ECE 201 LAB 8 TRANSFORMERS & SINUSOIDAL STEADY STATE ANALYSIS

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1 Version of 8 ECE 201 LAB 8 TRANSFORMERS & SINUSOIDAL STEADY STATE ANALYSIS BEFORE YOU BEGIN PREREQUISITE LABS Introduction to MATLAB Introduction to Lab Equipment Introduction to Oscilloscope Capacitors, Inductors, and First Order Circuits EXPECTED KNOWLEDGE You should be familiar with Phasors, steadystate sinusoidal analysis, and the equations governing magnetically coupled coils EQUIPMENT Digital Multimeter Oscilloscope Arbitrary Function Generator MATERIALS Variable Capacitor Two 741 operational amplifiers Speaker Bobbin, core, and magnet wire OBJECTIVES After completing this lab you should know how to: Characterize a linear circuit component by making a series of measurements. Measure the properties of magnetically coupled coils using sinusoidal analysis. INTRODUCTION Resistors, inductors, and capacitors are the three most common passive components in electric circuits. Many of the nonideal effects in wires and connectors can be modeled with inductors and capacitors. Even when capacitors and inductors are not explicitly placed in a circuit, capacitance and inductance must often be taken into account to make a circuit operate correctly. For example, computer engineers must account for capacitance in circuit board wires during their design of the board layout. The equation that relates voltage and current for resistors, Ohm s law, is independent of time. It does not matter if the voltages and currents are time varying; their relationship remains the same.

2 Version of 8 In contrast, the relationship of voltage and current for capacitors and inductors is described by a differential equation that is time dependent. Thus, when working with capacitors and inductors you must take into account the time varying properties of the voltage and current. Intuitively, you should understand that capacitors resist rapid changes in voltage and inductors resist rapid changes in current. In previous labs you learned how to characterize resistors by analyzing data that you obtained with the lab equipment. For resistors, you accomplished this by measuring the resistance directly with the DMM. The accuracy of your analysis depended on your ability to accurately characterize circuit components. Many components can be modeled as a network of resistors, capacitors, and inductors. Motors, for example, have a great deal of inductance and a little resistance. To build a circuit that drives the motor efficiently, you would probably need to estimate the impedance of the motor from a series of measurements. This is often more accurate than the nominal specifications provided by the manufacturer. Transformers can be thought of as two magnetically coupled inductors with a high coefficient of coupling. Transformers are used in communications circuits to eliminate DC voltages and to match impedance between different portions of the circuit. They are also widely used in power distribution circuits. Power lines are less power efficient at low voltages, so the crosscountry power transmission lines carry electrical power at tens of thousands of volts. Transformers are used to convert this high voltage to a lower voltage (e.g. 120 V), which is safer for local use. CAPACITORS Capacitors come in many varieties. Two of the most common types are electrolytic and ceramic. Electrolytic capacitors are shaped like small cylinders. These capacitors are sensitive to polarity. One of the leads in these capacitors is usually longer than the other and there is often a + or sign printed on the cylinder that indicates the polarity. It is important that the voltage across this type of capacitor always conforms to the required polarity. If you connect this capacitor such that the lead marked with the has a higher potential (voltage) than the other lead, the capacitor may explode. Ceramic capacitors are shaped like small discs and usually have smaller values than electrolytic capacitors. They are not polarity sensitive and are not prone to explosion. Large capacitors, such as 10 uf (ten microfarads), have their value printed directly on them. Smaller disk type capacitors along with plastic film types often have just two or three numbers printed on them. If there are just two numbers on the capacitor, the value is read as PicoFarads. An example: 47 printed on a small disk capacitor has a nominal value of 47 pf. The capacitors with three numbers are read like the resistor code. The first two numbers are the first and second significant digits and the third is a multiplier code. Note that even when the third digit is given, the units of the capacitance are pf. Table 1 gives the multiplier codes and their meanings.

3 Version of 8 Third digit Multiplier , , ,000 6 not used 7 not used Table 1: Capacitor Multiplier Codes. Occasionally the manufacturer will also include a letter after the numbers. This letter is similar to the tolerance band on resistors and indicates how much the true value may vary from the nominal value printed on the case. Table 2 lists the tolerance codes for capacitors.

