Pecht, M, Lall, P,, Ballou, G, Sankaran, C, Angelopoulos, N."Passive Components The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Pecht, M., Lall, P., Ballou, G., Sankaran, C., Angelopoulos, N. “Passive Components” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
Passive components Michael Pecht 1.1 Resistors University of maryland Resistor Characteristics.Resistor Types 1.2 Capacitors and Inductors Capacitors. Types of Capacitors. Inductors motorola 1.3 Transformers Glen ballou Types of Transformers. Principle of sformation. Electromagnetic Equation. Transformer Core· Transformer losses· Transformer C. Sankaran Connections Transformer Impedance 1.4 Electrical fuses atings. Fuse Performance. Selective Nick Angelopoulos Coordination· Standards· Products· Standard- Class h Gould Shawmut Company 1 Resistors Michael Pecht and Pradeep lall The resistor is an electrical device whose primary function is to introduce resistance to the flow of electric current. The magnitude of opposition to the flow of current is called the resistance of the resistor. A larger resistance value indicates a greater opposition to current flow The resistance is measured in ohms. An ohm is the resistance that arises when a current of one ampere is passed through a resistor subjected to one volt across its terminals. The various uses of resistors include setting biases, controlling gain, fixing time constants, matching and loading circuits, voltage division, and heat generation. The following sections discuss resistor characteristi and various resistor types. Resistor characteristics Voltage and Current Characteristics of Resistors The resistance of a resistor is directly proportional to the resistivity of the material and the length of the resistor and inversely proportional to the cross-sectional area perpendicular to the direction of current flow. The resistance R of a resistor is given by R A where p is the resistivity of the resistor material( Q2.cm), l is the length of the resistor along direction of current flow(cm), inherent property of materials. Good resistor materials typically have resistivities between 2 x 10- and 200x c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 1 Passive Components 1.1 Resistors Resistor Characteristics • Resistor Types 1.2 Capacitors and Inductors Capacitors • Types of Capacitors • Inductors 1.3 Transformers Types of Transformers • Principle of Transformation • Electromagnetic Equation • Transformer Core • Transformer Losses • Transformer Connections • Transformer Impedance 1.4 Electrical Fuses Ratings • Fuse Performance • Selective Coordination • Standards • Products • Standard— Class H • HRC • Trends 1.1 Resistors Michael Pecht and Pradeep Lall The resistor is an electrical device whose primary function is to introduce resistance to the flow of electric current. The magnitude of opposition to the flow of current is called the resistance of the resistor. A larger resistance value indicates a greater opposition to current flow. The resistance is measured in ohms. An ohm is the resistance that arises when a current of one ampere is passed through a resistor subjected to one volt across its terminals. The various uses of resistors include setting biases, controlling gain, fixing time constants, matching and loading circuits, voltage division, and heat generation. The following sections discuss resistor characteristics and various resistor types. Resistor Characteristics Voltage and Current Characteristics of Resistors The resistance of a resistor is directly proportional to the resistivity of the material and the length of the resistor and inversely proportional to the cross-sectional area perpendicular to the direction of current flow. The resistance R of a resistor is given by (1.1) where r is the resistivity of the resistor material (W · cm), l is the length of the resistor along direction of current flow (cm), and A is the cross-sectional area perpendicular to current flow (cm2 ) (Fig. 1.1). Resistivity is an inherent property of materials. Good resistor materials typically have resistivities between 2 ¥ 10–6 and 200 ¥ 10–6 W · cm. R l A = r Michael Pecht University of Maryland Pradeep Lall Motorola Glen Ballou Ballou Associates C. Sankaran Electro-Test Nick Angelopoulos Gould Shawmut Company
The resistance can also be defined in terms of sheet resistivity. If the sheet resistivity is used, a standard sheet thickness is assumed and factored into resistivity. Typically, resistors are rectangular in shape; therefore the length I divided by the width w gives the number of squares within the resistor(Fig. 1. 2). The number of squares multiplied by the resistivity is the resistance Cross-sectional area(A) FIGURE 1.1 Resistance of a rectangular l heet p sheet (1.2) cross-section resistor with cross-sectional where Psheet is the sheet resistivity(Q2/square), I is the length of resistor(cm), w is the width of the resistor(cm), resistance(Q2) The resistance of a resistor can be defined in terms of the voltage drop across the resistor and current through V (1.3) where R is the resistance(Q2), Vis the voltage across the resistor(V), and I is the current through the resistor (A). Whenever a current is passed through a resistor, a voltage is dropped across the ends of the resistor Figure 1.3 depicts the symbol of the resistor with the Ohms law relation. All resistors dissipate power when a voltage is applied. The power dissipated by the resistor is represented by (1.4) R where P is the power dissipated (W), V is the voltage across the resistor(V), and R is the resistance(Q2).An ideal resistor dissipates electric energy without storing electric or magnetic energy Resistor Networks Resistors may be joined to form networks. If resistors are joined in series, the effective resistance(Rr) is the m of the individual resistances(Fig 1.4) R WWWW 1-R THE ABOVE RESISTOR IS 3. 25 SQUARES FIGURE 1.3 A resistor with IFp=100, THEN R=325ax1000=3259 flowing through it will have a FIGURE 1.2 Number of squares in a rectangular resistor. oltage drop of IR across it
