Authors: Denard Lynch Date: July, 16, 2012 Corrections: Sep 16, 2012 D. Lynch, M. R. Avendi Revised: Sep 22, 2012 D. Lynch Revised: Sep 9, 2013 Description: This laboratory exercise explores resistance capacitance (R-C) and resistance inductance (R-L) static and transient behaviour in Direct Current (DC) circuits. The student will assemble circuits composed of resistive, capacitive and inductive elements and energize them with a DC source. Theoretical circuit behavior will be predicted and then verified within practical limits. Learning Objectives: In this laboratory, the student will: Understand and learn how to use a solderless breadboard and construct simple circuits; Learn how to measure circuit parameters using a digital multimeter and the Digilent Discovery module; Verify the behaviour of capacitors and inductors in a static (steady-state) DC circuit Verify the transient behavior of R-C and R-L circuits in response to a step change in potential in a DC circuit Reporting: Use your lab notebook (logbook) to document the key objectives of this laboratory, your theoretical calculations (note what you would expect to see) Parts List: your equipment and circuit components used, including circuit and test equipment set up any measured values of components your measurements verifying your theoretical expectations (you can paste in screen shots from your ADM where appropriate, or use annotated hand sketches), your observations and comments about how closely your observations matched your expectations, related comments on practical limitations for your observations and comments on possible sources of error Denard Lynch Page 1 of 11 Sep 9, 2013
Safety Considerations: In addition to general electrical safety considerations, the student should also be aware of the following considerations specific to this laboratory exercise: Resistors carrying current will generate heat energy, which can raise the temperature of the component significantly, especially when over-driven. Use your olfactory sense (smell) to alert you to overloaded components; remove the energy source immediately if you suspect any overheating and check your circuit. You can check for heat by feeling carefully in the proximity of a suspected component, but don t touch anything directly! Capacitors generally shouldn t generate significant heat unless they are subjected to potentials above their rating and suffer dielectric breakdown. If this happens, the same considerations as over-loaded resistors apply. In addition, capacitors can store a significant amount of energy, even after the circuit is de-energized. Or even when the capacitor is removed from the circuit! Be sure to discharge capacitors before contacting the leads. Inductors usually have some resistance in the wire from which they are made. This can lead to some heating affect as mentioned for resistors. Subjecting inductors to potentials or other conditions above their rating can also cause breakdown of the insulation inside the component leading to partial short circuits and rapid heating. In addition, when the flow of current through an inductor is interrupted or stopped for any reason, the collapsing magnetic field will cause an induced voltage across the inductor which can be many times greater than the source voltage! This can cause sparks, shocks (if touched) or component breakdown if not handled appropriately in circuit design and laboratory procedure. Be sure to allow sufficient time for fields to dissipate before handling circuit components. Background and Preparation: In preparation, especially for your first lab, become familiar with the items in your Lab Kit and how to use them. Pay particular attention to the following three items: 1. Solderless breadboard you will use this to assemble experimental circuits throughout the course. It is used in conjunction with a wire kit or other 22ga (~.67mm /.025 diameter) wire with 7.5mm (.33 ) insulation stripped for insertion into the board connectors. Please consult this brief and very helpful tutorial by Hernando Baragan about the use of solderless breadboard like the ones supplied in your Lab Kit. http://www.wiring.org.co/learning/tutorials/breadboard/index.html 2. Digital Multimeter (DMM) you will use this to check various circuit conditions and components, including resistance, continuity, voltage and current. Be very cautious to select the correct scale (volts, amperes, milliamperes, resistance or continuity etc.) and an appropriate range. If in doubt, always start with the highest range for voltage and current and the lowest range for resistance, and then adjust downward if necessary. Never connect a DMM set on the current scale directly across a source it will almost certainly destroy the meter and cause a Denard Lynch Page 2 of 11 Sep 9, 2013
