Electric Circuits, 9th Edition P20 docx

166 The Operational Amplifier Figure P5.7 Figure P5.10 10 kfl AAV Section 5.3 DESIGN PROBLEM 5.8 a) Design an inverting amplifier using an ideal op amp that has a gain of 3. Use a set of identical resistors from Appendix H. b) If you wish to amplify a 5 V input signal using the circuit you designed in part (a), what are the smallest power supply signals you can use? 5.9 The op amp in the circuit in Fig. P5.9 is ideal. MULTISIM a ) ^ind the range of values for a in which the op amp does not saturate. b) Find i () (in microamperes) when a = 0.272. Figure P5.9 12 kfl a50 kfl 1.6 kfl -AAWW- 50 kn 6 250 rnV 6.4 kfl t t l?n i io kn 5.10 a) The op amp in the circuit shown in Fig. P5.10 is PSPICE ideal. The adjustable resistor R± has a maxi- mum value of 100 kfl, and a is restricted to the range of 0.2 < a < 1. Calculate the range of v n if v s = 40 mV. b) If a is not restricted, at what value of a will the op amp saturate? 10 kfl Section 5.4 5.11 Refer to the circuit in Fig. 5.12, where the op amp PSPICE is assumed to be ideal. Given that R a = 4 kfl, .ULTISIM Rh = 5klli ^ = 2Qka ^ VA S 200 mV, v b = 150 mV, v c = 400 mV, and V cc = ±6 V, spec- ify the range of Rf for which the op amp operates within its linear region. 5.12 The op amp in Fig. P5.12 is ideal. PSPICE a ) what circuit configuration is shown in this figure? b) Find v Q if 4 V. = IV, v h = 1.5 V, and c) The voltages v a and v c remain at 1 V and -4 V, respectively. What are the limits on v b if the op amp operates within its linear region? Figure P5.12 44 kfl • VA, + 27.5 kfl 220 kfl AAA- 0 a • W^ + 80 kfl v h v„ 53.3 kfl 5.13 Design an inverting-summing amplifier so that v a = -(3¾ + 5v h + 4¾ + 2v d ). DE5IGN PROBLEM MULTISIM Start by choosing a feedback resistor (Rf) from Appendix H. Then choose single resistors from Appendix H or construct resistor neworks from resis- tors in Appendix H to satisfy the design values for /? a , /? b , R c , and i? d . Draw your final circuit diagram. Problems 167 5.14 a) The op amp in Fig. P5.14 is ideal. Find v a if PSPICE ? ; a = 4 V, v b = 9 V, v c = \3 V, and v d = 8 V. 4ULTISIM b) Assume v. A v c , and v L \ retain their values as given in (a). Specify the range of v. x such that the op amp operates within its linear region. Figure P5.17 Figure P5.14 40 kil • VvV + 22kft • VW 220 kil 'VW ii, T T Okil PSPICE MULTISIM 5.15 Tlie 220 kil feedback resistor in the circuit in Fig. P5.14 is replaced by a variable resistor Rf. The voltages v. d - v d have the same values as given in Problem 5.14(a). a) What value of Rf will cause the op amp to satu- rate? Note that 0 < R f < oo. b) When Rf has the value found in (a), what is the current (in microamperes) into the output ter- minal of the op amp? Section 5.5 5.16 The op amp in the circuit of Fig. P5.16 is ideal. PSPICE a \ -yvhat 0 p am p circuit configuration is this? MULTISIM b) Calculate v u . Figure P5.16 40 kH —A/VV 80 kil -A<W 5.17 The op amp in the circuit of Fig. P5.17 is ideal. a) What op amp circuit configuration is this? b) Find v a in terms of v s . c) Find the range of values for v s such that v n does not saturate and the op amp remains in its linear region of operation. 28 kO 5.18 The op amp in the circuit shown in Fig. P5.18 is ideal. PSPI " a) Calculate v a when v., equals 4 V. MULTISIM ' " ." n b) Specify the range of values of v s so that the op amp operates in a linear mode. c) Assume that v„ equals 2 V and that the 63 kil resistor is replaced with a variable resistor. What value of the variable resistor will cause the op amp to saturate? Figure P5.18 63 kil AAA- i.'„527kn 5.19 a) Design a non-inverting amplifier with a gain of 4. Use resistors from Appendix H. You might need to combine resistors in series and in par- allel to get the desired resistance. Draw your final circuit, b) If you use ± 12 V power supplies for the op amp, what range of input values will allow the op amp to stay in its linear operating region? 