1 INTRODUCTION 2 Digital Oscilloscope
Contents
1. quickly analyze the response of various circuits You may be tempted to use a DMM instead of an oscilloscope to measure Vin and Vout but you should beware that DMMs typically only work up to a maximum frequency of about 5 to 10 kHz Consult the specifications for a particular DMM if in doubt Physics 218 AC Filters Page 2 2 1 Voltage Measurements Plug the Hi Q output of the function generator into the CH 1 input of the oscilloscope Set the function generator to 1000 Hz sine waves and put the amplitude about half way up to the maximum Note that on the right hand side of the screen there is space for a menu The menu available is selected by pressing the appropriate button on the front panel For example you can select either CH 1 menu or CH 2 menu Math menu this one includes the Fast Fourier Transform or FFT option Measure or Cursor Try pressing each one and looking at the different options available For the Measure button the freq frequency and Pk Pk peak to peak voltage settings are often quite useful Note that when you press the Cursor menu small lights come on beside the vertical position knobs these allow you to move two cursors on the screen These will be useful for measuring phase differences Experiment with the various buttons and dials on the front of the oscilloscope until you are comfortable with how to use it to make measurements 2 2 Calibration In this experiment you will use the oscilloscope in du2. Analysis Plot log A as a function of log f The log log plot is a useful way to show a wide range of data on a single plot Include on your graph the theoretical prediction for each stage of the filter operating independently You don t need to compute a combined theoretical response Similarly plot as a function of log f and include the the theoretical predictions for each stage of the filter operating independently Revision 1361 Physics 218 AC Filters Page 7 Discuss your observations With more complex circuits it is possible to get a much sharper frequency response but this simple circuit illustrates the basic features of a bandpass filter Revision 1361
3. Physics 218 Alternating Current Circuits and Filters Due Monday February 16 2015 1 INTRODUCTION Many of the ideas we will discuss in the context of mechanical oscillations carry over into the realm of oscillations in electrical circuits Broadly speaking the process of analyzing time varying signals is known as signal processing In this experiment you will examine the effects of resistors and capacitors on alternating current signals You will construct high pass low pass and bandpass filters These circuits will have a response that depends on the frequency of the incoming signal 1 1 Notation Conventions We will typically use lower case letters e g v for time varying quantities and upper case letters e g V for constant quantities Of course sometimes those constant quantities themselves will be slowly varying in time so the distinction is not absolute Typically we will consider an input signal of the form Vin t Vin cos wt and the corresponding output signal will be of the form Vout t Vout cos wt The constants Vin and Vout are known as amplitudes The ratio A Vouz Vin is known as the voltage gain Even though A is less than 1 in the absence of amplification of some sort it is still called the voltage gain 2 Digital Oscilloscope For this experiment we will use the Tektronix TDS 1012 digital oscilloscope These oscil loscopes have several built in tools that will enable us to
4. al trace mode Channel 1 will be used to measure Vin and Channel 2 will be used to measure Vout The gain A will then simply be the amplitude of Ch 2 divided by the amplitude of Ch 1 Before getting started it is important to check that the two channels are calibrated Set the function generator to 1500 Hz and turn the amplitude knob about half way up Connect both Ch 1 and Ch 2 to to function generator HIQ and GND outputs Adjust the Variable Sensitivity knobs until both channels agree on the input voltage 3 RC High Pass Filter In this part you will study the voltage gain and phase shift of a simple RC circuit as a function of frequency Construct the circuit shown in Fig 1 Use R 10 0002 and C 0 01yuF These are nominal values only Measure record and use the actual resistance and capacitance values Set the function generator to sine waves It is useful to think of this as a voltage divider The amplitude of the output voltage is Revision 1361 Physics 218 AC Filters Page 3 Function Generator A R v Figure 1 RC High Pass Filter out then Vout Vine where the Z is the total impedance given by 1 Z R TEF The voltage gain A w of the circuit is defined to be Vout Vin and is given for this circuit by Vou _R_ wRC 4a Vin Z JS1 WRO where the last expression follows from simple algebra At small w the gain is near 0 but as the frequency increases the gain rises and approac