safety incident! View the following YouTube video (title: THE BEST Multimemeter Tutorial at: http://www.youtube.com/watch?v=bf3oyq3hwfu&feature=related Note: NEVER CONNECT THE PROBES TO YOUR SKIN TO MEASURE RESISTANCE AS SHOWN IN THIS VIDEO THIS IS AN UNSAFE PRACTICE AND COULD LEAD TO ELECTROCUTION!) Otherwise, it is a good explanation of basic DMM operation. 3. Digilent Analog Discovery Module this will be your main piece of test gear. In conjunction with the associated Waveforms software and a computer running Windows XP or later, this will provide virtual instrument capability for your experiments. This module is USB port connected and powered; provides a 2- channell oscilloscope with differential inputs, a 2-channel signal generator, a ± 5VDC supply and 16 digital lines that can be used to monitor digital signals or for static digital input and output. More information on the specifications and use can be found at: http://www.digilentinc.com/products/detail.cfm?navpath=2,842,1018&prod=an ALOG-DISCOVERY. The associated Waveforms software can be downloaded at no cost from here: http://www.digilentinc.com/products/detail.cfm?navpath=2,66,849&prod=wav EFORMS Please refer to the Class Notes for background theory on capacitive and inductive transients. (There is a summary of key points in Appendix A at the end of this Laboratory.) Terms: ADM Digilent s Analog Discovery Module DMM Digital Multimeter separate instrument often used to measure voltage, current, resistance, capacitance, continuity and occasionally other parameters Steady-state A circuit condition where all relevant parameters (e.g. V, I) are Steady not changing over time. WVDC Working Volts DC, often used to specify the voltage conditions for which a capacitor, or other component, was designed Nominal value The target value for a component. Due to manufacturing tolerances, each part may vary by a specified amount (e.g. a resistor specified as having a 5% tolerance, may in fact actually be any value between ~ 950Ω and 1050Ω) Trigger Level On an oscilloscope, the level at which it will initiate drawing a trace of a signal on the screen (e.g. if set to +1V, it will start drawing the signal on the screen once the input level goes above 1V) scope Common abbreviation for oscilloscope Denard Lynch Page 3 of 11 Sep 9, 2013
Procedure: The procedure will involve three phases. In each part, the student will use a solderless breadboard to assemble a simple circuit using resistive, capacitive or inductive components. Theoretical calculations of various circuit parameters should be performed as part of the lab preparation (i.e. prior to your lab period). During the lab procedure, you will use your test equipment to measure the same circuit parameters and compare the results to your theoretical expectations. A note on measuring current: A simple way to measure current with your ADM is to measure the voltage across a resistor that happens to be in series in the circuit leg of interest. If a suitable series resistor is not already in the circuit, you can insert a small sense resistor (say 10Ω) in series where you want to measure current and then use the differential oscilloscope inputs from one channel of your ADM (e.g. 1+ and 1-). The differential inputs essentially measure each point with reference to ground, and then subtract the two so you read the voltage difference between the two points of interest. You can display the measurement directly in current terms by adding a Mathematical Channel: and in the Enter Function box, typing C1/4700 (or C2 if you wish to use that channel; you should also use the actual value of your resistor if not 4700Ω) (you can also change the units of display under the settings icon on the M? dialog box). Alternately, for static conditions, an ammeter (DMM on one of the current scales) can be inserted in series where you want to measure the current. Be sure you have the leads plugged into the appropriate jacks on the DMM and that you ve selected the right scale. If in doubt, always start with a high scale and then increase the sensitivity if necessary. If you don t have a multimeter, or for dynamic conditions, as in a transient circuit where you want to observe the change in current over time, you can measure the voltage across a resistor in the circuit and calculate the current. Parts List The following parts, or suitable substitutes, are required for this laboratory: Item Quantity ADM 1 Solderless breadboard 1 100Ω ¼ W 1 1000Ω ¼ W 2 3300Ω ¼ W 1 4700Ω ¼ W 1 0.1 µf capacitor 1 10 mh inductor 1 Denard Lynch Page 4 of 11 Sep 9, 2013
Modeling- (determining what you would expect to see) This simply means using circuit theory to predict the circuit parameters for each circuit (e.g. v(t), i(t), τ). The required parameters are given in each section below. Calculating the expected currents and voltages will also allow you to determine the required ratings for your components (i.e. how much power they must dissipate, how much voltage they must withstand etc.). Note that in this case, you are using a practical inductor, which has some internal resistance. You should account for this fact in your theoretical calculations as much as possible, and adjust your predictions accordingly. Measurements- I. I R-L-C Circuit Static Behaviour Use your solderless breadboard and set up the circuit shown in Figure 1 below. A good first step is to examine the circuit, make a list of the parts you will need, obtain the necessary parts and construct the circuit (again, refer to the brief tutorial linked above if you are unfamiliar with use of these boards). You may also need to measure the