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Microelectronic Circuits

Adel S. Sedra, Kenneth C. Smith

Chapter 4

Diodes - all with Video Answers

Educators

Chapter Questions

01:26

Problem 1

An AA flashlight cell, whose Thévenin equivalent is a voltage source of $1.5 \mathrm{V}$ and a resistance of $1 \Omega$, is connected to the terminals of an ideal diode. Describe two possible situations that result. What are the diode current and terminal voltage when (a) the connection is between the diode cathode and the positive terminal of the battery and (b) the anode and the positive terminal are connected?

Anand Jangid
Anand Jangid
Numerade Educator
00:52

Problem 2

For the circuits shown in Fig. P4.2 using ideal diodes, find the values of the voltages and currents indicated.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
00:52

Problem 3

For the circuits shown in Fig. P4.3 using ideal diodes, find the values of the labeled voltages and currents.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
14:20

Problem 4

In each of the ideal-diode circuits shown in Fig. $\mathrm{P} 4.4,$ $v_{1}$ is a $1-\mathrm{kHz}, 10-\mathrm{V}$ peak sine wave. Sketch the waveform resulting at $v_{o} .$ What are its positive and negative peak values?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
15:58

Problem 5

The circuit shown in Fig. P4.5 is a model for a battery charger. Here $v_{1}$ is a 10 -V peak sine wave, $D_{1}$ and $D_{2}$ are ideal diodes, $I$ is a 60 -mA current source, and $B$ is a 3 -V battery. Sketch and label the waveform of the battery current $i_{B}$ What is its peak value? What is its average value? If the peak value of $v_{1}$ is reduced by $10 \%,$ what do the peak and average values of $i_{B}$ become?

Ryan Kutayiah
Ryan Kutayiah
Texas A&M University
01:57

Problem 6

The circuits shown in Fig. $\mathrm{P} 4.6$ can function as logic gates for input voltages that are either high or low. Using "1" to denote the high value and "0" to denote the low value, prepare a table with four columns including all possible input combinations and the resulting values of $X$ and $Y$. What logic function is $X$ of $A$ and $B ?$ What logic function is $Y$ of $A$ and $B ?$ For what values of $A$ and $B$ do $X$ and $Y$ have the same value? For what values of $A$ and $B$ do $X$ and $Y$ have opposite values?

Ajay Singhal
Ajay Singhal
Numerade Educator
02:37

Problem 7

For the logic gate of Fig. $4.5(\mathrm{a}),$ assume ideal diodes and input voltage levels of $0 \mathrm{V}$ and $+5 \mathrm{V}$. Find a suitable value for $R$ so that the current required from each of the input signal sources does not exceed $0.2 \mathrm{mA}$.

James Kiss
James Kiss
Numerade Educator
01:05

Problem 8

Repeat Problem 4.7 for the logic gate of Fig. 4.5 (b).

Carson Merrill
Carson Merrill
Numerade Educator
00:52

Problem 9

Assuming that the diodes in the circuits of Fig. P4.9 are ideal, find the values of the labeled voltages and
currents.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:37

Problem 10

Assuming that the diodes in the circuits of Fig. P4.10 are ideal, utilize Thévenin's theorem to simplify the circuits and thus find the values of the labeled currents and voltages.

James Kiss
James Kiss
Numerade Educator
01:12

Problem 11

For the rectifier circuit of Fig. $4.3(\mathrm{a}),$ let the input sine wave have 120 - $\mathrm{V}$ rms value and assume the diode to be ideal. Select a suitable value for $R$ so that the peak diode current does not exceed 50 mA. What is the greatest reverse voltage that will appear across the diode?

Narayan Hari
Narayan Hari
Numerade Educator
02:37

Problem 12

Consider the rectifier circuit of Fig. 4.3 in the event that the input source $v_{1}$ has a source resistance $R_{s}$. For the case $R_{s}=R$ and assuming the diode to be ideal, sketch and clearly label the transfer characteristic $v_{o}$ versus $v_{1}$.

James Kiss
James Kiss
Numerade Educator
01:40

Problem 13

A symmetrical square wave of $4-\mathrm{V}$ peak-to-peak amplitude and zero average is applied to a circuit resembling that in Fig. $4.3(\mathrm{a})$ and employing a $100-\Omega$ resistor. What is the peak output voltage that results? What is the average output voltage that results? What is the peak diode current? What is the average diode current? What is the maximum reverse voltage across the diode?

Narayan Hari
Narayan Hari
Numerade Educator
01:08

Problem 14

Repeat Problem 4.13 for the situation in which the average voltage of the square wave is $1 \mathrm{V}$, while its peak-to-peak value remains at $4 \mathrm{V}$.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:40

Problem 15

Design a battery-charging circuit, resembling that in Fig. 4.4 and using an ideal diode, in which current flows to the 12 -V battery $20 \%$ of the time with an average value of $100 \mathrm{mA} .$ What peak-to-peak sine-wave voltage is required? What resistance is required? What peak diode current flows? What peak reverse voltage does the diode endure? If resistors can be specified to only one significant digit, and the peak-to-peak voltage only to the nearest volt, what design would you choose to guarantee the required charging current? What fraction of the cycle does diode current flow? What is the average diode current? What is the peak diode current? What peak reverse voltage does the diode endure?

Narayan Hari
Narayan Hari
Numerade Educator
View

Problem 16

The circuit of Fig. $P 4.16$ can be used in a signalling system using one wire plus a common ground return. At any moment, the input has one of three values: $+3 \mathrm{V}, 0 \mathrm{V},-3 \mathrm{V}$ What is the status of the lamps for each input value? (Note that the lamps can be located apart from each other and that there may be several of each type of connection, all on one wire!)

