Electronic Diode and Diode Circuits

Abstract

Knowledge of basic circuit analysis

Appendices

Summary

Common diode circuits—circuits with diodes and resistors
Sensors, voltage references/regulators
1. Diode temperature sensor			1.Uses temperature dependence of diode pn-junction parameters2. Resistor R determines necessary diode current3. Typical sensitivity is minus 2 mV to minus 4 mV per 1 °C
2. Forward-bias voltage reference/voltage regulator			1. Provides a fixed reference voltage in a circuit2. Provides a constant DC voltage to the load3. Solved using the constant-voltage-drop model or the small-signal diode model
3. Zener voltage regulator			For high-resistance load: $\begin{array}{l}{V}_L={r}_Z\frac{V_S-{V}_{Z0}}{R+{r}_Z}+{V}_{Z0},\\ {}{V}_{Z0}={V}_{Z T}-{r}_Z{I}_{Z T}\end{array}$
Rectifiers and clippers
4. Half-wave rectifier
5. Full-wave rectifier
6. Full-wave bridge rectifier
7. Positive clipper/limiter		Clips positive voltages
8. Negative clipper/limiter		Clips negative voltages
9. Double clipper/limiter		Clips pos./neg. voltages
10. ESD protection circuit		Clips signals outside power rails
11. Zener diode clipper/limiter		Clips positive/negative voltages
12. Zener diode double clipper/limiter		Clips positive/negative voltages
13. Soft clipper/limiter		Smoothly clips positive voltages
Common diode circuits—circuits with diodes, capacitors, and resistors
14. Envelope detector or peak detector			Outputs signal envelope$\tau ={R}_LC$ $\tau >>{T}_{\mathrm{carrier}}, \tau <<{T}_{\mathrm{modulation}}$ $\begin{array}{l}\frac{d{\upsilon}_{out}}{dt}+\frac{\upsilon_{out}}{\tau }=\frac{R_L{I}_S}{\tau}\times \\ {} \exp \left[\left({\upsilon}_{in}+{V}_{bias}-{\upsilon}_{out}\right)/{V}_T\right]\end{array}$
15. Clamper circuit or DC restorer			1. Lowest peak of a signal is clamped to zero volts versus ground2. Has no effect on already clamped signals3. Used in clock recovery circuits and in PWM
16. Diode voltage doubler			1. Outputs the DC voltage of 2V m if the input signal has the amplitude of V m 2. Constructed as a combination of the clamper and the envelope detector
17. Diode voltage tripler			1. Outputs the DC voltage of 3V m if the input signal has the amplitude of V m 2. Constructed as a combination of the voltage doubler and the envelope detector
18. Diode voltage quadrupler			1. Outputs the DC voltage of 4V m if the input signal has the amplitude of V m 2. Constructed as a combination of two voltage doublers

Problems

2.1 16.1 Diode Operation and Classification

16.1.1 Circuit Symbol and Terminals

16.1.2 Three Regions of Operation

16.1.3 Mechanical Analogy of Diode Operation

16.1.4 Forward-Bias Region: Switching Diode

16.1.5 Reverse-Bias Region: Varactor Diode

16.1.6 Breakdown Region: Zener Diode

16.1.7 Other Diode Types

Problem 16.1

Draw the circuit symbol for the diode, labeling the anode and the cathode. In what direction does the electric current flow?

Problem 16.2

A package for a small-signal 1N4148 Si switching diode (yellow package) is shown in the figure. Where is its anode, on the left or on the right?

Problem 16.3

• A. Sketch the typical v–i diode curve

• B. Indicate three regions of diode operation and write the name of each region on the figure.

Problem 16.4

Determine thermal voltage, which is present in Shockley equation at:

• A. 0 °C

• B. 10 °C

• C. 20 °C

• D. 40 °C

Problem 16.5

Plot the v–i characteristic of a diode with:

• A. $n=1.0,{I}_{\mathrm{S}}=1.1\;\mathrm{nA}$

• B. $n=2.0,{I}_{\mathrm{S}}=1.1\;\mathrm{nA}$

at room temperature of 25 °C on the same figure. Use the figure that follows as a template. Label each curve. Use the value of 1.60218×10⁻¹⁹ C for the electron charge and the value of 1.38066×10⁻²³ J/K for the Boltzmann constant.

