Hudgins, J L, Bogart, Jr, T.F., Mayaram, K, Kennedy, M. P, Kolumban, G. " Nonlinear Circuits The electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRc Press llc. 2000
Hudgins, J.L., Bogart, Jr., T.F., Mayaram, K., Kennedy, M.P., Kolumbán, G. “Nonlinear Circuits” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
5 Nonlinear circuits Jerry L Hudgins Limiting Circuits. Precision Rectifying Circuits Theodore F. Bogart, r 5.3 Distortion University of Southern Mississippi Method Three- Point Method Five- Point Method Kartikeya Mayaram Modulation.compressionandInterceptPointsCrossove Distortion. Failure-to-Follow Distortion. Frequency Distortion Michael Peter Kennedy PhaseDistortion.computerSimulationofDistortionComponents 5.4 Communicating with Chaos Elements of Chaotic Digital Communications Systems. Chaotic Digital Geza kolumban Modulation Schemes.Low-Pass Equivalent Models for Chaoti Technical University of Budapest Communications Systems. Multipath Performance of FM-DCSK 5.1 Diodes and rectifiers Jerry L. hudgins a diode generally refers to a two-terminal solid-state semiconductor device that presents a low impedance to current flow in one direction and a high impedance to current flow in the opposite direction. These properties allow the diode to be used as a one-way current valve in electronic circuits. Rectifiers are a class of circuits whose purpose is to convert ac waveforms(usually sinusoidal and with zero average value) into a waveform that has a significant non-zero average value(dc component). Simply stated, rectifiers are ac-to-dc energy converter circuits. Most rectifier circuits employ diodes as the principal elements in the energy conversion process; thus the almost inseparable notions of diodes and rectifiers. The general electrical characteristics of common diodes and some simple rectifier topologies incorporating diodes are discussed. Diodes Most diodes are made from a host crystal of silicon(Si) with appropriate impurity elements introduced to modify, in a controlled manner, the electrical characteristics of the device. These diodes are the typical Pn-junction (or bipolar)devices used in electronic circuits. Another type is the Schottky diode(unipolar), produced by placing a metal layer directly onto the semiconductor [Schottky, 1938; Mott, 1938. The metal emiconductor interface serves the same function as the pn-junction in the common diode structure. Other semiconductor materials such as gallium-arsenide( GaAs)and silicon-carbide(Sic) are also in use for new and ecialized applications of diodes. Detailed discussion of diode structures and the physics of their operation can be found in later paragraphs of this section. The electrical circuit symbol for a bipolar diode is shown in Fig. 5. 1. The polarities associated with the forward voltage drop for forward current flow are also included Current or voltage opposite to the polarities indicated in Fig. 5. 1 are considered to be negative values with respect to the diode conventions shown. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC 5 Nonlinear Circuits 5.1 Diodes and Rectifiers Diodes • Rectifiers 5.2 Limiters Limiting Circuits • Precision Rectifying Circuits 5.3 Distortion Harmonic Distortion • Power-Series Method • Differential-Error Method • Three-Point Method • Five-Point Method • Intermodulation Distortion • Triple-Beat Distortion • Cross Modulation • Compression and Intercept Points • Crossover Distortion • Failure-to-Follow Distortion • Frequency Distortion • Phase Distortion • Computer Simulation of Distortion Components 5.4 Communicating with Chaos Elements of Chaotic Digital Communications Systems • Chaotic Digital Modulation Schemes • Low-Pass Equivalent Models for Chaotic Communications Systems • Multipath Performance of FM-DCSK 5.1 Diodes and Rectifiers Jerry L. Hudgins A diode generally refers to a two-terminal solid-state semiconductor device that presents a low impedance to current flow in one direction and a high impedance to current flow in the opposite direction. These properties allow the diode to be used as a one-way current valve in electronic circuits. Rectifiers are a class of circuits whose purpose is to convert ac waveforms (usually sinusoidal and with zero average value) into a waveform that has a significant non-zero average value (dc component). Simply stated, rectifiers are ac-to-dc energy converter circuits. Most rectifier circuits employ diodes as the principal elements in the energy conversion process; thus the almost inseparable notions of diodes and rectifiers. The general electrical characteristics of common diodes and some simple rectifier topologies incorporating diodes are discussed. Diodes Most diodes are made from a host crystal of silicon (Si) with appropriate impurity elements introduced to modify, in a controlled manner, the electrical characteristics of the device. These diodes are the typical pn-junction (or bipolar) devices used in electronic circuits. Another type is the Schottky diode (unipolar), produced by placing a metal layer directly onto the semiconductor [Schottky, 1938; Mott, 1938]. The metalsemiconductor interface serves the same function as the pn-junction in the common diode structure. Other semiconductor materials such as gallium-arsenide (GaAs) and silicon-carbide (SiC) are also in use for new and specialized applications of diodes. Detailed discussion of diode structures and the physics of their operation can be found in later paragraphs of this section. The electrical circuit symbol for a bipolar diode is shown in Fig. 5.1. The polarities associated with the forward voltage drop for forward current flow are also included. Current or voltage opposite to the polarities indicated in Fig. 5.1 are considered to be negative values with respect to the diode conventions shown. Jerry L. Hudgins University of South Carolina Theodore F. Bogart, Jr. University of Southern Mississippi Kartikeya Mayaram Washington State University Michael Peter Kennedy University College Dublin Géza Kolumbán Technical University of Budapest
