From Eqs. (1.14)and(.17)the equivalent constant k, for the series combination of varistors is given as Thermistors. Thermistors are resistors that change their resistance exponentially with changes in temperature If the resistance decreases with increase in temperature, the resistor is called a negative temperature coefficient (NTC)resistor. If the resistance increases with temperature, the resistor is called a positive temperature coef- ficient(PTC) resistor. NTC thermistors are ceramic semiconductors made by sintering mixtures of heavy metal oxides such manganese, nickel, cobalt, copper, and iron. The resistance temperature relationship for NTC thermistors is R_= debt where T is temperature(K), Rr is the resistance( 92), and A, B are constants whose values are determined by conducting experiments at two temperatures and solving the equations simultaneously PTC thermistors are prepared from BaTiO, or solid solutions of PbTiO, or SrTiO, The resistance temperature relationship for PTC thermistors is a+ c where T is temperature(K), Rr is the resistance(Q2), and A, B are constants determined by conducting experiments at two temperatures and solving the equations simultaneously. Positive thermistors have a PtC only between certain temperature ranges. Outside this range the temperature is either zero or negative. Typically, the absolute value of the temperature coefficient of resistance for PtC resistors is much higher than for NTC Defining Ter Doping: The intrinsic carrier concentration of semiconductors(e.g, Si)is too low to allow controlled charge ransport. For this reason some impurities called dopants are purposely added to the semiconductor. The process of adding dopants is called doping Dopants may belong to group IIIA (e. g, boron) or group VA(e.g, phosphorus) in the periodic table. If the elements belong to the group IIIA, the resulting semiconductor is called a p-type semiconductor. On the other hand, if the elements belong to the group VA, the resulting semiconductor is called an n-type semiconductor. Epitaxial la itaxy refers to processes used to grow a thin crystalline layer on a crystalline substrate. In the epitaxial process the wafer acts as a seed crystal. The layer grown by this process is called an epitaxial Resistivity: The resistance of a conductor with unit length and unit cross-sectional area. Temperature coefficient of resistance: The change in electrical resistance of a resistor per unit change in Time stability: The degree to which the initial value of resistance is maintained to a stated degree of certainty under stated conditions of use over a stated period of time. Time stability is usually expressed as a percent or parts per million change in resistance per 1000 hours of continuous use Voltage coefficient of resistance: The change in resistance per unit change in voltage, expressed as a percentage of the resistance at 10% of rated voltage Voltage drop: The difference in potential between the two ends of the resistor measured in the direction of flow of current. The voltage drop is V= IR, where V is the voltage across the resistor, I is the current through the resistor, and r is the resistance. Voltage rating: The maximum voltage that may be applied to the resistor
© 2000 by CRC Press LLC From Eqs. (1.14) and (1.17) the equivalent constant k2 for the series combination of varistors is given as (1.18) Thermistors. Thermistors are resistors that change their resistance exponentially with changes in temperature. If the resistance decreases with increase in temperature, the resistor is called a negative temperature coefficient (NTC) resistor. If the resistance increases with temperature, the resistor is called a positive temperature coef- ficient (PTC) resistor. NTC thermistors are ceramic semiconductors made by sintering mixtures of heavy metal oxides such as manganese, nickel, cobalt, copper, and iron. The resistance temperature relationship for NTC thermistors is RT = AeB/T (1.19) where T is temperature (K), RT is the resistance (W), and A, B are constants whose values are determined by conducting experiments at two temperatures and solving the equations simultaneously. PTC thermistors are prepared from BaTiO3 or solid solutions of PbTiO3 or SrTiO3. The resistance temperature relationship for PTC thermistors is RT = A + Ce BT (1.20) where T is temperature (K), RT is the resistance (W), and A, B are constants determined by conducting experiments at two temperatures and solving the equations simultaneously. Positive thermistors have a PTC only between certain temperature ranges. Outside this range the temperature is either zero or negative. Typically, the absolute value of the temperature coefficient of resistance for PTC resistors is much higher than for NTC resistors. Defining Terms Doping: The intrinsic carrier concentration of semiconductors (e.g., Si) is too low to allow controlled charge transport. For this reason some impurities called dopants are purposely added to the semiconductor. The process of adding dopants is called doping. Dopants may belong to group IIIA (e.g., boron) or group VA (e.g., phosphorus) in the periodic table. If the elements belong to the group IIIA, the resulting semiconductor is called a p-type semiconductor. On the other hand, if the elements belong to the group VA, the