Problem 16.6

Plot the v–i characteristic of a diode with:

• A. $n=1.0,{I}_{\mathrm{S}}=1\;\mathrm{nA}$

• B. $n=1.0,{I}_{\mathrm{S}}=0.01\;\mathrm{nA}$

at room temperature of 25 °C on the same figure. Use the figure to the previous problem as a template. Label each curve. Use the value of 1.60218×10⁻¹⁹ C for the electron charge and the value of 1.38066×10⁻²³ J/K for the Boltzmann constant.

Problem 16.7

For a diode with $n=2.0$, the following measurement is taken: ${\upsilon}_{\mathrm{D}}=0.65\;\mathrm{V}$ and ${i}_{\mathrm{D}}=1\;\mathrm{m}\mathrm{A}$. Given thermal voltage of 26 mV, determine diode’s saturation current I _S.

Problem 16.8

For a diode with ${I}_{\mathrm{S}}=1\;\mathrm{p}\mathrm{A}$, the following measurement is taken: ${\upsilon}_{\mathrm{D}}=0.62\;\mathrm{V}$ and ${i}_{\mathrm{D}}=1\;\mathrm{m}\mathrm{A}$. Given thermal voltage of 26 mV, determine diode’s ideality constant, n.

Problem 16.9

At which forward-bias voltage in terms of V _T does the diode conduct a current of 10⁴ I _S given the ideality factor of two?

Problem 16.10

A diode with $n=2.0$ is to be used as a temperature sensor in the forward-bias region (it is a common diode application). Determine:

• A. The corresponding change in the diode voltage (initial value, final value, and the difference) when the temperature rises from 20 to 60 °C

• B. Sensitivity of the device in mV/°C

The diode current is fixed at 1 mA. You are given that ${I}_{\mathrm{S}}=1\;\mathrm{nA}$ at 20 °C and that I _S doubles in value for every 5 °C. Use the value of 1.60218×10⁻¹⁹ C for the electron charge and the value of 1.38066×10⁻²³ J/K for the Boltzmann constant.

Problem 16.11

Answer the following questions:

• A. Which diode is used as a variable capacitor? Draw its symbol.

• B. Which diode operates in the breakdown region? Draw its symbol.

• C. Draw the circuit symbol for the Schottky barrier diode.

• D. Draw the circuit symbol for the photodiode.

2.2 16.2 Diode Models

16.2.1 Ideal-Diode Model: Method of Assumed States

Problem 16.12

• A. What is an ideal-diode model?

• B. Draw its volt-ampere characteristic using the voltage axis from −5 V to 5 V and the current axis from −10 mA to +10 mA as shown in the figure that follows. On the same graph draw the v–i characteristic for a 250 Ω resistor to scale.

Problem 16.13

After solving a circuit with ideal diodes, what check is necessary for diodes initially assumed to be ON? OFF?

Problem 16.14

Present equivalent circuits for the two-diode configurations shown in the figure, assuming ideal diodes.

Problem 16.15

Determine the electric current through the 1 kΩ resistor for the circuit shown in the figure below, assuming the ideal diode.

Problem 16.16

Assuming the ideal-diode model, find the voltage across the diode and the diode current for the circuit shown in the following figure. Denote the solution for the diode voltage and diode current in the DC steady state by capital letters V _D and I _D, respectively.

Problem 16.17

For the circuits shown in the figure that follows, find values of the diode current and voltage across the diode assuming that the diodes are ideal. Use capital letters V _D and I _D to denote the solution for the diode voltage and diode current in the DC steady state.

Problem 16.18

Using the ideal-diode model, you need to design a circuit for the diode temperature sensor described in Problem 16.10. The diode current must be fixed at 1 mA. The power supply voltage is fixed at 9 V.

• A. Present the corresponding circuit diagram and specify the component(s) values.

• B. Label the sensor output voltage.

Problem 16.19

A diode circuit is shown in the figure that follows. Find the values of the diode current and the voltage across the diode, assuming that the diode is ideal.

Problem 16.20

For the diode circuit shown in the following figure, determine the values of the diode current and the voltage across the diode, assuming that the diode is ideal.

Problem 16.21

Assuming the ideal-diode model, find current I for the circuit shown in the figure below.

Problem 16.22

Assuming the ideal-diode model, find current I for the circuit shown in the figure below.

Problem 16.23

For the circuit shown in the figure below, determine circuit current I, assuming that the diode is ideal. The ground path is simultaneously the current return path.