© 2000 by CRC Press LLC The resistance can also be defined in terms of sheet resistivity. If the sheet resistivity is used, a standard sheet thickness is assumed and factored into resistivity. Typically, resistors are rectangular in shape; therefore the length l divided by the width w gives the number of squares within the resistor (Fig. 1.2). The number of squares multiplied by the resistivity is the resistance. (1.2) where rsheet is the sheet resistivity (W/square), l is the length of resistor (cm), w is the width of the resistor (cm), and Rsheet is the sheet resistance (W). The resistance of a resistor can be defined in terms of the voltage drop across the resistor and current through the resistor related by Ohm’s law, (1.3) where R is the resistance (W), V is the voltage across the resistor (V), and I is the current through the resistor (A). Whenever a current is passed through a resistor, a voltage is dropped across the ends of the resistor. Figure 1.3 depicts the symbol of the resistor with the Ohm’s law relation. All resistors dissipate power when a voltage is applied. The power dissipated by the resistor is represented by (1.4) where P is the power dissipated (W), V is the voltage across the resistor (V), and R is the resistance (W). An ideal resistor dissipates electric energy without storing electric or magnetic energy. Resistor Networks Resistors may be joined to form networks. If resistors are joined in series, the effective resistance (RT) is the sum of the individual resistances (Fig. 1.4). (1.5) FIGURE 1.1 Resistance of a rectangular cross-section resistor with cross-sectional area A and length L. R l w sheet = rsheet R V I = P V R = 2 R R T i i n = = Â 1 FIGURE 1.2 Number of squares in a rectangular resistor. FIGURE 1.3 A resistor with resistance R having a current I flowing through it will have a voltage drop of IR across it
R1 R WWwr-o0···WWW0···0WW FIGURE 1. 4 Resistors connected in series If resistors are joined in parallel, the effective resistance(Rr)is the reciprocal of the sum of the reciprocals of individual resistances(Fig. 1.5 (16) Ry Temperature Coefficient of Electrical Resistance The resistance for most resistors changes with temperature. The tem perature coefficient of electrical resistance is the change in electrical WW resistance of a resistor per unit change in temperature. The tempera- ture coefficient of resistance is measured in S/C. The temperature coefficient of resistors may be either positive or negative. A positive temperature coefficient denotes a rise in resistance with a rise in tem erature; a negative temperature coefficient of resistance denotes a decrease in resistance with a rise in temperature. Pure metals typically have a positive temperature coefficient of resistance, while some metal alloys such as constantin and manganin have a zero temperature coef- ficient of resistance. Carbon and graphite mixed with binders usually fIGuRE 15 Resistors connected exhibit negative temperature coefficients, although certain choices of binders and process variations may yield positive temperature coeff.parallel. cients. The temperature coefficient of resistance is given by R(T2)=R(T1)[1+an(T2-T1) (1.7) where an is the temperature coefficient of electrical resistance at reference temperature T, R(T))is the resistance (32), and R(T,) is the temperature T,(S2). Th aken to be 20oC. Because the variation in resistance between any two temperatures is usually not linear as predicted by Eq(1.7), common practice is to apply the equation between temperature increments and the to plot the resistance change versus temperature for a number of incremental temperatures High-Frequency Effects Resistors show a change in their resistance value when subjected to ac voltages. The change in resistance with voltage frequency is W known as the Boella effect. The effect occurs because all resistors have some inductance and capacitance along with the resistive component and thus can be approximated by an equivalent circuit shown in Fig. 1.6. Even though the definition of useful frequency FIGURE 1.6 Equivalent circuit for a resistor range is application dependent, typically, the useful range of the resistor is the highest frequency at which the impedance differs from the resistance by more than the tolerance of the resistor The frequency effect on resistance varies with the resistor construction. wire-wound resistors typically exhibit an increase in their impedance with frequency. In composition resistors the capacitances are formed by the many conducting particles which are held in contact by a dielectric binder. The ac impedance for film resistors remains constant until 100 MHz(1 MHz =10 Hz) and then decreases at higher frequencies( Fig. 1.7).For film resistors, the decrease in dc resistance at higher frequencies decreases with increase in resistance. Film resistors have the most stable high-frequency performance. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC If resistors are joined in parallel, the effective resistance (RT) is the reciprocal of the sum of the reciprocals of individual resistances (Fig. 1.5). (1.6) Temperature Coefficient of Electrical Resistance The resistance for most resistors changes with temperature. The temperature coefficient of electrical resistance is the change in electrical resistance of a resistor per unit change in temperature. The temperature coefficient of resistance is measured in W/°C. The temperature coefficient of resistors may be either positive or negative. A positive temperature coefficient denotes a rise in resistance with a rise in temperature; a negative temperature coefficient of resistance denotes a decrease in resistance with a rise in temperature. Pure metals typically have a positive temperature coefficient of resistance, while some metal alloys such as constantin and manganin have a zero temperature coef- ficient of resistance. Carbon and graphite mixed with binders usually exhibit negative temperature coefficients, although certain choices of binders and process variations may yield positive temperature coeffi- cients. The temperature coefficient of resistance is given by R(T2) = R(T1)[1 + aT1(T2 – T1)] (1.7) where aT1 is the temperature coefficient of electrical resistance at reference temperature T1, R(T2) is the resistance at temperature T2 (W), and R(T1) is the resistance at temperature T1 (W). The reference temperature is usually taken to be 20°C. Because the variation in resistance between any two temperatures is usually not linear as predicted by Eq. (1.7), common practice is to apply the equation between temperature increments and then to plot the resistance change versus temperature for a number of incremental temperatures. High-Frequency Effects Resistors show a change in their resistance value when subjected to ac voltages. The change in resistance with voltage frequency is known as the Boella effect. The effect occurs because all resistors have some inductance and capacitance along with the resistive component and thus can be approximated by an equivalent circuit shown in Fig. 1.6. Even though the definition of useful frequency range is application dependent, typically, the useful range of the resistor is the highest frequency at which the impedance differs from the resistance by more than the tolerance of the resistor. The frequency effect on resistance varies with the resistor construction.Wire-wound resistors typically exhibit an increase in their impedance with frequency. In composition resistors the capacitances are formed by the many conducting particles which are held in contact by a dielectric binder. The ac impedance for film resistors remains constant until 100 MHz (1 MHz = 106 Hz) and then decreases at higher frequencies (Fig. 1.7). For film resistors, the decrease in dc resistance at higher frequencies decreases with increase in resistance. Film resistors have the most stable high-frequency performance. FIGURE 1.4 Resistors connected in series. 1 1 1 R R T i i n = = Â FIGURE 1.5 Resistors connected in parallel. FIGURE 1.6 Equivalent circuit for a resistor
Frequency (MHz) FIGURE 1.7 Typical graph of impedance as a percentage of dc resistance versus frequency for film resistors. The smaller the diameter of the resistor the better is its frequency response. Most high-frequency resistors have a length to diameter ratio between 4: 1 to 10: 1. Dielectric losses are kept to a minimum by proper choice of base material Voltage Coefficient of Resistance Resistance is not always independent of the applied voltage. The voltage coefficient of resistance is the change in resistance per unit change in voltage, expressed as a percentage of the resistance at 10% of rated voltage. The voltage coefficient is given by the relationship Voltage coefficient 100(R1-R2) (18) R2(V-V2) where R, is the resistance at the rated voltage Vi and R2 is the resistance at 10% of rated voltage V2. Resistors exhibit electrical noise in the form of small ac voltage fluctuations when dc voltage is applied. Noise in a resistor is a function of the applied voltage, physical dimensions, and materials. The total noise is a sum of Johnson noise, current flow noise, noise due to cracked bodies, resistors the noise can also be caused by the jumping of a moving contact over turns and by an imperfect electrical path between the contact and resistance element. The Johnson noise is temperature-dependent thermal noise(Fig. 1. 8). Thermal noise is also called"white noise" because the noise level is the same at all frequencies. The magnitude of thermal ERMs (V), is dependent on the resistance value and the temperature of the resistance due to thermal agitation kRT△f where ERMs is the root-mean-square value of the noise voltage(V), R is the resistance(]2), K is the Boltzmann constant(1.38x 102J/K), Tis the temperature( K), and Af is the bandwidth(Hz)over which the noise energy Figure 1. 8 shows the variation in current noise versus voltage frequency. Current noise varies inversely with frequency and is a function of the current flowing through the resistor and the value of the resistor. The magnitude of current noise is directly proportional to the square root of current. The current noise magnitude is usually expressed by a noise index given as the ratio of the root-mean-square current noise voltage(ERMs
