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electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA chapter 9 Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 The Basic Capacitor Capacitors are one of the fundamental passive components. In its most basic form, it is composed of two conductive plates separated by an insulating dielectric. The ability to store charge is the definition of capacitance. Conductors Electronics Fundamentals 8th edition Floyd/Buchla Dielectric © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 The Basic Capacitor VVSS The charging process… Leads Initially Source Fully Charging charged removed uncharged ++ +++ +++ +++ ++ +++ ++ + ++ + ++ + + + AA + A + Dielec tric ++ Plates + + + + Elec trons + B BB A capacitor with stored charge can act as a temporary battery. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitance Capacitance is the ratio of charge to voltage C Q V Rearranging, the amount of charge on a capacitor is determined by the size of the capacitor (C) and the voltage (V). Q CV If a 22 mF capacitor is connected to a 10 V source, the charge is 220 mC Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitance An analogy: Imagine you store rubber bands in a bottle that is nearly full. You could store more rubber bands (like charge or Q) in a bigger bottle (capacitance or C) or if you push them in more (voltage or V). Thus, Q CV Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitance A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two plates. The energy of a charged capacitor is given by the equation W 1 CV 2 2 where W = the energy in joules C = the capacitance in farads V = the voltage in volts Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitance The capacitance of a capacitor depends on three physical characteristics. A C 8.85 1012 F/m r d C is directly proportional to the relative dielectric constant and the plate area. C is inversely proportional to the distance between the plates Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitance Find the capacitance of a 4.0 cm diameter sensor immersed in oil if the plates are separated by 0.25 mm. r 4.0 for oil r A C 8.85 10 F/m d 2 2 3 2 The plate area is A πr 0.02 m 1.26 10 m 12 The distance between the plates is 0.25 103 m 4.0 1.26 103 m2 C 8.85 1012 F/m 0.25 103 m Electronics Fundamentals 8th edition Floyd/Buchla 178 pF © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor types Mica Mica capacitors are small with high working voltage. The working voltage is the voltage limit that cannot be exceeded. Foil Mic a Foil Mic a Foil Mic a Foil Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor types Ceramic disk Ceramic disks are small nonpolarized capacitors They have relatively high capacitance due to high r. Lead wire soldered to silver elec trode Solder Ceramic dielec tric Electronics Fundamentals 8th edition Floyd/Buchla Dipped phenolic c oating Silv er elec trodes deposited on top and bottom of c eram ic disk © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor types Plastic Film Plastic film capacitors are small and nonpolarized. They have relatively high capacitance due to larger plate area. High-purity foil elec trodes Plastic film dielec tric Outer wrap of polyester film Capac itor sec tion (alternate strips of film dielec tric and Lead wire foil elec trodes) Solder c oated end Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor types Electrolytic (two types) Electrolytic capacitors have very high capacitance but they are not as precise as other types and tend to have more leakage current. Electrolytic types are polarized. + _ Al electrolytic Ta electrolytic Symbol for any electrolytic capacitor Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor types Variable Variable capacitors typically have small capacitance values and are usually adjusted manually. A solid-state device that is used as a variable capacitor is the varactor diode; it is adjusted with an electrical signal. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor labeling + ++ + 47VTTMFVTT Capacitors use several labeling methods. Small capacitors values are frequently stamped on them such as .001 or .01, which have implied units of microfarads. Electrolytic capacitors have larger values, so are read as mF. The unit is usually stamped as mF, but some older ones may be shown as MF or MMF). . 022 Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitor labeling A label such as 103 or 104 is read as 10x103 (10,000 pF) or 10x104 (100,000 pF) respectively. (Third digit is the multiplier.) When values are marked as 330 or 6800, the units are picofarads. 222 2200 What is the value of each capacitor? Both are 2200 pF. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Series capacitors When capacitors are connected in series, the total capacitance is smaller than the smallest one. The general equation for capacitors in series is CT 1 1 1 1 1 ... C1 C2 C3 CT The total capacitance of two capacitors is CT 1 1 1 C1 C2 …or you can use the product-over-sum rule Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Series capacitors If a 0.001 mF capacitor is connected in series with an 800 pF capacitor, the total capacitance is 444 pF C 1 0 .0 0 1µ F Electronics Fundamentals 8th edition Floyd/Buchla C 2 8 0 0p F © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Parallel capacitors When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors. The general equation for capacitors in parallel is CT C1 C2 C3 ...Cn If a 0.001 mF capacitor is connected in parallel with an 800 pF capacitor, the total capacitance is 1800 pF Electronics Fundamentals 8th edition Floyd/Buchla C 1 C 2 0 .0 0 1 µ F 8 0 0 p F © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Vfinal The RC time constant When a capacitor is charged through a series resistor and dc source, the charging curve is exponential. 0 t (a) Capacitor c harging voltage Iinitial R C 0 (b) Charging current Electronics Fundamentals 8th edition Floyd/Buchla t © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 The RC time constant When a capacitor is discharged through a resistor, the discharge curve is also an exponential. (Note that the current is negative.) R Vinitial t 0 (a) Capacitor disc harging voltage Iinitial C 0 t (b) Disc harging current Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 The RC time constant The same shape curves are seen if a square wave is used for the source. What is the shape of the current curve? VS VC R VS C VR The current has the same shape as VR. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Universal exponential curves τ RC 100% 95% 99% Rising exponential 63% 60% 40% 37% Falling exponential 20% 14% 5% 0 0 Electronics Fundamentals 8th edition Floyd/Buchla 98% 86% 80% Percent of final value Specific values for current and voltage can be read from a universal curve. For an RC circuit, the time constant is 1t 2% 2t 3t 4t Number of time constants 1% 5t © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Universal exponential curves The universal curves can be applied to general formulas for the voltage (or current) curves for RC circuits. The general voltage formula is v =VF + (Vi VF)et/RC VF = final value of voltage Vi = initial value of voltage v = instantaneous value of voltage The final capacitor voltage is greater than the initial voltage when the capacitor is charging, or less than the initial voltage when it is discharging. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitive reactance Capacitive reactance is the opposition to ac by a capacitor. The equation for capacitive reactance is 1 XC 2πfC The reactance of a 0.047 mF capacitor when a frequency of 15 kHz is applied is 226 W Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitive reactance When capacitors are in series, the total reactance is the sum of the individual reactances. That is, X C(tot ) X C1 X C2 X C3 X Cn Assume three 0.033 mF capacitors are in series with a 2.5 kHz ac source. What is the total reactance? The reactance of each capacitor is 1 1 1.93 kW 2πfC 2π 2.5 kHz 0.033 μF X C(tot ) X C1 X C2 X C3 XC 1.93 kW 1.93 kW 1.93 kW 5.79 kW Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitive reactance When capacitors are in parallel, the total reactance is the reciprocal of the sum of the reciprocals of the individual reactances. That is, X C(tot ) 1 1 1 1 1 X C1 X C2 X C3 X Cn If the three 0.033 mF capacitors from the last example are placed in parallel with the 2.5 kHz ac source, what is the total reactance? The reactance of each capacitor is 1.93 kW X C(tot ) Electronics Fundamentals 8th edition Floyd/Buchla 1 1 643 W 1 1 1 1 1 1 + + X C1 X C2 X C3 1.93 kW 1.93 kW 1.93 kW © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitive Voltage Divider Two capacitors in series are commonly used as a capacitive voltage divider. The capacitors split the output voltage in proportion to their reactance (and inversely proportional to their capacitance). What is the output voltage for the capacitive voltage divider? 1 1 4.82 kW 2πfC1 2π 33 kHz 1000 pF 1 1 482 W 2πfC2 2π 33 kHz 0.01 μF X C1 XC2 X C (tot ) X C1 X C 2 4.82 kW 482 W 5.30 kW Vout XC2 482 W Vs 1.0 V = 91 mV X 5.30 kW C (tot ) Electronics Fundamentals 8th edition Floyd/Buchla 1.0 V f = 33 kHz C1 1000 pF C2 Vout 0.01 µF © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitive Voltage Divider Instead of using a ratio of reactances in the capacitor voltage divider equation, you can use a ratio of the total series capacitance to the output capacitance (multiplied by the input voltage). The result is the same. For the problem presented in the last slide, C(tot ) Vout 1000 pF 0.01 μF 909 pF C1C2 C1 C2 1000 pF 0.01 μF C 909 pF (tot ) Vs 1.0 V = 91 mV C 0.01 μF 2 Electronics Fundamentals 8th edition Floyd/Buchla C1 1000 pF 1.0 V f = 33 kHz C2 Vout 0.01 µF © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Capacitive phase shift When a sine wave is applied to a capacitor, there is a phase shift between voltage and current such that current always leads the voltage by 90o. Electronics Fundamentals 8th edition Floyd/Buchla VC 0 90o I 0 © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Power in a capacitor Energy is stored by the capacitor during a portion of the ac cycle and returned to the source during another portion of the cycle. Voltage and current are always 90o out of phase. For this reason, no true power is dissipated by a capacitor, because stored energy is returned to the circuit. The rate at which a capacitor stores or returns energy is called reactive power. The unit for reactive power is the VAR (volt-ampere reactive). Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Power supply filtering There are many applications for capacitors. One is in filters, such as the power supply filter shown here. Rectifier 60 Hz ac C Load resistance The filter smoothes the pulsating dc from the rectifier. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Coupling capacitors Coupling capacitors are used to pass an ac signal from one stage to another while blocking dc. 3V 0V 0V +V The capacitor isolates dc Input between the amplifier stages, preventing dc in one stage from affecting the other stage. Electronics Fundamentals 8th edition Floyd/Buchla C R1 Amplifier stage 1 Amplifier stage 2 Output R2 © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Bypass capacitors Another application is to bypass an ac signal to ground but retain a dc value. This is widely done to affect gain in amplifiers. dc plus ac 0V dc only 0V The bypass capacitor places point A at ac ground, keeping only a dc value at point A. Electronics Fundamentals 8th edition Floyd/Buchla R1 A Point in circuit where R 2 only dc is required C © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Selected Key Terms Capacitor An electrical device consisting of two conductive plates separated by an insulating material and possessing the property of capacitance. Dielectric The insulating material between the conductive plates of a capacitor. Farad The unit of capacitance. RC time A fixed time interval set by the R and C values, constant that determine the time response of a series RC circuit. It equals the product of the resistance and the capacitance. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Selected Key Terms Capacitive The opposition of a capacitor to sinusoidal reactance current. The unit is the ohm. Instantaneous The value of power in a circuit at a given power (p) instant of time. True power The power that is dissipated in a circuit (Ptrue) usually in the form of heat. Reactive The rate at which energy is alternately stored power (Pr ) and returned to the source by a capacitor. The unit is the VAR. VAR The unit of reactive power. (volt-ampere reactive) Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 1. The capacitance of a capacitor will be larger if a. the spacing between the plates is increased. b. air replaces oil as the dielectric. c. the area of the plates is increased. d. all of the above. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 2. The capacitance of two capacitors connected in series will is analogous to a. two resistors connected in series b. two resistors connected in parallel c. none of the above. d. all of the above. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 3. Electrolytic capacitors are useful in applications where a. a precise value of capacitance is required. b. low leakage current is required. c. large capacitance is required. d. all of the above. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 4. If a 0.015 mF capacitor is in series with a 6800 pF capacitor, the total capacitance is a. 1568 pF. b. 4678 pF. c. 6815 pF. d. 0.022 mF. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 5. Two capacitors that are initially uncharged are connected in series with a dc source. Compared to the larger capacitor, the smaller capacitor will have a. the same charge. b. more charge. c. less voltage. d. the same voltage. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 6. When a capacitor is connected through a resistor to a dc voltage source, the charge on the capacitor will reach 50% of its final charge in a. less than one time constant. b. exactly one time constant. c. greater than one time constant. d. answer depends on the amount of voltage. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 7. When a capacitor is connected through a series resistor and switch to a dc voltage source, the voltage across the resistor after the switch is closed has the shape of a. a straight line. b. a rising exponential. c. a falling exponential. d. none of the above. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 8. The capacitive reactance of a 100 mF capacitor to 60 Hz is a. 6.14 kW. b. 265 W. c. 37.7 W. d. 26.5 W. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 9. If an sine wave from a function generator is applied to a capacitor, the current will a. lag voltage by 90o. b. lag voltage by 45o. c. be in phase with the voltage. d. none of the above. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz 10. When a capacitor is used to pass an AC signal while removing DC, it is a a. decoupling capacitor. b. ripple filter capacitor. c. bypass capacitor. d. coupling capacitor. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 9 Quiz Answers: Electronics Fundamentals 8th edition Floyd/Buchla 1. c 6. a 2. b 7. c 3. c 8. d 4. b 9. d 5. a 10. d © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.