EE 221 L CIRCUIT II LABORATORY 4: AC CIRCUITS, CAPACITORS AND INDUCTORS UNIVERSITY OF NEVADA, LAS VEGAS OBJECTIVE COMPONENTS & EQUIPMENT BACKGROUND

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1 EE 221 L CIRCUIT II LABORATORY 4: AC CIRCUITS, CAPACITORS AND INDUCTORS DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING UNIVERSITY OF NEVADA, LAS VEGAS OBJECTIVE Compare the difference between DC and AC circuits. Implement basic non-linear electrical components, i.e. capacitors and inductors, on breadboards. Achieve better understanding on the characteristics of AC circuits, as well as capacitors and inductors, through practicing in real world. COMPONENTS & EQUIPMENT Power Supply Multimeter Oscilloscope Breadboard Resistors Capacitors Inductors PC & LTspice Jump wires BACKGROUND AC Circuits: Alternating current (AC) is an electric current which periodically reverses direction, in contrast to DC which flows only in one direction. Due to the advantages of AC over DC in power generation, transmission, consumption and many more, AC are widely used in businesses and residences, especially in some relatively high voltage/power applications. The usual waveforms of AC include sine and square waves (widely used in digital logic circuits); sometimes triangular waves are also employed. Generally, an AC signal can be characterized by its DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 1

2 Amplitude: peak voltage/current if DC offset is 0, or peak-to-peak voltage/current in some occasions, Period (or frequency), Phase, DC offset. Two signals with same amplitudes (V m ), periods (2π/ω)/frequencies (ω) and DC offsets, but different phases are depicted as Fig. 1. Capacitors: Fig. 1 Two AC signals Fig. 2 A capacitor A capacitor is a passive element designed to store energy in its electric field. Capacitors are used extensively in electronics, communications, computers, and power systems, e.g. in the tuning circuits of radio receivers and as dynamic memory elements in computer systems. A capacitor consists of two conducting plates separated by an insulator (or dielectric) as Fig. 2, and is determined by the surface area of the plates, the spacing between the plates and the permittivity of the material (i.e. C = εa/d), with a unit of farads (F). Other basic capacitor related equations include (but not exhaustive): q = Cv i = C dv dt Serial Connected 1 = N = 1 C eq C 1 C 2 C N C i DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 2

3 Capacitor Impedance in AC circuits Z C = 1 jωc Parallel Connected EE 221L CIRCUITS II C eq = C 1 + C C N = C i **** Equations above hold true for ideal theoretical capacitors, whereas a real capacitor in practical has some resistance and inductance (see next subsection), and can be modelled as Fig. 3. Such parasitic resistance and inductance would affect the resistor performance in certain frequency ranges, but could be neglected in other frequencies. Such facts do not impact our labs much, but it is good to keep in mind that real world may not work as well as we ideally expect. N Fig. 3. A more practical model for real capacitors. Fig. 4. Three main types of capacitors There are three broad categories of capacitors available in our lab (Fig. 4). These are electrolytic, film and ceramic. There are other types of capacitors as well, such as paper-in-oil, but these are rarely used. Table 1 shows typical characteristics of each type. Choose smart for your applications! Table 1. Characteristics of the three main types of capacitors Characteristic Electrolytic Film Ceramic General Practical Range of 1uF 0.1F (standard) Values 1F 10F (supercaps) 10pf 10uF 1pF 1uF Polarized Yes No No Equivalent Series Resistance 0.1Ω ~ 1 Ω Negligible Negligible Leakage Current High (up to 1uA per uf) Low Low Inductance High Medium Low Max Freq. Range < 1MHz 10MHz ~ 100MHz 100MHz ~ 10GHz Typical Max Voltage Rating 1V ~ 500V 50V ~ 1KV 25V ~ 10KV Applications Power supply filtering, Audio circuits, filters, Bypassing, filters, energy storage precision applications RF applications DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 3

