Physics Electronics Temple University, Fall C. J. Martoff, Instructor

Transcription

1 Physics Electronics Temple University, Fall C. J. Martoff, Instructor Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) in 100 Ritter Annex to coordinate reasonable accommodations for students with documented disabilities. Lab Exercise 1: Basic DC Circuits and RC Filters The purpose of this Exercise is to get started with Electronics class. The first order of business is to become familiar with the breadboard, the main tool for the semester s work. This device allows circuits and circuit fragments to be very easily assembled and studied, without bothering with soldering, PC boards, batteries, etc. References to specific pages or figures in the text refer to Horowitz and Hill, a copy of which is available in the lab. Discussions or ideas referred to as in the text can be found in any electronics textbook, for example Curtis Meyer s book. Secondly, the breadboard will be put to work to build and study some small circuits composed of two or three resistors connected to a DC power supply. ( DC means that all voltages are constant in time.) These circuits will illustrate the important principles of the DC voltage divider and the concepts of input and output impedance. To design any electronic circuit that is going to do something (ring a bell, turn on a light bulb, turn on a heater), an understanding of input and output impedance is necessary. Finally some circuits in which voltages vary with time will be studied. Out of this vast subject only the case of filter circuits will be selected. Here, a capacitor (with its frequency-dependent behavior) will be incorporated into a voltage divider circuit, allowing circuits to be built which select or block input signals depending on the signal frequency. A. The Breadboard In this section the breadboard is first described, then the description is verified by the student through some simple exercises. 1

2 The breadboard is designed to provide a convenient framework for building and testing small circuits. It consists of a grid of hundreds of little plugs ( tie-points or nodes ), into each of which a fine wire can easily be inserted, by hand or preferably using needle-nose pliers. Each plug makes good electrical contact with any wire inserted into it. Such a wire may be one of the leads that stick out of the ends of a resistor or other component. Or it could be just a plain piece of wire (a jumper ) which we use in order to connect one plug on the breadboard to another one. Some groups of nodes are permanently connected together by wires hidden inside the breadboard. Clues to some of these connections are given by lines painted on the faceplate; others are completely hidden (but logical, once discovered). These connections make things much easier to build. They insure that connecting points to each of the three power supplies and to ground (guaranteed 0 Volts) are available very close to any location on the breadboard. The first kind of permanent connections on the breadboard are the power and ground busses. Any connection that distributes power or ground over some distance on a board (in this case from the right edge to the left) is called a power [or ground] buss. The busses are the four uppermost horizontal rows of nodes at the top of the grid. Notice the painted lines on the faceplate between these four top rows of nodes, and the colored binding post terminals labeled with voltages. This is supposed to indicate that the three internal power supplies of the breadboard (adjustable + and - 15 Volts and fixed +5) and the ground connection (0 volts) are each connected to one of these rows of nodes. And within each row, all the nodes are connected together. (It is easier to check with a voltmeter than it is to explain.) Thus each row provides a couple dozen nodes through which other things can be connected to a power supply or to ground. To extend the power and ground busses, the student must make some further connections to the top-row busses, by adding some jumper wires. Vertical columns of nodes at the edges of each section of the board are also connected together by fixed connections inside the breadboard ( bussed ). These must be used to extend the top-row power and ground busses down onto the main part of the breadboard. Any of the power supplies, or the ground reference, can then be reached from anywhere on the breadboard with just a short jumper wire. This is very convenient and quite important for ease of use. It keeps the breadboard neat (free of rat s nests of long tangled jumpers) when more complex circuits are constructed. Finally, within each main breadboard section the nodes are bussed in horizontal groups of 5 (but not permanently connected to anything else). This is done to make it easy to connect several components together or to one circuit point. To connect a pair of leads to one another, just stick them both into nodes within any single row of 5. If more than 5 connections to one point are needed (unlikely), use a jumper to connect one group of 5 to a neighboring group. That gives room for 8 connections to the single point (2 x 5-2 for the jumper). To verify these connections and understand the details of them, do the 2

