Électronics 1 - Chapitre 2 DIODES 1. UNDERSTANDING DIODES MATERIALS Silicon and germanium are semiconductor materials used in the manufacture of diodes, transistors, and integrated circuits. DOPING Semiconductor material is refined to an extreme level of purity, and then minute, controlled amounts of a specific impurity are added (a process called doping). Based on which impurity is added to a region of a semiconductor crystal, that region is said to be N type or P type. In addition to electrons (which are negative charge carriers used to conduct charge in a conventional conductor), semiconductors contain positive charge carriers called holes. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 2 DOPING (continued) The impurities added to an N type region increases the number of electrons capable of conducting charge, whereas the impurities added to a P type region increase the number of holes capable of conducting charge. DIODE JUNCTION When a semiconductor chip contains an N doped region adjacent to a P doped region, a diode junction (often called a PN junction) is formed. Diode junctions can also be made with either silicon or germanium. However, silicon and germanium are never mixed when making PN junctions. QUESTION Which diagrams in Figure 2.1 show diode junctions? Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 3 FIGURE 2.1 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 4 2. ANODE / CATHODE In a diode, the P material is called the The N material is called the cathode : Figure 2.2 anode. CURRENT FLOW Diodes are useful because electric current can flow through a PN junction in one direction only. Figure 2.3 shows the direction in which the current flows. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 5 DIODE SYMBOL Figure 2.4 shows the circuit symbol for a diode. The arrowhead points in the direction of current flow. Although the anode and cathode are indicated here, they are not usually indicated in circuit diagrams. In a diode, current flows from anode to cathode In the circuit shown in Figure 2.5, an arrow shows the direction of current flow. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 6 CONNECT THE DIODE IN A CIRCUIT Forward-biased In the circuit shown in Figure 2.5, The anode connects to the positive battery terminal, and the cathode connects to the negative battery terminal. Therefore, the anode is at a higher voltage than the cathode. When the diode is connected so that the current flows, it is forward-biased. In a forward biased diode, the anode connects to a higher voltage than the cathode, and current flows. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 7 Reverse-biased In the circuit shown in Figure 2.6, The cathode is connected to the positive battery terminal, and the anode is connected to the negative battery terminal. Therefore, the cathode is at a higher voltage than the anode. When the cathode is connected to a higher voltage level than the anode, the diode cannot conduct. In this case, the diode is reverse-biased. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 8 Perfect diode In many circuits, the diode is often considered to be a perfect diode to simplify calculations. A perfect diode has zero voltage drop in the forward direction and conducts no current in the reverse direction. A forward-biased perfect diode can be compared to a closed switch, Figure 2.7 (2). It has no voltage drop across its terminals, and current flows through it. A reverse-biased perfect diode can be compared to an open switch, Figure 2.7 (1). No current flows through it, and the voltage difference between its terminals equals the supply voltage. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 9 PROJECT 2 : DIODE ● OBJECTIVE The objective of this project is to plot the V-I curve (also called a characteristic curve) of a diode, which shows how current flow through the diode varies with the applied voltage. As shown in Figure 2.8, the I-V curve for a diode demonstrates that if low voltage is applied to a diode, current does not flow. However, when the applied voltage exceeds a certain value, the current flow increases quickly. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 10 FIGURE 2.8 : the I-V curve for a diode Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 11 ● GENERAL INSTRUCTIONS While the circuit is set up, measure the current for each voltage value. As you perform the project, observe how much more rapidly the current increases for higher applied voltages. ● PARTS LIST ❑ One 9 V battery ❑ One snap battery connector ❑ One multimeter set to measure current (mA) ❑ One multimeter set to measure DC voltage Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 12 PARTS LIST (continued) ❑ One 330-ohm, 0.5-watt resistor ❑ One 1N4001 diode ❑ One breadboard ❑ One 1 MΩ potentiometer ❑ One terminal block Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 13 STEP-BY-STEP INSTRUCTIONS Set up the circuit as shown in Figure 2.9. The circled “A” designates a multimeter set to measure current, and the circled “V” designates a multimeter set to measure DC voltage. If you have some experience in building circuits, this schematic (along with the previous parts list) should provide all the information you need to build the circuit. If you need a bit more help in building the circuit, look at the photos of the completed circuit in the “Expected Results” section. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 14 FIGURE 2.9 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 15 Carefully check your circuit against Figure 2.9, especially the direction of the battery and the diode. The diode has a band at one end. Connect the lead at the end of the diode with the band to the ground bus on the breadboard. After you check your circuit, follow these steps, and record your measurements in the blank table following the steps: 1. Set the potentiometer to its highest value. This sets the voltage applied to the diode to its lowest possible value. 2. Measure and record the voltage applied to the diode. 3. Measure and record the current. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 16 4. Adjust the potentiometer slightly to give a higher voltage. 5. Measure and record the new values of voltage and current. 