Repeat P10.16 for Vs = 4 V, Rs = 1 , and ix = vx + 2v2 x,

Describe a fluid-flow analogy for a diode.

Draw the circuit symbol for a diode, labeling the anode and cathode.

Sketch the voltampere characteristic of a typical diode and label the various regions.

Write the Shockley equation and define all of the terms

Determine the values of VT for temperatures of 20C and 175C.

Suppose that we have a junction diode that has iD = 0.5 mA for vD = 0.6 V. Assume that n = 2 and VT = 0.026 V. Use the Shockley equation to compute the diode current at vD = 0.65 V and at vD = 0.70 V.

A diode operates in forward bias, in which it is described by Equation 10.4, with VT = 0.026 V. For vD1 = 0.600 V, the current is iD1 = 1 mA. For vD2 = 0.680 V, the current is iD2 = 10 mA. Determine the values of Is and n.

Sketch i versus v to scale for the circuits shown in Figure P10.8. The reversebreakdown voltages of the Zener diodes are shown. Assume voltages of approximately 0.6 V for all diodes including the Zener diodes when current flows in the forward direction. i v + (a) (b) i v + 6.8 V (c) i v + 5.6 V 5.6 V Figure P10.8

Repeat Problem P10.8 for the circuits shown in Figure P10.9. (a) v + i (b) 3.3 V 5.6 V v + i (c) v + i (d) v 5.6 V + i Figure P10.9

As a rule of thumb, with constant current flowing in the forward direction in a smallsignal silicon diode, the voltage across the diode decreases with temperature by about 2 mV/K. Such a diode has a voltage of 0.650 V, with a current of 1 mA at a temperature of 25C. Find the diode voltage at 1 mA and a temperature of 150C.

We have a silicon diode described by the Shockley equation. The diode has n = 2 and operates at 100C with a current of 1 mA and voltage of 0.5 V. Determine the current after the voltage is increased to 0.6 V

Consider a junction diode operating at a constant temperature of 300 K. With a forward current of 1 mA, the voltage is 600 mV. Furthermore, with a current of 10 mA, the voltage is 700 mV. Find the value of n for this diode.

Assume a diode with n = 2,Is = 20 nA, and VT =26 mV. a. Using a computer program of your choice, obtain a plot of iD versus vD for iD ranging from 10 A to 10 mA. Choose a logarithmic scale foriD and a linear scale for vD. What type of curve results? b. Place a 100-resistance in series with the diode, and plot current versus voltage across the series combination on the same axes used for part (a). Compare the two curves. When is the added series resistance significant?

The diodes shown in Figure P10.14 are identical and have n = 1. The temperature of the diodes is constant at 300 K. Before the switch is closed, the voltage v is 600 mV. Find v after the switch is closed. Repeat for n = 2. v + 1 mA Figure P10.14

Current hogging. The diodes shown in Figure P10.15 are identical and have n = 1. For each diode, a forward current of 100 mA results in a voltage of 700 mV at a temperature of 300 K. a. If both diodes are at 300 K, what are the values of IA and IB? b. If diode A is at 300 K and diode B is at 305 K, again find IA and IB, given that Is doubles in value for a 5-K increase in temperature. [Hint: Answer part (a) by use of symmetry. For part (b), a transcendental equation for the voltage across the diodes can be found. Solve by trial and error. An important observation to be made from this problem is that, starting at the same temperature, the diodes should theoretically each conduct half of the total current. However, if one diode conducts slightly more, it becomes warmer, resulting in even more current. Eventually, one of the diodes hogs most of the current. This is particularly noticeable for devices that are thermally isolated from one another with large currents, for which significant heating occurs.] 200 mA IA IB Figure P10.15

The nonlinear circuit element shown in Figure P10.16 has ix = [exp(vx) 1]/10, in which the units of vx and ix are V and A, respectively. Also, we have Vs = 3 V and Rs = 1 . Use graphical load-line techniques to solve for ix and vx. (You may prefer to use a computer program to plot the characteristic and the load line.) + Rs Vs vx + ix Figure P10.16

Repeat Problem P10.16 for Vs = 4 V, Rs = 1 , and ix = vx + 2v2 x, in which the units of vx and ix are V and A, respectively.

