# NEAMEN ELECTRONIC CIRCUIT ANALYSIS AND DESIGN PDF

Microelectronics: circuit analysis and design / Donald A. Neamen. — 4th ed. p. cm. Includes and devices courses and electronic circuits courses. He is still a. Donald Neamen is a great author and his book on semiconductors is definitely a for Electronic Circuit Analysis and Design by Donald Neamen (3rd edition)?. Electronic Circuit Analysis and Design by Neamen - Free ebook download as PDF File .pdf), Text File .txt) or read book online for free. Electronics 2.

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Neamen - Electronic Circuit Analysis and Design compwalsoihassre.gq - Ebook download as PDF File .pdf) or read book online. Circuit Analysis and Design Fourth Edition Donald A. Neamen University of semiconductor physics and devices courses and electronic circuits courses. by Donald A Neamen · electronic circuit analysis. Preview Microelectronics Circuit Analysis and Design Donald Neamen 4th Solutions. Pages·· .

Test Your Understanding 1. The applied voltage V R induces an applied electric field, EA, in the semiconductor. The direction of this applied field is the same as that of the E-field in the space-charge region. Since the electric fields in the areas outside the space-charge region are essentially zero, the magnitude of the electric field in the space-charge region increases above the thermal equilibrium value.

This increased electric field holds back the holes in the p-region and the electrons in the n-region, so there is essentially no current across the pn junction. By definition, this applied voltage polarity is called reverse bias. When the electric field in the space-charge region increases, the number of positive and negative charges also increases. If the doping concentrations are not changed, the increases in the charges can only occur if the width W of the J w l L..

Jure 1. Because of the additional positive and negative charges in rhe space-charge region, a capacitance is associated with the pn junction when a reverse-bias voltage ill ,I pplied.

This juDctien capacitaace. The capacitance-voltage characteristics make the pn junction useful for electrically tunable resonant circuits. J Simple Series-Pass Regulator " L4 Body Effect is. Classifications and Ardritectur: Qnly Memory I Preview B.

Chapter 3 lntroduces the btpotartranststor, presents the de analysii! A basic electronic device is the pn junction diode, One of the more interesting characteristics of the diode is its nonlinear current-voltage properties. The resistor, for example, has a linear relation between the current through it and the voltage across the element The diode is also a two-terminal device, but the i-'I' relationship is nonlinear.

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The current is all exponential function of voltage in one direction and is essentially rem in the other direction. As we will sec, this nonlinear characteristic makes possible the generation of a de voltage lrorn nil ac voltage source and the design of digital logic circuits.

Since the diode is a nonlinear element. A mathematical model of the diode, describing the nonlinear i-v properties. In many engineering problems. We develop one such approximation te-chnique using the piecewise linear model of the diode. In this case, we replace the nonlinear diode properties by linear characteristics that are approximately valid over a limited region of operation.

This concept is used throughout tile study of electronics. Besides the pn junction diode, we consider five other types of diodes that are used in specialized electronic applications. These include the solar celt.

The general properties of the diode are considered in this chapter. Simple diode circuits are analyzed with the intent of developing a basic understanding of analysis rcchniqucs and diode circuit characteristics. Chapter 2 then conSiders applications of diodes in circuits that perform 'Various electronic functions. Silicon is by far the most common semiconductor material used for semiconductor devices and integrated circuits.

Other semiconductor materiaJs are used for specialized applications, For example, gallium arsenide and related compounds are used for very-highspeed devices and optical devices, 1. The electrons are distributed in various "shells" at different distances from the nucleus, and electron energy increases as shell radius increases.

Elements in the period table can be grouped according to the number of valence electrons. Table 1. As silicon atoms come into dose proximity to each other, the valence electrons interact to fonn a crystal. The final crystal structure is 11 tetrahedral configuration in which each silicon atom has four nearest neighbors, as shown in Figure 1.