5. als of the oscilloscope probes are connected internally to the oscilloscope ground which is also connected to the third prong on the power cord Thus the negative terminals of both probes must always be connected to the same spot in the circuit In fact you don t even need to connect the negative terminal of the second probe though it s good practice to do so Revision 1361 Physics 218 AC Filters Page 6 than fiowpass That is the combination of filters will tend to pass through only frequencies f in the range highpass lt f lt lowpass 4 If possible design the second stage of the filter to have a higher impedance to prevent it from loading down the first stage Include a diagram of your working circuit Qualitatively your design should look something like Fig 2 Function Generator A Low pass Filter High pass Filter Vout Figure 2 Block diagram of a bandpass filter consisting of a low pass filter followed by a high pass filter 5 1 Data Acquisition Measure the voltage gain and phase difference for your circuit as a function of frequency over a vary wide range of frequencies Again don t waste time taking too many closely spaced data points You are looking for the general overall behavior over a very wide range of frequencies If you plot your data as you go along it should become clear when you have enough data See the Analysis section below for further details 5 2
6. hes 1 Hence this circuit is known as a high pass filter high frequency signals are passed through but low frequency signals are blocked A w The breakpoint frequency is defined to be w 1 RC At this frequency A has decreased to a value 1 2 and the power has decreased to 1 2 of its peak value Calculate the expected linear breakpoint frequency f w 27 1 27RC for your circuit The phase of the output voltage also varies with frequency and is given by lw tan lt a 2 Set up the oscilloscope for dual trace mode Monitor the input voltage on Channel 1 and the output voltage The voltage across R on Channel 2 Use the DC settings for both channels The AC setting is effectively just a high pass filter that subtracts out the average value of the incoming signal Revision 1361 Physics 218 AC Filters Page 4 3 1 Voltage Gain and Phase Difference Use the Measure feature to measure the voltage gain Note that since you are taking a ratio Vout Vin it doesn t matter if you use the peak or the peak to peak values To measure the phase difference use the Cursor menu Note that if you use Cursor 1 and Cursor 2 to mark the horizontal positions of two peaks the oscilloscope can calculate the time difference At for you The phase is then given by o on 2n At f where T 1 f is the oscillation period 3 1 1 Data Acquisition Take the data necessary to measu
7. re the voltage gain and phase difference over a wide range of frequencies going from well below fp to well above f Record your raw data in a clear table Note that the raw data is the data you get directly from the oscilloscope not the results of calculations you perform on that data You don t need a lot of data points Take a few data points near the ends of the range and more near the breakpoint frequency If you plot your data as you go along it should become clear when you have enough data Don t waste time taking lots of closely spaced data points 3 1 2 Analysis From your raw data calculate the voltage gain A and phase shift as a function of frequency Plot your results Include the theoretical curve on your graph as well This is easy to do in Excel LoggerPro and Mathematica Please feel free to ask for help setting up the graphs and calculations in any of them Discuss your findings If everything agrees well there is usually little more to say If there are significant discrepancies try to resolve them perhaps by going back and re measuring some points if necessary No sophisticated error analysis is required for this lab just a qualitative assessment of how well the theory fits the data See the example Measuring Ring Frequency on pg 48 of the User Manual for step by step instruc tions Revision 1361 Physics 218 AC Filters Page 5 4 RC Low Pass Filter Interchange the position of the re
8. sistor and capacitor in Fig 1 Measure the output voltage across the capacitor The theoretical gain for this circuit is Vou Xe 1 A 3 V Z y1 WRO The breakpoint frequency is the same as before 4 1 Data Acquisition Measure the voltage gain and phase difference over a wide range of frequencies going from well below f to well above fp 4 2 Analysis Again plot the theoretical predictions along with your measured values for A vs f and us f Discuss your results briefly 5 Bandpass Filter A bandpass filter is a filter that passes only a narrow range or band of frequencies Signals with frequencies either higher or lower than that band are blocked One simple way to build a bandpass filter is to start with a low pass filter which blocks high frequencies and follow it with a high pass filter which blocks low frequencies Design and build a bandpass filter by combining low pass and high pass filters Start by using your low pass filter from the previous part This will tend to pass all signals with frequencies lower than fliowpass Use the output of your low pass filter as the input to a high pass filter Your high pass filter should have a breakpoint frequency fhighpass Slightly lower 2You may be tempted to simply move the oscilloscope probes to measure the voltage across the capacitor but this won t work because of the way the oscilloscope probes are grounded The negative termin
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