3 following exercises: 1. With power off, use an ohmmeter to investigate the following connections and functions of the breadboard. The ohmmeter measures resistance between points to which its two leads are connected. Both ohmmeter leads must be connected to test points in order to get a meaningful reading. The leads must also be connected to the right plugs on the meter itself- study the markings or ask your instructor. Connect to the breadboard nodes using a jumper wire with an uninsulated end tightly wrapped around a meter probe or clipped to a gripper probe. The Ohmmeter will read 0 Ohms for pairs of nodes which are electrically connected, and will give an open-circuit indication (OFLO or blinking display or resistance number higher than several MegOhms) for points which are not electrically connected. Measure the resistance between the following locations on the breadboard: Top busses to power connectors Any pair of nodes within one top bus Any pair of nodes where one is on one top bus and one on another top bus Side busses to each other and to main sections Several pairs of nodes within the same row of five in one of the three main sections Several pairs of nodes in different rows of five in one of the three main sections Between the three main sections 2. Understand the 10K and 1K pots located at the bottom of the breadboard. A Pot, short for potentiometer is a physically extended resistor with the normal connections one at each end, plus a third connection called the wiper. The wiper can be mechanically moved to any point between the ends of the resistor by turning a screw. The resistance from either end to the wiper is proportional to the distance from that end to the wiper connection on the resistor. To see the behavior of the pot, measure the resistance between one end lead and the wiper while turning the knob. To protect the pots against certain short circuits and resultant damage there may be a 100 Ohm fixed resistor in series with the wiper lead underneath the board. This makes the minimum resistance between the wiper and either end equal to 100 Ohms, preventing unintentional short circuits. Note: it is important to check these pots carefully now, because they have been found to fail prematurely on some boards. 3. Next turn on the power (toggle switch at upper right) and check the power supply voltages at the labeled terminal posts. If necessary, readjust the two adjustable voltages to +/- 15 volts using a screwdriver. 3

4 4. Connect and verify the vertical bus jumpers for the power supply voltages. Note that the voltage busses should be connected in order from most positive to most negative: + 15V, +5V, OV, -15V from left to right in each of the three sections. 5. Find the connections for the function generator (a source of AC signals) and the built-in speaker on the breadboard. Connect the function generator to one lead of the speaker by hopping with jumper wires in a few steps across the board. Just as in most of the circuit diagrams in the book, the function generator has only one output wire because the other one is grounded (and hidden). Therefore, complete the speaker circuit by connecting the second speaker lead to ground. Play with the various function generator settings and listen to the results on the speaker. (Listen carefully; this is a function generator with rather high output impedance (see below). Therefore it can only produce a very faint sound when driving the speaker directly. Next, connect the signal generator to the center pin of the BNC connector located near the bottom of the breadboard, using a jumper. The BNC is a venerable, rugged type of round coaxial cable connector just like the ones on the inputs of the lab oscilloscope. To use it, align the bump on the connector with the slot in the mating connector on the end of a BNC cable, press the two together, and twist to lock. Then view the signal generator output on the oscilloscope at the same time as it is used to drive the speaker. B. Voltage Dividers and Thevenin Equivalent Circuit The voltage divider is probably the most important circuit concept there is. It also provides a simple model for many complicated circuit behaviors. This exercise shows how to build some voltage dividers and study their behavior. The Thevenin Theorem and Thevenin Equivalent Circuit theory are discussed in the textbook and at the end of this section. For us, the main importance of Thevenin is that it allows us to predict and understand how and why signal sources almost always sag (give less and less output voltage) as they are loaded more and more heavily (asked to supply more and more output current). 1. Referring to the discussion in the textbook, design a voltage divider to provide a source of 10 V (relative to ground), starting with the 15V power supply on the breadboard. Use fixed resistors from the resistor kit, with values of at least 10K Ohms but not more than 100 K Ohms. ( Design in this case just means determine the resistor values needed.) Sketch the proposed circuit and give the necessary calculations. 2. Build your 10 V divider on the breadboard and verify the output voltage with a meter (measure voltage between the output point at 4