The valence electrons are shared between atoms, forming what ale called covalent bonds. Germanium, gallium arsenide, and many other semiconductor materials have the same tetrahedral configuration. I c is a two-dimensional representation or the lattice formed by the: An important property of such a lattice is that valence electrons are always available 00 the outer edge of the silicon crystal so that additional atoms can be added to form very large single-crystal structures.

A two-dimensional representation of a silicon single crystal is shown in Ftgure 1. IF a small electric field is applied to this material, the electrons will not move, because they will still be bound to their individual atoms. The electron will then be free to move within the crystal, Since the net charge of thematerial is neutral, ir a negatively charged electron breaks its covalent bond and moves away from Its original position, a positively charged "empty state" is created at that position Figure 1.

As the temperature increases, more covalent bonds are broken and more free electrons and positive empty stales are created. In order 10 break the covalent bond. Materials that have large bandgap energies. In contrast, materials that contain very large numbers of free electrons at room temperature are ctlnductors.

In a semiconductar, the bandgap energy is on the order of I eV.

The net flow or free electrons in a semiconductor causes. This positively charged "particle" is called a hole. III semiconductors, then, two types or charged particles contribute to the current: This description of a hole is I An eleciron-vott is the energy of an electron that hoi. The concentrations! An bltrinsit semiconductor is a single-crystal semiconductor materia! In an intrinsic semiconductor, the densities of electrons and holes ale equal, since the thermally generated eleerrons and Roles are the only source of such particles.

Therefore, we use the notation n, as the intrinsic carrier eoneeatration for the concentration of the free electrons. The equation for II; is as follows: BT' "e m 1,1 where B is a constant related to the specific semiconductor material, E'J is he bandgap energy ev , Tis rhe temperature CK , and k is Boltzmann's constant 86 eV j"K , The values for Band Eg for several semiconductor materials are given in Table 1.

An inuinsic electron concenirauon of I. The intrmsic concentration A, is an important parameter that appears often in the current-voltage equations for semiconductor devices.

Chapter J Semiconductor Materials and D! Si, IIi;;: However, these concentrations can be greatly increased by adding controlled amounts of certain impurities. A desirable impurity is one that enters the crystal lattice and replaces i. For silicon. The most common group V elements used for this purpose are phosphorus and arsenic.

For example, when a phosphorus atom substitutes for a silicon atom. At room temperature. The phosphorus atom is called a doaor impurity, since it donates an electron that is free to move. Although the remaining phosphorus atom has a net positive charge, the atom is immobile in the crystal and cannot contribute to thecurrent.

This process is called dopiDg, and it allows us to control me concentration of free electrons in a semiconductor. A semiconductor that contains donor impurity atoms is called an n-type sc: The most common group III element used for silicon doping is boron. When a boron atom replaces a silicon atom, its three valence electrons are used to satisfy he covalent bond requirements for three of the four nearest siacon atoms Figure 1.

This leaves one bond position open. At room temperature, adjacent silicon valence electrons have sufficient thermal energy to move into this position, thereby creating a hole.

The boron atom then has a net negative charge. Acceptor atoms lead to the creation of holes without electrons being generated. This process, also called doping, can be used to control the concentration of holes in a semiconductor.

UCtors, or doped semicOllductors. The doping process, which allows us to control the concentrations of free electrons and holes, determines the conductivity and currents in the material. If the donor concentration Nd is much larger than the intrinsic concentration, we can approximate Theil, from Equation 1.

Recall from Example 1. In an extrinsic semiconductor, the electron and hole concentrations normally differ by many orders of magnitude. Chapter I Semiconductor Materials and Diodes In an n-type semiconductor, electrons are called the majority carrier because they far outnumber the holes, which are termed the minority carrier, The results obtained in Example 1.

Test Your Understanding 1. Such gradients can be caused by a nonhomogeneous doping distribution, or by the injection of: To understand drift, assume an electric field is applied to a semiconductor.