Victor Salazar
Victor Salazar
Numerade Educator
01:31

Problem 17

Calculate the value of the thermal voltage, $V_{T},$ at $-40^{\circ} \mathrm{C}$, $0^{\circ} \mathrm{C},+40^{\circ} \mathrm{C},$ and $+150^{\circ} \mathrm{C} .$ At what temperature is $V_{T}$ exactly $25 \mathrm{mV} ?$

Supratim Pal
Supratim Pal
Numerade Educator
02:54

Problem 18

At what forward voltage does a diode conduct a current equal to $1000 I_{S} ?$ In terms of $I_{s},$ what current flows in the same diode when its forward voltage is $0.7 \mathrm{V} ?$

Narayan Hari
Narayan Hari
Numerade Educator
01:50

Problem 19

A diode for which the forward voltage drop is $0.7 \mathrm{V}$ at $1.0 \mathrm{mA}$ is operated at $0.5 \mathrm{V}$. What is the value of the current?

Aman Kumar
Aman Kumar
Numerade Educator
03:01

Problem 20

A particular diode is found to conduct $0.5 \mathrm{mA}$ with a junction voltage of $0.7 \mathrm{V}$. What is its saturation current $I_{S} ?$ What current will flow in this diode if the junction voltage is raised to $0.71 \mathrm{V} ?$ To $0.8 \mathrm{V} ?$ If the junction voltage is lowered to 0.69 V? To 0.6 V? What change in junction voltage will increase the diode current by a factor of $10 ?$

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:54

Problem 21

The following measurements are taken on particular junction diodes for which $V$ is the terminal voltage and 1 is the diode current. For each diode, estimate values of $I_{S}$ and the terminal voltage at $10 \%$ of the measured current.
(a) $V=0.700 \mathrm{V}$ at $I=1.00 \mathrm{A}$
(b) $V=0.650 \mathrm{V}$ at $I=1.00 \mathrm{mA}$
(c) $V=0.650 \mathrm{V}$ at $I=10 \mu \mathrm{A}$
(d) $V=0.700 \mathrm{V}$ at $I=10 \mathrm{mA}$

Narayan Hari
Narayan Hari
Numerade Educator
02:56

Problem 22

Listed below are the results of measurements taken on several different junction diodes. For each diode, the data provided are the diode current $I$ and the corresponding diode voltage $V .$ In each case, estimate $I_{S},$ and the diode voltage at $10 I$ and $I / 10$.
(aa) $10.0 \mathrm{mA}, 700 \mathrm{mV}$
(b) $1.0 \mathrm{mA}, 700 \mathrm{mV}$
(c) $10 \mathrm{A}, 800 \mathrm{mV}$
(d) $1 \mathrm{mA}, 700 \mathrm{mV}$
(e) $10 \mu \mathrm{A}, 700 \mathrm{mV}$

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
02:54

Problem 23

The circuit in Fig. $P 4.23$ utilizes three identical diodes having $I_{S}=10^{-16} \mathrm{A}$. Find the value of the current 1 required to obtain an output voltage $V_{o}=2.4 \mathrm{V}$. If a current of $1 \mathrm{mA}$ is drawn away from the output terminal by a load, what is the change in output voltage?

Narayan Hari
Narayan Hari
Numerade Educator
01:49

Problem 24

A junction diode is operated in a circuit in which it is supplied with a constant current $I$. What is the effect on the forward voltage of the diode if an identical diode is connected in parallel?

Jorge Villanueva
Jorge Villanueva
Numerade Educator
03:55

Problem 25

In the circuit shown in Fig. $\mathrm{P} 4.25, D_{1}$ has 10 times the junction area of $D_{2}$. What value of $V$ results? To obtain a value for $V$ of $50 \mathrm{mV}$, what current $I_{2}$ is needed?

Vishal Gupta
Vishal Gupta
Numerade Educator
00:46

Problem 26

For the circuit shown in Fig. $P 4.26,$ both diodes are identical. Find the value of $R$ for which $V=80 \mathrm{mV}$.

Sana Maqsad
Sana Maqsad
Numerade Educator
02:16

Problem 27

A diode fed with a constant current $I=1 \mathrm{mA}$ has a voltage $V=690 \mathrm{mV}$ at $20^{\circ} \mathrm{C}$. Find the diode voltage at $-20^{\circ} \mathrm{C}$ and $\mathrm{at}+70^{\circ} \mathrm{C}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:11

Problem 28

In the circuit shown in Fig. P4.28, $D_{1}$ is a large-area high-current diode whose reverse leakage is high and independent of applied voltage, while $D_{2}$ is a much smaller, low-current diode. At an ambient temperature of $20^{\circ} \mathrm{C}$, resistor $R_{1}$ is adjusted to make $V_{1}=V_{2}=520 \mathrm{mV}$. Subsequent measurement indicates that $R_{1}$ is $520 \mathrm{k} \Omega$. What do you expect the voltages $V_{R 1}$ and $V_{2}$ to become at $0^{\circ} \mathrm{C}$ and at $40^{\circ} \mathrm{C}?$

Chai Santi
Chai Santi
Numerade Educator
02:50

Problem 29

When a 15 -A current is applied to a particular diode. it is found that the junction voltage immediately becomes $700 \mathrm{mV}$. However, as the power being dissipated in the diode raises its temperature, it is found that the voltage decreases and eventually reaches $600 \mathrm{mV}$. What is the apparent rise in junction temperature? What is the power dissipated in the diode in its final state? What is the temperature rise per watt of power dissipation? (This is called the thermal resistance.)

Narayan Hari
Narayan Hari
Numerade Educator
01:50

Problem 30

A designer of an instrument that must operate over a wide supply-voltage range, noting that a diode's junction-voltage drop is relatively independent of junction current, considers the use of a large diode to establish a small relatively constant voltage. A power diode, for which the nominal current at $0.8 \mathrm{V}$ is $10 \mathrm{A}$, is available. If the current source feeding the diode changes in rhe range $0.5 \mathrm{mA}$ to $1.5 \mathrm{mA}$ and if, in addition, the temperature changes by $\pm 25^{\circ} \mathrm{C}$, what is the expected range of diode voltage?

Aman Kumar
Aman Kumar
Numerade Educator
03:05

Problem 31

As an alternative to the idea suggested in Problem $4.30,$ the designer considers a second approach to producing a relatively constant small voltage from a variable current supply: It relies on the ability to make quite accurate copies of any small current that is available (using a process called current mirroring). The designer proposes to use this idea to supply two diodes of different junction areas with the same current and to measure their junction-voltage difference.

