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EECS 100 Frequency Domain Signals B. Boser Page 1 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 εr from one (air or vacuum) to a much larger value (εr ≈80EECS 100 Frequency Domain Signals B. Boser Page 2 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.EECS 100 Frequency Domain Signals B. Boser Page 3 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 (100kΩ 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.EECS 100 Frequency Domain Signals B. Boser Page 4 2. RC Lowpass First we will analyze the touch sensor board. Calculate and sketch the magnitude and phase response of ܸ஼ଵܸ஺஼ൗand ܸ஼ଶܸ஺஼ൗusing R1= 100kΩ, R2=150kΩ, 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=100kΩ): _____ Hz ___ of 1 P 3-dB frequency (R2=150kΩ): _____ Hz ___ of 1 P Maximum magnitude difference: _____ dB ___ of 1 P Maximum phase difference: _____ deg ___ of 1 P Repeat your analysis for R1=R2=100kΩ, 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=100kΩ, and CT1= CT2=20pF b) R1= 100kΩ, R2=150kΩ, and CT1= CT2=20pF c) R1=R2=100kΩ, 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 PEECS 100 Frequency Domain Signals B. Boser Page 5 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


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Berkeley ELENG 40 - FREQUENCY DOMAIN

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