The field prodeces a force that acts on free electrons and holes, which then experience a net drill velocity and net movement. Consider an a-type semiconductor with a large number of free electrons Figure 1. An electric field E applied in one direction produces a force on he electrons in the opposite direction, because of the electrons' negative charge. The electrons acquire a drift velocity I'J. For low-doped silicon, the value of IJ.. Tile negative sign in Equation I.

The conventional drift current is in the opposite direction [rom the flow of negative charge, which means that the drift current in an n-type semiconductor is in he same direction as the applied electric field. Next consider a p-type semiconductor with a large number of holes Figure 1,7 bn. An electric field E applied in one direction produces a force on the holes in the same direction, because of the positive charge on the holes. The holes acquire a drift velocity l'Jp in cmjs which can be written as t.

For low-doped silicon, the value of p. The positive sign in Equation 1. The conventional drift current IS in the same direction as the flow of positive charge, which means that the drift curreni m a p-type material is also in the same direction as the applied electric field.

Since a semiconductor contains both electrons and holes. The total drift current density is then written as 1. IHa becomes a linear relationship between current lind voltage and is one form of Olun's law. From Equation 1. With diffusion. This is a statistical phenomenon related 10 kinetic theory. To explain. Statistically, we can assume that, at any particular instant. We can also assume that, at the same time. However, by definition, there are fewer particles in the lower-concentration region than there are in the high-concentration region.

Therefore, the net result is a flow ofparucles away from the high-concentration region and toward the tower-concentration region. This is the basic: For example, consider an electron concentration that varies as a function of distance. The diffusion of electrons from a highconcentration region 10 a Iow-cohcenlralion region produces a flov..

If eiectrons in the negative x direction. Since electrons are negatively charged, the conventional current direction is in the positive x direction.

Chapter I Scm iconducror M.. The diITusion of holes from a high-concentration region to a low-ccncentrauon region produces a flow of holes in the negative x direction. The totat current density is the sum of the drift and diffusion components.

In the discussion of drift and diffusion currents. Yet, when a voltage is applied [0. Valence electrons may acquire sufficient energy to break the covalent bond and become free elect rous if they interact with high-energy photons incident on the semiconductor.

When this occurs, both all electron and a hole are produced, thus generating an electron-hole pair. These additional electrons and holes are called excess electrons and excess holes. When these excess electrons and hob are created. This may be represented by 1. Both the free electron and the hole disappear causing the excess concentration to reach a steady-state value. The mean time over which an excess electron and hole exist before recombination is called the excess carrier lifeCime.

Assume hat Ii. The real power of semiconductor electronics occurs when p- and n-regions are directly adjacent to each other, forming a pDjunction. One important concept to remember is 'that in most integrated circuit applications, the entire semiconductor material is a single crystal, with one region doped to be p-type and the adjacent region doped to be n-type.

A large density gradient in both the hole and electron concentrations occurs across this junction. The flow of holes from rhe p-region uncovers negatively charged acceptor ions, and the flow of electrons from the n-region uncovers positively Charter J Semiconductor Materials and Diodes p I p-region Potemisl b Electron diffusloo -,,,0 Figure 1. This action creates a charge separation Figure 1.

If no voltage is applied to tbe pn junction. The direction of tbe induced electric field will cause rbe resulting force to repel the diffusion of holes from the p-region and the diffusion of electrons from the n-region.

Thermal equilibrium occurs when the force produced by the electric field and the "force" produced by the density gradient exactly balance. The parameter VT is called the the Example 1.

Calculate the buill-ill potennal barrier of a pn junction. Consider a silicon p!

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QZ6 ln 10 l:: Because of the log function. The applied voltage V R induces an applied electric field, EA, in the semiconductor. The direction of this applied field is the same as that of the E-field in the space-charge region.

Since the electric fields in the areas outside the space-charge region are essentially zero, the magnitude of the electric field in the space-charge region increases above the thermal equilibrium value.

This increased electric field holds back the holes in the p-region and the electrons in the n-region, so there is essentially no current across the pn junction.

