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 C Vin R Vout Figure 1 RC filter with series capacitor and output resistor R vin vout Figure 2 Two port circuit Recall that we customarily represent an AC voltage as a periodic function of time such as V t V0cos t where V0 is the amplitude of the voltage t is time and 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 2 f For example if the frequency f of the ordinary power line voltage in the U S is 60 Hz then the associated angular frequency is 377 radians s 2 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 j C you can show that the magnitude of the transfer function is EECS 40 Fall 2005 P Godoy A Neureuther Vout RC Vin 1 RC 2 An approximate log log plot of transfer function magnitude vs frequency is shown in Figure 3 Vo ut Vi n 1 RC 1 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 RC 1 or 1 where 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 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 R C Vin Vout Figure 4 Circuit with a series resistor R and the capacitor C as the output element V out 1 2 Vin RC 1 Vo ut Vi n 1 1 RC Figure 5 Log log plot of transfer function magnitude vs frequency times RC for the circuit of Fig 4 EECS 40 Fall 2005 P Godoy A Neureuther Lab Equipment Personal computer running Windows XP with LabVIEW 7 1 installed Printer 10k resistor 0 1 F 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 10k resistor and a non polarized 0 1 F 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 CDROM in the envelope inside the back cover of the book LabVIEW is a graphical programming language that shares some aspects with traditional nongraphical 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 appropriate software drivers any button or knob that can be pressed manually can be controlled automatically by one of these function blocks Finally certain special blocks can control the flow of a program by specifying that a few tasks should be performed in a certain order or that a task should be repeated a certain number of times All of these types of blocks are used in this lab In addition to placing blocks on
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