6. Repeat steps 4 and 5 until the lowest resistance of the potentiometer is reached, taking as many readings as possible. This results in the highest voltage and current readings for this circuit. At this point, the potentiometer resistance is zero ohms, and the current is limited to approximately 27 mA by the 330ohm resistor. This resistor is included in the circuit to avoid overheating the components when the potentiometer is set to zero ohms. If your circuit allows currents significantly above this level as you adjust the potentiometer, something is wrong. You should disconnect the battery and examine the circuit to see if it were connected incorrectly. If V gets large—above 3 or 4 volts—and I remains small, then the diode is backward. Reverse it and start again. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 17 FIGURE 2.10 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 18 7. Graph the points recorded in the table using the blank graph shown in Figure 2.11. Your curve should look like the one shown in Figure 2.8. FIGURE 2.11 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 19 ● EXPECTED RESULTS Figure 2.12 shows the breadboarded circuit for this project. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 20 FIGURE 2.12 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 21 Figure 2.13 shows the test setup for this project. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 22 CHAPTER 2 (continued) The V-I curve (or diode characteristic curve) is repeated in Figure 2.14 with three important regions marked on it. The most important region is the knee region. This is not a sharply defined changeover point, but it occupies a narrow range of the curve where the diode resistance changes from high to low. The ideal curve is shown for comparison. For the diode used in this project, the knee voltage is about 0.7 volt, which is typical for a silicon diode. This means (and your data should verify this) that at voltage levels below 0.7 volt, the diode has such a high resistance that it limits the current flow to a low value. This characteristic knee voltage is sometimes referred to as a threshold voltage. If you use a germanium diode, the knee voltage is approximately 0.3 volt. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 23 Figure 2.14 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 24 NOTE For any given diode, the knee voltage is not exactly 0.7 volt or 0.3 volt. Rather, it varies slightly. But when using diodes in practice (that is, imperfect diodes), you can make two assumptions : ■ The voltage drop across the diode is either 0.7 volt or 0.3 volt. ■ You can prevent excessive current from flowing through the diode by using the appropriate resistor in series with the diode. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 25 Current through the diode Calculate the current through the diode in the circuit shown in Figure 2.15 using the steps in the following questions. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 26 QUESTIONS A. The voltage drop across the diode is known. It is 0.7 volt for silicon and 0.3 volt for germanium. (“Si” near the diode means it is silicon.) Write down the diode voltage drop. VD = B. Find the voltage drop across the resistor. This can be calculated using VR = VS - VD. This is taken from KVL. VR = C. Calculate the current through the resistor. Use I = VR / R. I= D. Finally, determine the current through the diode. ID = Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 27 QUESTIONS A. The voltage drop across the diode is known. It is 0.7 volt for silicon and 0.3 volt for germanium. (“Si” near the diode means it is silicon.) Write down the diode voltage drop. VD = B. Find the voltage drop across the resistor. This can be calculated using VR = VS - VD. This is taken from KVL. VR = C. Calculate the current through the resistor. Use I = VR / R. I= D. Finally, determine the current through the diode. ID = Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 28 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 29 NOTE In practice, when the battery voltage is 10 volt or above, the voltage drop across the diode is often considered to be 0 volt, instead of 0.7 volt. The assumption here is that the diode is a perfect diode, and the knee voltage is at 0 volts, rather than at a threshold value that must be exceeded. As discussed later, this assumption is often used in many electronic designs. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 30 POWER DISSIPATION When a current flows through a diode, it causes heating and power dissipation, just as with a resistor. The power formula for resistors is P = V x I. This same formula can be applied to diodes to find the power dissipation. To calculate the power dissipation in a diode, you must first calculate the current as shown previously. The voltage drop in this formula is assumed to be 0.7 volt for a silicon diode, even if you considered it to be 0 volts when calculating the current. For example, a silicon diode has 100 mA flowing through it. Determine how much power the diode dissipates. P = (0.7 volt)(100 mA) = 570 mW Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 31 NOTE Diodes are made to dissipate a certain amount of power, and this is quoted as a maximum power rating in the manufacturer’s specifications of the diode. Assume a silicon diode has a maximum power rating of 2 watts. How much current can it safely pass? Provided the current in the circuit does not exceed this, the diode cannot overheat and burn out. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 32 QUESTIONS Look at the circuit shown in Figure 2.16. To find ID, you need to go through the following steps because there is no way to find ID directly : Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 33 DIODE BREAKDOWN If you place the diode in the circuit backward—as shown on the right in Figure 2.17—then almost no current flows. In fact, the current flow is so small, it can be said that no current flows. The V-I curve for a reversed diode looks like the one shown on the left in Figure 2.17. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 34 The V-I curve for a perfect diode would show zero current for all voltage values. But for a real diode, a voltage is reached where the diode “breaks down” and the diode allows a large current to flow. The V-I curve for the diode breakdown would then look like the one in Figure 2.18. If this condition continues, the diode will burn out. You can avoid burning out the diode, even though it is at the breakdown voltage, by limiting the current with a resistor. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 35 QUESTION The diode in the circuit shown in Figure 2.19 is known to break down at 100 volts, and it can safely pass 1 ampere without overheating. Find the resistance in this circuit that would limit the current to 1 ampere. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 36 ANSWER Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 37 Breakdown voltage All diodes break down when connected in the reverse direction if excess voltage is applied to them. The breakdown voltage (which is a function of how the diode is made) varies from one type of diode to another. This voltage is quoted in the manufacturer’s data sheet. Breakdown is not a catastrophic process and does not destroy the diode. If the excessive supply voltage is removed, the diode can recover and operate normally. You can use it safely many more times, provided the current is limited to prevent the diode from burning out. A diode always breaks down at the same voltage, no matter how many times it is used. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 38 The breakdown voltage is often called the peak inverse voltage (PIV) or the peak reverse voltage (PRV). Following are the PIVs of some common diodes : Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 39 INSIDE THE DIODE At the junction of the N and P type regions of a diode, electrons from the N region are trapped by holes in the P region, forming a depletion region as illustrated in the following figure. When the electrons are trapped by holes, they can no longer move, which is what produces this depletion region that contains no mobile electrons. The static electrons give this region the properties of an Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 40 electrical insulator. Forward-biased You apply a forward-biased voltage to a diode by applying negative voltage to the N region and positive voltage to the P region. Electrons in the N region are repelled by the negative voltage, pushing more electrons into the depletion region. However, the electrons in the N region are also repelled by the electrons already in the depletion region. (Remember that like charges repel each other.) When the forward-biased voltage is sufficiently high (0.7 volts for silicon diodes, and 0.3 volts for germanium diodes), the depletion region is eliminated. As the voltage is raised further, the negative voltage, in repelling electrons in the N region, pushes them into the P region, where they are attracted by the positive voltage. This combination of repulsive and attractive forces allows current to flow, as illustrated in the following figure. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 41 This combination of repulsive and attractive forces allows current to flow, as illustrated in the following figure. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 42 Note that an interesting aspect of diodes is that while the N and P regions of the diode have mobile charges, they do not have a net charge. The mobile charges (electrons in N regions and holes in P regions) are simply donated by the impurity atoms used to dope the semiconductor material. The impurity atoms have more electrons in the N region and less in the P region than are needed to bond to the adjacent silicon or germanium atoms in the crystalline structure. However, because the atoms have the same number of positive and negative charges, the net charge is neutral. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 43 In a similar way, metal is a conductor because it has more electrons than are needed to bond together the atoms in its crystalline structure. These excess electrons are free to move when a voltage is applied, either in a metal or an N type semiconductor, which makes the material electrically conductive. Electrons moving through the P region of the diode jump between the holes, which physicists model as the holes moving. In a depletion region, where electrons have been trapped by holes, there is a net negative charge. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 44 Reverse-biased You apply a reverse-biased voltage to a diode by applying positive voltage to the N type region and negative voltage to the P type region. In this scenario, electrons are attracted to the positive voltage, which pulls them away from the depletion region. No current can flow unless the voltage exceeds the reverse breakdown voltage. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 45 Diode symbol Diodes are marked with one band indicating the cathode (the N region) end of the diode. The band on the diode corresponds to the bar on the diode symbol, as shown in the following figure. Use this marking to orient diodes in a circuit. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 46 Part number The part number is marked on diodes. However, the part numbers don’t tell you much about the diode. For example, the 1N4001 is a silicon diode that can handle a peak reverse voltage of 50 volts, whereas the 1N270 is a germanium diode that can handle a peak reverse voltage of 80 volts. Your best bet is to refer to the manufacturer’s data sheet for the diode peak reverse voltage and other characteristics. You can easily look up data sheets on the Internet. Also, you can find links to the data sheets for the components used on the website at : www.buildinggadgets.com/index_datasheets.htm. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 47 3. THE ZENER DIODE Diodes can be manufactured so that breakdown occurs at lower and more precise voltages than those just discussed. These types of diodes are called zener diodes, so named because they exhibit the “Zener effect”—a particular form of voltage breakdown. At the zener voltage, a small current flows through the zener diode. This current must be maintained to keep the diode at the zener point. In most cases, a few milliamperes are all that is required. Figure 2.20 shows the zener diode symbol and a simple circuit. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 48 FIGURE 2.20 In this circuit, the battery determines the applied voltage. The zener diode determines the voltage drop (labeled Vz) across it. The resistor determines the current flow. Zeners are used to maintain a constant voltage at some point in a circuit. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 49 APPLICATION Examine an application in which a constant voltage is wanted—for example, a lamp driven by a DC generator. In this example, when the generator turns at full speed, it puts out 50 volts. When it runs more slowly, the voltage can drop to 35 volts. You want to illuminate a 20-volt lamp with this generator. Assume that the lamp draws 1.5 amperes. Figure 2.21 shows the circuit. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 50 FIGURE 2.21 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 51 A) You need to determine a suitable value for the resistance. Follow these steps to find a suitable resistance value: Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 52 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 53 B) Assume now that the 20-ohm resistor calculated is in place, and the voltage output of the generator drops to 35 volts, as shown in Figure 2.21. This is similar to what happens when a battery gets old. Its voltage level decays and it will no longer have sufficient voltage to produce the proper current. This results in the lamp glowing less brightly, or perhaps not at all. Note, however, that the resistance of the lamp stays the same. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 54 QUESTIONS Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 55 ANSWER Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 56 C) In many applications, a lowering of voltage across the lamp (or some other component) may be unacceptable. You can prevent this by using a zener diode, as shown in the circuit in Figure 2.22. If you choose a 20-volt zener (that is, one that has a 20-volt drop across it), then the lamp always has 20 volts across it, no matter what the output voltage is from the generator (provided, of course, that the output from the generator is always above 20 volts). Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 57 QUESTIONS Say that the voltage across the lamp is constant, and the generator output drops. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 58 ZENER ACTION To make this circuit work and keep 20 volts across the lamp at all times, you must find a suitable value of R. This value should allow sufficient total current to flow to provide 1.5 amperes required by the lamp, and the small amount required to keep the diode at its zener voltage. To do this, you start at the “worst case” condition. (“Worst case” design is a common practice in electronics. It is used to ensure that equipment can work under the most adverse conditions.) The worst case here would occur when the generator puts out only 35 volts. Figure 2.23 shows the paths that current would take in this circuit. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 59 Figure 2.23 shows the paths that current would take in this circuit. Find the value of R that enables 1.5 amperes to flow through the lamp. How much current can flow through the zener diode? You can choose any current you like, provided it is above a few milliamperes, and provided it does not cause the zener diode to burn out. In this example, assume that the zener current IZ is 0.5 amperes. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 60 QUESTIONS Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 61 ZENER ACTION (continued) Now, take a look at what happens when the generator supplies 50 volts, as shown in Figure 2.24. Because the lamp still has 20 volts across it, it can still draw only 1.5 amperes. But the total current and the zener current change. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 62 QUESTIONS Although the lamp voltage and current remain the same, the total current and the zener current both changed. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 63 QUESTIONS The increase in IT flows through the zener diode and not through the lamp. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 64 POWER DISSIPATED The power dissipated by the zener diode changes as the generator voltage changes. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 65 PROJECT 3 : The Zener Diode Voltage Regulator ● OBJECTIVE The objective of this project is to measure the voltage applied to the lamp, and the current through the lamp for different supply voltages, demonstrating the use of a zener diode to provide a steady voltage and current to a lamp when the supply voltage changes. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 66 OBJECTIVE The objective of this project is to measure the voltage applied to the lamp, and the current through the lamp for different supply voltages, demonstrating the use of a zener diode to provide a steady voltage and current to a lamp when the supply voltage changes. GENERAL INSTRUCTIONS While the circuit is set up, measure the lamp current, zener diode current, and supply voltage as the voltage from the 9-volt battery drops. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 67 PARTS LIST Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 68 STEP-BY-STEP INSTRUCTIONS Set up the circuit shown on Figure 2.25. The circled “A” designates a multimeter set to measure current, and the circled “V” designates a multimeter set to measure DC voltage. If you have some experience in building circuits, this schematic (along with the previous parts list) should provide all the information you need to build the circuit. If you need a bit more help in building the circuit, look at the photos of the completed circuit in the “Expected Results” section. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 69 STEP-BY-STEP INSTRUCTIONS (continued) FIGURE 2.25 Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 70 STEP-BY-STEP INSTRUCTIONS (continued) Carefully check your circuit against the diagram, especially the direction of the battery and the diode. The diode has a band at one end. Connect the lead at the end of the diode without the band to the ground bus on the breadboard. After you check your circuit, follow these steps, and record your measurements in the blank table following the steps: Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 71 STEP-BY-STEP INSTRUCTIONS (continued) Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 72 EXPECTED RESULTS Figure 2.26 shows the breadboarded circuit for this project. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 73 Figure 2.27 shows the test setup for this project. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 74 Complete your measurements like the ones shown in the following table. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 75 NOTE You must see in the recorded datas that, even though the supply voltage dropped by approximately 15 percent, the lamp current stayed roughly constant, showing less than a 1 percent drop. Pr. G. G. ALLOGHO / Electronique 1 / Chapitre 2 : DIODES 76