By definition, this applied voltage polarity is called reverse bias. When the electric field in the space-charge region increases, the number of positive and negative charges also increases. If the doping concentrations are not changed, the increases in the charges can only occur if the width W of the J w l L.. Jure 1. Because of the additional positive and negative charges in rhe space-charge region, a capacitance is associated with the pn junction when a reverse-bias voltage ill ,I pplied.

This juDctien capacitaace. The capacitance-voltage characteristics make the pn junction useful for electrically tunable resonant circuits. Junctions fa bricated specifically for this purpose are called varaeter diodes. Varactor diodes can be used in electrically tunable oscillators. Calculate tile Junction capacitance of a pn junction. Calculate the junction capacitance at VI";: The built-in potential is determined by J'.

A, implied in the previous section, the magnitude of the electric field in the space-charge region increases as the reverse-bias voltage increases. This concept will be described in detail later ill this chapter. The junction capacitance is to be C,: Find the zero-biased junction capacitance C,,,.

With zero applied voltage. The electric fields in the space-charge region are l'er, large compared to those in the remainder of the p- and n-regions, so essentially all of the applied voltage exists across the pn junction region. The applied electric field. EA- induced by the applied voltage is in the opposite direction from that If the thermal equilibrium space-charge E-field. This upsets the delicate balance between diffusion and [he E-tield force.

Majority carrier electrons from the n-region diffuse into the p-region, and majority carrier holes from the p-region diffuse into the n-region, The process continues as long ii,' the voltage.

This process would be analogous to lowering. As the majority carriers cross into the opposite regions, they become rnrnority carriers in those regions. Figure 1. These excess minority carriers diffuse into the neutral n- and p-regions, where they recombine with majority carriers, thus establishing a steady-state condition, as shown in Figure 1. The theoretical relationship between the voltage and the current in the pn junction is given by 1.

For silicon pn junctions, typical values of t. The actual value depends on the doping concentrations and the cross-sectional area of the junction. The parameter Vj is the thermal voltage. The parameter It is usually called the emission coefficient or ideality factor, and Its value is in the range I s fI: The emission coefficient n takes into account any recombination of electrons and holes in the space-charge region.

At very low current levels, recombinauon may be a significant factor and the value of fI may be close to 2. AI higher current levels, recombination is less a factor, and the value of n will be I. Determine the current in a pn junction. With a reverse-bias voltage applied, the junction current is virtually zero. Test Your Understanding t. A, ii I05 J. Determine 'n' Ans.

For a forward-bias voltage, the current is an exponential function 2 iD mA 4 Beverse-bias regiDn Figur-c 1. I V, the - I term in Equation 1. In the reverse-bias direction, the current is almost zero. Figure L 17 shows the diode circui 1 symbol iI nd the conventional current direction and voltage polarity.

The diode can be thought of and used as a voltage controlled switch that is "off" for a reverse-bias voltage and "on" for a forward-bias voltage. In the forward-bias or "on" stale, a relatively large current is produced by a fairly small applied voltage: The current is in the reverse direction and is a constant. Real diodes. This additional current is called a generation current and is due to electrons and holes being generated within the space-charge region.

Whereas a typical value of is may be A. Even though this current is much larger than Is, it is still small arid negligible in most cases. Temperature Effects Since both ls and Vr are functions of temperature, the diode characteristics also vary with temperature, The temperature-related variations in forward-bias characteristics are illustrated in Figure 1. For a given current, the required 19 a b Flgure1. As an example of the importance of this effect, in germanium, the relative value of n, is large.

Increases in this reverse current with increases in the temperature make the germanium diode highly impractical for most circuit applications. Breakdown Voltage When a reverse-bias voltage is applied to a pn junction, the electric field in the: The electric field may become large enough that covalent bonds are broken and electron-hole pairs are created.