Narayan Hari
Narayan Hari
Numerade Educator
04:44

Problem 32

Consider the graphical analysis of the diode circuit of Fig. 4.10 with $V_{D D}=1 \mathrm{V}, R=1 \mathrm{k} \Omega,$ and a diode having $I_{S}=$ $10^{-15}$ A. Calculate a small number of points on the diode characteristic in the vicinity of where you expect the load line to intersect it, and use a graphical process to refine your estimate of diode current. What value of diode current and voltage do you find? Analytically, find the voltage corresponding to your estimate of current. By how much does it differ from the graphically estimated value?

Pawan Yadav
Pawan Yadav
Numerade Educator
04:44

Problem 33

Use the iterative-analysis procedure to determine the diode current and voltage in the circuit of Fig. 4.10 for $V_{D D}=$ 1 $\mathrm{V}, R=1 \mathrm{k} \Omega,$ and a diode having $I_{S}=10^{-15} \mathrm{A}$.

Pawan Yadav
Pawan Yadav
Numerade Educator
02:54

Problem 34

A "1-mA diode" (i.e., one that has $v_{D}=0.7 \mathrm{V}$ at $i_{D}=$ 1 $\mathrm{mA}$ ) is connected in series with a $200-\Omega$ resistor to a $1.0-\mathrm{V}$ supply.
(a) Provide a rough estimate of the diode current you would expect.
(b) Estimate the diode current more closely using iterative analysis.

Narayan Hari
Narayan Hari
Numerade Educator
02:21

Problem 35

Assuming the availability of diodes for which $v_{D}=$ $0.7 \mathrm{V}$ at $i_{D}=1 \mathrm{mA},$ design a circuit that utilizes four diodes connected in series, in series with a resistor $R$ connected to a 10-V power supply. The voltage across the string of diodes is to be $3.0 \mathrm{V}$.

Anand Jangid
Anand Jangid
Numerade Educator
02:54

Problem 36

A diode operates in a series circuit with $R$ and $V$. A designer, considering using a constant-voltage model, is uncertain whether to use $0.7 \mathrm{V}$ or $0.6 \mathrm{V}$ for $V_{D} .$ For what value of $V$ is the difference in the calculated values of current only $1 \% ?$ For $V=2 \mathrm{V}$ and $R=1 \mathrm{k} \Omega$, what two currents would result from the use of the two values of $V_{D} ?$ What is their percentage difference?

Narayan Hari
Narayan Hari
Numerade Educator
02:21

Problem 37

A designer has a supply of diodes for which a current of $2 \mathrm{mA}$ flows at $0.7 \mathrm{V}$. Using a $1-\mathrm{mA}$ current source, the designer wishes to create a reference voltage of $1.25 \mathrm{V}$. Suggest a combination of series and parallel diodes that will do the job as well as possible. How many diodes are needed? What voltage is actually achieved?

Vinnu M
Vinnu M
Numerade Educator
04:44

Problem 38

Solve the problems in Example 4.2 using the constant-voltage-drop $\left(V_{D}=0.7 \mathrm{V}\right)$ diode model.

Pawan Yadav
Pawan Yadav
Numerade Educator
04:44

Problem 39

For the circuits shown in Fig. P4.2, using the constant-voltage-drop $\left(V_{D}=0.7 \mathrm{V}\right)$ diode model, find the voltages and currents indicated.

Pawan Yadav
Pawan Yadav
Numerade Educator
04:44

Problem 40

For the circuits shown in Fig. P4.3, using the constant-voltage-drop $\left(V_{D}=0.7 \mathrm{V}\right)$ diode model, find the voltages and currents indicated.

Pawan Yadav
Pawan Yadav
Numerade Educator
04:44

Problem 41

For the circuits in Fig. P4.9, using the constant-voltage-$\operatorname{drop}\left(V_{D}=0.7 \mathrm{V}\right)$ diode model, find the values of the labeled currents and voltages.

Pawan Yadav
Pawan Yadav
Numerade Educator
01:32

Problem 42

For the circuits in Fig. P4.10, utilize Thévenin's theorem to simplify the circuits and find the values of the labeled currents and voltages. Assume that conducting diodes can be represented by the constant-voltage-drop model $\left(V_{D}=0.7 \mathrm{V}\right)$.

Narayan Hari
Narayan Hari
Numerade Educator
02:22

Problem 43

Repeat Problem 4.11 , representing the diode by the constant-voltage-drop $\left(V_{D}=0.7 \mathrm{V}\right)$ model. How different is the resulting design?

Narayan Hari
Narayan Hari
Numerade Educator
01:32

Problem 44

The small-signal model is said to be valid for voltage variations of about $5 \mathrm{mV}$. To what percentage current change does this correspond? (Consider both positive and negative signals.) What is the maximum allowable voltage signal (positive or negative) if the current change is to be limited to $10 \% ?$

Amany Waheeb
Amany Waheeb
Numerade Educator
08:21

Problem 45

In a particular circuit application, ten "20-mA diodes" (a 20 -mA diode is a diode that provides a 0.7 -V drop when the current through it is $20 \mathrm{mA}$ ) connected in parallel operate at a total current of 0.1 A. For the diodes closely matched, what current flows in each? What is the corresponding small-signal resistance of each diode and of the combination? Compare this with the incremental resistance of a single diode conducting 0.1 A. If each of the $20-\mathrm{mA}$ diodes has a series resistance of $0.2 \Omega$ associated with the wire bonds to the junction, what is the equivalent resistance of the 10 parallel-connected diodes? What connection resistance would a single diode need in order to be totally equivalent? (Note: This is why the parallel connection of real diodes can often be used to advantage.)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:17