© 2000 by CRC Press LLC The smaller the diameter of the resistor the better is its frequency response. Most high-frequency resistors have a length to diameter ratio between 4:1 to 10:1. Dielectric losses are kept to a minimum by proper choice of base material. Voltage Coefficient of Resistance Resistance is not always independent of the applied voltage. The voltage coefficient of resistance is the change in resistance per unit change in voltage, expressed as a percentage of the resistance at 10% of rated voltage. The voltage coefficient is given by the relationship (1.8) where R1 is the resistance at the rated voltage V1 and R2 is the resistance at 10% of rated voltage V2. Noise Resistors exhibit electrical noise in the form of small ac voltage fluctuations when dc voltage is applied. Noise in a resistor is a function of the applied voltage, physical dimensions, and materials. The total noise is a sum of Johnson noise, current flow noise, noise due to cracked bodies, and loose end caps and leads. For variable resistors the noise can also be caused by the jumping of a moving contact over turns and by an imperfect electrical path between the contact and resistance element. The Johnson noise is temperature-dependent thermal noise (Fig. 1.8). Thermal noise is also called “white noise” because the noise level is the same at all frequencies. The magnitude of thermal noise, ERMS (V), is dependent on the resistance value and the temperature of the resistance due to thermal agitation. (1.9) where ERMS is the root-mean-square value of the noise voltage (V), R is the resistance (W), K is the Boltzmann constant (1.38 ¥ 10–23 J/K), T is the temperature (K), and Df is the bandwidth (Hz) over which the noise energy is measured. Figure 1.8 shows the variation in current noise versus voltage frequency. Current noise varies inversely with frequency and is a function of the current flowing through the resistor and the value of the resistor. The magnitude of current noise is directly proportional to the square root of current. The current noise magnitude is usually expressed by a noise index given as the ratio of the root-mean-square current noise voltage (ERMS) FIGURE 1.7 Typical graph of impedance as a percentage of dc resistance versus frequency for film resistors. Voltage coefficient = 100( ( 1 2 1 R R R V V – ) – ) 2 2 E kRT f RMS = 4 D
I Volts I=0.5mA 00001000c IGURE 1. 8 The total resistor noise is the sum of current noise and thermal noise. The current noise approaches the thermal noise at higher frequencies.( Source: Phillips Components, Discrete Products Division, 1990-91 Resistor/Capacitor Data Book, 1991. with permission. over one decade bandwidth to the average voltage caused by a specified constant current passed through the resistor at a specified hot-spot temperature [ Phillips, 1991] Noise voltage 1.10) dc vo V×10 (1.11) f where N.I. is the noise index, Va is the dc voltage drop across the resistor, and fi and f represent the frequency range over which the noise is being computed. Units of noise index are uV/V. At higher frequencies, the current noise becomes less dominant compared to Johnson noise. Precision film resistors have extremely low noise. Composition resistors show some degree of noise due internal electrical contacts between the conducting particles held together with the binder Wire-wound resistors re essentially free of electrical noise unless resistor terminations are faulty Power Rating and Derating Curves Resistors must be operated within specified temperature limits to avoid permanent damage to the materials. The temperature limit is defined in terms of the maximum power, called the power rating, and derating curve. The power rating of a resistor is the maximum power in watts which the resistor can dissipate. The maximum power rating is a function of resistor material, maximum voltage rating, resistor dimensions, and maximum allowable hot-spot temperature. The maximum hot-spot temperature is the temperature of the hottest part on the resistor when dissipating full-rated power at rated ambient temperature. The maximum allowable power rating as a function of the ambient temperature is given by the derating curve Figure 1.9 shows a typical power rating curve for a resistor. The derating curve is usually linearly drawn from the full-rated load temperature to the maximum allowable no-load temperature. A resistor may be operated at ambient temperatures above the maximum full-load ambient temperature if operating at lower an full-rated power capacity. The maximum allowable no-load temperature is also the maximum storage temperature for the resistor. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC over one decade bandwidth to the average voltage caused by a specified constant current passed through the resistor at a specified hot-spot temperature [Phillips, 1991]. (1.10) (1.11) where N.I. is the noise index, Vdc is the dc voltage drop across the resistor, and f1 and f2 represent the frequency range over which the noise is being computed. Units of noise index are mV/V. At higher frequencies, the current noise becomes less dominant compared to Johnson noise. Precision film resistors have extremely low noise. Composition resistors show some degree of noise due to internal electrical contacts between the conducting particles held together with the binder.Wire-wound resistors are essentially free of electrical noise unless resistor terminations are faulty. Power Rating and Derating Curves Resistors must be operated within specified temperature limits to avoid permanent damage to the materials. The temperature limit is defined in terms of the maximum power, called the power rating, and derating curve. The power rating of a resistor is the maximum power in watts which the resistor can dissipate. The maximum power rating is a function of resistor material, maximum voltage rating, resistor