Problem 16.24

For the circuit below find circuit current I, assuming that both diodes are ideal. The ground path is simultaneously the current return path.

Problem 16.25

For the circuit shown in the figure below, find circuit current I, assuming that the diodes are ideal. The ground path is simultaneously the current return path.

Problem 16.26

The circuit shown in the figure below can be used as a signaling system using one wire plus a common ground return. At any moment, the input has one of three voltage values shown in the figure. What is the status of the lamps for each input value?

Problem 16.27

Sketch I versus V to scale for the circuit shown in the following figure. Assume the ideal-diode model and allow V to range from −3 V to 3 V.

Problem 16.28

Sketch I versus V to scale for the circuit shown in the figure. Assume the ideal-diode model and allow V to range from −5 V to 5 V.

Problem 16.29

For the circuit shown in the figure below, fill out Table 16.5.

Table 16.5 Output voltage of the diode circuit as a function of two input voltages

What type of logic gate is it?

Problem 16.30

A freshman ECE student attends class if all of the following conditions are satisfied:

• A. He/she feels that this lecture might be useful.

• B. There are no other more important things to do.

• C. The way to the Department is cleaned up from snow.

Every morning he/she “votes” by simultaneously pushing any appropriate combination of three 5-V buttons (A, B, C) placed in parallel. A simple diode circuit is needed that lights a green LED when there is time to go to the lecture.

Problem 16.31

A small county board is composed of three commissioners. Each commissioner votes on measures presented to the board by pressing a 5-V button indicating whether the commissioner votes for or against a measure. If two or more commissioners vote for a measure, it passes. You are asked to help with a an ideal-diode circuit that takes the three votes as inputs and lights a green LED to indicate that a measure passed. You can use as many diodes/resistors as you need.

• 1. Explain your reasoning for building the diode circuit.

• 2. Present the appropriate circuit diagram.

16.2.2. Constant-Voltage-Drop Model

Problem 16.32

What is the constant-voltage-drop-diode model? Draw the corresponding v–i diagram.

Problem 16.33

Sketch I versus V to scale for the circuit shown in the following figure using:

• A. Ideal-diode model

• B. Constant-voltage-drop-diode model with the turn-on voltage of 1 V

Allow V to range from −3 V to 3 V.

Problem 16.34

Sketch I versus V to scale for the circuit shown in the figure using:

• A. Ideal-diode model

• B. Constant-voltage-drop-diode model with the turn-on voltage of 1 V

Allow V to range from −5 V to 5 V.

Problem 16.35

Sketch I versus V to scale for the circuit shown in the figure using:

• A. Ideal-diode model

• B. Constant-voltage-drop-diode model with the turn-on voltage of 1 V

Allow V to range from −5 V to 5 V.

Problem 16.36

Present equivalent circuit for the two-diode configuration shown in the figure, assuming the constant-voltage-drop-diode model with the turn-on voltage of 1 V.

Problem 16.37

Using the constant-voltage-drop-diode model, you need to design a circuit for the diode temperature sensor described in Problem 16.10. The diode current must be fixed at 1 mA. The power supply voltage is fixed at 9 V.

• A. Present the corresponding circuit diagram and specify the component(s) values.

• B. Label the sensor output voltage.

16.2.3 Exponential Model in the Forward-Bias Region and Its Use

16.2. 4 Load-Line Analysis

16.2. 5 Iterative Solution

Problem 16.38

A 1N4148 diode manufactured by Fairchild has a current of 0.7 mA at 0.6 V and a current of 8 mA at 0.725 V, all at 25°. Determine the ideality factor and the saturation current of Shockley equation at this temperature.

Problem 16.39

A 1N4148 diode manufactured by Hitachi has a current of 0.15 mA at 0.6 V and a current of 1.5 mA at 0.7 V, all at minus 25°. Determine the ideality factor and the saturation current of Shockley equation at this temperature.

Problem 16.40

In the circuit shown in the figure below, the diode is described in terms of the exponential forward-bias model with the Shockley equation plotted in the figure.

• A. Graphically determine the solution—the DC operating point V _D, I _D using the load-line method.

• B. Compare the obtained diode current with that found in the constant-voltage-drop model.

  

Problem 16.41

Repeat the previous problem for the circuit shown in the figure that follows.