4 Version of 8 Letter symbol D Tolerance ± 0.5 pf F ± 1% G ± 2% H ± 3% J ± 5% K ± 10% M ± 20% P +100%,0% Z +80%, 20% Table 2. Capacitor Tolerance Codes For example, a 103J is a 10,000 pf capacitor with ±5% tolerance. If the capacitor marking begins with a decimal point, the value is read directly in microfarads. If a letter follows the numbers, it is read using the tolerance code in Table 2. For example, a capacitor marked.001m has a value of.001 µf (or 1 nf) and a tolerance of +/ 20%. INDUCTORS Inductor nominal values are usually printed directly on the inductor. Some manufacturers code their inductors by giving the multiplier first, followed by the first and second significant digits. In this case, the value is read in micro Henries. For example, if the inductor has 410 printed on it, it is read as (10 * 10000) µh, or 100 mh. PRELAB You will need to cut the wire in your kit into two pieces, one piece twice as long as the other. The easiest way to do this is to stretch the wire out and then bend it into thirds. Then cut the wire on one of the bends. Wrap your inductor bobbin using the two pieces of wire. Make the ratio of turns 2:1. You should be able to wrap one wire approximately 40 times, and the other wire approximately 20 times around the bobbin. Place both halves of the E shaped core into the bobbin with the two pieces of the core touching. Secure the core in place with a piece of wire.

5 Version of 8 The easiest way to do this is to pass a piece of wire between the core and rectangular opening on the bobbin on both sides of the core, then twist both ends of the wire together. Answer Questions 1 4. MAGNETICALLY COUPLED COILS In this section, you will determine the self inductance and mutual inductance of your transformer. For this lab, the side of your transformer with the smaller inductance will be called the primary side. The side with the larger inductance will be called the secondary side. SINUSOIDAL CHARACTERIZATION You can use sinusoidal analysis to determine the inductance of each winding of the transformer, L1 and L2, and to find the mutual inductance M in Figure Ω V Sine Wave V i V 1 L Figure 1. Sinusodial Characterization for an Inductor Figure 1 shows the circuit you will be using to determine the inductance of your transformer. To determine the value of the primary side of your transformer, you need to find V 1 as a phasor o relative to V i. If we choose to use V i as our reference ( V i = 1 0 ), V 1 should have a smaller amplitude and a negative angle. To find V 1, construct the circuit shown in Figure 1. Measure the peak to peak amplitude of V i and V 1 with the oscilloscope. To make your readings more accurate, you will need to average the input from your circuit on the oscilloscope. To do this, press the Menu button directly below the waveform intensity knob. Then press the screen menu button below the Mode label and then the screen menu button next to the Average label. In this mode, the oscilloscope takes the average of the input over a specified length of time. You can change this length of time using the selector knob just to the left of the Measure and Cursor buttons. As you increase the time, your waveform will appear cleaner. For this experiment, set this time to 32. The current setting is displayed just below the Average label in the Acquire menu. Next, use the cursors to measure the phase shift of the two sinusoids. To do this, you will need to have Channel 1 and Channel 2 coupling set to AC. (Use the vertical menu button to make this change.) Next push the Cursor button and select vertical bars. You will need to line up one of the vertical bars on the spot where the rising portion of one of the waves crosses the horizontal axis. Line up the other vertical bar on the spot where the rising portion of the second wave crosses the horizontal axis as in Figure 2.

6 Version of 8 Estimating Relative Phase Figure 2. Sample Phase Measurement In Figure 2, the signal on Channel 2 crosses 0 V approximately 312 µs before the signal on Channel 1. If these sinusoidal signals have a frequency of 500 Hz (period = 2 ms), the phase of 312µs o o the signal on Channel 2 is 360 = 56.16, relative to the signal on Channel 1. 2ms To decrease your error, repeat the above procedure using the falling portions of the waves. Then average the two measurements.

7 Version of 8 Estimating Signal Amplitude You should know how to use the oscilloscope to measure the amplitude of sinusoidal voltages. Be careful to distinguish between peaktopeak, amplitude, and RMS estimates. Use the techniques described above and your previous answers to estimate the inductance on each winding of the transformer. You will need to use the DMM to find the exact value of your 47 Ω resistor. Repeat this process using three different frequencies for V i : 500 Hz, 1 khz, and 2 khz. Answer Question 5. + i M + 1 V Sine Wave V in V 1 + L 1 L 2 V 2 47 Ω Figure 3. Circuit For Determining M To find the mutual inductance of your transformer, construct the circuit shown in Figure 3. Since there is no current flowing through L 2, there will be no reflected impedance, and therefore, V2 = jω M i. V 1 can be foud using Ohm s law and i. (Be sure to measure V 1 and V 2 with respect to V in.) Answer Question 6 7. SPEAKER CHARACTERIZATION Using the method described in the previous section, estimate the inductance of the speaker in your lab kit at three different frequencies: 500 Hz, 1 khz and 2 khz. Limit the amplitude of your input voltage to 1 V. Don t forget to account for the 8 Ω resistance in the speaker. Answer Questions Connect your transformer to the speaker to boost the power delivered to the speaker. Answer Questions Design a circuit that will maximize power transfer to your speaker at 2 khz. You should find that this will require at least one capacitor. Answer Questions

8 Version of 8 OPAMPS AND SPEAKERS Design and build a circuit using opamps that will amplify a 1 V signal by a factor of 10. Make sure that the circuit does not invert the signal. Connect your circuit to the speaker. Answer Questions