5.20 The op amp in the circuit of Fig. P5.20 is ideal. PSPICE MULTISIM a) What op amp circuit configuration is this? b) Find v <y in terms of v s . c) Find the range of values for v s such that v a does not saturate and the op amp remains in its linear region of operation. Figure P5.20 60 kil AA/V- 168 The Operational Amplifier 5.21 The op amp in the circuit shown in Fig. P5.21 is PSPICE ideal. The signal voltages v and v b are 800 mV and MULTISIM .„., ., 400 mv, respectively. a) What circuit configuration is shown in the figure? b) Calculate v a in volts. c) Find / a and / b in microamperes. d) What are the weighting factors associated with v a and v b ? Figure P5.21 110 kO 'VW »„£47kft T T 5.22 The circuit in Fig. P5.22 is a noninverting summing PROBLEM amplifier. Assume the op amp is ideal. Design the PSPICE circuit so that MULTISIM v <> = y a + 2«^ + 3v c . a) Specify the numerical values of R a and R c . b) Calculate / a , / b , and / c (in microamperes) when v a = 0.7 V, v b = 0.4 V, and u c = 1.1 V. Figure P5.22 loo kn 5.23 The op amp in the noninverting summing amplifier of Fig. P5.23 is ideal. a) Specify the values of Rf, R b , and R c so that v 0 = 6v. A + 3v h + 4v c . PSPICE MULTISIM b) Using the values found in part (a) for R ( , R h , and JR C , find (in microamperes) i a , / b , i c , L, and / s when v. a = 0.5 V, % = 2.5 V, and v c = 1 V. Figure P5.23 «3.3 kO Section 5.6 5.24 a) Use the principle of superposition to derive Eq. 5.22. b) Derive Eqs. 5.23 and 5.24. 5.25 The resistors in the difference amplifier shown PSPICE in Fig. 5.15 are K a = 24kO, R b = 75 kll, MULTISIM Rc = 130ka and ^ - 120 kH. The signal volt- ages v. d and v b are 8 and 5 V, respectively, and V cc = ±20 V. a) Find v (> . b) What is the resistance seen by the signal source y a ? c) What is the resistance seen by the signal source v b ? 5.26 The op amp in the circuit of Fig. P5.26 is ideal. What value of R { will give the equation v () = 5 - 4v u , for this circuit? Figure P5.26 Problems 169 DESIGN PROBLEM PSPICE MULTISIM 5.27 Design the difference-amplifier circuit in Fig. P5.27 so that v (l = 10(¾¾ - v a ), and the voltage source v b sees an input resistance of 220 kfi. Specify the val- ues of R a ,Rb» and R t using single resistors or com- binations of resistors from Appendix H. Use the ideal model for the op amp. Figure P5.27 4.7 kft DESIGN PROBLEM PSPrCE MULTISIM 5.30 Design a difference amplifier (Fig. 5.15) to meet the following criteria: v () = 3t> b — 4i> a . The resist- ance seen by the signal source v b is 470 kft, and the resistance seen by the signal source v. d is 22 kft when the output voltage v () is zero. Specify the values of R a , R b , R c , and R d using single resistors or combinations of resistors from Appendix H. 5.31 »'„$22 kft 5.28 The op amp in the adder-subtracter circuit shown in PSPICE pig. P5.28 is ideal. MULTISIM a) Find v 0 when v a = 1 V, v b = 2 V, v c = 3 V, and V d = 4 V. b) If v a , v b , and v d are held constant, what values of v c will not saturate the op amp? The resistor R £ in the circuit in Fig. P5.31 is adjusted until the ideal op amp saturates. Specify R t in kilohms. Figure P5.31 1.6 kO 18 V 5.6 kH Figure P5.28 20 kft V W W/ 180 kH ^vw- <v 18 kft -AW 30 kO v B 147 kfi 20 kH 5.29 Select the values of R a and R{ in the circuit in DESIGN Fig. P5.29 so that PROBLEM ° PSPICE MULTISIM 5.32 The op amp in the circuit of Fig. P5.32 is ideal. a) Plot v„ versus a when Rf = 4R-[ and v g =* 2 V. Use increments of 0.1 and note by hypothesis thatO < a < 1.0. b) Write an equation for the straight line you plot- ted in (a). How are the slope and inter- cept of the line related to v g and the ratio Rf/Ri? c) Using the results from (b), choose values for v g and the ratio Rf/R\ such that v a = -6a + 4. Figure P5.32 v a = 5000(; b - Q. Use single resistors or combinations of resistors from Appendix H.The op amp is ideal. Figure P5.29 »«t*L t) %** 170 The Operational Amplifier 5.33 