Problem 16.42

In the circuit shown in the figure that follows, the diode is described in terms of the exponential forward-bias model where the ideality factor and the saturation current of Shockley equation are $n=1.5,{I}_{\mathrm{S}}=1\;\mathrm{nA}$. Given thermal voltage of 0.026 V, determine the exact DC operating point (diode voltage and diode current V _D, I _D) with the help of the iterative solution.

Problem 16.43

Repeat the previous problem when the diode saturation current changes to 3 nA. All other parameters remain the same.

16.2.6 Linearization About a Bias Point: Small-Signal Diode Model

16.2.7 Superposition Principle for Small-Signal Diode Model

Problem 16.44

Determine the small-signal diode resistance for two limiting cases:

• A. When diode bias voltage (DC operating voltage) V _D tends to zero

• B. When diode bias current (DC operating current) I _D tends to infinity

Problem 16.45

In the circuit shown in the following figure, ${\upsilon}_{\mathrm{S}}(t)=10+0.005 \cos \omega t\left[\mathrm{V}\right]$. Determine diode voltage. Use the constant-voltage-drop-diode model for the diode with the turn-on voltage of 0.7 V. Assume the operating temperature of 25 °C and $n=2.0$.

Problem 16.46

Repeat the previous problem for the circuit shown in the following figure.

Problem 16.47

• A. Obtain the next term of the asymptotic expansion in Eq. (16.7c) so that the error will be on the order of (υ _d/nV _T)³.

• B. Derive the expression of the nonlinear small-signal diode resistance as a constant term plus a term that depends on the small-signal diode voltage.

2.3 16.3 Diode Voltage Regulators and Rectifiers

16.3.1 Voltage reference and voltage regulator

Problem 16.48

You are given a variable voltage source ${V}_{\mathrm{S}}=5\;\mathrm{V}\pm 0.5\;\mathrm{V}$ represented by its Thévenin equivalent shown in the figure below. You are also given a load represented by its equivalent resistance of ${R}_{\mathrm{L}}=1000\;\Omega$. Construct a diode voltage regulator circuit which outputs the constant voltage of 2.1 V to the load.

• A. Present the corresponding circuit diagram.

• B. Determine load voltage and diode current for the regulator circuit for two extreme cases ${V}_{\mathrm{S}}=5\;\mathrm{V}\pm 0.5\;\mathrm{V}$ of the supply voltage variation. Use the constant-voltage-drop-diode model with the turn-on voltage of 0.7 V.

Problem 16.49

Repeat the previous problem when Thévenin resistance of the source changes to 1 kΩ.

Problem 16.50

You are given a (variable) voltage source V _S represented by its Thévenin equivalent with resistance R _T and a load represented by its equivalent resistance of R _L. A forward-bias diode voltage regulator is used to keep the load voltage constant. Using the constant-voltage-drop-diode model, answer two questions:

• A. What is the maximum possible regulated load voltage if ${R}_{\mathrm{L}}={R}_{\mathrm{T}}$?

• B. What is the maximum possible regulated load voltage if ${R}_{\mathrm{L}}=10{R}_{\mathrm{T}}$?

16.3.2 Voltage regulator with Zener diode

Problem 16.51

A 1N5231B Zener diode with the test point ${V}_{\mathrm{ZT}}=5.1\;\mathrm{V},{I}_{\mathrm{ZT}}=20\;\mathrm{m}\mathrm{A}$ and with the dynamic resistance ${r}_{\mathrm{Z}}=17\;\Omega$ is used in the voltage regulator circuit shown in the figure below.

• A. Determine load voltage for the regulator circuit given that ${V}_{\mathrm{S}}=9\;\mathrm{V}\pm 1\;\mathrm{V}$ and that the load has a very high (infinite) resistance.

• B. Determine line regulation

Problem 16.52

In a typical 12-V automotive application, battery voltage may vary between 10.5 and 14.1 V. The ECM (engine control module) determines fuel delivery and spark advance to control emissions based on several sensors connected to the engine. Many of these sensors require a stable 5-V reference that can be achieved through the use of a Zener diode. The figure that follows shows the corresponding circuit using a 1N4733A Zener diode to provide a stable 5-V reference.

The Zener diode has a reference (test) voltage of 5.1 V at a reference (test) current of 49 mA.

• A. Choose a value for resistor R ₁ to limit the current through the Zener diode to approximately 50 mA with the sensor disconnected (switch OPEN).