resulting semiconductor is called an n-type semiconductor. Epitaxial layer: Epitaxy refers to processes used to grow a thin crystalline layer on a crystalline substrate. In the epitaxial process the wafer acts as a seed crystal. The layer grown by this process is called an epitaxial layer. Resistivity: The resistance of a conductor with unit length and unit cross-sectional area. Temperature coefficient of resistance: The change in electrical resistance of a resistor per unit change in temperature. Time stability: The degree to which the initial value of resistance is maintained to a stated degree of certainty under stated conditions of use over a stated period of time. Time stability is usually expressed as a percent or parts per million change in resistance per 1000 hours of continuous use. Voltage coefficient of resistance: The change in resistance per unit change in voltage, expressed as a percentage of the resistance at 10% of rated voltage. Voltage drop: The difference in potential between the two ends of the resistor measured in the direction of flow of current. The voltage drop is V = IR, where V is the voltage across the resistor, I is the current through the resistor, and R is the resistance. Voltage rating: The maximum voltage that may be applied to the resistor. k k n 2 = b
Related Topics 22 1 Physical Properties.25.1 Integrated Circuit Technology. 51.1 Introduction References Phillips Components, Discrete Products Division, 1990-91 Resistor/Capacitor Data Book, 1991 CC. Wellard, Resistance and Resistors, New York: McGraw-Hill. 1960 Further information EEE Transactions on Electron Devices and IEEE Electron Device Letters: Published monthly by the Institute of Electrical and Electronics Engin IEEE Components, Hybrids and Manufacturing Technology: Published quarterly by the Institute of Electrical and Electronics Engineers. G.W.A. Dummer, Materials for Conductive and Resistive Functions, New York: Hayden Book Co., 1970 H.E. Littlejohn and C.E. Burckel, Handbook of Power Resistors, Mount Vernon, N Y: Ward Leonard Electric Company, 1951 I.R. Sinclair, Passive Components: A User's Guide, Oxford: Heinmann Newnes, 1990 1.2 Capacitors and Inductors Glen ballou Capacitors If a potential difference is found between two points, an electric field exists that is the result of the separation of unlike charges. The strength of the field will depend on the amount the charges have been separated. Capacitance is the concept of energy storage in an electric field and is restricted to the area, shape, and pacing of the capacitor plates and the property of the material separating them. When electrical current flows into a capacitor, a force is established between two parallel plates separated by dielectric. This energy is stored and remains even after the input is removed. By connecting a conductor( resistor, hard wire, or even air)across the capacitor, the charged capacitor can regain electron balance, that is, discharge its stored The value of a parallel-plate capacitor can be found with the equation x∈[(N-1)A] 10-13 (1.21) where C=capacitance, F; E=dielectric constant of insulation; d spacing between plates; N= number of plates; A=area of plates; and x=0.0885 when A and d are in centimeters, and x=0. 225 when A and d are in inches. The work necessary to transport a unit charge from one plate to the other is where e volts expressing energy per unit charge, g= coulombs of charge already transported, and k proportionality factor between work necessary to carry a unit charge between the two plates and charge already transported. It is equal to 1/C, where C is the capacitance, E. The value of a capacitor can now be calculated from the equation e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Related Topics 22.1 Physical Properties • 25.1 Integrated Circuit Technology • 51.1 Introduction References Phillips Components, Discrete Products Division, 1990–91 Resistor/Capacitor Data Book, 1991. C.C. Wellard, Resistance and Resistors, New York: McGraw-Hill, 1960. Further Information IEEE Transactions on Electron Devices and IEEE Electron Device Letters: Published monthly by the Institute of Electrical and Electronics Engineers. IEEE Components, Hybrids and Manufacturing Technology: Published quarterly by the Institute of Electrical and Electronics Engineers. G.W.A. Dummer, Materials for Conductive and Resistive Functions, New York: Hayden Book Co., 1970. H.F. Littlejohn and C.E. Burckel, Handbook of Power Resistors, Mount Vernon, N.Y.: Ward Leonard Electric Company, 1951. I.R. Sinclair, Passive Components: A User’s Guide, Oxford: Heinmann Newnes, 1990. 