The characteristic curve shown in Fig. 5. 2 is representative of the current voltage dependencies of typical diodes. The diode conducts forward current with a small forward voltage drop across the device, simulating a closed switch. The relationship between the forward current and forward voltage is approximately given by the Shockley diode equation Shockley, 1949: FIGURE5.1 Circuit symbol for a diode indicating ip=I exp (5.1) ity associated with the oltage and current directions. where I is the leakage current through the diode, q is the electronic charge, n is a correction factor, k Boltzmanns constant, and Tis the temperature of the semiconductor. Around the knee of the curve in Fig 5.2 is a positive voltage that is termed the turn-on or sometimes the threshold voltage for the diode. This valu an approximate voltage above which the diode is considered turned"on"and can be modeled to first degree as a closed switch with constant forward drop. Below the threshold voltage value the diode is considered weakly conducting and approximated as an open switch. The exponential relationship shown in Eq (5.1)means that the diode forward current can change by orders of magnitude before there is a large change in diode voltage, thus providing the simple circuit model during conduction. The nonlinear relationship of Eq (5.1)also provides a means of frequency mixing for applications in modulation circuits Reverse voltage applied to the diode causes a small leakage current(negative according to the sign convention to flow that is typically orders of magnitude lower than current in the forward direction. The diode can withstand reverse voltages up to a limit determined by its physical construction and the semiconductor material used. Beyond this value the reverse voltage imparts enough energy to the charge carriers to cause large increases in current. The mechanisms by which this current increase occurs are impact ionization(avalanche)[McKay, 1954] and a tunneling phenomenon(Zener breakdown)[Moll, 1964 ]. Avalanche breakdown results in large power dissipation in the diode, is generally destructive, and should be avoided at all times. Both breakdown regions are superimposed in Fig 5.2 for comparison of their effects on the shape of the diode characteristic curve. Avalanche breakdown occurs for reverse applied voltages in the range of volts to kilovolts depending on ne exact design of the diode. Zener breakdown occurs at much lower voltages than the avalanche mechanisn Diodes specifically designed to operate in the Zener breakdown mode are used extensively as voltage regulators During forward conduction the power loss in the diode can become excessive for large current flow. Schottky diodes have an inherently lower turn-on voltage than pn-junction diodes and are therefore more desirable the energy losses in the diodes cant(such as output rectifiers in switching power supplies). Other considerations such as recovery characteristics from forward conduction to reverse blockin iD(A) Vo ((not to scale) 00 FIGURE 5.2 a typical diode dc characteristic curve showing the current dependence on e 2000 by CRC Press LLC
© 2000 by CRC Press LLC The characteristic curve shown in Fig. 5.2 is representative of the currentvoltage dependencies of typical diodes. The diode conducts forward current with a small forward voltage drop across the device, simulating a closed switch. The relationship between the forward current and forward voltage is approximately given by the Shockley diode equation [Shockley, 1949]: (5.1) where Is is the leakage current through the diode, q is the electronic charge, n is a correction factor, k is Boltzmann’s constant, and T is the temperature of the semiconductor. Around the knee of the curve in Fig. 5.2 is a positive voltage that is termed the turn-on or sometimes the threshold voltage for the diode. This value is an approximate voltage above which the diode is considered turned “on” and can be modeled to first degree as a closed switch with constant forward drop. Below the threshold voltage value the diode is considered weakly conducting and approximated as an open switch. The exponential relationship shown in Eq. (5.1) means that the diode forward current can change by orders of magnitude before there is a large change in diode voltage, thus providing the simple circuit model during conduction. The nonlinear relationship of Eq. (5.1) also provides a means of frequency mixing for applications in modulation circuits. Reverse voltage applied to the diode causes a small leakage current (negative according to the sign convention) to flow that is typically orders of magnitude lower than current in the forward direction. The diode can withstand reverse voltages up to a limit determined by its physical construction and the semiconductor material used. Beyond this value the reverse voltage imparts enough energy to the charge carriers to cause large increases in current. The mechanisms by which this current increase occurs are impact ionization (avalanche) [McKay, 1954] and a tunneling phenomenon (Zener breakdown) [Moll, 1964]. Avalanche