Experiment Guide RC Filters and Simulation Instrumentation Software Description and Background In this lab you will a manipulate instruments manually to determine the input output characteristics of RC filters b use software systems to simulate the characteristics as functions of frequency and c use a software system to control equipment to measure and plot the filter characteristics automatically A 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 Vout R 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 socalled 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 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 Vout Vo ut Vi n RC Vin 1 RC 2 1 Eq 1 An approximate log log plot of transfer function magnitude vs frequency is shown in RC Figure 3 1 Fig 3 Log log plot of transfer function magnitude vs angular frequency times RC Note the horizontal axis is really a frequency axis since R and C are constants 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 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 Vin R C Vout Fig 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 RC Fig 5 Log log plot of transfer function magnitude vs frequency times RC for the circuit of Fig 4 Procedures 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 43 100 web site P2 Reverse the order of the two components and repeat P3 Observe the effects of filtering on square and triangular waves P4 Using software SignalExpress 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 Description and Background Graphical circuit stimulation software such as LabVIEW National Instruments Inc 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 an oscilloscope to get the graph that shows the transfer functions the ratios of the output and input 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 A recent development from National Instruments is the application SignalExpress which enables you to set up and control the measurement equipment easily SignalExpress actually creates the LabVIEW programs that run the equipment Each piece of equipment you use here the function generator and the oscilloscope for instance has a cable connected to it to provide control signals set the function generator frequency to 300 Hz and to collect data from a real circuit under test here the actual voltages input to and output from the RC circuit are measured by the real oscilloscope whose measurement go to the computer via the cable connected in the back of the oscilloscope Each piece of equipment has a unique number so that the SignalExpress or LabVIEW program can recognize it These cables are identified as GPIB buses GPIB General Purpose Interface Bus 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 On the class web site you should find the brief document Simulation and Instrumentation Software that describes in simple terms what several popular and useful simulation and instrumentation applications do Included are LabVIEW and SignalExpress along with Orcad the schematic capture program on a CD inside the back cover of your text PSpice a very popular and useful circuit simulation program use it to check your homework and MultiSIM a versatile circuit simulation program that even shows pictorial views of circuit components and circuits built on protoboards like those you ve used in this laboratory Some Comments About LabVIEW for the Computer Oriented Student LabVIEW is a graphical programming language that shares some aspects with traditional non graphical programming languages C BASIC Pascal etc and some
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