1.2 Capacitors and Inductors Glen Ballou Capacitors If a potential difference is found between two points, an electric field exists that is the result of the separation of unlike charges. The strength of the field will depend on the amount the charges have been separated. Capacitance is the concept of energy storage in an electric field and is restricted to the area, shape, and spacing of the capacitor plates and the property of the material separating them. When electrical current flows into a capacitor, a force is established between two parallel plates separated by a dielectric. This energy is stored and remains even after the input is removed. By connecting a conductor (a resistor, hard wire, or even air) across the capacitor, the charged capacitor can regain electron balance, that is, discharge its stored energy. The value of a parallel-plate capacitor can be found with the equation (1.21) where C = capacitance, F; e = dielectric constant of insulation; d = spacing between plates; N = number of plates; A = area of plates; and x = 0.0885 when A and d are in centimeters, and x = 0.225 when A and d are in inches. The work necessary to transport a unit charge from one plate to the other is e = kg (1.22) where e = volts expressing energy per unit charge, g = coulombs of charge already transported, and k = proportionality factor between work necessary to carry a unit charge between the two plates and charge already transported. It is equal to 1/C, where C is the capacitance, F. The value of a capacitor can now be calculated from the equation (1.23) C x N A d = ¥ e[( – 1) ] – 10 13 C q e =
where q= charge(C)and e is found with Eq. (1. 22) The energy stored in a capacitor is (1.24) The dielectric constant of a material determines the electrostatic Dielectric Constants on of Capacitor where W= energy, J; C= capacitance, F; and V= applied voltage, V. TABLE 1.4 Compar energy which may be stored in that material per unit volume voltage. The value of the dielectric constant expresses the ratio of a Dielectric. Dielectric Constant) air is 1, the reference unit employed for expressing the dielectric constant. Pane vacuum capacitor in a vacuum to one using a given dielectric. The dielectric of As the dielectric constant is increased or decreased, the capacitance will Mineral oil increase or decrease, respectively. Table 1. 4 lists the dielectric constants Quartz The dielectric constant of most materials is affected by both temper. porcelain ature and frequency, except for quartz, Styrofoam, and Teflon, whose Aluminum oxide dielectric constants remain essentially constant. Ceram 12-400,000 The equation for calculating the force of attraction between two plates Source: G. Ballou, Handbook for Sound Engineers, The New Audio Cyclopedia, Car- mel, Ind. Macmillan Computer Publish- Av2 ing Company, 199 (1.25) k(1504S)2 where F= attraction force, dyn; A= area of one plate, cm V= potential energy difference, V;k= dielectric coefficient; and S=separation between plates,cm The Q for a capacitor when the resistance and capacitance is in series is 2兀fRC where Q= ratio expressing the factor of merit; f= frequency, Hz;R= resistance, $; and C= capacitance, F. When capacitors are connected in series, the total capacitance is (1.27) 1/C1+1/C2+ and is always less than the value of the smallest capacitor. When capacitors are connected in parallel, the total capacitance Cr=C1+C2+…+Cn and is always larger than the largest capacitor. When a voltage is applied across a group of capacitors connected in series, the voltage drop across the combination is equal to the applied voltage. The drop across each individual capacitor is inversely proportional to its capacitance. (1.29)
© 2000 by CRC Press LLC where q = charge (C) and e is found with Eq. (1.22). The energy stored in a capacitor is (1.24) where W = energy, J; C = capacitance, F; and V = applied voltage, V. The dielectric constant of a material determines the electrostatic energy which may be stored in that material per unit volume for a given voltage. The value of the dielectric constant expresses the ratio of a capacitor in a vacuum to one using a given dielectric. The dielectric of air is 1, the reference unit employed for expressing the dielectric constant. As the dielectric constant is increased or decreased, the capacitance will increase or decrease, respectively. Table 1.4 lists the dielectric constants of various materials. The dielectric constant of most materials is affected by both temperature and frequency, except for quartz, Styrofoam, and Teflon, whose dielectric constants remain essentially constant. The equation for calculating the force of attraction between two plates is (1.25) where F = attraction force, dyn; A = area of one plate, cm2 ; V = potential energy difference, V; k = dielectric coefficient; and S = separation between plates, cm. The Q for a capacitor when the resistance and capacitance is in series is (1.26) where Q = ratio expressing the factor of merit; f = frequency, Hz; R = resistance, W; and C = capacitance, F. When capacitors are connected in series, the total capacitance is (1.27) and is always less than the value of the smallest capacitor. When capacitors are connected in parallel, the total capacitance is CT = C1 + C2 + · · · + Cn (1.28) and is always larger than the largest capacitor. When a voltage is applied across a group of capacitors connected in series, the voltage drop across the combination is equal to the applied voltage. The drop across each individual capacitor is inversely proportional to its capacitance. (1.29) W CV = 2 2 TABLE 1.4 Comparison of Capacitor Dielectric Constants K Dielectric (Dielectric Constant) Air or vacuum 1.0 Paper 2.0–6.0 Plastic 2.1–6.0 Mineral oil 2.2–2.3 Silicone oil 2.7–2.8 Quartz 3.8–4.4 Glass 4.8–8.0 Porcelain 5.1–5.9 Mica 5.4–8.7 Aluminum oxide 8.4 Tantalum pentoxide 26 Ceramic 12–400,000 Source: G. Ballou, Handbook for Sound Engineers, The New Audio Cyclopedia, Carmel, Ind.: Macmillan Computer Publishing Company, 1991. With permission. F AV k S = 2 2 ( ) 1504 Q fRC = 1 2p C C C C T n = + + × × × + 1 1 1 1 1 2 / / / V V C C C A X T =