Electrons are swept to the n-region and boles to the p-region by the electric fieldgenerating II reverse-bias current. This breakdown mechanism is called the Zener effect. Another breakdown mechanism is caged avalanche breakdown. The generated electron-hole pairs can themselves be in v olved in a. The reverse-bias current for each breakdown mechanism will be limited by the external circuit.

The PIV of a diode must never be exceeded in circuit operation ir reverse breakdown is to be avoided.

Zener diodes are fabricated with a specifically designed breakdown voltage and are designed 0 operate in the breakdown region. These diodes are discussed later in this chapter. SWitching Transumt Since the pn junction diode can be used as an electrical switch, an important parameter is its transient response, that is, its speed and characteristics, as it is switched from one state to the other.

Here, we neglect he change in the space charge region width, When a forward-bias voltage is applied. This happens because the excess minority carrier electrons! The large reverse-bias current is initially limited by resistor RII to approximately 1. After this time. The fall time " is lypically defined as the lime required for the current to fall to 10 perc-ent of its initial value.

The total hlrfl--off time is the sum of the storage time and the fall time. These same transient effects impact [he switching of transistors. For example. The transient tdm-t 1l time is the time required to establish the forward-bias minority carrier distributions. During this time, the Chapter t Semiconductor Materials and Diodes voltage across the junction gradually increases toward its steady-state value. Although the turn-on time for the pn junction diode is not zero.

If Vp ;;;;; U. As we have seen, the diode is a two-terminal device with nonlinear i-v characteristics. The analysis of nonlinear electronic ci rcui ts is not 1: IS straightforward as the analysis of linen electric circuits.

Mathematical relationships, or models, that describe. An example is Ohm's law. When a reverse-bias voltage is applied, the current through the diode is zero Figure I. Assume that the input voltage "lis a sinusoidal signal. During the positive half-cycle of the sinusoidal input, a forward-bias current exists in the diode and the voltage across the diode is zero. The equivalent circuit fOI this condition is shown in Figure 1. The output voltage Vo is then equal to the input voltage, During tae negative half-cycle of the sinusoidal input, the diode is reverse biased.

The equivalent circuit for this condition is shown in Figure L23 d , In this part of tile cycle. The output voltage of the circuit is shown in Figure 1. Over the entire cycle, the input signal is sinusoidal and has a zero average value; however, the output signal contains only positive values and therefore has a positive average value- Conseqently, this circuit is said to rectify the input signal, which is tne first step in generating a de voltage from a sinusoidal ac voltage.

A de voltage is required in virtually all electronic circuits. As mentioned. Methods a and b are closely related and are therefore presented together. The graphical analysis technique involves plotting two simultaneous equations and locating their point of intersection, which is the solution to the two equations. We will use both techniques to solve the circuit equations. These equations are difficult 10 solve by hand because they contain both linear and exponential terms.

Kirdaboff's voltage 1. In the remainder of this section in which de analysis is emphasized, the de variables are denoted by uppercase letters and uppercase subscripts. Combining Equations 1. Equation 1. The use of iteration to find a solution to this equation is demonstrated in the following example. Determine the diode voltage and current for the circuit shown in Figure 1. We can write Equation '. This equation is referred to as the circuit load line, which can be plotted on a graph with Tn and VD as the axes.

From Equation I. The load line can be drawn between these two points. Using the values given in Example 1. The seco.. The intersection of the load line and the device characteristics curve provides ile dc current 'D This point is referred to as the qliesce".

However, the concept of the load line and the graphical approach are useful for "visualizing" the response of a circuit, and the load line is used extensively in the evaluation of electronic circuits. Test Your Understanding "1. Determine VD and lv, using the ideal diode equation and tbe iteration method.

## Neamen Electronic Circuit Analysis And Design ( 4th Edition)

VY' we assume a straight-line approximation whose slope is 1 rf. The equivalent circuit for this linear approximation is a constant-voltage source in series with a resistor Figure 1. In this case, the equivalent circuit is an open circuit Figure I. For V C! Determine the diode voltage and current in the circuit shown in Figure 1. Assume piece-wise linear diode parameters of Vr The equivalent circuit is shown ill Figure 1.

