Laboratory 3 Daniel Choi 904169061 a We plug in our scope into the function generator and we run a 1kHz sine wave We go to the math menu and we change it to the FFT Fourier transform We see a graph with a spike This spike moves to the right as we raise the frequency 1kHz 44kHz We then change the function to a square wave at 1kHz We see the images below because the generator scope is picking up all frequencies and building the wave that we want 1kHz 63kHz b We build our circuit as the following Using a LCR meter we measured our inductor to be 9 4mH and our capacitor to be 9 74nF We can calculate the resonant frequency by using the inductance and capacitance of our circuit We see that the resonant angular frequency is w 0 1 LC w 0 1 104 500 rad sec 9 4 mH 9 74 nF 104 500 16 63 kHz We then find the resonant frequency experimentally by comparing our V 2 and V out We wiggle the frequency around until we get the greatest peak a graph that looks closest to our CH2 or V f 0 16 kHz 17 1 kHz 18 6 kHz Using the function generator s sweep feature we set the start frequency to 12kHz and the stop frequency to 20kHz We then set the sweep time to be 5 seconds and we see a sine wave whose amplitude increases hits a maximum then decreases We then drive the circuit with a square wave and we gradually lower the frequency We lower it until we get a peak response We do this carefully and find the first five terms of the Fourier series 2 5 kHz 1 92 kHz 5 8 kHz 1 59 kHz 3 4 kHz 1 35 kHz We now run the function generator with a 100 Hz square wave We use the cursor tool to find the time it takes from one peak to the other We find it to take 58 s which is 1 17 24 kHz resonant frequency We t now want to find the Q quality factor which we do by using the equation Q 2 Energy Stored 100 mV We find Q to be Q 2 2 2 4 Energy Dissapated per Cycle 50 mV c Using a transformer we build the circuit as the following We use the scope to look at the output of our half wave rectifier circuit We see below that the graph that we get on our scope is what we d expect The peak voltage is around 16V We then switch the direction of our diode and we can see that there is indeed a polarity The polarity is shown the following figure We see that V peak 9 V because 9V is the rms root mean square We get which is very close to 9 V 2 d We will build our circuit as the following V peak to be about 16V We see that when everything is properly connected we get a graph like the following We see that the peak voltage on the full wave rectifier is around 14V This is lower than that of the half wave rectifier because when we add more diodes we have a voltage drop of around 0 6 for each diode If we connect a second ground lead of the scope to one side of the secondary it could blow the diodes The peak amplitudes are less than those of the last circuit because there is a voltage drop for each diode The diodes fail closed When one of the diodes is reversed change of polarity its partner the diode that is adjacent will also blow We then zoomed in at the region of the output waveform that is near zero volts There are flat regions that last for about 400 s These periods are the time when the diodes are charging and discharging e We then take the same circuit but we now replace the diodes with LEDs and we now plug the fullwave rectifier to our signal generator on 0 5Hz We see that two of the diodes light up at a time f Keeping the LEDs on the circuit we added a 15 F capacitor across the output so that we can measure a ripple The peak to peak of a ripple was around 2V We then replaced the 15 F capacitor with a 470 F capacitor and we measured our ripple to be about 0 4V g We will build a rectified differentiator using diodes as the following We will drive the function generator with a 10kHz square wave at maximum output amplitude 10V Using both channels we observed the input and output The 2 2k resistor acts as a drain fore the current to flow through The RC time constant is dependent of this resistor and we see that the RC time constant decreases when we remove the resistor We see this as a steeper slope on our graph h We build the following circuit We max out the amplitude of our function generator and we run a 1kHz sine wave We see the output to be similar to a sine wave but truncated at the top i We build the following circuit We run the function generator with a 1kHz sine wave square wave and triangle wave figures shown below respectively Sine Wave Square Wave Triangle Wave The diode limiter is a circuit that limits voltages 1V This occurs because the diodes block both the low and high end of the frequencies The flat portions are not perfectly flat This is an important circuit because we could use this if our voltage source is too high and if we want to protect a device or instrument that only runs on small voltages j Using the same voltage divider as part i above diode limiter we will take measurements using the scope probe We use it both on the x1 and x10 switch We see from the two pictures show graphs that are exactly the same but the input voltages are different The first graph CH4 shows that the scaling is 200mV and the second graph CH4 is 2V The difference or attenuation is by a factor of 10 yet they both give the same answer