Repeat Problem P10.16 for Vs = 15 V, Rs = 3 k, and ix = 0.01/(1vx/4)3, in which the units of vx and ix areV and mA, respectively.

Repeat Problem P10.16 for Vs = 8 V, Rs = 2 , and ix = v3 x # 4, in which the units of vx and ix are V and A, respectively.

Several types of special-purpose diodes exist. One is the constant-current diode for which the current is constant over a wide range of voltage. The circuit symbol and voltampere characteristic for a particular constant-current diode are shown in Figure P10.20(a). Another special type is the LED for which the circuit symbol and a typical voltampere characteristic are shown in Figure P10.20(b). Sometimes, the series combination of these two devices is used to provide constant current to the LED from a variable voltage cource. a. Sketch the overall voltampere characteristic to scale for the series combination shown in Figure P10.20(c). b. Sketch the overall volt ampere characteristic to scale for the parallel combination shown in Figure P10.20(d). (a) Voltampere characteristic of a constant-current diode i (mA) v (V) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 012345 0.5 1.5 2.5 3.5 4.5 i + v (b) Voltampere characteristic of a light-emitting diode (LED) i (mA) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 012345 0.5 1.5 2.5 3.5 4.5 v (V) i + v (c) + v i (d) + v i Figure P10.20

Determine the values for i and v for the circuit of Figure P10.21. The diode is the LED having the characteristic shown in Figure P10.20(b). 5 k 15 V v + + i Figure P10.21

What is a Zener diode? For what is it typically used? Draw the voltampere characteristic of an ideal 5.8-V Zener diode.

Draw the circuit diagram of a simple voltage regulator.

Consider the Zener-diode regulator shown in Figure 10.14 on page 478. What is the smallest load resistance for which vo is 10V?

A simple voltage regulator is shown in Figure P10.25. The source voltage Vs varies from 8 to 12 V, and the load current iL varies from 50 to 150 mA. Assume that the Zener diode is ideal. Determine the largest value allowed for the resistance Rs so that the load voltage vL remains constant with variations in load current and source voltage. Determine the maximum power dissipation in Rs. vL iz + VS RS iL 5 V Figure P10.25

You are required to design a simple voltageregulator circuit that provides a constant voltage of 5 V to a load from a variable supply voltage. The load current varies from 0 to 100 mA, and the source voltage varies from 8 to 10 V. You may assume that ideal Zener diodes are available. Resistors of any value may be specified. Draw the circuit diagram of your regulator, and specify the value of each component. Also, find the worst case (maximum) power dissipated in each component in your regulator. Try to use good judgment in your design.

Repeat Problem P10.26 given that the supply voltage ranges from 6 to 10 V.

Repeat Problem P10.26 given that the load current varies from 0 to 1 A.

Explain in general terms the method for solving a circuit that contains a single nonlinear element plus resistors, dc voltage sources, and dc current sources, given the voltampere characteristic of the nonlinear device.

A certain linear two-terminal circuit has terminals a and b. Under open-circuit conditions, we have vab = 10 V. A short circuit is connected across the terminals, and a current of 2 A flows from a to b through the short circuit. Determine the value of vab when a nonlinear element that has iab = 3 vab is connected across the terminals.

Determine the values for i1 and i2 for the circuit of Figure P10.31. The device is the constant-current diode having the characteristic shown in Figure P10.20(a). 10 mA i2 i1 500 500 Figure P10.31

Determine the values for i and v for the circuit of Figure P10.32. The diode is the LED having the characteristic shown in Figure P10.20(b). v + + 5 k 5 V i 1 mA Figure P10.32

Repeat Problem P10.32 for the circuit of Figure P10.33. The diode is the LED having the characteristic shown in Figure P10.20(b). v + + 2 k 4 V i ix 1.5 ix Figure P10.33

What is an ideal diode? Draw its volt ampere characteristic.After solving a circuit with ideal diodes, what check is necessary for diodes initially assumed to be on? Off?

Consider two ideal diodes in series, pointing in opposite directions. What is the equivalent circuit for the combination?What is the equivalent circuit if the diodes are in parallel and pointing in opposite directions?