5 V supply R 2 V out R 1 Figure 1: Voltage Divider the junction of the two voltage divider resistors and ground). Report the measured voltage and explain any discrepancy. The measured voltage of the bare divider is close to the open circuit output voltage of the divider circuit. According to the discussion in the textbook, this is also equal to V Th, the Thevenin Voltage of the divider circuit. This is the voltage of the fictitious battery in the Thevenin Equivalent circuit. If the voltmeter drew exactly zero current from the divider, the measured voltage would be exactly the open circuit output voltage (by definition). All the real meters in the lab do draw low enough current to make the measured voltage of this divider be essentially indistinguishable from the open circuit output voltage. A measuring device that draws very little current when measuring a finite voltage is said to have high input resistance (or impedance) since it acts like a very high-value resistor in this respect. **Make sure you understand the preceding very important sentence.** 3. Next, study how the divider output voltage sags (decreases) when it is loaded more and more heavily (forced to drive larger and larger currents into a series of loads). (a) First, let s load the divider with 1 Meg Ohm. This resistor value is large much larger than the resistors in the divider itself. Such a large resistor will draw little current compared to that in the divider itself. It therefore constitutes a light load for the divider. To set this up, connect a 1 Meg Ohm resistor from the 10 V output point to ground. In this condition the divider is forced to supply its output voltage (10 V) to the 1 Meg Ohm resistor. The divider is said to be loaded with (or by) 1 MΩ. 5

6 Now measure the output voltage that the divider manages to supply to this load. To do this, connect a voltmeter from the 10 V output point to ground as before. Of course, this also measures the voltage across the load resistor. The measured voltage should be practically the same as the open circuit voltage. The divider is said to be lightly loaded by the 1 MΩ resistor. Little current flows through this big resistor (big compared to what?) when the divider s output voltage is placed across it. As a result (some calculation is needed to see this explicitly) the divider s output voltage remains nearly the same as when the 1M resistor was absent. We say that the output voltage barely sags because it is lightly loaded. (b) Now study some intermediate loadings. Load the divider with 100 K Ohms, then 50 K Ohms, then 25 K, and so forth. Measure and record the output voltage in each case. Notice that the output voltage sags more and more (drops farther and farther below 10 V) as the load resistance decreases and the load current therefore increases. Notice that a lower load resistance presents a heavier load to the divider. (c) For what load resistance R 1 does the output voltage sag to half 2 its open circuit value? (It is easiest to estimate this from a plot of output voltage vs. load resistance, rather than playing around trying to find exactly the right load resistor.) From the discussion in the textbook, R1 is in fact equal to R Th, the Thevenin 2 Equivalent resistance of the divider. (d) Compare R f rac12 with R Th as calculated from the divider circuit diagram and the textbook formula R Th = R 1 R 2 /(R 1 + R 2 ). Comment on any discrepancy. (e) Finally, load the divider as heavily as possible by replacing the 1 M resistor with a short circuit (a jumper wire). Measure the output voltage again. The output voltage (voltage across the 0 Ohm load resistor) should be found to sag right down to zero volts. Obviously the divider cannot supply its rated (10 V) output voltage across a short circuit! The divider circuit is said to be shorted out by the low value (0 Ohm) resistor. The circuit cannot supply any output voltage at all when it is as heavily loaded as this. The circuit still tries to supply voltage, though. In fact it supplies the maximum current of which it is capable. Calculate this current from the shorted divider circuit using Ohm s Law. (f) Measure the short-circuit current I s using the ammeter setting of the ohmmeter and compare to the calculation from the previous item. (g) The short circuit current I s can be used to calculate the Thevenin Equivalent Resistance of the divider circuit, using R Th = V Th /I s 6

