EECS 40 Fall 2005 P Godoy, A Neureuther Experiment Guide: RC Filters and LabVIEW Objective In this lab you will (a) manipulate instruments manually to determine the input-output characteristics of an RC filter, and then (b) use an instrument control system called LabVIEW (made by National Instruments, Inc.) to measure and plot RC filter characteristics automatically. Background: RC Filter Characteristics Figure 1 below shows an RC filter connected to a sinusoidal voltage source. This circuit is termed a two-port circuit (see Fig. 2) where the voltage source produces the input voltage Vin and the output voltage Vout appears across resistor R. Recall that we customarily represent an AC voltage as a periodic function of time such as V(t) = V0cos(ωt) where V0 is the amplitude of the voltage, t is time, and ω is the so-called angular frequency, whose units are radians per second. The angular frequency is related to the “ordinary” frequency, f, measured in Hertz, by ω = 2πf. For example, if the frequency, f, of the ordinary power line voltage in the U. S. is 60 Hz, then the associated angular frequency, ω, is 377 radians/s (2π×60). Background: Transfer Function A two-port circuit is characterized by its so-called transfer function, whose magnitude is defined as |Vout/Vin|, where Vout and Vin are phasor voltages (as indicated by the boldface type). The variation of the transfer function with frequency characterizes the circuit, whether the circuit is an amplifier (does it amplify high frequencies more than low frequencies?) or a filter (does the filter pass the low frequencies or the high frequencies better?). If you analyze the RC circuit of Fig. 1 using Kirchhoff’s voltage law, the phasor voltages Vout and Vin, the resistance R and the impedance of the capacitor ZC = 1/jωC, you can show that the magnitude of the transfer function is +-VoutVin+-RCFigure 1. RC filter with series capacitor and output resistor R. vinvoutFigure 2. Two-port circuit.EECS 40 Fall 2005 P Godoy, A Neureuther 2)ωRC(1ωRC+=inoutVV An approximate log-log plot of transfer function magnitude vs. frequency is shown in Figure 3: 1|Vout/Vin|ωRC1 Figure 3. Log-log plot of transfer function magnitude vs. frequency times RC. The filter characteristic has been simplified to appear as two lines that intersect at the angular frequency for which ωRC = 1, or ωτ = 1, where τ is the time constant RC for this circuit. If plotted precisely, the characteristic would transition smoothly from the upward sloping line to the horizontal line, but for many purposes the two-straight-line approximation is adequate. This circuit is called a high-pass filter, since for frequencies above ω = 1/RC the output voltage equals the input voltage. If we reverse the positions of R and C in the filter circuit (Figure 4), we obtain the transfer function and filter characteristic shown below: +-VoutVin+-RC Figure 4. Circuit with a series resistor R and the capacitor C as the output element. 1|Vout/Vin| ωτ =ωRC1 Figure 5. Log-log plot of transfer function magnitude vs. frequency times RC for the circuit of Fig. 4. VoutVin---------1ωRC()21+---------------------------------·=EECS 40 Fall 2005 P Godoy, A Neureuther Lab Equipment • Personal computer running Windows XP with LabVIEW 7.1 installed • Printer • 10kΩ resistor • 0.1µF non-polarized capacitor • HP 54645D oscilloscope • HP 33120A function generator • HP 34401A multimeter • the file “RC Circuit.vi” on the EECS 40 website • External Interface Command Set Manual for HP 34401A multimeter and HP 33120A function generator (also on EECS 40 website) Procedures (Manual Plot) P1. Connect a 10kΩ resistor and a (non-polarized) 0.1 µF capacitor in series with a signal generator, making sure that your oscilloscope ground and the signal generator ground are connected together. Set the signal generator to output a 1-volt peak sine wave. Measure and plot the amplitude of the voltage between the components versus frequency on log-log graph paper. You can download log-log graph paper from the EECS 40 website. P3. Reverse the order of the two components and repeat. P2. Observe the effects of filtering on square and triangular waves. References (on Reserve for EE 40 in Engineering Library) • P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. (Cambridge U. Press, 1989), pp. 35-8. • R. White and R. Doering, Electrical Engineering Uncovered, 2nd ed. (Prentice Hall, 2001). See p. 27 ff. for explanation of decibels, and pp. 285-7 on transfer functions and Bode plots. Background: LabVIEW Graphical circuit stimulation software, such as LabVIEW, is popular among engineers working in industry and researchers in universities because it reduces the tedium and cost of circuit and system testing. So far in this lab, you’ve used an analog function generator and oscilloscope to get the graph that shows the ratio of the voltages versus the frequency. Plotting the graph by hand is time-consuming and it may give inaccurate results. With LabVIEW, however, you can obtain accurate tabular and graphical results automatically after you program the system. Note that your EECS 40 text (A. R. Hambley, “Electrical Engineering: Principles and Applications”, 3rd Ed.) discusses LabVIEW on pages 425-437, and contains a LabVIEW CD-ROM in the envelope inside the back cover of the book. LabVIEW is a graphical programming language that shares some aspects with traditional non-graphical programming languages (C, BASIC, Pascal, etc.) and some aspects of hardware definition languages (VHDL, Verilog). It combines the generality and power of traditional programming data structures such as loops, if-then branches, and arithmetic operators with the ability of hardware definition languages to perform multiple tasks simultaneously.EECS 40 Fall 2005 P Godoy, A Neureuther Programming in a graphical environment consists of placing functional blocks that perform specific tasks on a worksheet and wiring them together to send data from one block to another. These blocks can do anything from simple tasks (add the data on the two input wires together and place the answer on the output wire) to complex tasks (take two arrays of data as input and display the contents on a log-log graph as x,y pairs). These functional blocks can also translate data in the graphical program into a form that external equipment can use. With the
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