Find the values of I and V for the circuits of Figure P10.36, assuming that the diodes are ideal. (a) (b) (c) V 10 k + 10 k +15 V 5 k 5 k I D1 D2 1 k I V + +6 V +3 V D1 D2 1 k 1.5 k +15 V D1 2.2 k D2 I + V 15 V Figure P10.36

Find the values of I and V for the circuits of Figure P10.37, assuming that the diodes are ideal.

Find the values of I and V for the circuits of Figure P10.38, assuming that the diodes are ideal. For part (b), consider Vin = 0, 2, 6, and 10 V. Also, for part (b) of the figure, plot V versus Vin for Vin ranging from 10 V to 10 V. 1 k 15 V D1 D2 D3 I 1 k + V 1 k 1 k +15 V (a) (b) V + + Vin 1 k +10 V I 1 k 1 k 10 V D3 D4 D1 D2 Figure P10.38

a. Figure P10.39(a) shows a type of logic gate. Assume that the diodes are ideal. The voltagesVA andVB independently have values of either 0 V (for logic 0, or low) or 5 V (for logic 1, or high). For which of the four combinations of input voltages is the output high (i.e.,Vo = 5 V)?What type of logic gate is this? b. Repeat for Figure P10.39(b). (a) + VA VB + Vo + (b) +5 V + VA VB + Vo + Figure P10.39

Sketch a plot of i versus v to scale for each of the circuits shown in Figure P10.40. Assume that the diodes are ideal and allow v to range from 10 V to +10 V. v + i 1 k (a) (b) i 2 k v + 5 V + (c) v + 1 k A 2 k B i (d) v + 1 k C D i Figure P10.40

Sketch vo(t) to scale versus time for the circuit shown in Figure P10.41. Assume that the diodes are ideal. vo(t) 5 sin(2pt) + + D1 D2 R R R Figure P10.41

If a nonlinear two-terminal device is modeled by the piecewise-linear approach, what is the equivalent circuit of the device for each linear segment?

A resistor Ra is in series with a voltage source Va. Draw the circuit. Label the voltage across the combination as v and the current asi. Draw and label the voltampere characteristic (i versus v).

The voltampere characteristic of a certain two-terminal device is a straight line that passes through the points (2 V, 5 mA) and (3 V, 15 mA). The current reference points into the positive reference for the voltage. Determine the equivalent circuit for this device.

Assume that we have approximated a nonlinear voltampere characteristic by the straight-line segments shown in Figure P10.45(c). Find the equivalent circuit for each segment. Use these equivalent circuits to find v in the circuits shown in Figure P10.45(a) and (b). v + 2 1 3 k 15 V + (a) (b) v + 40 mA 2 1 50 1 10 11 i (mA) 0.8 1.2 2.0 v (V) i + v 1 2

Consider the voltampere characteristic of an ideal 10-V Zener diode shown in Figure 10.14 on page 478. Determine the piecewiselinear equivalent circuit for each segment of the characteristic.

The Zener diode shown in Figure P10.47 has a piecewise-linear model shown in Figure 10.19 on page 481. Plot load voltage vL versus load current iL for iL ranging from 0 to 100 mA. vL + + 100 13 V iL Figure P10.47

In this problem, we will assume that the diode shown in Figure P10.48 can be represented by the model of Figure 10.23 on page 483, with Vf = 0.7 V. a. Assume that the diode operates as an open-circuit and solve for the node voltages v1 and v2. Are the results consistent with the model? Why or why not? b. Repeat part (a), assuming that the diode operates as a 0.7-V voltage source. v1 + + 16 V v2 vD 100 200 200 300 iD Figure P10.48

Draw the circuit diagram of a half-wave rectifier for producing a nearly steady dc voltage from an ac source. Draw two different full-wave circuits (one of which requires two ac sources).

We have a 15-V rms 60-Hz ac source is in series with an ideal diode and a 50- resistance. Determine the peak current and peak inverse voltage (PIV) for the diode.

This problem relates to the half-wave recti- fier shown in Figure 10.26 on page 485. The ac source has an rms value of 15 V and a frequency of 60 Hz. The diodes are ideal, and the capacitance is very large, so the ripple voltage Vr is very small. The load is a 50- resistance. Determine the peak inverse voltage across the diode and the charge that passes through the diode per cycle. What can you say about the peak current through the diode?