7 V Th RTh + Equivalent Circuit R L V out Figure 2: Equivalent circuit for voltage divider with load. (see the textbook). Measure R Th this way, compare to the result previously obtained from R1, and comment on any discrepancy. 2 C. Improving the Divider with Lower Output Impedance This section ascribes how to make the divider better - that is, how to make it able to drive heavier (lower resistance) loads. 1. The measurement above of R Th = R1 (and the discussion in the text) 2 show why R Th is often referred to as the output impedance of the divider. It is equal to the ratio dv out /di out. This quantity clearly has the dimensions of a resistance. In the Thevenin equivalent circuit, it is the value of the fictitious resistor in series with V th. If the output impedance R Th = dv out /di out is large, the voltage divider will not work very well. Rather than always providing the design voltage independent of load, the output voltage will change a lot depending on what load it has to drive (i.e., how much current is drawn from the divider). Thus high output impedance is in most cases a bad thing. I jokingly refer to low output impedance as the First Holy Grail of Electronics. To see how to fix this, consider the formula for R Th in terms of the resistors used to construct the divider: R Th = R 1 R 2 /(R 1 + R 2 ). Evidently in order to reduce R Th, the resistor values used must be reduced. 2. Re-design the divider to have lower output impedance so that it can drive a 5 K Ohm load without sagging more than 10%. Do not use resistors smaller than 200 Ohms or they will get too hot. The values needed can be calculated by referring to the Thevenin Equivalent Circuit diagram given in the textbook or the diagram below. In this imaginary (but useful!) circuit, the load resistor R L is seen to form a voltage divider with R Th! It is simple to calculate what R Th must be in order to have V o ut only 5% less than V Th. Then the values of the real resistors R 1 and R 2 can be estimated from R Th = R 1 R 2 /(R 1 + R 2 ). 7

8 3. Build the improved divider circuit and check that it performs as expected with a 5 K Ohm load. 4. Measure and compare the output impedance of the new divider with the original one. Note that the measuring instruments may present an appreciable load to some circuits. The load presented by an instrument or other device is discussed in terms of a concept called input impedance, defined as R in = V in /I in. One can see that for a voltmeter, bigger input impedances is better - it means that the meter draws less current from the divider or whatever other circuit it is measuring. This is just the opposite of the case of output impedance, where smaller is generally better. High Input Impedance is the Second Holy Grail of electronics. The mechanical voltmeter has an input impedance of 25K Ohms times the full scale reading of whatever scale is being used (e.g. 250K on the 1OV scale). Our oscilloscopes have 1 Megohm input impedance, or 10 Megohms if the divide-by-10-probe is used. The electronic voltmeters have input impedance of 10 Megohms. From the previous discussion, it should be clear that measurements of voltages in a circuit will be accurately equal to the open circuit voltage if the input impedance of the meter is large compared to the Thevenin impedance of the circuit it is probing, If not, the meter itself will be a significant load to the source circuit, and the output voltage will sag. The meter reading will no longer be equal to the open circuit output voltage. The reading will depend not only on the source circuit but also on the characteristics of the meter (its input impedance). D. An AC Measurement The output impedance of AC sources is defined very similarly to that of DC sources. This section discusses how to measure the output impedance of the function generator on the breadboard. This is a further development based on Thevenin s theorem- not only voltage dividers but any ordinary circuit has a Thevenin equivalent circuit and therefore has a definite Thevenin resistance (output impedance). 1. Use a BNC cable and the oscilloscope to measure the open circuit sine wave output voltage V 0 of the generator. Report the value. 2. Next load the generator with various resistors connected from its output to ground. (The second output terminal of the generator is internally connected to ground.) Find the load resistance that causes the sine wave amplitude at the top of the resistor to decrease from V 0 by about half. Just as in the DC case, this resistance is the generator s Thevenin Equivalent Resistance, which is the same as its output impedance. Give the measured value of R Th and a drawing of the Thevenin Equivalent Circuit. E. RC Circuits and Filters 8