4 Inductors: An inductor is also a passive element designed to store energy but in its magnetic field. They are widely used in power supplies, transformers, radios, TVs, electric motors and so on. Also, inductors are usually formed into a cylindrical coil with many turns of conducting wire to enhance the inductive effect, as Fig. 5. Various inductors and transformers are shown in Fig. 6, and a model of a real inductor (with parasitic resistance and capacitance) can be depicted as Fig. 7. Fig. 5 Typical form of an inductor Fig. 6. Various inductors and transformers Fig. 7. A model of a real inductor Fig. 8. Inductor schematic symbols. Basic inductor related equations/formulas include (but not exhaustive): L = N2 μa l v = L di dt Serial Connected L eq = L 1 + L L N = L i N Inductor Impedance in AC circuits Z L = jωl Parallel Connected 1 = = 1 L eq L 1 L 2 L N L i N DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 4

5 Inductor Color Code LAB DELIVERIES PRELAB: 1. Review the knowledge of AC circuits, capacitors and inductors. Part of them are listed in the previous section of this manual. 2. Use both hand-calculations and LTspice to find the voltages at each node of the following circuits. Set voltage source freq. (i.e. f ) in Circuit (b) to 0Hz (DC), 10Hz, 1kHz, 100kHz. Fill in the following table. (a) (b) DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 5

6 Hand Calc. (Ideal) LTspice Measured Circuit (a) Ckt. (b) 0Hz Ckt (b) 10Hz Ckt (b) 1kHz Ckt (b) 100kHz V 1 V 2 V 3 V 1 V 2 V 1 V 2 V 1 V 2 V 1 V 2 LAB EXPERIMENTS: 1. Implement the Circuit (a) in Prelab on breadboard. 1) Use the DC power supply as voltage source. 2) Measure the node peak-to-peak voltages with multimeter, and fill in the table above. 3) Compare the measured results with hand calculation and simulations. 2. Implement the Circuit (b) in Prelab on breadboard. 1) Use the DC power supply as DC voltage source, and function generator as AC voltage source, respectively. 2) Measure the node peak-to-peak voltages (Vpp) with oscilloscope, and fill in the table above. 3) Compare the measured Vpp with hand calculations and simulations. 4) Compare the measured Vpp of various frequencies. What do you see, and why? Can you explain in a mathematic way? 3. Change the waveform of AC voltage source in Circuit (b) to square waveform, and observe the measurement at V 1 and V 2, respectively. 1) Set the AC voltage source frequency as 10Hz, 1kHz, and 100kHz, respectively. 2) Observe the waveform changes at V 1 and V 2. Can you see the slopes/sparks in waveforms? Why does that happen? POSTLAB REPORT: Include the following elements in the report document: Section Element 1 Theory of operation Include a brief description of every element and phenomenon that appears during the experiments. 2 Prelab report 1. Hand calculations of each circuit for voltages and currents. 2. LTspice simulations of circuit (b) and (c) for voltages and currents. Results of the experiments Experiments Experiment Results 3 1 Measured waveforms in Experiment 1. 2 Measured waveforms in Experiment 2. 3 Measured waveforms in Experiment 3. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 6

7 Answer the questions Questions Questions 4 1 Answer the questions in Experiment 2. 2 Answer the questions in Experiment 3. 5 Conclusions Write down your conclusions, things learned, problems encountered during the lab and how they were solved, etc. 6 Images Paste images (e.g. scratches, drafts, screenshots, photos, etc.) in Postlab report document (only.docx,.doc or.pdf format is accepted). If the sizes of images are too large, convert them to jpg/jpeg format first, and then paste them in the document. Attachments (If needed) 1. Zip your projects. Send through WebCampus as attachments, or provide link to the zip file on Google Drive / Dropbox, etc. REFERENCES & ACKNOWLEDGEMENT 1. C. K. Alexander and M. Sadiku, Fundamentals of Electric Circuits, 4 th Ed, I appreciate the help from faculty members and TAs during the composing of this instruction manual. I would also thank students who provide valuable feedback so that we can offer better higher education to the students. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 7