breakdown results in large power dissipation in the diode, is generally destructive, and should be avoided at all times. Both breakdown regions are superimposed in Fig. 5.2 for comparison of their effects on the shape of the diode characteristic curve. Avalanche breakdown occurs for reverse applied voltages in the range of volts to kilovolts depending on the exact design of the diode. Zener breakdown occurs at much lower voltages than the avalanche mechanism. Diodes specifically designed to operate in the Zener breakdown mode are used extensively as voltage regulators in regulator integrated circuits and as discrete components in large regulated power supplies. During forward conduction the power loss in the diode can become excessive for large current flow. Schottky diodes have an inherently lower turn-on voltage than pn-junction diodes and are therefore more desirable in applications where the energy losses in the diodes are significant (such as output rectifiers in switching power supplies). Other considerations such as recovery characteristics from forward conduction to reverse blocking FIGURE 5.2 A typical diode dc characteristic curve showing the current dependence on voltage. FIGURE 5.1 Circuit symbol for a bipolar diode indicating the polarity associated with the forward voltage and current directions. i I qV nkT D s D = Ê Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ exp – 1
PoV(not to scale IGURE 5.3 The effects of temperature variations on the forward voltage drop and the avalanche breakdown voltage in Iso make one diode type more desirable than another. Schottky diodes condu charge carrier and are therefore inherently faster to turn off than bipolar diodes. However, one of the limitations of Schottky diodes is their excessive forward voltage drop when designed to support reverse biases above about 200 V. Therefore, high-voltage diodes are the pn-junction ty polar diode are many. The forward voltage drop uring conduction will decrease over a large current range, the reverse leakage current will increase, and the reverse avalanche breakdown voltage(Vap) will increase as the device temperature climbs. A family of static haracteristic curves highlighting these effects is shown in Fig. 5. 3 where T3> T2>T. In addition, a major effect on the switching characteristic is the increase in the reverse recovery time during turn-off. Some of the key parameters to be aware of when choosing a diode are its repetitive peak inverse voltage rating, VRRM(relates to the avalanche breakdown value), the peak forward surge current rating, IEsM(relates to the maximum allowable transient heating in the device), the average or rms current rating, Io(relates to the steady-state heating in the device), and the reverse recovery time, tr, (relates to the switching speed of the device) Rectifiers This section discusses some simple uncontrolled rectifier circuits that are commonly encountered. The term uncontrolled refers to the absence of any control signal necessary to operate the primary switching elements(diodes) in the rectifier circuit. The discussion of controlled rectifier circuits, and the controlled switches themselves, is more appropriate in the context of power electronics applications [Hoft, 1986]. Rectifiers are the fundamental building block in dc power supplies of all types and in dc power transmission used by some electric utilities. A single-phase full-wave rectifier circuit with the accompanying input and output voltage waveforms is show half-cycles of the input voltage. The forward drop across the diodes is ignored on the output graph, whid.a in Fig. 5.4. This topology makes use of a center-tapped transformer with each diode conducting on opposi a valid approximation if the peak voltages of the input and output are large compared to 1 V. The circuit changes a sinusoidal waveform with no dc component(zero average value)to one with a dc component of 2 Vpeak/. The rms value of the output is 0. 707Vpeak The dc value can be increased further by adding a low-pass filter in cascade with the output. The usual form of this filter is a shunt capacitor or an LC filter as shown in Fig. 5.5. The resonant frequency of the LC filter should be lower than the fundamental frequency of the rectifier output for effective performance. The ac portion of the output signal is reduced while the dc and rms values are increased by adding the filter. The remaining c portion of the output is called the ripple. Though somewhat confusing, the transformer, diodes, and filter are often collectively called the rectifier circuit. Another circuit topology commonly encountered is the bridge rectifier. Figure 5.6 illustrates single-and three-phase versions of the circuit. In the single-Phase circuit diodes DI and D4 half-cycle of the input while D2 and D3 conduct on the negative half-cycle of the input. Alternate pairs of diodes conduct in the three-phase circuit depending on the relative amplitude of the source signals. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC may also make one diode type more desirable than another. Schottky diodes conduct current with one type of charge carrier and are therefore inherently faster to turn off than bipolar diodes. However, one of the limitations of Schottky diodes is their excessive forward voltage drop when designed to support reverse biases above about 200 V. Therefore, high-voltage diodes are the pn-junction type. The effects due to an increase in the temperature in a bipolar diode are many. The forward voltage drop during conduction will decrease over a large current range, the reverse leakage current will increase, and the reverse avalanche breakdown voltage (VBD) will increase as the device temperature climbs. A family of static characteristic curves highlighting these effects is shown in Fig. 5.3 where T3 > T2 > T1. In addition, a major effect on the switching characteristic is the increase in the reverse recovery time during turn-off. Some of the key parameters to be aware of when choosing a diode are its repetitive peak inverse voltage rating, VRRM (relates to the avalanche breakdown value), the peak forward surge current rating, IFSM (relates to the maximum allowable transient heating in the device), the average or rms current rating, IO (relates to the steady-state heating in the device), and the reverse recovery time, trr (relates to the switching speed of the device). Rectifiers This section discusses some simple uncontrolled rectifier circuits that are commonly encountered. The term uncontrolled refers to the absence of any control signal necessary to operate the primary switching elements (diodes) in the rectifier circuit. The discussion of controlled rectifier circuits, and the controlled switches themselves, is more appropriate in the context of power electronics applications [Hoft, 1986]. Rectifiers are the fundamental building block in dc power supplies of all types and in dc power transmission used by some electric utilities. A single-phase full-wave rectifier circuit with the accompanying input and output voltage waveforms is shown in Fig. 5.4. This topology makes use of a center-tapped transformer with each diode conducting on opposite half-cycles of the input voltage. The forward drop across the diodes is ignored on the output graph, which is a valid approximation if the peak voltages of the input and output are large compared to 1 V. The circuit changes a sinusoidal waveform with no dc component (zero average value) to one with a dc component of 2Vpeak/p. The rms value of the output is 0.707Vpeak. The dc value can be increased further by adding a low-pass filter in cascade with the output. The usual form of this filter is a shunt capacitor or an LC filter as shown in Fig. 5.5. The resonant frequency of the LC filter should be lower than the fundamental frequency of the rectifier output for effective performance. The ac portion of the output signal is reduced while the dc and rms values are increased by adding the filter. The remaining ac portion of the output is called the ripple. Though somewhat confusing, the transformer, diodes, and filter are often collectively called the rectifier circuit. Another circuit topology commonly encountered is the bridge rectifier. Figure 5.6 illustrates single- and three-phase versions of the circuit. In the single-phase circuit diodes D1 and D4 conduct on the positive half-cycle of the input while D2 and D3 conduct on the negative half-cycle of the input. Alternate pairs of diodes conduct in the three-phase circuit depending on the relative amplitude of the source signals. FIGURE 5.3 The effects of temperature variations on the forward voltage drop and the avalanche breakdown voltage in a bipolar diode
Conducting Diode D1 I D2 I DI I D2 I D1 ID2 FIGURE 5.4 A single-Phase full-wave rectifier circuit using a center-tapped transformer with the associated input and Filter FIGURE 5.5 A single-Phase full-wave rectifier with the addition of an output filter. 本D本D3 Filter D2 AD4 D32D5 te D4本D6 FIGURE 5.6 Single- and three-phase bridge rectifier circuits. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC FIGURE 5.4 A single-phase full-wave rectifier circuit using a center-tapped transformer with the associated input and output waveforms. FIGURE 5.5 A single-phase full-wave rectifier with the addition of an output filter. FIGURE 5.6 Single- and three-phase bridge rectifier circuits. Vin L C C + – Filter Load
S4b6甲32p4D6甲甲 ⅩXX E5.7 Three-phase rectifier output compared to the input signals. The input signals as well as the labels are those referenced to Fig. 5.6. The three-phase inputs with the associated rectifier output voltage are shown in Fig. 5. 7 as they would appear without the low-pass filter section. The three-phase bridge rectifier has a reduced ripple content of 4%as diodes that conduct are also shown at the top of the figure. This output waveform assumes a purely resistive load connected as shown in Fig. 5.6. Most loads(motors, transformers, etc. and many sources(power grid) clude some inductance, and in fact may be dominated by inductive properties. This causes phase shifts between the input and output waveforms. The rectifier output may thus vary in shape and phase considerably from that shown in Fig. 5.7 (Kassakian et al, 1991]. When other types of switches are used in these circuits the inductive elements can induce large voltages that may damage sensitive or expensive components. Diodes are used regularly in such circuits to shunt current and clamp induced voltages at low levels to protect expensive One variation of the typical rectifier is the Cockroft Walton circuit used to obtain high voltages without the necessity of providing a high-voltage transformer. The uit in Fig. 5. 