In the difference amplifier shown in Fig. P5.33, what range of values of R x yields a CMRR > 1000? Figure P5.33 50kil 'WW 5.34 In the difference amplifier shown in Fig. P5.34, compute (a) the differential mode gain, (b) the common mode gain, and (c) the CMRR. Figure P5.34 1 kO ^L <b x i vJ [ Y i ikn ) < i 25kfl r^f 10V ^"S-iov 124 kO 1 + »„ r Sections 5.1-5.6 5.35 Assume that the ideal op amp in the circuit seen in Fig. P5.35 is operating in its linear region. a) Show that v 0 = [(/?, + R 2 )/R x \v s . b) What happens if R 1 —• oo and R 2 -» 0? c) Explain why this circuit is referred to as a volt- age follower when Z?j = oo and R 2 = 0. Figure P5.35 5.36 The voltage v g shown in Fig. P5.36(a) is applied to PSPICE tne inverting amplifier shown in Fig. P5.36(b). 1ULTISIM <-,,,, ,, 11 Sketch v„ versus f, assuming the op amp is ideal. Figure P5.36 v 0.5 V -0.5 V (a) 120 kO 7.5 kO —AMs •o "»%6.8ka (b) 5.37 Tlie signal voltage v g in the circuit shown in Fig. P5.37 PSPICE j s described by the following equations: MULTISIM *• v e = 0, 0, v g = 10 sin(ir/3)/ V, 0 < / < oo. Sketch v a versus r, assuming the op amp is ideal. Figure P5.37 15 kO 75 kH »,, f 6.8 kfi 5.38 a) Show that when the ideal op amp in Fig. P5.38 is operating in its linear region, . 3V 8 *• = -R- b) Show that the ideal op amp will saturate when R(±V CC ~ 2v g ) R* = 3v g Problems 171 Figure P5.38 5.39 Assume that the ideal op amp in the circuit in PSPICE Fig. P5.39 is operating in its linear region. MULTISIM a) Calculate the power delivered to the 16 kO resistor. b) Repeat (a) with the op amp removed from the circuit, that is, with the 16 kfit resistor connected in the series with the voltage source and the 48 kft resistor. c) Find the ratio of the power found in (a) to that found in (b). d) Does the insertion of the op amp between the source and the load serve a useful purpose? Explain. Figure P5.39 320 mV 5.40 The circuit inside the shaded area in Fig. P5.40 is a con- PSPICE s tant current source for a limited range of values of R f . MULTISIM a) Find the value of i L for R L = 4 kft. b) Find the maximum value for R L for which i L will have the value in (a). c) Assume that R L = 16 kft. Explain the operation of the circuit. You can assume that i n = i p ~ 0 under all operating conditions. d) Sketch i L versus R L for 0 < R L < 16 kft. Figure P5.40 50 kfl 'v© ,. -20V [ IA R L ( t Jh l t-\: :4 left 5.41 The two op amps in the circuit in Fig. P5.41 are PSPICE ideal. Calculate v„\ and v o2 . MULTISIM Figure P5.41 15 V 15 V 10 V «4,2 f5kft 5.42 The op amps in the circuit in Fig. P5.42 are ideal. PSPICE a) Find/ a . ULTISIM b) Find the value of the left source voltage for which / n = 0. Figure P5.42 10 kn i—vvv—4 47 kD -vw 220 kH AAA- IV © 33 kH AA/v—i 6 150 mV 172 The Operational Amplifier Section 5.7 5.43 Repeat Assessment Problem 5.6, given that the PSPICE inverting amplifier is loaded with a 500 ft resistor. MULTISIM 5.44 Assume the input resistance of the op amp in PSPKE Fig. P5.44 is infinite and its output resistance is zero. MULTISIM a) Find v 0 as a function of v g and the open-loop gain A. b) What is the value of v 0 if v g - 1 V and A = 150? c) What is the value of v 0 if v g = 1 V and A - oo? d) How large does A have to be so that v {) is 99% of its value in (c)? Figure P5.44 10 kfl 'VW- 5.46 PSPICE MULTISIM a) Find the Thevenin equivalent circuit with respect to the output terminals a,b for the inverting amplifier of Fig. P5.46. The dc signal source has a value of 880 mV. The op amp has an input resistance of 500 kft, an output resistance of 2 kft and an open-loop gain of 100,000. b) What is the output resistance of the inverting amplifier? c) What is the resistance (in ohms) seen by the sig- nal source v s when the load at the terminals a,b is 330 ft? Figure P5.46 24 kO AW- 5.45 The op amp in the noninverting amplifier circuit of PSPICE Fig. P5.45 has an input resistance of 560 kft, an out- WLTISIM p Ut res { s t ance 0 f § kO, and