This problem relates to the battery-charging circuit shown in Figure 10.25 on page 484. The ac source voltage is vs(t) = Vm sin(t) = 24 sin(120t). The resistance is 0.5 , the diode is ideal, and VB = 12 V. Determine the average current (i.e., the value of the charge that passes through the battery in 1 second). Suppose that the battery starts from a totally discharged state and has a capacity of 100 ampere hours. How long does it take to fully charge the battery?

Dc voltmeters produce readings equal to the average values of the voltages measured. The average value of a periodic waveform is Vavg = 1 T T 0 v(t)dt in which T is the period of the voltage v(t) applied to the meter. a. What does a dc voltmeter read if the applied voltage is v(t) = Vm sin(t)? b. What does the meter read if the applied voltage is a half-wave rectified version of the sinewave? c. What does the meter read if the applied voltage is a full-wave rectified version of the sinewave?

A half-wave rectifier is needed to supply 15-V dc to a load that draws an average current of 250 mA. The peak-to-peak ripple is required to be 0.2 V or less. What is the minimum value allowed for the smoothing capacitance? If a full-wave rectifier is needed?

Design a half-wave rectifier power supply to deliver an average voltage of 9 V with a peak-to-peak ripple of 2 V to a load. The average load current is 100 mA.Assume that ideal diodes and 60-Hz ac voltage sources of any amplitudes needed are available. Draw the circuit diagram for your design. Specify the values of all components used.

Repeat Problem P10.55 with a full-wave bridge rectifier.

Repeat Problem P10.55 with two diodes and out-of-phase voltage sources to form a full-wave rectifier.

Repeat Problem P10.55, assuming that the diodes have forward drops of 0.8 V.

Consider the battery-charging circuit shown in Figure 10.25 on page 484, in which vs(t) = 20 sin(200t), R = 80 , VB = 12 V, and the diode is ideal. a. Sketch the current i(t) to scale versus time. b. Determine the average charging current for the battery. (Hint: The average current is the charge that flows through the battery in one cycle, divided by the period.)

a. Consider the full-wave rectifier shown in Figure 10.27 on page 486, with a large smoothing capacitance placed in parallel with the load RL and Vm = 12 V. Assuming that the diodes are ideal, what is the approximate value of the load voltage? What peak inverse voltage (PIV) appears across the diodes? b. Repeat for the full-wave bridge shown in Figure 10.28 on page 487.

Figure P10.61 shows the equivalent circuit for a typical automotive battery charging system. The three-phase delta-connected source represents the stator coils of the alternator. (Three-phase ac sources are discussed in Section 5.7. Actually, the alternator stator is usually wye connected, but the terminal voltages are the same as for the equivalent delta.) Not shown in the figure is a voltage regulator that controls the current applied to the rotor coil of the alternator and, consequently, Vm and the charging current to the battery. a. Sketch the load voltage vL(t) to scale versus time. Assume ideal diodes and that Vm is large enough that current flows into the battery at all times. (Hint: Each Problems 507 source and four of the diodes form a fullwave bridge rectifier.) b. Determine the peak-to-peak ripple and the average load voltage in terms of Vm. c. Determine the value of Vm needed to provide an average charging current of 30 A. d.What additional factors would need to be considered in a realistic computation of Vm? vAB vBC vCA + + + 12 V 0.1 A C B + + vL vAB = Vm cos(vt) vBC = Vm cos(vt 120) vCA = Vm cos(vt + 120) Figure P10.61 Idealized model of an automotive battery-charging system.

What is a clipper circuit? Draw an example circuit diagram, including component values, an input waveform, and the corresponding output waveform.

Sketch the transfer characteristic (vo versus vin) to scale for the circuit shown in Figure P10.63. Allow vin to range from 10 V to +10 V and assume that the diodes are ideal. 1 k vo + 2 k + vin Figure P10.63

Sketch to scale the output waveform for the circuit shown in Figure P10.64. Assume that the diodes are ideal.

Sketch the transfer characteristic (vo versus vin) to scale for the circuit shown in Figure P10.65. Allow vin to range from 10 V to +10 V and assume that the diodes are ideal. + vin 1 k 1 k 1 k D2 D1 vo Figure P10.65

Sketch the transfer characteristic (vo versus vin) to scale for the circuit shown in Figure P10.66. Allow vin to range from 10 V to +10 V and assume that the diodes are ideal. vo + 3 k + 1 k vin 3 V Figure P10.66

Sketch the transfer characteristic (vo versus vin) for the circuit shown in Figure P10.67, + vin 10 V 1.2 k 2 k 3 k + vo + Figure P10.67 508 Chapter 10 Diodes carefully labeling the breakpoint and slopes. Allow vin to range from 10 V to +10 V and assume that the diodes are ideal.