dimensions, and maximum allowable hot-spot temperature. The maximum hot-spot temperature is the temperature of the hottest part on the resistor when dissipating full-rated power at rated ambient temperature. The maximum allowable power rating as a function of the ambient temperature is given by the derating curve. Figure 1.9 shows a typical power rating curve for a resistor. The derating curve is usually linearly drawn from the full-rated load temperature to the maximum allowable no-load temperature. A resistor may be operated at ambient temperatures above the maximum full-load ambient temperature if operating at lower than full-rated power capacity. The maximum allowable no-load temperature is also the maximum storage temperature for the resistor. FIGURE 1.8 The total resistor noise is the sum of current noise and thermal noise. The current noise approaches the thermal noise at higher frequencies. (Source: Phillips Components, Discrete Products Division, 1990–91 Resistor/Capacitor Data Book, 1991. With permission.) N.I. Noise voltage dc voltage = Ê Ë Á ˆ ¯ ˜ 20 10 log E V f f RMS dc N.I. = ¥ Ê Ë Á ˆ ¯ ˜ 10 20 2 1 / log
No-load maximum temperature( deg c) FIGURE 1.9 Typical derating curve for resistors. The maximum voltage that may be applied to the resistor is called the voltage rating and is related to the power rating by √PR (1.12) where V is the voltage rating(V), P is the power rating(W), and R is the resistance( 2). For a given value of wer rating, a critical value of resistance can be calculated. For values of resistance below the critical value, the maximum voltage is never reached; for values of resistance above the critical value, the power dissipated is lower than the rated power(Fig. 1.10) Color coding of resistors Resistors are generally identified by color coding or direct digital marking. The color code is given in Table 1.1 The color code is commonly used in composition resistors and film resistors. The color code essentially consists of four bands of different colors. The first band is the most significant figure, the second band is the second significant figure, the third band is the multiplier or the number of zeros that have to be added after the first two significant figures, and the fourth band is the tolerance on the resistance value. If the fourth band is not present, the resistor tolerance is the standard 20% above and below the rated value. When the color code is used on fixed wire-wound resistors, the first band is applied in double width. 小 FIGURE 1.10 Relationship of applied voltage and power above and below the critical value of resistance
© 2000 by CRC Press LLC Voltage Rating of Resistors The maximum voltage that may be applied to the resistor is called the voltage rating and is related to the power rating by (1.12) where V is the voltage rating (V), P is the power rating (W), and R is the resistance (W). For a given value of voltage and power rating, a critical value of resistance can be calculated. For values of resistance below the critical value, the maximum voltage is never reached; for values of resistance above the critical value, the power dissipated is lower than the rated power (Fig. 1.10). Color Coding of Resistors Resistors are generally identified by color coding or direct digital marking. The color code is given in Table 1.1. The color code is commonly used in composition resistors and film resistors. The color code essentially consists of four bands of different colors. The first band is the most significant figure, the second band is the second significant figure, the third band is the multiplier or the number of zeros that have to be added after the first two significant figures, and the fourth band is the tolerance on the resistance value. If the fourth band is not present, the resistor tolerance is the standard 20% above and below the rated value. When the color code is used on fixed wire-wound resistors, the first band is applied in double width. FIGURE 1.9 Typical derating curve for resistors. FIGURE 1.10 Relationship of applied voltage and power above and below the critical value of resistance. V = PR
TABLE 1.1 Color Code Table for Resistors Fourth band Color First Band Second Band Third Band Tolerance, 0 123 10000 678 001 No band Blanks in the table represent situations which do not exist in the color code. Resistors can be broadly categorized as fixed, variable, and special-purpose. Each of these resistor types is discussed in detail with typical ranges of their characteristics The fixed resistors are those whose value cannot be varied after manufacture. Fixed resistors are classified into composition resistors, wire-wound resistors, and metal-film resistors. Table 1.2 outlines the characteristics of ome typical fixed resistors. Wire-Wound Resistors. Wire-wound resistors are made by winding wire of nickel-chromium alloy on a ceramic tube covering with a vitreous coating. The spiral winding has inductive and capacitive characteristics that make it unsuitable for operation above 50 kHz. The frequency limit can be raised by noninductive winding so that the magnetic fields produced by the two parts of the winding cancel Composition Resistors. Composition resistors are composed of carbon particles mixed with a binder. This mixture is molded into a cylindrical shape and hardened by baking. Leads are attached axially to each end, and the assembly is encapsulated in a protective encapsulation coating Color bands on the outer surface indicate the resistance value and tolerance. Composition resistors are economical and exhibit low noise