This solution, obtained using the piecewise linear model, is nearly equal to the solution obtained in Example 1. In addition, if the cut-in voltage is 0. Which is not significantly different from the previous results. Therefore, the calculated diode current is not a strong function of the cui-in voltage, Consequently, we will often assume a cut-in voltage of 0. The Q-point changes for each load line.

## Microelectronics Circuit Analysis and Design

The load line concept is also useful when the diode is reverse biased. The diode current lD and voltage V D shown are the usual forward-biased parameters. Applying Kirchhoff's voltage law, we can write 1. The diode characteristics and the load line are plotted in Figure 1. Although the piecewise linear model may yield solutions that are less accurate than those obtained with the ideal diode equation, the analysis is much easier.

## Neamen - Electronic Circuit Analysis and Design 2e.pdf

The power dissipated ill the diode is to be no more than 1,05 mW. Determine the maximum diode current and the minimum value of R to meet che power specification. Such models can factor in many diverse conditions, such as the temperature dependence of various parameters.

One of the earliest, and now he most widely used. Determine the diode current and voltage characteristics of the circuit shown in Figure 1. The input voltage VI was varied de sweep from 0 to: Figure I ,30 b and c shows the diode voltage and diode current characteristics versus he input voltage.

I YI'I b Figure 1. Several observauons may be made from the results. The diode voltage increases at aunost: The piecewise linear model predicts quite accurate remits at the maximum mput voltage, However, these results show that there IS definitelya nonlinear rci: Jlillfl between the diode current and diode voltage. We must keep in mind [hal the piecewise linear model IS an approximation technique that works very well in many applications. For the ideal diode equation. For the piecewise linear model.

In most cases, however, '1 is assumed to be zero unless otherwise given. When semiconductor devices with pn junctions are used in linear amplifier circuits. The rollowing sections examine these HC cha racteristics. To investigate this circuit.

I J Q is the de quiescent diode current. In addition, the diode voltage will contain a de value with an ac signal superimposed, as shown in Figure 1. The relationship between the diode current and voltage can be written as 1.

We are neglecting the -I term in the diode equation. We see from these two equations that t', r. Circuit Analysis To analyze the circuit shown in Figure 1. Eumple 1.

Analyze tile circuit shown in Figure 1. Dl'iiLk the analysis into two parts: In other words. TDQ 0. The ac diode current is. JI IlA The ac component of the output voltage. Throughout the text. To do so, we will use separate equivalent circuit models for each analysis. Frequency Response In the previous analysis, we implicitly assumed that the frequency or tile uc signal was small enough thai capacitance effects in the circuit would be negligible. If the frequency of the ac input signal increases, the diffusion taplicitalH..

We must also add the junction capacitance, which is in parallel with the diffusion resistance and capacitance, and a series resistance.

What is the quiescent diode current? The solar cell, photodiode, light-emitting diode, and Zener diode are types of pn junction diodes with specific characteristics that make them useful in particular circuit applica tions. When Light hits the spacecharge region, electrons and holes are generated. They are quickly separated and swept out of the space-charge region by the electric field, thus creating a photocurrent. The generated photocurrent will produce a voltage across the load, which means that the solar cell has supplied power.

Solar cells are usually fabricated from silicon. Solar cells nave long been used to power he electronics in satellites and space vehicles, and also as the power supply to some calculators. Solar cells are also used to power race cars in a Sunrayce event. Collegiate teams in the United Stales design, build and drive the race cars. The power from the solar array can be used either to power an electric motor or to charge a battery pack 1.

An example is the pbotooMJde. Incident photons or light waves create excess electrons and holes in the space-charge region. As previously explained, when a forward-bias voltage is applied across a pn junction, electrons and holes Row across he space-charge region and become excess minority carriers.