Problem 46

In the circuit shown in Fig. $\mathrm{P} 4.46, I$ is a dc current and $v_{s}$ is a sinusoidal signal. Capacitors $C_{1}$ and $C_{2}$ are very large; their function is to couple the signal to and from the diode but block the dc current from flowing into the signal source or the load (not shown). Use the diode small-signal model to show that the signal component of the output voltage is $$v_{o}=v_{s} \frac{V_{T}}{V_{T}+I R_{s}}$$ If $v_{s}=10 \mathrm{mV},$ find $v_{o}$ for $I=1 \mathrm{mA}, 0.1 \mathrm{mA},$ and $1 \mu \mathrm{A}$. Let $R_{s}=1 \mathrm{k} \Omega$. At what value of $I$ does $v_{o}$ become one-half of $v_{s}?$ Note that this circuit functions as a signal attenuator with the attenuation factor controlled by the value of the dc current $I$.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:39

Problem 47

In the attenuator circuit of Fig. P4.46, let $R_{s}=10 \mathrm{k} \Omega$. The diode is a $1-\mathrm{mA}$ device; that is, it exhibits a voltage drop of $0.7 \mathrm{V}$ at a dc current of $1 \mathrm{mA}$. For small input signals, what value of current $I$ is needed for $v_{o} / v_{s}=0.50 ?$ $0.10 ? 0.01 ? 0.001 ?$ In each case, what is the largest input signal that can be used while ensuring that the signal component of the diode current is limited to $\pm 10 \%$ of its dc current? What output signals correspond?

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
10:52

Problem 48

In the capacitor-coupled attenuator circuit shown in Fig. P4.48, I is a dc current that varies from 0 $\mathrm{mA}$ to 1 $\mathrm{mA}$, and $C_{\mathrm{l}}$ and $C_{2}$ are large coupling capacitors. For very small input sig. nals, so that the diodes can be representedby their small-signal resistances $r_{d 1}$ and $r_{d 2},$ show that $\frac{v_{o}}{v_{i}}=\frac{r_{d 2}}{r_{d 1}+r_{d 2}}$ and hence that $\frac{v_{o}}{v_{i}}=I,$ where $I$ is in $\mathrm{mA}$. Find $v_{o} / v_{i}$ for $I=0 \mu \mathrm{A}$ $1 \mu \mathrm{A}, 10 \mu \mathrm{A}, 100 \mu \mathrm{A}, 500 \mu \mathrm{A}, 600 \mu \mathrm{A}, 900 \mu \mathrm{A}, 990 \mu \mathrm{A}$
and $1 \mathrm{mA}$.

Vishal Gupta
Vishal Gupta
Numerade Educator
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Problem 49

In the circuit shown in Fig. P4.49, diodes $D_{1}$ through $D_{4}$ are identical and each exhibits a voltage drop of $0.7 \mathrm{V}$ at a $1-\mathrm{mA}$ current.
(a) For small input signals (e.g., $10 \mathrm{mV}$ peak), find values of the small-signal transmission $v_{o} / v_{i}$ for various values of $I: 0 \mu A, 1 \mu A, 10 \mu A, 100 \mu A, 1 m A,$ and $10 \mathrm{mA}$.
(b) For a forward-conducting diode, what is the largest signal-voltage magnitude that it can support while the corresponding signal current is limited to $10 \%$ of the dc bias current. Now, for the circuit in Fig. P4.49, for 10-mV peak input, what is the smallest value of 1 for which the diode currents remain within $\pm 10 \%$ of their dc value?
(c) For $I=1 \mathrm{mA}$, what is the largest possible output signal for which the diode currents deviate by at most $10 \%$ of their dc values? What is the corresponding peak input? What is the total current in each diode?

Lainey Roebuck
Lainey Roebuck
Numerade Educator
03:17

Problem 50

In Problem 4.49 we investigated the operation of the circuit in Fig. P4.49 for small input signals. In this problem we wish to find the voltage transfer characteristic (VTC) $v_{O}$ versus $v_{I}$ for $-12 \mathrm{V} \leq v_{1} \leq 12 \mathrm{V}$ for the case $I=$ 1 $\mathrm{mA}$ and each of the diodes exhibits a voltage drop of $0.7 \mathrm{V}$ at a current of $1 \mathrm{mA}$. Toward this end, use the diode exponential characteristic to construct a table that gives the values of: the current $i_{O}$ in the $10-\mathrm{k} \Omega$ resistor, the current in each of the four diodes, the voltage drop across each of the four diodes, and the input voltage $v_{I},$ for $v_{O}=0,+1 \mathrm{V}$ $+2 \mathrm{V},+5 \mathrm{V},+9 \mathrm{V},+9.9 \mathrm{V},+9.99 \mathrm{V},+10.5 \mathrm{V},+11 \mathrm{V},$ and $+12 \mathrm{V} .$ Use these data, with extrapolation to negative values of $v_{I}$ and $v_{O},$ to sketch the required $\mathrm{VTC}$. Also sketch the VTC that results if $I$ is reduced to $0.5 \mathrm{mA}$.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:24

Problem 51

In the circuit shown in Fig. P4.51, $I$ is a dc current and $v_{i}$ is a sinusoidal signal with small amplitude (less than $10 \mathrm{mV}$ ) and a frequency of $100 \mathrm{kHz}$. Representing the diode by its small-signal resistance $r_{d},$ which is a function of $I,$ sketch the circuit for determining the sinusoidal output voltage $V_{o},$ and thus find the phase shift between $V_{i}$ and $V_{o}$ Find the value of $I$ that will provide a phase shift of $-45^{\circ}$ and find the range of phase shift achieved as $I$ is varied over the range of 0.1 times to 10 times this value.