levels for resistances above 1 MQ2 Composition resistors are usually rated for temperatures in the neighborhood of 70.0 for power ranging from 1/8 to 2 W. Composition resistors have end-to-end shunted capacitance that may be noticed at frequencies in the neighborhood of 100 kHz, especially for resistance values above 0.3 MQ2 Metal-Film Resistors. Metal-film resistors are commonly made of nichrome, tin-oxide, or tantalum nitride, either hermetically sealed or using molded-phenolic cases. Metal-film resistors are not as stable as the TABLE 1.2 Characteristics of Typical Fixed Resistors resistor Types Resistance Range Watt Range Temp. Range a, ppm/C Precisio 0.1 to 1.2 MQ2 l/8tol/4-55to145 0.ltol80klto210-55to275260 Power 5 to 100 k I to 5 55to15520-100 General purpose 2.7 to 100 MS 1/8 to 2 -55 to 130 1500 e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Resistor Types Resistors can be broadly categorized as fixed, variable, and special-purpose. Each of these resistor types is discussed in detail with typical ranges of their characteristics. Fixed Resistors The fixed resistors are those whose value cannot be varied after manufacture. Fixed resistors are classified into composition resistors, wire-wound resistors, and metal-film resistors. Table 1.2 outlines the characteristics of some typical fixed resistors. Wire-Wound Resistors. Wire-wound resistors are made by winding wire of nickel-chromium alloy on a ceramic tube covering with a vitreous coating. The spiral winding has inductive and capacitive characteristics that make it unsuitable for operation above 50 kHz. The frequency limit can be raised by noninductive winding so that the magnetic fields produced by the two parts of the winding cancel. Composition Resistors. Composition resistors are composed of carbon particles mixed with a binder. This mixture is molded into a cylindrical shape and hardened by baking. Leads are attached axially to each end, and the assembly is encapsulated in a protective encapsulation coating. Color bands on the outer surface indicate the resistance value and tolerance. Composition resistors are economical and exhibit low noise levels for resistances above 1 MW. Composition resistors are usually rated for temperatures in the neighborhood of 70°C for power ranging from 1/8 to 2 W. Composition resistors have end-to-end shunted capacitance that may be noticed at frequencies in the neighborhood of 100 kHz, especially for resistance values above 0.3 MW. Metal-Film Resistors. Metal-film resistors are commonly made of nichrome, tin-oxide, or tantalum nitride, either hermetically sealed or using molded-phenolic cases. Metal-film resistors are not as stable as the TABLE 1.1 Color Code Table for Resistors Fourth Band Color First Band Second Band Third Band Tolerance, % Black 0 0 1 Brown 1 1 10 Red 2 2 100 Orange 3 3 1,000 Yellow 4 4 10,000 Green 5 5 100,000 Blue 6 6 1,000,000 Violet 7 7 10,000,000 Gray 8 8 100,000,000 White 9 9 1,000,000,000 Gold 0.1 5% Silver 0.01 10% No band 20% Blanks in the table represent situations which do not exist in the color code. TABLE 1.2 Characteristics of Typical Fixed Resistors Operating Resistor Types Resistance Range Watt Range Temp. Range a, ppm/°C Wire-wound resistor Precision 0.1 to 1.2 MW 1/8 to 1/4 –55 to 145 10 Power 0.1 to 180 kW 1 to 210 –55 to 275 260 Metal-film resistor Precision 1 to 250 MW 1/20 to 1 –55 to 125 50–100 Power 5 to 100 kW 1 to 5 –55 to 155 20–100 Composition resistor General purpose 2.7 to 100 MW 1/8 to 2 –55 to 130 1500
wire-wound resistors. Depending on the application, fixed resistors are manufactured as precision resistors, semiprecision resistors, standard general-purpose resistors, or power resistors. Precision resistors have low voltage and power coefficients, excellent temperature and time stabilities, low noise, and very low reactance These resistors are available in metal-film or wire constructions and are typically designed for circuits havin very close resistance tolerances on values. Semiprecision resistors are smaller than precision resistors and are have arily used for current-limiting or voltage-dropping functions in circuit applications. Semiprecision resistors resistance tolerances or long-term stability. For general-purpose resistors, initial resistance variation may be in the neighborhood of 5% and the variation in resistance under full-rated power may approach 20%. Typically general-purpose resistors have a high coefficient of resistance and high noise levels. Power resistors are used for power supplies, control circuits, and voltage dividers where operational stability of 5%is acceptable. Power resistors are available in wire-wound and film constructions. Film-type power resistors have the advantage of tability at high frequencies and have higher resistance values than wire-wound resistors for a given size Variable resistors Potentiometers. The potentiometer is a special form of variable resistor with three terminals. Two terminal are connected to the opposite sides of the resistive element, and the third connects to a sliding contact that can be adjusted as a voltage divider. Potentiometers are usually circular in form with the movable contact attached to a shaft that rotates Potentiometers are manufactured as carbon composition, metallic film, and wire-wound resistors available in gle-turn or multiturn units. The movable contact does not go all the way toward the end of the resistive element, and a small resistance called the hop-off resistance is present to prevent accidental burning of the resistive element Rheostat. The