an open-loop gain of 50,000. Assume that the op amp is operating in its linear region. a) Calculate the voltage gain (v () /v g ). b) Find the inverting and noninverting input volt- ages v n and v p (in millivolts) if v g — 1 V. c) Calculate the difference (v p - v n ) in microvolts when Vg ~ 1 V. d) Find the current drain in picoamperes on the signal source v R when v g = 1 V. e) Repeat (a)-(d) assuming an ideal op amp. 5.47 Repeat Problem 5.46 assuming an ideal op amp. Figure P5.45 200 kft 20 kCL PSPICE MULTISIM 5.48 Derive Eq. 5.60. Sections 5.1-5.7 5.49 Suppose the strain gages in the bridge in Fig. 5.21 PRACTICAL have the value 120 ft ± 1%. The power supplies PERSPECTIVE r r r to the op amp are ±15V, and the refer- ence voltage, v rc{ , is taken from the positive power supply. a) Calculate the value of Rf so that when the strain gage that is lengthening reaches its maximum length, the output voltage is 5 V. b) Suppose that we can accurately measure 50 mV changes in the output voltage. What change in strain gage resistance can be detected in milliohms? Problems 173 5.50 PRACTICAL PERSPECTIVE a) For the circuit shown in Fig. P5.50, show that if AR « R, the output voltage of the op amp is approximately show that the percent error in the approxima- tion of v„ in Problem 5.50 is R 2 (R + 2R t ) (~AR)v h AR (R + Re) % error = — 7½ TTTT X 100. R (R + 2R { ) b) Find v () if R f = 470 kfl, R = 10 kf>, AR = 95 ft, and v in = 15 V. c) Find the actual value of v a in (b). Figure P5.50 5.51 a) If percent error is defined as PRAOICAL PERSPECTIVE PSPICE MULTISIM % error = approximate value true value - 1 x 100, b) Calculate the percent error in v a for Problem 5.50. 5.52 Assume the percent error in the approximation of PRACTICAL v t) in the circuit in Fig. P5.50 is not to exceed 1%. PERSPECTIVE " ° PSPICE What is the largest percent change in R that can be MULTisiM tolerated? 5.53 Assume the resistor in the variable branch of the PRACTICAL bridge circuit in Fig. P5.50 is R PERSPECTIVE n ° L ° R + AR. AR instead of PSPICE MULTISIM a) What is the expression for v () if AR « R? b) What is the expression for the percent error in v a as a function of R, i? f , and AR1 c) Assume the resistance in the variable arm of the bridge circuit in Fig. P5.50 is 9810 fi and the values of R, R ( , and v m are the same as in Problem 5.50(b). What is the approximate value of v a '? d) What is the percent error in the approximation of v (} when the variable arm resistance is 9810 a? • t _•< aBniri r 6.1 The Inductor p. 176 6.2 The Capacitor p. 182 6.3 Series-Parallel Combinations of Inductance and Capacitance p. 187 6.4 Mutual Inductance p. 189 6.5 A Closer Look at Mutual Inductance p. 193 1 Know and be able to use the equations for voltage, current, power, and energy in an inductor; understand how an inductor behaves in the presence of constant current, and the requirement that the current be continuous in an inductor. 2 Know and be able to use the equations for voltage, current, power, and energy in a capacitor; understand how a capacitor behaves in the presence of constant voltage, and the requirement that the voltage be continuous in a capacitor. 3 Be able to combine inductors with initial conditions in series and in parallel to form a single equivalent inductor with an initial condition; be able to combine capacitors with initial conditions in series and in parallel to form a single equivalent capacitor with an initial condition. 4 Understand the basic concept of mutual inductance and be able to write mesh-current equations for a circuit containing magnetically coupled coils using the dot convention correctly. 