M Hassan Anwar
M Hassan Anwar
Numerade Educator
04:44

Problem 52

Consider the voltage-regulator circuit shown in Fig. P4.52. The value of $R$ is selected to obtain an output voltage $V_{o}(\text { across the diode })$ of $0.7 \mathrm{V}$.
(a) Use the diode small-signal model to show that the change in output voltage corresponding to a change of $1 \mathrm{V}$ in $V^{+}$ is $$\frac{\Delta V_{O}}{\Delta V^{+}}=\frac{V_{T}}{V^{+}+V_{T}-0.7}$$ This quantity is known as the line regulation and is usually expressed in $\mathrm{mV} / \mathrm{V}$.
(b) Generalize the expression above for the case of $m$ diodes connected in series and the value of $R$ adjusted so that the voltage across each diode is $0.7 \mathrm{V}$ (and $V_{o}=0.7 \mathrm{m}$ V).
(c) Calculate the value of line regulation for the case $V^{+}=$ $10 \mathrm{V}$ (nominally) and (i) $m=1$ and (ii) $m=3$.

Chai Santi
Chai Santi
Numerade Educator
View

Problem 53

Consider the voltage-regulator circuit shown in Fig $\mathrm{P} 4.52$ under the condition that a load current $I_{L}$ is drawn from the output terminal.
(a) If the value of $I_{L}$ is sufficiently small that the corresponding change in regulator output voltage $\Delta V_{o}$ is small enough to justify using the diode small-signal model, show that $$\frac{\Delta V_{O}}{I_{L}}=-\left(r_{d} \| R\right)$$ This quantity is known as the load regulation and is usually expressed in $\mathrm{mV} / \mathrm{mA}$.
(b) If the value of $R$ is selected such that at no load the voltage across the diode is $0.7 \mathrm{V}$ and the diode current is $I_{D}$ show that the expression derived in (a) becomes $$\frac{\Delta V_{O}}{I_{L}}=-\frac{V_{T}}{I_{D}} \frac{V^{+}-0.7}{V^{+}-0.7+V_{T}}$$ Select the lowest possible value for $I_{D}$ that results in a load regulation $\leq 5 \mathrm{mV} / \mathrm{mA}$. If $V^{+}$ is nominally $10 \mathrm{V}$, what value of $R$ is required? Also, specify the diode required in terms of its $I_{S}$ (c) Generalize the expression derived in (b) for the case of $m$ diodes connected in series and $R$ adjusted to obtain $V_{o}=$ $0.7 m \mathrm{V}$ at no load.

Lainey Roebuck
Lainey Roebuck
Numerade Educator
11:47

Problem 54

Design a diode voltage regulator to supply $1.5 \mathrm{V}$ to a $150-\Omega$ load. Use two diodes specified to have a $0.7-V$ drop at a current of $10 \mathrm{mA}$. The diodes are to be connected to a $+5-\mathrm{V}$ supply through a resistor $R$. Specify the value for $R$. What is the diode current with the load connected? What is the increase resulting in the output voltage when the load is disconnected? What change results if the load resistance is reduced to $100 \Omega ?$ To $75 \Omega ?$ To $50 \Omega ?$ (Hint: Use the small signal diode model to calculate all changes in output voltage.)

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
02:21

Problem 55

A voltage regulator consisting of two diodes in series fed with a constant-current source is used as a re for a single carbon-zinc cell (battery) of nominal voltage $1.5 \mathrm{V} .$ The regulator load current varies from $2 \mathrm{mA}$ to $7 \mathrm{mA}$ Constant-current supplies of $5 \mathrm{mA}, 10 \mathrm{mA}$, and $15 \mathrm{mA}$ are available. Which would you choose, and why? What change in output voltage would result when the load current varies over its full range?

Vinnu M
Vinnu M
Numerade Educator
08:21

Problem 56

A particular design of a voltage regulator is shown in Fig. P4.56. Diodes $D_{1}$ and $D_{2}$ are 10 -mA units; that is, each has a voltage drop of $0.7 \mathrm{V}$ at a current of $10 \mathrm{mA}$. Use the diode exponential model and iterative analysis to answer the following questions:
(a) What is the regulator output voltage $V_{o}$ with the $150-\Omega$ load connected?
(b) Find $V_{o}$ with no load.
(c) With the load connected, to what value can the $5-\mathrm{V}$ supply be lowered while maintaining the loaded output voltage within $0.1 \mathrm{V}$ of its nominal value?
(d) What does the loaded output voltage become when the 5-V supply is raised by the same amount as the drop found in $(\mathrm{c}) ?$
(e) For the range of changes explored in (c) and (d), by what percentage does the output voltage change for each percentage change of supply voltage in the worst case?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
11:47

Problem 57

Partial specifications of a collection of zener diodes are provided below. For each, identify the missing parameter, and estimate its value. Note from Fig. 4.17 that $V_{Z K} \simeq V_{Z 0}$.
(a) $V_{z}=10.0 \mathrm{V}, V_{2 \mathrm{K}}=9.6 \mathrm{V},$ and $I_{T_{T}}=50 \mathrm{mA}$
(b) $I_{Z T}=10 \mathrm{mA}, V_{2}=9.1 \mathrm{V},$ and $r_{2}=30 \Omega$
(c) $r_{z}=2 \Omega, V_{z}=6.8 \mathrm{V},$ and $V_{\mathrm{zK}}=6.6 \mathrm{V}$
(d) $V_{z}=18 \mathrm{V}, I_{\text {IT }}=5 \mathrm{mA}$, and $V_{\mathrm{ZK}}=17.6 \mathrm{V}$
(e) $I_{T I}=200 \mathrm{mA}, V_{2}=7.5 \mathrm{V},$ and $r_{z}=1.5 \Omega$
Assuming that the power rating of a breakdown diode is established at about twice the specified zener current $\left(l_{Z}\right)$ what is the power rating of each of the diodes described above?

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
01:03

Problem 58

A designer requires a shunt regulator of approximately $20 \mathrm{V}$. Two kinds of zener diodes are available: $6.8-\mathrm{V}$ devices with $r_{z}$ of $10 \Omega$ and $5.1-V$ devices with $r_{z}$ of $30 \Omega$ For the two major choices possible, find the load regulation. In this calculation neglect the effect of the regulator resistance $R$.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
01:13

Problem 59

A shunt regulator utilizing a zener diode with an incremental resistance of $5 \Omega$ is fed through an $82-\Omega$ resistor. If the raw supply changes by $1.0 \mathrm{V},$ what is the corresponding change in the regulated output voltage?