These excess minority carriers diffuse into the neutral semiconductor regions, where: LEDs are fabricated from GaAs or other compound semiconductor materials, In an LED, the diode current is directly proportional to the recombination rate, which means that the output light intensity is also proportional to the diode current. Monolithic arrays of LEDs are fabricated for numeric and alphanumeric displays.

An LED may be integrated into In optical cavity 10 produce a. Such a device is a laser diode. The current-voltage characteristics of a Schottky diode ase very similar to those of a pn junction diode.

The same ideal diode equation can be used for both devices. The current in a [ junction diode is controlled by the diffusion of minority carriers, The current in a Schottky diode results from the flow of majority carriers over the potential barrier at the metallurgical junction, This me-all, that there is no minority carrier storage in the Schottky diode.

S c -cond, the reverse-saturation current Is for a Schottky diode is larger than ,hat or a pn junction diode for comparable device areas. Figure I.. U compares the characrerisucs of t he two diodes. Applying the piecewise linear model.

In later chapters. Consider the circuit shown ill Figure J. The de calculations for a circuit containing a Schottky diode are [he same as those for a circuit containing a pn junction diode.

Another type of metal-semiconductor junction is also possible. A metal applied to a heavily doped semiconductor forms, in most cases, an ohmic contact: Determine the forward-bias voltages required to produce I rnA in each diode. The difference in forward-bias voltages is 0.

Determine the reverse-saturation current of the Schottky diode. At some point, breakdown occurs and the current in the reverse-bias direction increases rapidly. The voltage at this point is called the breakdown voltage. The diode I-JI characteristics. Allhougll the breakdown voltage is on the negative voltage axis reverse-bias , its value is given as a positive quantity.

The large current that may exist at breakdown can cause heating effects and catastrophic failure or the diode due to the large power dissipation in the device. However, diodes can be operated in the breakdown region by limiting the current to a value within the capabilities of the device. Such a diode can be Figure 1. The diode breakdown voltage is essentially constant over a wide range of currents and temperatures, The slope of the I-V characteristics curve in.

Typically, r" is in the range of a few ohms or tens of ohms. The circuit symbol of the Zener diode is shown in Figure 1. Note the difference between this symbol and the Schottky diode symbol.

TIle voltage V z 1S the Zener breakdown voltage, and the current Iz is the reverse-bias current when the diode is operating in the breakdown region. Design Example 1. Consider a simple constant-voltage reference circuit and design the value of resistance required to limit the current in this circuit. Consider the circuit shown ill Figure 1. Assume that the Zeller diode breakdown voltage is Vz '" 5,6 V and the Zener resistance is t: As before, we can determine the current from the voltage difference across R divided by the resistance.

That is, The resistance is then Comment The resistance external to the Zener diode limits the current when the diode is operating In the breakdown region.

In the circuit shown in the figure. We will see further applications If the Zener diode in the next chapter. If the voltage across the Zener diode is 5. The current-voltage characteristics of the diode are nonlinear: The current IS an exponential function of voltage in the forward-bias condition, and is essentially zero in the reverse-bias condition. A piecewise-linear model of the diode was developed so that approximate hand calcularion results can be easily obtained.

The i-v characteristics If the diode arc broken into linear segments, wh. A srnull-ssgnal linear equivalent circuit wa, developed and is used Hl determine the rclanonship between the ac current and ac vohage.

This Slime equivalent circuit will be applied extensively when the frequency response of rransistots is discussed.Junctions fa bricated specifically for this purpose are called varaeter diodes. If we assume that the diode turns off immediately when the input voltage starts to decrease from its peak value.

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Ripple Voltage, and Diode Current lf a capacitor is added in parallel with Ihe load resistor of a half-wave rectifier to form a simple filter circuit Figure 2. Therefore, the net result is a flow ofparucles away from the high-concentration region and toward the tower-concentration region.

If either Va approaches minus infinity or V6 approaches plus infinity, then the circuit reverts to a single limiter.

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