actual value of your components versus their nominal value, and note it for calculations and future reference (many times the nominal value will be sufficiently accurate to allow you to verify the principles involved). For example: Component Nominal Measured 1/4W resistor 1000Ω 986Ω Capacitor 100WVDC 0.1µF 0.092µF Etc. Your instructor will indicate where to obtain the necessary parts if they are not already in your parts kit, and how to measure their actual value using a DMM or the component tester in the lab. You can generally use the power supply provided in your Analog Discovery Module (ADM). (Note: there is a very limited amount of current available from the ADM; ~90mA maximum. Check your theoretical calculation to make sure this supply isn t overloaded whenever you use it.) Assemble the components as shown in Figure 1. Place the components as close as possible to each other, but with enough spacing to allow for insertion of measurement leads; you can use connectors from your wiring kit to connect components on the board if required. Your lab instructors can help with layout suggestions. Denard Lynch Page 5 of 11 Sep 9, 2013
Digilent ADM +5V Figure 1: Static DC R-L-C Circuit Once you have checked your breadboarded circuit for correctness, energize the circuit and measure the voltages and currents indicated using the Voltmeter on your ADM, as well as verify Kirchhoff s voltage and current laws by measuring the voltages around each loop (e.g. 5V source R1 R3 C1 GND, etc.), and to verify that the total current drawn from the source is equal to the sum of the currents in each leg (I S = I 1 + I 2 + I 3 ) You may want to use a table similar to Table 1 to record your measurements and results in your laboratory notebook (logbook). Table 1 Circuit Parameter V 1 V 2 V 3 V R1 I 1 I 2 I 3 I T Expected Measured Comments Note: It may not be useful to try to determine an Expected in every case. Try to determine what you should see at relevant points in the circuit that will help you verify the theoretical operation. II. Resistive Capacitive Transient Behaviour Modify your breadboard circuit so that it reflects the circuit shown in Figure 2. Again, inventory and measure any new components if needed. Use one of the signal generator outputs on your Analog Discovery Module (ADM) (e.g. W1 or W2) as an input to this circuit. Set the output for a 0 5V square wave (e.g. 2.5V with an offset 2.5V). Select a suitable frequency so you can observe and measure the charging and discharging transients. (Based on your theoretical calculation of the time constant, τ, select a frequency that will result in a high signal between about 5 10 time constants. Connect the oscilloscope inputs from your ADM to Denard Lynch Page 6 of 11 Sep 9, 2013
monitor and measure the driving signal, and the resulting voltage across the capacitor. Be sure to make good ground connections between your ADM (, any black wire) and your circuit board. Figure 2: R - C Transient Circuit Adjust the trace on your oscilloscope display so you can measure the observed time constant as accurately as possible for both the charging and discharging phases. There are two ways to verify your theoretical calculations: 1) determine the expected voltage across the capacitor at t = one time constant and then measure the actual time observed when it reaches that voltage, or 2) measure the voltage at one (calculated) time constant on the horizontal (time) axis and compare it to the expected value. Use the X1, X2 and Y1, Y2 cursors on your ADM oscilloscope to aid with your measurements. Table 2 Circuit Parameter V i charge V f charge I i charge I f charge τ charge V i decay V f decay I i decay I f decay τ decay Digilent ADM WaveGen (W1) Amplitude: 2.5V Offset: 2.5V f ~ (10τ) -1 Expected Measured Comments Note: You can add a Measurement to your scope display to measure various parameters of the input signals. If the ADM cannot adequately determine the values, a? -- will be shown in the display. In these cases, read the values off the display visually or using the X, Y cursors. III. Resistive Inductive Transient Behaviour (This is very similar in procedure to part II except that you are using a practical inductor instead of the capacitor) Modify your breadboard circuit so that it reflects Denard Lynch Page 7 of 11 Sep 9, 2013
the circuit shown in Figure 3. Again, inventory and measure any new components if needed. Use one of the signal generator outputs on your Analog Discovery Module (ADM) (e.g. W1 or W2) as an input to this circuit. Again set the output for a 0 5V square wave (e.g. 2.5V with 2.5V offset). This simulates a DC source alternating periodically between 5V and 0V. Again select a suitable frequency so you can observe and measure the charging and discharging transients. (Based on your theoretical calculation of the time constant, τ, select a frequency that will result in a high signal for 5 10 time constants. First use one of the oscilloscope inputs to check your input. Then use the oscilloscope inputs to monitor the resulting voltage across the inductor and the voltage across the resistor (again using a Mathematical channel) to observe the current through the inductor. Be sure to make good