Vinnu M
Vinnu M
Numerade Educator
01:39

Problem 60

A $9.1-\mathrm{V}$ zener diode exhibits its nominal voltage at a test current of $28 \mathrm{mA}$. At this current the incremental resistance is specified as $5 \Omega$. Find $V_{z 0}$ of the zener model. Find the zener voltage at a current of $10 \mathrm{mA}$ and at $100 \mathrm{mA}$.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:34

Problem 61

Design a 7.5 -V zener regulator circuit using a $7.5 . \mathrm{V}$ zener specified at 12 mA. The zener has an incremental resistance $r_{z}=30 \Omega$ and a knee current of $0.5 \mathrm{mA}$. The regulator operates from a 10 -V supply and has a $1.2-\mathrm{k} \Omega$ load. What is the value of $R$ you have chosen? What is the regulator output voltage when the supply is $10 \%$ high? Is $10 \%$ low? What is the output voltage when both the supply is $10 \%$ high and the load is removed? What is the smallest possible load resistor that can be used while the zener operates at a current no lower than the knee current while the supply is $10 \%$ low? What is the load voltage in this case?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:18

Problem 62

Provide two designs of shunt regulators utilizing the $1 \mathrm{N} 5235$ zener diode, which is specified as follows: $V_{2}=$ $6.8 \mathrm{V}$ and $r_{z}=5 \Omega$ for $I_{z}=20 \mathrm{mA} ;$ at $I_{z}=0.25 \mathrm{mA}$ (nearer the knee), $r_{z}=750 \Omega$. For both designs, the supply voltage is nominally $9 \mathrm{V}$ and varies by $\pm 1 \mathrm{V}$. For the first design, assume that the availability of supply current is not a problem, and thus operate the diode at $20 \mathrm{mA}$. For the second design, assume that the current from the raw supply is limited, and therefore you are forced to operate the diode at $0.25 \mathrm{mA}$. For the purpose of these initial designs, assume no load. For each design find the value of $R$ and the line regulation.

James Kiss
James Kiss
Numerade Educator
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Problem 63

A zener shunt regulator employs a 9.1 -V zener diode for which $V_{z}=9.1 \mathrm{V}$ at $I_{\mathrm{Z}}=9 \mathrm{mA},$ with $r_{z}=30 \Omega$ and $I_{\mathrm{Zx}}=0.3$ mA. The available supply voltage of $15 \mathrm{V}$ can vary as much as $\pm 10 \% .$ For this diode, what is the value of $V_{20} ?$ For a nominal load resistance $R_{L}$ of $1 \mathrm{k} \Omega$ and a nominal zener current of 10 $\mathrm{mA},$ what current must flow in the supply resistor $R ?$ For the nominal value of supply voltage, select a value for resistor $R$, specified to one significant digit, to provide at least that current. What nominal output voltage results? For $a \pm 10 \%$ change in the supply voltage, what variation in output voltage results? If the load current is reduced by $50 \%,$ what increase in $V_{o}$ results? What is the smallest value of load resistance that can be tolerated while maintaining regulation when the supply voltage is low? What is the lowest possible output voltage that results? Calculate values for the line regulation and for the load regulation for this circuit using the numerical results obtained in this problem.

Lainey Roebuck
Lainey Roebuck
Numerade Educator
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Problem 64

It is required to design a zener shunt regulator to provide a regulated voltage of about $10 \mathrm{V}$. The available $10-\mathrm{V}, 1-\mathrm{W}$ zener of type $1 \mathrm{N} 4740$ is specified to have a $10-\mathrm{V}$ drop at a test current of $25 \mathrm{mA}$. At this current, its $r_{z}$ is $7 \Omega$ The raw supply, $V_{s},$ available has a nominal value of $20 \mathrm{V}$ but can vary by as much as $\pm 25 \% .$ The regulator is required to supply a load current of $0 \mathrm{mA}$ to $20 \mathrm{mA}$. Design for a minimum zener current of $5 \mathrm{mA}$.
(a) Find $V_{20}$
(b) Calculate the required value of $R$
(c) Find the line regulation. What is the change in $V_{o}$ expressed as a percentage, corresponding to the $\pm 25 \%$ change in $V_{S} ?$
(d) Find the load regulation. By what percentage does $V_{o}$ change from the no-load to the full-load condition?
(e) What is the maximum current that the zener in your design is required to conduct? What is the zener power dissipation under this condition?

Lainey Roebuck
Lainey Roebuck
Numerade Educator
01:12

Problem 65

Consider the half-wave rectifier circuit of Fig. $4.21(\mathrm{a})$ with the diode reversed. Let $v_{s}$ be a sinusoid with 12 -V peak amplitude, and let $R=1.5 \mathrm{k} \Omega$. Use the constant-voltage-drop diode model with $V_{D}=0.7 \mathrm{V}$.
(a) Sketch the transfer characteristic.
(b) Sketch the waveform of $v_{o}$
(c) Find the average value of $v_{o}$
(d) Find the peak current in the diode
(e) Find the PIV of the diode.

Narayan Hari
Narayan Hari
Numerade Educator
02:26

Problem 66

Using the exponential diode characteristic, show that for $v_{S}$ and $v_{o}$ both greater than zero, the circuit of Fig. $4.21(\mathrm{a})$ has the transfer characteristic $$v_{O}=v_{S}-v_{D}\left(\operatorname{at} i_{D}=1 \mathrm{mA}\right)-V_{T} \ln \left(v_{O} / R\right)$$ where $v_{s}$ and $v_{o}$ are in volts and $R$ is in kilohms. Note that this relationship can be used to obtain the voltage transfer characteristic $v_{o}$ vs $v_{s}$ by finding $v_{s}$ corresponding to various values of $v_{O}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 67

Consider a half-wave rectifier circuit with a triangular-wave input of $5-\mathrm{V}$ peak-to-peak amplitude and zero average, and with $R=1 \mathrm{k} \Omega$. Assume that the diode can be represented by the constant-voltage-drop model with $V_{D}=$ $0.7 \mathrm{V} .$ Find the average value of $v_{O}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 68

A half-wave rectifier circuit with a $1-\mathrm{k} \Omega$ load operates from a $120-\mathrm{V}(\mathrm{rms}) 60-\mathrm{Hz}$ household supply through a $10-$ to-1 step-down transformer. It uses a silicon diode that can be modeled to have a $0.7-\mathrm{V}$ drop for any current. What is the peak voltage of the rectified output? For what fraction of the cycle does the diode conduct? What is the average output voltage? What is the average current in the load?