8 multiplies the peak secondary voltage y a factor of six. The steady-state voltage level at each filter capacitor node is shown in the figure. Adding s, max s ma 2vs.max additional stages increases the load voltage further. As in other rectifier circuits, the value of the capacitors will determine the amount of ripple in the output FIGURE 5.8 Cockroft-Walton circuit used for voltage actors in a lower voltage stage than in the next highest voltage stage Defining Terms Bipolar device: Semiconductor electronic device that uses positive and negative charge carriers to conduct electric current Diode: Two-terminal solid-state semiconductor device that presents a low impedance to current flow in one direction and a high impedance to current flow in the opposite direction. Pn-junction: Metallurgical interface of two regions in a semiconductor where one region contains impurity elements that create equivalent positive charge carriers(p-type) and the other semiconductor region ontains impurities that create negative charge carriers(n-type) Ripple: The ac(time-varying) portion of the output signal from a rectifier circuit. hottky diode: A diode formed by placing a metal layer directly onto a unipolar semiconductor substrate Uncontrolled rectifier: A rectifier circuit employing switches that do not require control signals to operate them in their“on”or“off” states. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC The three-phase inputs with the associated rectifier output voltage are shown in Fig. 5.7 as they would appear without the low-pass filter section. The three-phase bridge rectifier has a reduced ripple content of 4% as compared to a ripple content of 47% in the single-phase bridge rectifier [Milnes, 1980]. The corresponding diodes that conduct are also shown at the top of the figure. This output waveform assumes a purely resistive load connected as shown in Fig. 5.6. Most loads (motors, transformers, etc.) and many sources (power grid) include some inductance, and in fact may be dominated by inductive properties. This causes phase shifts between the input and output waveforms. The rectifier output may thus vary in shape and phase considerably from that shown in Fig. 5.7 [Kassakian et al., 1991]. When other types of switches are used in these circuits the inductive elements can induce large voltages that may damage sensitive or expensive components. Diodes are used regularly in such circuits to shunt current and clamp induced voltages at low levels to protect expensive components such as electronic switches. One variation of the typical rectifier is the CockroftWalton circuit used to obtain high voltages without the necessity of providing a high-voltage transformer. The circuit in Fig. 5.8 multiplies the peak secondary voltage by a factor of six. The steady-state voltage level at each filter capacitor node is shown in the figure. Adding additional stages increases the load voltage further. As in other rectifier circuits, the value of the capacitors will determine the amount of ripple in the output waveform for given load resistance values. In general, the capacitors in a lower voltage stage should be larger than in the next highest voltage stage. Defining Terms Bipolar device: Semiconductor electronic device that uses positive and negative charge carriers to conduct electric current. Diode: Two-terminal solid-state semiconductor device that presents a low impedance to current flow in one direction and a high impedance to current flow in the opposite direction. pn-junction: Metallurgical interface of two regions in a semiconductor where one region contains impurity elements that create equivalent positive charge carriers (p-type) and the other semiconductor region contains impurities that create negative charge carriers (n-type). Ripple: The ac (time-varying) portion of the output signal from a rectifier circuit. Schottky diode: A diode formed by placing a metal layer directly onto a unipolar semiconductor substrate. Uncontrolled rectifier: A rectifier circuit employing switches that do not require control signals to operate them in their “on” or “off” states. FIGURE 5.7 Three-phase rectifier output compared to the input signals. The input signals as well as the conducting diode labels are those referenced to Fig. 5.6. FIGURE 5.8 Cockroft-Walton circuit used for voltage multiplication
Related Topics 22.2 Diodes.30.1 Power Semiconductor Devices References R.G. Hoft, Semiconductor power electronics, New York: Van Nostrand Reinhold. 1986. J.G. Kassakian, M.E. Schlecht, and G.C. Verghese, Principles of Power Electronics, Reading, Mass.: Addison K.G. McKay, Avalanche breakdown in silicon, "Physical Review, voL 94, P. 877, 1954 A.G. Milnes, Semiconductor Devices and Integrated Electronics, New York: Van Nostrand Reinhold, 1980 J.L. Moll, Physics of Semiconductors, New York: McGraw-Hill, 1964 N.F. Mott, Note on the contact between a metal and an insulator or semiconductor, Proc. Cambridge philos. Soc,vol.34,p.568,1938 W. Schottky,"Halbleitertheorie der Sperrschicht, " Naturwissenschaften, vol 26, P. 843, 1938 W. Shockley, The theory of p-n junctions in semiconductors and p-n junction transistors, "Bell System Tech Jvol.28,p.435,1949 Further information A good introduction to solid-state electronic devices with a minimum of mathematics and physics is Solid State Electronic Devices, 3rd edition, by B.G. Streetman, Prentice-Hall, 1989. A rigorous and more detailed discussion is provided in Physics of Semiconductor Devices, 2nd edition, by S M. Sze, John Wiley Sons, 1981. Both of these books discuss many specialized diode structures as well as other semiconductor devices. Advanced material on the most recent developments in semiconductor devices, including diodes, can be found in technical journals such as the IEEE Transactions on Electron Devices, Solid State Electronics, and Journal of Applied Physics. a good summary of advanced rectifier topologies and characteristics is given in Basic Principles of Power Electronics by K. Heumann, Springer-Verlag, 1986. Advanced material on rectifier designs as well as other power electronics circuits can be found in IEEE Transactions on Power Electronics, IEEE Transactions on Industry Applications, and the EPE Journal. Two good industry magazines that cover power devices such as diodes and power converter circuitry are Power Control and Intelligent Motion(PCIM) and Power Technics. 