174 Inductance, Capacitance, and Mutual Inductance We begin this chapter by introducing the last two ideal circuit elements mentioned in Chapter 2, namely, inductors and capaci- tors. Be assured that the circuit analysis techniques introduced in Chapters 3 and 4 apply to circuits containing inductors and capac- itors. Therefore, once you understand the terminal behavior of these elements in terms of current and voltage, you can use Kirchhoff s laws to describe any interconnections with the other basic elements. Like other components, inductors and capacitors are easier to describe in terms of circuit variables rather than electromagnetic field variables. However, before we focus on the circuit descriptions, a brief review of the field concepts under- lying these basic elements is in order. An inductor is an electrical component that opposes any change in electrical current. It is composed of a coil of wire wound around a supporting core whose material may be mag- netic or nonmagnetic. The behavior of inductors is based on phe- nomena associated with magnetic fields. The source of the magnetic field is charge in motion, or current. If the current is varying with time, the magnetic field is varying with time. A time- varying magnetic field induces a voltage in any conductor linked by the field. The circuit parameter of inductance relates the induced voltage to the current. We discuss this quantitative rela- tionship in Section 6.1. A capacitor is an electrical component that consists of two conductors separated by an insulator or dielectric material. The capacitor is the only device other than a battery that can store electrical charge. The behavior of capacitors is based on phenom- ena associated with electric fields. The source of the electric field is separation of charge, or voltage. If the voltage is varying with time, the electric field is varying with time. A time-varying electric field produces a displacement current in the space occupied by the field. The circuit parameter of capacitance relates the dis- placement current to the voltage, where the displacement current is equal to the conduction current at the terminals of the capaci- tor. We discuss this quantitative relationship in Section 6.2. Practical Perspective Proximity Switches The electrical devices we use in our daily lives contain many switches. Most switches are mechanical, such as the one used in the flashlight introduced in Chapter 2. Mechanical switches use an actuator that is pushed, pulled, slid, or rotated, caus- ing two pieces of conducting metal to touch and create a short circuit. Sometimes designers prefer to use switches without moving parts, to increase the safety, reliability, con- venience, or novelty of their products. Such switches are called proximity switches. Proximity switches can employ a variety of sensor technologies. For example, some elevator doors stay open whenever a light beam is obstructed. Another sensor technology used in proximity switches detects people by responding to the disruption they cause in electric fields. This type of proximity switch is used in some desk lamps that turn on and off when touched and in elevator buttons with no moving parts (as shown in the figure). The switch is based on a capacitor. As you are about to discover in this chapter, a capacitor is a circuit element whose terminal characteristics are determined by electric fields. When you touch a capacitive proximity switch, you produce a change in the value of a capacitor, causing a voltage change, which acti- vates the switch. The design of a capacitive touch-sensitive switch is the topic of the Practical Perspective example at the end of this chapter. 175 . with electric fields. The source of the electric field is separation of charge, or voltage. If the voltage is varying with time, the electric field is varying with time. A time-varying electric. capacitor is an electrical component that consists of two conductors separated by an insulator or dielectric material. The capacitor is the only device other than a battery that can store electrical . concepts under- lying these basic elements is in order. An inductor is an electrical component that opposes any change in electrical current. It is composed of a coil of wire wound around a supporting