where Vc=voltage across the individual capacitor in the series( Cl, C2, Cn),V; VA= applied voltage, V; CT total capacitance of the series combination, F; and Cx=capacitance of individual capacitor under consideration,E the impedance, of the capacitor where Xc= capacitive reactance, Q2; f= frequency, Hz; and C=capacitance, E. The current will lead the voltage y 90% in a circuit with a pure capacitor When a dc voltage is connected across a capacitor, a time t is required to charge the capacitor to the applied voltage. This is called a time constant and is calculated with the equation t=RC (1.31) where t= time, s;R=resistance, Q2; and C= capacitance, E In a circuit consisting of pure resistance and capacitance, the time constant t is defined as the time required to charge the capacitor to 63. 2% of the applied voltage. uring the next time constant, the capacitor charges to 63. 2% of the remaining difference of full va to 86.5% of the full value. The charge on a capacitor can never actually reach 100% but is considered to be 100% after five time constants. When the voltage is removed, the capacitor discharges to 63. 2% of the full value. Capacitance is expressed in microfarads(uF, or 10-F)or picofarads(pe, or 10-2F)with a stated accuracy derange. toley also be stated teed minimum value referred All capacitors have a maximum working voltage that must not be exceeded and is a combination of the dc value plus the peak ac value which may be applied during operation Quality Factor(Q) Quality factor is the ratio of the capacitors reactance to its resistance at a specified frequency and is found by the equation 2兀CR where Q= quality factor; f= frequency, Hz; C= value of capacitance, F;R= internal resistance, Q2; and PF Power Factor(PF) Power factor is the preferred measurement in describing capacitive losses in ac circuits. It is the fraction of input volt-amperes(or power)dissipated in the capacitor dielectric and is virtually independent of the capac itance, applied voltage, and frequency. Equivalent Series Resistance(ESR) Equivalent series resistance is expressed in ohms or milliohms(Q2, mQ2)and is derived from lead resistance, termination losses, and dissipation in the dielectric material. Equivalent Series Inductance(ESL The equivalent series inductance can be useful or detrimental. It reduces high-frequency performance; however, it can be used in conjunction with the internal capacitance to form a resonant circuit e 2000 by CRC Press LLC
© 2000 by CRC Press LLC where VC = voltage across the individual capacitor in the series (C1, C2, ...,Cn), V; VA = applied voltage, V; CT = total capacitance of the series combination, F; and CX = capacitance of individual capacitor under consideration, F. In an ac circuit, the capacitive reactance, or the impedance, of the capacitor is (1.30) where XC = capacitive reactance, W ; f = frequency, Hz; and C = capacitance, F. The current will lead the voltage by 90° in a circuit with a pure capacitor. When a dc voltage is connected across a capacitor, a time t is required to charge the capacitor to the applied voltage. This is called a time constant and is calculated with the equation t = RC (1.31) where t = time, s; R = resistance, W; and C = capacitance, F. In a circuit consisting of pure resistance and capacitance, the time constant t is defined as the time required to charge the capacitor to 63.2% of the applied voltage. During the next time constant, the capacitor charges to 63.2% of the remaining difference of full value, or to 86.5% of the full value. The charge on a capacitor can never actually reach 100% but is considered to be 100% after five time constants. When the voltage is removed, the capacitor discharges to 63.2% of the full value. Capacitance is expressed in microfarads (mF, or 10–6 F) or picofarads (pF, or 10–12 F) with a stated accuracy or tolerance. Tolerance may also be stated as GMV (guaranteed minimum value), sometimes referred to as MRV (minimum rated value). All capacitors have a maximum working voltage that must not be exceeded and is a combination of the dc value plus the peak ac value which may be applied during operation. Quality Factor (Q) Quality factor is the ratio of the capacitor’s reactance to its resistance at a specified frequency and is found by the equation (1.32) where Q = quality factor; f = frequency, Hz; C = value of capacitance, F; R = internal resistance, W; and PF = power factor Power Factor (PF) Power factor is the preferred measurement in describing capacitive losses in ac circuits. It is the fraction of input volt-amperes (or power) dissipated in the capacitor dielectric and is virtually independent of the capacitance, applied voltage, and frequency. Equivalent Series Resistance (ESR) Equivalent series resistance is expressed in ohms or milliohms (W , mW) and is derived from lead resistance, termination losses, and dissipation in the dielectric material. Equivalent Series Inductance (ESL) The equivalent series inductance can be useful or detrimental. It reduces high-frequency performance; however, it can be used in conjunction with the internal capacitance to form a resonant circuit. X fC C = 1 2p Q fCR PF = = 1 2 1 p