rheostat is a current-setting device in which one terminal is connected to the resistive element and the second terminal is connected to a movable contact to place a selected section of the resistive element into the circuit. Typically, rheostats are wire-wound resistors used as speed controls for motors, ovens, and heater controls and in applications where adjustments on the voltage and current levels are required, such voltage dividers and bleeder circuits Special-Purpose Resistors Integrated Circuit Resistors. Integrated circuit resistors are classified into two general categories: semicon- ductor resistors and deposited film resistors. Semiconductor resistors use the bulk resistivity of doped ser conductor regions to obtain the desired resistance value. Deposited film resistors are formed by depositing resistance films on an insulating substrate which are etched and patterned to form the desired resistive network. Depending on the thickness and dimensions of the deposited films, the resistors are classified into thick-film nd thin-film resistors Semiconductor resistors can be divided into four types: diffused, bulk, pinched, and planted. Table 1.3 lows some typical resistor properties for semiconductor resistors. Diffused semiconductor resistors use resis- vity of the diffused region in the semiconductor substrate to introduce a resistance in the circuit. Both n-type and p-type diffusions are used to form the diffused resistor. a bulk resistor uses the bulk resistivity of the semiconductor to introduce a resistance into the circuit Mathematically the sheet resistance of a bulk resistor is given by Pe d where R,heet is the sheet resistance in(Q/square),P is the sheet resistivity(Q/square), and d is the depth of the n-type epitaxial layer Pinched resistors are formed by reducing the effective cross-sectional area of diffused resistors. The reduced cross section of the diffused length results in extremely high sheet resistivities from ordinary diffused resistors
© 2000 by CRC Press LLC wire-wound resistors. Depending on the application, fixed resistors are manufactured as precision resistors, semiprecision resistors, standard general-purpose resistors, or power resistors. Precision resistors have low voltage and power coefficients, excellent temperature and time stabilities, low noise, and very low reactance. These resistors are available in metal-film or wire constructions and are typically designed for circuits having very close resistance tolerances on values. Semiprecision resistors are smaller than precision resistors and are primarily used for current-limiting or voltage-dropping functions in circuit applications. Semiprecision resistors have long-term temperature stability. General-purpose resistors are used in circuits that do not require tight resistance tolerances or long-term stability. For general-purpose resistors, initial resistance variation may be in the neighborhood of 5% and the variation in resistance under full-rated power may approach 20%. Typically, general-purpose resistors have a high coefficient of resistance and high noise levels. Power resistors are used for power supplies, control circuits, and voltage dividers where operational stability of 5% is acceptable. Power resistors are available in wire-wound and film constructions. Film-type power resistors have the advantage of stability at high frequencies and have higher resistance values than wire-wound resistors for a given size. Variable Resistors Potentiometers. The potentiometer is a special form of variable resistor with three terminals. Two terminals are connected to the opposite sides of the resistive element, and the third connects to a sliding contact that can be adjusted as a voltage divider. Potentiometers are usually circular in form with the movable contact attached to a shaft that rotates. Potentiometers are manufactured as carbon composition, metallic film, and wire-wound resistors available in single-turn or multiturn units. The movable contact does not go all the way toward the end of the resistive element, and a small resistance called the hop-off resistance is present to prevent accidental burning of the resistive element. Rheostat. The rheostat is a current-setting device in which one terminal is connected to the resistive element and the second terminal is connected to a movable contact to place a selected section of the resistive element into the circuit. Typically, rheostats are wire-wound resistors used as speed controls for motors, ovens, and heater controls and in applications where adjustments on the voltage and current levels are required, such as voltage dividers and bleeder circuits. Special-Purpose Resistors Integrated Circuit Resistors. Integrated circuit resistors are classified into two general categories: semiconductor resistors and deposited film resistors. Semiconductor resistors use the bulk resistivity of doped semiconductor regions to obtain the desired resistance value. Deposited film resistors are formed by depositing resistance films on an insulating substrate which are etched and patterned to form the desired resistive network. Depending on the thickness and dimensions of the deposited films, the resistors are classified into thick-film and thin-film resistors. Semiconductor resistors can be divided into four types: diffused, bulk, pinched, and ion-implanted. Table 1.3 shows some typical resistor properties for semiconductor resistors. Diffused semiconductor resistors use resistivity of the diffused region in the semiconductor substrate to introduce a resistance in the circuit. Both n-type and p-type diffusions are used to form the diffused resistor. A bulk resistor uses the bulk resistivity of the semiconductor to introduce a resistance into the circuit. Mathematically the sheet resistance of a bulk resistor is given by (1.13) where Rsheet is the sheet resistance in (W/square), re is the sheet resistivity (W/square), and d is the depth of the n-type epitaxial layer. Pinched resistors are formed by reducing the effective cross-sectional area of diffused resistors. The reduced cross section of the diffused length results in extremely high sheet resistivities from ordinary diffused resistors. R d e sheet = r