What is a clamp circuit? Draw an example circuit diagram, including component values, an input waveform, and the corresponding output waveform.

Sketch to scale the steady-state output waveform for the circuit shown in Figure P10.69. Assume that RC is much larger than the period of the input voltage and that the diodes are ideal. vo(t) vc vs(t) = 10 sin (200pt) + + + 5 V R C Figure P10.69

Design a clipper circuit to clip off the portions of an input voltage that fall above 3 V or below 5 V. Assume that diodes having a constant forward drop of 0.7 V are available. Ideal Zener diodes of any breakdown voltage required are available. Dc voltage sources of any value needed are available

Repeat Problem P10.70, with clipping levels of +5 V and +10 V (i.e., every part of the input waveform below +5 or above +10 is clipped off).

Consider the circuit shown in Figure P10.72, in which the RC time constant is very long compared with the period of the input and in which the diode is ideal. Sketch several cycles of vo(t) to scale versus time. vo(t) + + C R vs(t) = 10 sin(2000pt) Figure P10.72

Voltage-doubler circuit. Consider the circuit of Figure P10.73. The capacitors are very large, so they discharge only a very small amount per cycle. (Thus, no ac voltage appears across the capacitors, and the ac input plus the dc voltage of C1 must appear at point A.) Sketch the voltage at point A versus time. Find the voltage across the load. Why is this called a voltage doubler?What is the peak inverse voltage across each diode? + Vm sin(vt) RL C1 D2 A D1 C2 Figure P10.73 Voltage doubler

Design a clamp circuit to clamp the negative extreme of a periodic input waveform to 5 V. Use diodes, Zener diodes, and resistors of any values required. Assume a 0.6-V forward drop for all diodes and that the Zener diodes have an ideal characteristic in the breakdown region. Power-supply voltages of 15 V are available.

Repeat Problem P10.74 for a clamp voltage of +5 V.

Design circuits that have the transfer characteristics shown in Figure P10.76. Assume that vin ranges from 10 to +10 V. Use diodes, Zener diodes, and resistors of any values needed. Assume a 0.6-V forward drop for all diodes and that the Zener diodes have an ideal characteristic in the breakdown region. Power-supply voltages of 15 V are available. (a)

A certain diode has IDQ = 4 mA and id(t) = 0.5 cos(200t) mA. Find an expression for iD(t), and sketch several cycles to scale versus time.

Of what does the small-signal equivalent circuit of a diode consist? How is the dynamic resistance of a nonlinear circuit element determined at a given operating point?

With what are dc voltage sources replaced in a small-signal ac equivalent circuit? Why?

With what should we replace a dc current source in a small-signal ac equivalent circuit? Justify your answer.

A certain nonlinear device has iD = v3 D # 8. Sketch iD versus vD to scale for vD ranging from 2 V to +2 V. Is this device a diode? Determine the dynamic resistance of the device and sketch it versus vD to scale for vD ranging from 2 V to +2 V.

A breakdown diode has iD = 106 (1 + vD/7)2 for 7 V < vD < 0 where iD is in amperes. Plot iD versus vD for the ranges 10 mA iD 0 and 7 V

A diode is operating with an applied voltage given by vD(t) = 4 + 0.02 cos(t)V The current is given by iD(t) = 7 + 0.2 cos(t) mA Determine the dynamic resistance and Q point of the diode under the conditions given.

The voltage of an ideal Zener diode is constant in the breakdown region. What does this imply about the dynamic resistance in the breakdown region for an ideal Zener diode?

Consider the voltage-regulator circuit shown in Figure P10.85. The ac ripple voltage is 1 V peak to peak. The dc (average) load voltage is 5 V. What is the Q-point current in the Zener diode? What is the maximum dynamic resistance allowed for the Zener diode if the output ripple is to be less than 10 mV peak to peak? VL = 5 V + R Vripple 100 + 8 V 20 RL Figure P10.85