to observe phase shift vs frequency for f f and f f f f db dB Phase shift at 100Hz dB f f 3 dB We see a phase shift close to 0 Phase shift at 1060Hz f f 3 dB We see a phase shift of about 45 Phase shift at 10kHz f f 3 dB We see a phase shift of about 90 We will now find the attenuations for and f 10 f f 4 f 3 dB f 2 f 3 dB 3 dB f 2 f 3 dB V 544 V V out 272 V V 252V f 4 f 3 dB V 522V V out 176 V V 368V f 10 f dB V 544 V V out 88 mV V 456 V g Using the same low pass filter that we had previously used in part e we will generate a sine function from our function generator Because we used an older generating function when changing our start stop frequencies we had to stay in the same range Hz kHz etc for both the start and stop We then grabbed a speaker and plugged it in parallel with our function generator and we turned out start frequency to 0 2 kHz and our stop frequency to 2kHz We then set the sweep to 1 per second …