TABLE 1.3 Typical Characteristics of Integrated Circuit Resistors Sheet Resistivity Coefficient Resistor type (ppm/C Diffused 0.8to2609 1100to2000 003 to 10 kQ Pinched 100to1300 Thin-film 0.01 to 1 kQ 0.08 to 4 kQ 40to450g 0.03to2.5k Thick-film Ruthenium.silver 10 2 to 10 MQ Palladium-silver 0.01 to 100 k( 500to150 Ion-implanted resistors are formed by implanting ions on the semiconductor surface by bombarding the silicon lattice with high-energy ions. The implanted ions lie in a very shallow layer along the surface(0.1 to 0. 8 um). For similar thicknesses ion-implanted resistors yield sheet resistivities 20 times greater than diffused resistors. Table 1.3 shows typical properties of diffused, bulk, pinched, and ion-implanted resistors. Typical sheet resistance values range from 80 to 250Q2/square Varistors. Varistors are voltage-dependent resistors that show a high degree of nonlinearity between their resistance value and applied voltage. They are composed of a nonhomogeneous material that provides a rectifying action. Varistors are used for protection of electronic circuits, semiconductor components, collectors of motors, and relay contacts against overvoltage The relationship between the voltage and current of a varistor is given by (1.14) where Vis the voltage(V), I is the current(A), and k and B are constants that depend on the materials and manufacturing process. The electrical characteristics of a varistor are specified by its B and k values Varistors in Series. The resultant k value of n varistors connected in series is nk. This can be derived by considering n varistors connected in series and a voltage n Applied across the ends. The current through each varistor remains the same as for V volts over one varistor. Mathematically, the voltage and current are expressed nV=K,B (1.15) Equating the expressions(1. 14)and(1. 15), the equivalent constant k, for the series combination of varistors (1.16) Varistors in Parallel. The equivalent k value for a parallel combination of varistors can be obtained by connecting n varistors in parallel and applying a voltage Vacross the terminals. The current through the aristo will still be n times the current through a single varistor with a voltage V across it. Mathematically the current V=k(nD (1.17) e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Ion-implanted resistors are formed by implanting ions on the semiconductor surface by bombarding the silicon lattice with high-energy ions. The implanted ions lie in a very shallow layer along the surface (0.1 to 0.8 mm). For similar thicknesses ion-implanted resistors yield sheet resistivities 20 times greater than diffused resistors. Table 1.3 shows typical properties of diffused, bulk, pinched, and ion-implanted resistors. Typical sheet resistance values range from 80 to 250 W/square. Varistors. Varistors are voltage-dependent resistors that show a high degree of nonlinearity between their resistance value and applied voltage. They are composed of a nonhomogeneous material that provides a rectifying action. Varistors are used for protection of electronic circuits, semiconductor components, collectors of motors, and relay contacts against overvoltage. The relationship between the voltage and current of a varistor is given by V = kI b (1.14) where V is the voltage (V), I is the current (A), and k and b are constants that depend on the materials and manufacturing process. The electrical characteristics of a varistor are specified by its b and k values. Varistors in Series. The resultant k value of n varistors connected in series is nk. This can be derived by considering n varistors connected in series and a voltage nV applied across the ends. The current through each varistor remains the same as for V volts over one varistor. Mathematically, the voltage and current are expressed as nV = k1 I b (1.15) Equating the expressions (1.14) and (1.15), the equivalent constant k1 for the series combination of varistors is given as k1 = nk (1.16) Varistors in Parallel. The equivalent k value for a parallel combination of varistors can be obtained by connecting n varistors in parallel and applying a voltage V across the terminals. The current through the varistors will still be n times the current through a single varistor with a voltage V across it. Mathematically the current and voltage are related as V = k2(nI)b (1.17) TABLE 1.3 Typical Characteristics of Integrated Circuit Resistors Temperature Sheet Resistivity Coefficient Resistor Type (per square) (ppm/°C) Semiconductor Diffused 0.8 to 260 W 1100 to 2000 Bulk 0.003 to 10 kW 2900 to 5000 Pinched 0.001 to 10 kW 3000 to 6000 Ion-implanted 0.5 to 20 kW 100 to 1300 Deposited resistors Thin-film Tantalum 0.01 to 1 kW m100 SnO2 0.08 to 4 kW –1500 to 0 Ni-Cr 40 to 450 W m100 Cermet (Cr-SiO) 0.03 to 2.5 kW m150 Thick-film Ruthenium-silver 10 W to 10 MW m200 Palladium-silver 0.01 to 100 kW –500 to 150