• B. Given that the battery voltage may vary between 10.5 and 14.1 V, determine how much the Zener voltage (voltage across the Zener diode) fluctuates with the sensor disconnected (switch OPEN). Note: This Zener diode has a dynamic resistance of 7 Ω at the test current of 49 mA.

• C. What minimum load resistance can be connected to the circuit without the voltage drop more than 0.5 V from 5 V?

• D. Plot load voltage as function of the load resistance in the range 0–1000 Ω for two extreme battery voltages.

• E. If the switch is closed and the load resistance is 100 Ω, what is the power efficiency of this circuit for two extreme values of the battery voltage?Note: Efficiency percentage = P_LOAD/P_BAT × 100 %.

Problem 16.55

Using software of your choice (MATLAB is recommended), plot the output of a half-wave diode rectifier to scale over a time period from 0 to 8 s when the input voltage is given by

$$ {\upsilon}_{\mathrm{S}}(t)={V}_{\mathrm{m}} \sin \omega t+0.5{V}_{\mathrm{m}} \sin 2\omega t $$

with

Signal frequency—0.5 Hz

Signal amplitude—${V}_{\mathrm{m}}=9\;\mathrm{V}$.

Assume the ideal diode.

Problem 16.56

Using the constant-voltage-drop model for a diode with the turn-on voltage of 0.7 V, determine the following parameters for the circuit shown in the figure:

• A. The peak positive voltage across the load

• B. The average voltage across the load

• C. The peak diode current

• D. The average diode current

• E. The peak negative voltage across the diode

  

Note: The voltage source shown represents the output of a typical step-down transform and is given in rms.

16.3.4 Full-wave rectifier with a dual supply

16.3.5 Diode bridge rectifier

16.3.6 Application example: Automotive battery-charging system

Problem 16.57

Using the constant-voltage-drop model for the diode with the turn-on voltage of 0.7 V, determine the following parameters for the circuit shown in the figure:

• A. The peak positive voltage across the load

• B. The average voltage across the load

• C. The peak diode current

• D. The average diode current

• E. The peak negative voltage across each diode

  

Problem 16.58

• A. Draw a schematic of the full-wave diode bridge rectifier.

• B. Indicate current flow in the full-wave diode rectifier at positive and negative applied voltages.

• C. If all diodes in the rectifier are changed to the opposite direction, will the rectifier function or not?

Problem 16.59

Using the constant-voltage-drop model for the diode with the turn-on voltage of 0.7 V, determine the following parameters for the circuit shown in the figure:

• A. The peak positive voltage across the load

• B. The average voltage across the load

• C. The peak diode current

• D. The average diode current

• E. The peak negative voltage across each diode

  

Note: The voltage source shown represents the output of a typical step-down transform and is given in rms.

Problem 16.60

For an automotive battery-charging system schematically shown in Fig. 16.26c, plot the individual rectified voltages and the output voltage (voltage across the load) as a function of time over the interval 0–0.01 s. Every power supply in the figure is a sinusoidal AC voltage source with ${V}_{\mathrm{m}}=15\;\mathrm{V}$, $f=100\;\mathrm{Hz}$. All three voltage power supplies are 120° out of phase with regard to each other—have the phase angles of 0 and $\mp 120{}^{\circ}$. Any software can be used (MATLAB is recommended).

16.3.7 Application example: Envelope (or peak) detector circuit

Problem 16.61

• A. Explain the function of the envelope detector in your own words.

• B. What is the difference between linear and square-law regions of operation for the envelope detector?

• C. When does the envelope detector operate in the linear region? In the square-law region?

Problem 16.62

Design an envelope detector given the carrier frequency of $f=1.7\;\mathrm{MHz}$. The modulation is a human voice, with the maximum passing modulation frequency of 20 kHz.

• A. Draw the circuit diagram of the envelope detector.

• B. Specify one possible set of values for R _L, C.

Problem 16.63

Design an envelope detector (specify one possible set of values for R _L, C) given the carrier frequency of $f=10\;\mathrm{MHz}$. The modulation is a digital signal, with the bit rate of 100 kbps. Hint: The equivalent frequency of the digital signal is the bit rate in Hz.

