EECS 100 Frequency Domain Signals B Boser University of California Berkeley Department of Electrical Engineering and Computer Sciences EECS 100 Professor Bernhard Boser LABORATORY 8 v1 FREQUENCY DOMAIN Up to now we looked at signals as a function of time on the oscilloscope Signals can also be viewed in the frequency domain While in principle the information in the time and frequency domains is identical connected through a mathematical operation called Fourier transform depending on the application one or the other representation conveys more relevant information For example measuring the bandwidth of an amplifier in the frequency domain is much more straightforward than a time domain approach Simulators such as Multisim use the AC analysis to measure the frequency response In the laboratory the corresponding instrument is called network analyzer You will find this tool in every well equipped electronics laboratory and it is mandatory e g for the evaluation of wireless circuits such as cellular phones Since network analyzers are rather expensive we do not have them in the EE100 lab Fortunately with a few tricks the effects of the frequency response of a circuit can be demonstrated also with an oscilloscope The figure above shows the board that you will be using for this laboratory The touch pads are simple printed circuit board PCB traces close to one another and form capacitors Touching the sensor area with a finger increases the relative permittivity r from one air or vacuum to a much larger value r 80 Page 1 EECS 100 Frequency Domain Signals B Boser for water a finger is somewhere between one and this value The result is a significant increase in capacitance due to this effect Many gadgets such as MP3 players and appliances use this effect as a more versatile and reliable input device than conventional switches In this laboratory we will investigate these touch pads in a later laboratory we will actually build a touch sensor The diagram below shows the circuit implemented by the PCB Together with resistors R1 and R2 the touch sensor capacitors CT1 and CT2 form to RC lowpass filters driven from a source VAC Nominally the resistors and capacitors have identical values and hence the voltages VC1 and VC2 are identical However if one of the two capacitors is touched its value increases resulting in a drop of the voltage across it and an increased phase lag We will investigate these two effects in the laboratory Page 2 EECS 100 B Boser Frequency Domain Signals LAB REPORT Lab Session Name 1 SID Name 2 SID 1 Solder Printed Circuit Board First you need to assemble the PCB for the touch sensor experiments For this you need to solder the following components Resistors R1 and R2 100k each Jumpers J1 and J2 3 pin single inline do not add a component for zero adjust R3 The position of the components is marked on the PCB Use tweezers to bend the wires of the resistors so that the part fits exactly into the holes in the PCB Bending the wires too close to the resistor body may cause the electrical connection to fail Bending too far causes difficulty of inserting the resistor into the PCB and can also result in reliability problems So work accurately The component goes on the side with the white markings Cut the wires on the other side approximately 1mm from the surface of the board Now comes the fun part with the soldering iron These get very hot work in groups of two with one partner watching the other and making sure no hand touches the hot iron Turn the iron on and wait for a minute or two for it to get hot The iron is sufficiently hot when solder touching the tip melts into a shiny little bowl sticking to the tip With a little solder on the tip touch one of the cut off wires and surface of the PCB and add more solder to get a nice cone around the wire all around the eye on the PCB The solder solidifies almost instantly after removing the iron Clean off the tip of the soldering iron on a sponge wet first with water to get rid of burned flux an additive to the solder that makes it flow nicely Repeat for the other connections Then solder the jumpers Be careful not to touch the jumper on the other side of the PCB when soldering metal is a good heat conductor and you d burn your finger Check your work first visually and then with the continuity tester All the grounds must be connected and the AC input with the closer end of resistors R1 and R2 Congratulations You have just assembled your first printed circuit board Page 3 EECS 100 Frequency Domain Signals B Boser 2 RC Lowpass First we will analyze the touch sensor board Calculate and sketch the magnitude and phase response of and using R1 100k R2 150k and CT1 CT2 20pF Draw also the difference of the magnitude and phase response What are their values and at what frequencies do they occur 3 dB frequency R1 100k Hz of 1 P 3 dB frequency R2 150k Hz of 1 P Maximum magnitude difference dB of 1 P Maximum phase difference deg of 1 P Repeat your analysis for R1 R2 100k CT1 20pF and CT2 30pF 3 dB frequency CT1 20pF Hz of 1 P 3 dB frequency CT2 30pF Hz of 1 P Maximum magnitude difference dB of 1 P Maximum phase difference deg of 1 P Verify your result with Multisim use the AC analysis Now perform a transient analysis and plot VC2 versus VC1 for a R1 R2 100k and CT1 CT2 20pF b R1 100k R2 150k and CT1 CT2 20pF c R1 R2 100k CT1 20pF and CT2 30pF Note one possibility for generating an X Y plot in Multisim is to display VC2 and VC1 with a simulated oscilloscope and pressing the A B button Printout of simulation result of 8 P Page 4 EECS 100 Frequency Domain Signals B Boser 3 Touch Sensor Check out the touch sensor in the laboratory Connect the sinusoidal function generator to the AC port Set the amplitude to 2 5V and the frequency to 100kHz Connect oscilloscope probes to points S A and S B set the probes to 10x attenuation Display the waveforms on the oscilloscope in Y T and X Y mode Touch the sensor areas Do you get a nice ellipsoid Adjust the frequency to maximize the opening of the ellipsoid for the biggest finger in the team How close does the finger have to be to the sensor area to produce a noticeable change on the scope screen Try setting the function generator to other waveform types e g square wave Can you produce a triangle on the scope screen Why not Show your result the ellipsoid to the lab TA Touch sensor ellipsoid test of 10 M 4 Physics When you touch the sensor is current flowing through your finger Note that the green film on the PCB is
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