ground connections between your ADM ( ) and your circuit board. Digilent ADM WaveGen (W1) Amplitude: 2.5V Offset: 2.5V f ~ (10τ) -1 Figure 3: R - L Transient Circuit Adjust the trace on your oscilloscope display so you can measure the observed time constant as accurately as possible for both the charging and discharging phases. Again make use of the X1, X2 and Y2, Y2 cursors on your ADM oscilloscope to aid with your measurements. As mentioned above, you are using a practical inductor, which has some internal resistance. You should account for this fact in your theoretical calculations, and adjust your observed expectations accordingly. For the purposes of this lab, the following model will adequately represent your practical inductor: Be sure to account for the extra resistance in your time (τ) and voltage expectations. (E.g., during the charging phase, the final current will cause a voltage drop across the inductor resistance, so you may not measure 0V as you would theoretically expect. You should verify and explain. You can also estimate the internal resistance using the voltage measurements you have taken.) Denard Lynch Page 8 of 11 Sep 9, 2013
Table 3 Circuit Parameter V i charge V f charge I i charge I f charge Expected Measured Comments τ charge V i decay V f decay I i decay I f decay τ decay APPENDIX A: Background Theory As discussed in class, the three basic electrical elements, resistors, inductors and capacitors, exhibit certain characteristic behaviour in Direct Current (DC) circuits. In a steady-state or static DC circuit, a resistor obeys Ohm s Law, a capacitor looks like an open circuit, and an inductor looks like a short circuit (assuming ideal components). When subjected to non-static (i.e. changing or transient ) conditions, these elements, especially in combination, can act quite differently. The subsequent parts of this lab will investigate and verify this non-static or transient behaviour. You will be using the signal generator in your Anaolog Discovery Module (ADM) to impose instantaneous (well, very fast at least) changes to the source voltage impressed across a simple R L or R C circuit. Internal Impedance of Sources: Although the output impedance of the Digilent Arbitrary Waveform Generator (AWG) is not a factor for any of the experiments in this course, its affect should generally be considered in other cases. The following discussion provides an overview on this topic which can be used to assess whether or not it shoud be considered. An ideal voltage source has an internal resistance of 0Ω,. However, a real source, when it is providing, say, 5V DC, will look like an ideal 5V battery with a series resistance of R int, as shown in (a) in Figure 4. When this source changes to 0V, it will still have the internal resistance of the practical source, as shown in (b), even though there would be no voltage output at the terminals. Denard Lynch Page 9 of 11 Sep 9, 2013
Figure 4: Practical Voltage Source This internal resistance can affect the behavior (and measurements) in both static and transient conditions. You can estimate the internal resistance of your source by measuring the difference in output voltage with different load resistances (c). If your load resistances have a ratio of 2 (e.g. 200Ω and 100Ω), you can use the following estimate for R int of the source: R int = 2Δ 1 3Δ RLoad V 2 RL VRL Where Δ =, is the difference in measured voltage as a ratio of the source E voltage, E, and R Load is the smaller load value (e.g. use 100Ω and 200Ω). Of course the lower the test load resistance, the greater the ΔV, but also the more inaccurate the estimate is. If the R int turns out ~2-3% of the R Load, the estimate is satisfactory. The internal resistance of modern sources is usually quite low and can often be ignored, but it should be considered and checked if necessary. R-L and R-C Transient Behaviour The time constants in R-C and R-L circuits respectively is τ=r T C and τ= L RT, where R T in both cases is really the Thévènin equivalent resistance of the circuit, and should take into account the internal resistance of the source and the component. While the internal resistance of a capacitor in these circuits is probably negligible, the internal resistance of an inductor is probably not and will noticeably affect both the time constant and the end voltages (because of a voltage divider effect). The expressions describe the transient behaviour for Thévènin equivalent R-C and R-L circuits (for the charging phase) are summarized in Table 4 and Table 5 for reference. Table 4: Charging Transient Expressions i L il(t) = If 1 e t τ C ic(t) = Iie t τ vc(t) = Vf 1 e t τ v ( ) vl(t) = Vie t τ ( ) Denard Lynch Page 10 of 11 Sep 9, 2013
Table 5: Discharging Transient Expressions i v L il(t) = Iie t τ ' vl(t) = Vie t τ ' C ic(t) = Iie t τ ' vc(t) = Vie t τ ' In both cases, use KVL, KCL and Ohm s law to determine the required initial or final (static) values for current or voltage during the period of interest (i.e. from just after the circuit changes until it either reaches a steady-date or the circuit is changed again). References: (Lynch, 2011), EE201 Supplementary Course Notes p 29-51 Denard Lynch Page 11 of 11 Sep 9, 2013