5.2 Limiters Theodore F. Bogart, r Limiters are named for their ability to limit voltage excursions at the output of a circuit whose input may undergo unrestricted variations. They are also called clipping circuits because waveforms having rounded peaks that exceed the limit(s)imposed by such circuits appear, after limiting, to have their peaks flattened, or"clipped off. Limiters may be designed to clip positive voltages at a certain level, negative voltages at a different level, or to do both. The simplest types consist simply of diodes and dc voltage sources, while more elaborate designs incorporate operational amplifiers Limiting Circuits Figure 5.9 shows how the transfer characteristics of limiting circuits reflect the fact that outputs are clipped at certain levels In each of the examples shown, note that the characteristic becomes horizontal at the outpr level where clipping occurs. The horizontal line means that the output remains constant regardless of the input level in that region. Outside of the clipping region, the transfer characteristic is simply a line whose slope equals Excerpted from T. Bogart, Jr, Electronic Devices and Circuits, 3rd ed, Columbus, Ohio: Macmillan/Merrill, 1993, Pp. 689-697. with permission e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Related Topics 22.2 Diodes • 30.1 Power Semiconductor Devices References R.G. Hoft, Semiconductor Power Electronics, New York: Van Nostrand Reinhold, 1986. J.G. Kassakian, M.F. Schlecht, and G.C. Verghese, Principles of Power Electronics, Reading, Mass.: AddisonWesley, 1991. K.G. McKay, “Avalanche breakdown in silicon,” Physical Review, vol. 94, p. 877, 1954. A.G. Milnes, Semiconductor Devices and Integrated Electronics, New York: Van Nostrand Reinhold, 1980. J.L. Moll, Physics of Semiconductors, New York: McGraw-Hill, 1964. N.F. Mott, “Note on the contact between a metal and an insulator or semiconductor,” Proc. Cambridge Philos. Soc., vol. 34, p. 568, 1938. W. Schottky, “Halbleitertheorie der Sperrschicht,” Naturwissenschaften, vol. 26, p. 843, 1938. W. Shockley, “The theory of p-n junctions in semiconductors and p-n junction transistors,” Bell System Tech. J., vol. 28, p. 435, 1949. Further Information A good introduction to solid-state electronic devices with a minimum of mathematics and physics is Solid State Electronic Devices, 3rd edition, by B.G. Streetman, Prentice-Hall, 1989. A rigorous and more detailed discussion is provided in Physics of Semiconductor Devices, 2nd edition, by S.M. Sze, John Wiley & Sons, 1981. Both of these books discuss many specialized diode structures as well as other semiconductor devices.Advanced material on the most recent developments in semiconductor devices, including diodes, can be found in technical journals such as the IEEE Transactions on Electron Devices, Solid State Electronics, and Journal of Applied Physics. A good summary of advanced rectifier topologies and characteristics is given in Basic Principles of Power Electronics by K. Heumann, Springer-Verlag, 1986. Advanced material on rectifier designs as well as other power electronics circuits can be found in IEEE Transactions on Power Electronics, IEEE Transactions on Industry Applications, and the EPE Journal. Two good industry magazines that cover power devices such as diodes and power converter circuitry are Power Control and Intelligent Motion (PCIM) and Power Technics. 5.2 Limiters1 Theodore F. Bogart, Jr. Limiters are named for their ability to limit voltage excursions at the output of a circuit whose input may undergo unrestricted variations. They are also called clipping circuits because waveforms having rounded peaks that exceed the limit(s) imposed by such circuits appear, after limiting, to have their peaks flattened, or “clipped” off. Limiters may be designed to clip positive voltages at a certain level, negative voltages at a different level, or to do both. The simplest types consist simply of diodes and dc voltage sources, while more elaborate designs incorporate operational amplifiers. Limiting Circuits Figure 5.9 shows how the transfer characteristics of limiting circuits reflect the fact that outputs are clipped at certain levels. In each of the examples shown, note that the characteristic becomes horizontal at the output level where clipping occurs. The horizontal line means that the output remains constant regardless of the input level in that region. Outside of the clipping region, the transfer characteristic is simply a line whose slope equals 1 Excerpted from T.F. Bogart, Jr., Electronic Devices and Circuits, 3rd ed., Columbus, Ohio:Macmillan/Merrill, 1993, pp. 689–697. With permission