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 69

A full-wave rectifier circuit with a $1-\mathrm{k} \Omega$ load operates from a $120-\mathrm{V}(\mathrm{rms}) 60-\mathrm{Hz}$ household supply through a $5-\mathrm{to}-$ 1 transformer having a center-tapped secondary winding. It uses two silicon diodes that can be modeled to have a $0.7-\mathrm{V}$ drop for all currents. What is the peak voltage of the rectified output? For what fraction of a cycle does each diode conduct? What is the average output voltage? What is the average current in the load?

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 70

A full-wave bridge rectifier circuit with a $1-\mathrm{k} \Omega$ load operates from a $120-\mathrm{V}$ (rms) $60-\mathrm{Hz}$ household supply through a 10 -to-1 step-down transformer having a single secondary winding. It uses four diodes, each of which can be modeled to have a $0.7-\mathrm{V}$ drop for any current. What is the peak value of the rectified voltage across the load? For what fraction of a cycle does each diode conduct? What is the average voltage across the load? What is the average current through the load?

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 71

It is required to design a full-wave rectifier circuit using the circuit of Fig. 4.22 to provide an average output voltage of:
(a) $10 \mathrm{V}$
(b) $100 \mathrm{V}$
In each case find the required turns ratio of the transformer. Assume that a conducting diode has a voltage drop of $0.7 \mathrm{V}$ The ac line voltage is $120 \mathrm{V} \mathrm{rms}$.

Narayan Hari
Narayan Hari
Numerade Educator
05:06

Problem 72

Repeat Problem 4.71 for the bridge rectifier circuit of Fig. 4.23.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:40

Problem 73

Consider the full-wave rectifier in Fig. 4.22 when the transformer turns ratio is such that the voltage across the entire secondary winding is $24 \mathrm{V} \mathrm{rms}$. If the input ac line voltage $(120 \mathrm{V} \mathrm{rms})$ fluctuates by as much as $\pm 10 \%$, find the required PIV of the diodes. (Remember to use a factor of safety in your design.

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 74

The circuit in Fig. P4.74 implements a complementary-output rectifier. Sketch and clearly label the waveforms of $v_{O}^{+}$ and $v_{O}^{-} .$ Assume a 0.7 - $\mathrm{V}$ drop across each conducting diode. If the magnitude of the average of each output is to be 15 $\mathrm{V}$, find the required amplitude of the sine wave across the entire secondary winding. What is the PIV of each diode?

Narayan Hari
Narayan Hari
Numerade Educator
01:40

Problem 75

Augment the rectifier circuit of Problem 4.68 with a capacitor chosen to provide a peak-to-peak ripple voltage of
(i) $10 \%$ of the peak output and (ii) $1 \%$ of the peak output. In each case:
(a) What average output voltage results?
(b) What fraction of the cycle does the diode conduct?
(c) What is the average diode current?
(d) What is the peak diode current?

Narayan Hari
Narayan Hari
Numerade Educator
02:09

Problem 76

Repeat Problem 4.75 for the rectifier in Problem 4.69.

Chai Santi
Chai Santi
Numerade Educator
02:09

Problem 77

Repeat Problem 4.75 for the rectifier in Problem 4.70.

Chai Santi
Chai Santi
Numerade Educator
01:40

Problem 78

It is required to use a peak rectifier to design a dc the power supply that provides an average de output voltage of $15 \mathrm{V}$ on which a maximum of $\pm 1-\mathrm{V}$ ripple is allowed. The rectifier feeds a load of $150 \Omega$. The rectifier is fed from the line voltage $(120 \mathrm{V} \mathrm{rms}, 60 \mathrm{Hz})$ through a transformer. The diodes available have $0.7-\mathrm{V}$ drop when conducting. If the designer opts for the half-wave circuit:
(a) Specify the rms voltage that must appear across the transformer secondary.
(b) Find the required value of the filter capacitor.
(c) Find the maximum reverse voltage that will appear across the diode, and specify the PIV rating of the diode.
(d) Calculate the average current through the diode during conduction.
(e) Calculate the peak diode current.

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 79

Repeat Problem 4.78 for the case in which the designer opts for a full-wave circuit utilizing a center-tapped transformer.

Raj Bala
Raj Bala
Numerade Educator
05:06

Problem 80

Repeat Problem 4.78 for the case in which the designer opts for a full-wave bridge rectifier circuit.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:12

Problem 81

Consider a half-wave peak rectifier fed with a voltage $v_{s}$ having a triangular waveform with 20 -V peak-to-peak amplitude, zero average, and $1-\mathrm{kHz}$ frequency. Assume that the diode has a $0.7-\mathrm{V}$ drop when conducting. Let the load resistance $R=100 \Omega$ and the filter capacitor $C=$ $100 \mu \mathrm{F} .$ Find the average dc output voltage, the time interval during which the diode conducts, the average diode current during conduction, and the maximum diode current.

Narayan Hari
Narayan Hari
Numerade Educator
01:12

Problem 82

Consider the circuit in Fig. P4.74 with two equal filter capacitors placed across the load resistors $R$. Assume that the diodes available exhibit a $0.7-\mathrm{V}$ drop when con ducting. Design the circuit to provide $\pm 15-\mathrm{V}$ dc output voltages with a peak-to-peak ripple no greater than 1 V. Each supply should be capable of providing $200 \mathrm{mA}$ dc current to its load resistor $R$. Completely specify the capacitors, diodes and the transformer.