9 Figure 3: RC Filter Circuit Putting a capacitor in place of one of the resistors in a voltage divider gives some very interesting and useful effects. As discussed in the text, a capacitor is characterized by a quantity called impedance (Z), which is defined similarly to resistance; Z = V/I. However, as discussed in the text, impedance is a more general concept than resistance. Unlike resistance, an impedance may depend on signal frequency, and it may be a complex number. For a capacitor, it is shown in the text that Z = 1/iωC. Therefore the voltage division factor Z 2 /(Z 1 + Z 2 )becomes a complex number which is a function of frequency. This results in certain very useful behaviors which lead to the name RC filter for such a circuit. 1. Set up the circuit shown below. This is similar to Fig in the textbook, but the SPDT (single pole, double throw) switch allows the capacitor not only to be charged (connected to 5 volts through the resistor and switch) but also discharged (connected to ground). Design the circuit (that is, select values for R and C) to have a time constant τ = RC in the range 1-3 sec. This will allow the effect of throwing the switch by hand to be easily observed on the scope. Report the necessary values of R and C. 2. Observe the voltage across the capacitor while it is being charged (switch connection to +5 V) and discharged (switch connection to ground), using the scope and probe. To do this, use the oscilloscope, connect to the capacitor with a 10X probe (which actually divides the signal amplitude by 10!), a very slow sweep speed, and auto triggering. Watch the scope trace out the exponential equation derived in freshman physics for charging a capacitor C through a resistance R. (Note that this is a case where the high input impedance of the scope probe being used to measure the circuit behavior is very important. If its 9

10 Figure 4: Faster RC Filter Setup with TTL Drive impedance were not so high, connecting the probe across the capacitor would obliterate the phenomenon under study by discharging the capacitor through the probe itself.) This circuit gives an output voltage V = Q(t)/C which is proportional to the charge on the capacitor. This charge is proportional to the time integral of the current that has flowed through the filter. Hence this circuit is often called a current integrator or just an integrator. 3. Observe the TTL output of the function generator on the scope. Sketch the waveform. Note that the signal switches between about +4V and ground in a way very like throwing the switch above. The next sections show how to build a filter and drive it with this signal instead of the manually operated switch. To do this, first re-configure the circuit above, using component values close to 0.01 microfarad and 2.2 K Ohms. What charging time constant does this give? 4. Set the TTL generator frequency to the xlok scale for easy scope observation at fast sweep speed. Apply the TTL output to the integrating circuit in place of the +5V and switch, as shown in the diagram below. 5. Observe the output voltage wave form and compare it to the input (use the two channels of the scope and the alternate vertical display mode). Now vary the generator frequency over a wide range and describe the changing relationship between input and output wave forms. The appearance of the output varies quite a lot, depending on the frequency! The component values R or C may also be varied if desired. Sketch some typical waveforms and explain them qualitatively. 6. For what relationship of pulse length to RC time constant does the out- 10

11 put voltage accurately resemble the time integral of the input voltage (not the current)? [Hint; what shape is the time integral of a square voltage pulse?] 7. Repeat the previous part using the differentiating filter circuit of Fig in the textbook. 8. To quantitatively explore the filter behavior, the next few items will use sinusoidal signals. Set up the high pass filter circuit of Fig in the text, using the R and C values as above (0.01 microfarad and 2.2 KΩ). Drive the circuit with the sine wave output of the signal generator. Now, measure the ratio of the output voltage (voltage across R) to the input voltage for a number of different frequencies between 1 and 20,000 Hz. [Hint- around what frequency would anything interesting be expected to happen? Answer; ω = 1/RC or f=1/2πrc] Use the scope to measure the frequencies. See also Fig in the text. 9. Plot and report a graph of output amplitude vs. frequency for this high pass filter. Find the -3db frequency and compare with the expected value. The -3db frequency ( -3dB point ) is defined as the frequency at which the amplitude of the output signal has fallen to of the input value. Compare the measured result with that expected from equations in the text. Do not expect accuracy better than 15values are generally quite loose. 10. Observe the phase relationship between input and output signals over a wide range of frequencies. Record your results and comment, based on the discussion of phase shifts given in the textbook. 11. Interchange R and C to make a low pass filter and repeat. Ref