(a) Positive clippi (b) Negative clipping (c)Positive and negative clipping FIGURE 5.9 Waveforms and transfer characteristics of limiting circuits. Source: T.E. Bogart, Jr, Electronic Devices and Circuits, 3rd ed, Columbus, Ohio: Macmillan/Merrill, 1993, p 676. With permission. the gain of the device. This is the region of linear operation. In these examples, the devices are assumed to have unity gain, so the slope of each line in the linear region is 1. Figure 5.10 illustrates a somewhat different kind of limiting action. Instead of the positive or negative peaks being clipped, the output follows the input when the signal is above or below a certain level. The transfer characteristics show that linear operation occurs only when certain signal levels are reached and that the output remains constant below those levels. This form of limiting can also be thought of as a special case of that shown in Fig. 5.9. Imagine, for example, that the clipping level in Fig. 5.9(b) is raised to a positive value; then the result is the same as Fig. 5.10(a) Limiting can be accomplished using biased diodes. Such circuits rely on the fact that diodes have very low impedances when they are forward biased and are essentially open circuits when reverse biased. If a certain point in a circuit, such as the output of an amplifier, is connected through a very small impedance to a constant voltage, then the voltage at the circuit point cannot differ significantly from the constant voltage. We say in this case that the point is clamped to the fixed voltage. An ideal, forward-biased diode is like a closed switch if it is connected between a point in a circuit and a fixed voltage source, the diode very effectively holds the boint to the fixed voltage. Diodes can be connected in operational amplifier circuits, as well as other circuits, e 2000 by CRC Press LLC
© 2000 by CRC Press LLC the gain of the device. This is the region of linear operation. In these examples, the devices are assumed to have unity gain, so the slope of each line in the linear region is 1. Figure 5.10 illustrates a somewhat different kind of limiting action. Instead of the positive or negative peaks being clipped, the output follows the input when the signal is above or below a certain level. The transfer characteristics show that linear operation occurs only when certain signal levels are reached and that the output remains constant below those levels. This form of limiting can also be thought of as a special case of that shown in Fig. 5.9. Imagine, for example, that the clipping level in Fig. 5.9(b) is raised to a positive value; then the result is the same as Fig. 5.10(a). Limiting can be accomplished using biased diodes. Such circuits rely on the fact that diodes have very low impedances when they are forward biased and are essentially open circuits when reverse biased. If a certain point in a circuit, such as the output of an amplifier, is connected through a very small impedance to a constant voltage, then the voltage at the circuit point cannot differ significantly from the constant voltage. We say in this case that the point is clamped to the fixed voltage. An ideal, forward-biased diode is like a closed switch, so if it is connected between a point in a circuit and a fixed voltage source, the diode very effectively holds the point to the fixed voltage. Diodes can be connected in operational amplifier circuits, as well as other circuits, FIGURE 5.9 Waveforms and transfer characteristics of limiting circuits. (Source: T.F. Bogart, Jr., Electronic Devices and Circuits, 3rd ed., Columbus, Ohio: Macmillan/Merrill, 1993, p. 676. With permission.)
E FIGURE 5. 10 Another form of clipping. Compare with Fig. 5.9.(Source: T.E. Bogart, Jr, Electronic Devices and Circuits, 3rd ed, Columbus, Ohio: Macmillan/Merrill, 1993, P 690. With permission. +10=VD Vo>0 vvD=v-9 FIGURE 5.11 Examples of biased diodes and the signal voltages vi required to forward bias them.(Ideal diodes are ssumed.)In each case, we solve for the value of v, that is necessary to make Vp >0.(Source: T.E. Bogart, Jr, Electronic Devices and Circuits, 3rd ed, Columbus, Ohio: Macmillan/Merrill, 1993, P. 691. with permission. in such a way that they become forward biased when a signal reaches a certain voltage. When the forward-biasing level is reached, the diode serves to hold the output to a fixed voltage and thereby establishes a clipping level a biased diode is simply a diode connected to a fixed voltage source. The value and polarity of the voltage ource determine what value of total voltage across the combination is necessary to forward bias the diode Figure 5.11 shows several examples. (In prac ies resistor would be connected in each circuit to limit current flow when the diode is forward biased. In each part of the figure, we can write Kirchhoffs voltage law e 2000 by CRC Press LLC
© 2000 by CRC Press LLC in such a way that they become forward biased when a signal reaches a certain voltage.When the forward-biasing level is reached, the diode serves to hold the output to a fixed voltage and thereby establishes a clipping level. A biased diode is simply a diode connected to a fixed voltage source. The value and polarity of the voltage source determine what value of total voltage across the combination is necessary to forward bias the diode. Figure 5.11 shows several examples. (In practice, a series resistor would be connected in each circuit to limit current flow when the diode is forward biased.) In each part of the figure, we can write Kirchhoff’s voltage law FIGURE 5.10 Another form of clipping. Compare with Fig. 5.9. (Source: T.F. Bogart, Jr., Electronic Devices and Circuits, 3rd ed., Columbus, Ohio: Macmillan/Merrill, 1993, p. 690. With permission.) FIGURE 5.11 Examples of biased diodes and the signal voltages vi required to forward bias them. (Ideal diodes are assumed.) In each case, we solve for the value of vi that is necessary to make VD > 0. (Source: T.F. Bogart, Jr., Electronic Devices and Circuits, 3rd ed., Columbus, Ohio: Macmillan/Merrill, 1993, p. 691. With permission.)