Narayan Hari
Narayan Hari
Numerade Educator
01:12

Problem 83

The op amp in the precision rectifier circuit of Fig. $P 4.83$ is ideal with output saturation levels of ±12 V. Assume that when conducting the diode exhibits a constant voltage drop of $0.7 \mathrm{V} .$ Find $v_{-}, v_{0},$ and $v_{A}$ for:
(a) $v_{1}=+1 \mathrm{V}$
(b) $v_{1}=+2 \mathrm{V}$
(c) $v_{1}=-1 \mathrm{V}$
(d) $v_{1}=-2 \mathrm{V}$
Also, find the average output voltage obtained when $v_{l}$ is a symmetrical square wave of $1-\mathrm{kHz}$ frequency, $3-\mathrm{V}$ amplitude, and zero average.

Narayan Hari
Narayan Hari
Numerade Educator
01:58

Problem 84

The op amp in the circuit of Fig. P4.84 is ideal with output saturation levels of $\pm 12 \mathrm{V}$. The diodes exhibit a constant 0.7-V drop when conducting. Find $v_{-}, v_{A},$ and $v_{o}$ for:
(a) $v_{1}=+1 \mathrm{V}$
(b) $v_{1}=+2 \mathrm{V}$
(c) $v_{1}=-1 \mathrm{V}$
(d) $v_{1}=-2 \mathrm{V}$

Narayan Hari
Narayan Hari
Numerade Educator
02:37

Problem 85

Sketch the transfer characteristic $v_{o}$ versus $v_{1}$ for the limiter circuits shown in Fig. P4.85. All diodes begin conducting at a forward voltage drop of $0.5 \mathrm{V}$ and have voltage drops of $0.7 \mathrm{V}$ when conducting a current $i_{D} \geqslant 1 \mathrm{mA}$.

James Kiss
James Kiss
Numerade Educator
01:59

Problem 86

The circuits in Fig. P4.85(a) and (d) are connected as follows: The two input terminals are tied together, and the two output terminals are tied together. Sketch the transfer characteristic of the circuit resulting, assuming that the cut in voltage of the diodes is $0.5 \mathrm{V}$ and their voltage drop when conducting a current $i_{D} \geqslant 1 \mathrm{mA}$ is $0.7 \mathrm{V}$.

Vinnu M
Vinnu M
Numerade Educator
03:51

Problem 87

Repeat Problem 4.86 for the two circuits in Fig. P4.85(a) and (b) connected together as follows: The two input terminals are tied together, and the two output terminals are tied together.

Nishant Kumar
Nishant Kumar
Numerade Educator
01:11

Problem 88

Sketch and clearly label the transfer characteristic of the circuit in Fig. $\mathrm{P} 4.88$ for $-20 \mathrm{V} \leqslant v_{1} \leqslant+20 \mathrm{V}$. Assume that the diodes can be represented by the constant-voltage-drop model with $V_{D}=0.7 \mathrm{V}$. Also assume that the zener voltage is $8.2 \mathrm{V}$ and that $r_{z}$ is negligibly small.

Chai Santi
Chai Santi
Numerade Educator
01:32

Problem 89

Plot the transfer characteristic of the circuit in Fig.P4.89 by evaluating $v_{1}$ corresponding to $v_{o}=0.5 \mathrm{V}$ $0.6 \mathrm{V}, 0.7 \mathrm{V}, 0.8 \mathrm{V}, 0 \mathrm{V},-0.5 \mathrm{V},-0.6 \mathrm{V},-0.7 \mathrm{V},$ and $-0.8 \mathrm{V}$. Assume that the diodes have 0.7 -V drops at 1-mA currents Characterize the circuit as a hard or soft limiter. What is the value of $K ?$ Estimate $L_{+}$ and $L_{-}$.

Narayan Hari
Narayan Hari
Numerade Educator
00:56

Problem 90

Design limiter circuits using only diodes and $10-\mathrm{k} \Omega$ resistors to provide an output signal limited to the range:
(a) $-0.7 \mathrm{V}$ and above
(b) $-2.1 \mathrm{V}$ and above
(c) $\pm 1.4 \mathrm{V}$
Assume that each diode has a 0.7 -V drop when conducting.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
01:48

Problem 91

Design a two-sided limiting circuit using a resistor, two diodes, and two power supplies to feed a $1-k \Omega$ load with nominal limiting levels of $\pm 3 \mathrm{V}$. Use diodes modeled by a constant $0.7 \mathrm{V}$. In the nonlimiting region, the voltage gain should be at least $0.95 \mathrm{V} / \mathrm{V}$.

Narayan Hari
Narayan Hari
Numerade Educator
02:37

Problem 92

In the circuit shown in Fig. $\mathrm{P} 4.92,$ the diodes exhibit a $0.7-\mathrm{V}$ drop at $0.1 \mathrm{mA}$. For inputs over the range of $\pm 5 \mathrm{V}$, provide a calibrated sketch of the voltages at outputs $B$ and C versus $v_{A}$. For a 5 -V peak, 100 -Hz sinusoid applied at $A$, sketch the signals at nodes $B$ and $C$.

James Kiss
James Kiss
Numerade Educator
02:37

Problem 93

Sketch and label the voltage transfer characteristic $v_{o}$ versus $v_{l}$ of the circuit shown in Fig. P4.93 over a ±10 range of input signals. All diodes are 1 -mA units (i.e., each exhibits a $0.7-\mathrm{V}$ drop at a current of $1 \mathrm{mA}$ ). What are the slopes of the characteristic at the extreme ±10 -V levels?

James Kiss
James Kiss
Numerade Educator
01:12

Problem 94

A clamped capacitor using an ideal diode with cathode grounded is supplied with a sine wave of 10 -V rms. What is the average (dc) value of the resulting output?

Narayan Hari
Narayan Hari
Numerade Educator
02:37

Problem 95

For the circuits in Fig. $\mathrm{P} 4.95$, each utilizing an ideal diode (or diodes), sketch the output for the input shown. Label the most positive and most negative output levels. Assume $C R \gg T$.

James Kiss
James Kiss
Numerade Educator