Problem 16.64

A MATLAB script that follows models an envelope detector circuit in Fig. 16.27 by solving the exact circuit ODE given by Eq. (16.19b)

$$ \frac{d{\upsilon}_{\mathrm{out}}}{dt}=\frac{1}{\tau}\left({R}_{\mathrm{L}}{I}_{\mathrm{S}}\ \exp \left[\left({\upsilon}_{\mathrm{in}}+{V}_{\mathrm{bias}}-{\upsilon}_{\mathrm{out}}\right)/{V}_{\mathrm{T}}\right]\right.\left.-{\upsilon}_{\mathrm{out}}\right) $$

with a particular set of design parameters of your choice. Which bias voltage (0, 1, 4, or 8 V) is most beneficial for the performance of your circuit? Justify your answer.

2.4 16.4 Diode Wave-Shaping Circuits

16.4. 1 Diode clamper circuit (DC restorer)

16.4.2 Diode voltage doubler and multiplier

Problem 16.65

In the clamper circuit shown in the figure below, ${\upsilon}_{\mathrm{in}}(t)={V}_{\mathrm{m}} \sin \omega t$ and ${V}_{\mathrm{m}}=4\;\mathrm{V}$. The wave period is 2 ms. Given the ideal-diode model, plot the input voltage, voltage across capacitor C ₁, and voltage across diode D ₁ (the output voltage of the circuit) to scale versus time. Clearly label each curve.

Problem 16.66

In the clamper circuit shown in the figure for Problem 16.65, ${\upsilon}_{\mathrm{in}}(t)={V}_{\mathrm{m}}-{V}_{\mathrm{m}} \sin \omega t$ and ${V}_{\mathrm{m}}=4\;\mathrm{V}$. The wave period is 2 ms.

• A. Given the ideal-diode model, plot the input voltage, voltage across capacitor C ₁, and voltage across diode D ₁ to scale versus time. Clearly label each curve.

• B. Based on your solution, what conclusion could you make about the operation of a clamper circuit subject to strictly positive versus the ground point (already clamped) AC signals?

Problem 16.67

The input voltage for the voltage doubler circuit in Fig. 16.30a is shown in the figure below. Plot the voltage across capacitor C ₁ and the voltage across capacitor C ₂ (the output voltage) to scale versus time. Clearly label each curve.

Problem 16.68

• A. Construct a voltage tripler diode circuit, which outputs the DC voltage of 3V _m for the input AC signal of amplitude V _m and zero mean. Present the corresponding circuit diagram.

• B. How many capacitors and diodes are you using?

• C. Could you extrapolate your answer to a voltage multiplier diode circuit, which outputs the DC voltage of 5V _m?

16.4.3 Positive, negative, and double clipper

16.4. 4 Transfer characteristic of a diode circuit

Problem 16.69

For the positive clipper diode circuit, sketch the voltage transfer characteristic to scale assuming

• A. Ideal-diode model

• B. Constant-voltage drop model

  

Problem 16.70

Repeat Problem 16.69 for the diode circuit shown in the figure that follows.

Problem 16.71

Repeat Problem 16.69 for the diode circuit shown in the figure that follows.

Problem 16.72

Given the Zener breakdown voltage of 4 V for D₁, for the circuit shown in the figure below, sketch the voltage transfer characteristic to scale assuming:

• A. Ideal-diode model in the forward-bias region

• B. Constant-voltage drop model in the forward-bias region

Always use the constant-voltage-drop model in the breakdown region.

Problem 16.73

Repeat Problem 16.72 for the diode circuit shown in the following figure .

Problem 16.74

Repeat Problem 16.72 for the diode circuit shown in the figure below assuming the Zener breakdown voltage of 4 V for D₁ and 5 V for D₂.

Problem 16.75

Repeat Problem 16.72 for the diode circuit shown in the figure below assuming the Zener breakdown voltage of 2 V for D₁ and 4 V for D₂.

Problem 16.76

For the following diode circuit, sketch the voltage transfer characteristic to scale given that ${R}_1=1\;\mathrm{k}\Omega$ and ${R}_2=1\;\mathrm{k}\Omega$, and assuming:

• A. Ideal-diode model

• B. Constant-voltage drop model

Label the endpoint voltages.

Problem 16.77

Repeat Problem 16.76 for the diode circuit shown in the figure below. Assume ${R}_1=1\;\mathrm{k}\Omega$, ${R}_2=1\;\mathrm{k}\Omega$, and ${R}_3=1\;\mathrm{k}\Omega$. Label the endpoint voltages.