12b 12v FIGURE 5. 12 Examples of parallel clipping circuits. ( Source: T.E. Bogart, Jr, Electronic Devices and Circuits, 3rd ed, Columbus, Ohio: Macmillan/Merrill, 1993, p. 692. with permission. around the loop to determine the value of input voltage v, that is necessary to forward bias the diode. Assuming that the diodes are ideal (neglecting their forward voltage drops), we determine the value v; necessary to forward bias each diode by determining the value v; necessary to make vp >0. when v, reaches the voltage necessary to make Vp>0, the diode becomes forward biased and the signal source is forced to, or held at, the dc source voltage. If the forward voltage drop across the diode is not neglected, the clipping level is found by determining the value of vi necessary to make Vp greater than that forward drop(e.g ,Vp>0.7 V for a silicon diode Figure 5. 12 shows three examples of clipping circuits using ideal biased diodes and the waveforms that result when each is driven by a sine-wave input. In each case, note that the output equals the dc source voltage when ne input reaches the value necessary to forward bias the diode. Note also that the type of clipping we showed in Fig. 5. 9 occurs when the fixed bias voltage tends to reverse bias the diode, and the type shown in Fig. 5.10 occurs when the fixed voltage tends to forward bias the diode. When the diode is reverse biased by the input signal, it is like an open circuit that disconnects the dc source, and the output follows the input. These circuits are called parallel clippers because the biased diode is in parallel with the output. Although the circuits behave the same way whether or not one side of the dc voltage source is connected to the common(low) side of the input and output, the connections shown in Fig. 5. 12(a)and(c)are preferred to that in(b), because the latter Figure 5. 13 shows a biased diode connected in the feedback path of an inverting operational amplifier. The diode is in parallel with the feedback resistor and forms a parallel clipping circuit like that shown in Fig. 5.12 In an operational amplifier circuit, v = v, and since v+=0V in this circuit, v is approximately oV(virtual ground). Thus, the voltage across R is the same as the output voltage v, Therefore, when the output voltage reaches the bias voltage E, the output is held at E volts. Figure 5.13(b)illustrates this fact for a sinusoidal input. So long as the diode is reverse biased, it acts like an open circuit and the amplifier behaves like a conventional inverting amplifier. Notice that output clipping occurs at input voltage-(R/R)E, since the amplifier inverts and has closed-loop gain magnitude R/R, The resulting transfer characteristic is shown in Fig. 5.13(c) In practice, the biased diode shown in the feedback of Fig. 5.13(a) is often replaced by a Zener diode in series with a conventional diode. This arrangement eliminates the need for a floating voltage source. Zener diodes e 2000 by CRC Press LLC
© 2000 by CRC Press LLC around the loop to determine the value of input voltage vi that is necessary to forward bias the diode. Assuming that the diodes are ideal (neglecting their forward voltage drops), we determine the value vi necessary to forward bias each diode by determining the value vi necessary to make vD > 0. When vi reaches the voltage necessary to make VD > 0, the diode becomes forward biased and the signal source is forced to, or held at, the dc source voltage. If the forward voltage drop across the diode is not neglected, the clipping level is found by determining the value of vi necessary to make VD greater than that forward drop (e.g., VD > 0.7 V for a silicon diode). Figure 5.12 shows three examples of clipping circuits using ideal biased diodes and the waveforms that result when each is driven by a sine-wave input. In each case, note that the output equals the dc source voltage when the input reaches the value necessary to forward bias the diode. Note also that the type of clipping we showed in Fig. 5.9 occurs when the fixed bias voltage tends to reverse bias the diode, and the type shown in Fig. 5.10 occurs when the fixed voltage tends to forward bias the diode. When the diode is reverse biased by the input signal, it is like an open circuit that disconnects the dc source, and the output follows the input. These circuits are called parallel clippers because the biased diode is in parallel with the output. Although the circuits behave the same way whether or not one side of the dc voltage source is connected to the common (low) side of the input and output, the connections shown in Fig. 5.12(a) and (c) are preferred to that in (b), because the latter uses a floating source. Figure 5.13 shows a biased diode connected in the feedback path of an inverting operational amplifier. The diode is in parallel with the feedback resistor and forms a parallel clipping circuit like that shown in Fig. 5.12. In an operational amplifier circuit, v– ª v+, and since v+ = 0 V in this circuit, v– is approximately 0 V (virtual ground). Thus, the voltage across Rf is the same as the output voltage vo . Therefore, when the output voltage reaches the bias voltage E, the output is held at E volts. Figure 5.13(b) illustrates this fact for a sinusoidal input. So long as the diode is reverse biased, it acts like an open circuit and the amplifier behaves like a conventional inverting amplifier. Notice that output clipping occurs at input voltage –(R1/Rf )E, since the amplifier inverts and has closed-loop gain magnitude Rf /R1. The resulting transfer characteristic is shown in Fig. 5.13(c). In practice, the biased diode shown in the feedback of Fig. 5.13(a) is often replaced by a Zener diode in series with a conventional diode. This arrangement eliminates the need for a floating voltage source. Zener diodes FIGURE 5.12 Examples of parallel clipping circuits. (Source: T.F. Bogart, Jr., Electronic Devices and Circuits, 3rd ed., Columbus, Ohio: Macmillan/Merrill, 1993, p. 692. With permission.)
