# e-book Electronic Devices and Amplifier Circuits with MATLAB Applications

For this reason, silicon is not used in the manufacturing of tunnel diodes. The voltage at which the current begins to rise again is denoted as V v and typical values for silicon, germanium, and GaAs are , , and mV respectively. The backward diode is also used in circuits with small amplitude waveforms. Find the current i Figure 2. Circuit and tunnel diode i - v characteristics for Example 2.

Graphical solution for the determination of the current i for the circuit of Figure 2. For this reason, the symbol for a varactor is as shown in Figure 2. Symbol for varactor A varactor diode uses a PN junction in reverse bias and has a structure such that the capacitance of the diode varies with the reverse voltage. A voltage controlled capacitance is useful in tuning applications.

Typical capacitance values are small, in the order of picofarads. Presently, varactors are replacing the old variable capacitor tuning circuits as in television tuners. A light-emitting diode, when for- ward biased, produces visible light. The light may be red, green, or amber, depending upon the material used to make the diode. The circuit symbols for all optoelectronic devices have arrows pointing either toward them, if they use light, or away from them, if they produce light. The LED is designated by a standard diode symbol with two arrows pointing away from the cathode as shown in Figure 2.

The life expectancy of the LED is very long, over , hours of operation. LEDs arranged for seven segment display In Figure 2. When a negative voltage is applied to the proper cathodes, a number is formed. For example, if negative voltage is applied to all cathodes the number 8 is produced, and if a negative voltage is changed and applied to all cathodes except LED b and e the number 5 is displayed. Seven-segment displays are also available in common-cathode form, in which all cathodes are at the same potential.

When replacing LED displays, one must ensure the replacement display is the same type as the faulty display. Laser diodes are LEDs specifically designed to produce coherent light with a narrow bandwidth and are suitable for CD players and optical communications. Another optoelectronic device in common use today is the photodiode.

Unlike the LED, which produces light, the photodiode receives light and converts it to electrical signals. Basically, the photodiode is a light-controlled variable resistor. In total darkness, it has a relatively high resis- tance and therefore conducts little current. Elowever, when the PN junction is exposed to an external light source, internal resistance decreases and current flow increases. The symbol for a photodiode is shown in Figure 2.

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Symbol for photodiode Switching the light source on or off changes the conduction level of the photodiode and varying the light intensity controls the amount of conduction. Photodiodes respond quickly to changes in light intensity, and for this reason are extremely useful in digital applications such as photo- graphic light meters and optical scanning equipment. A phototransistor is another optoelectronic device that conducts current when exposed to light.

We will discuss phototransistor in the next chapter. An older device that uses light in a way similar to the photodiode is the photoconductive cell, or photocell, shown with its schematic symbol in Figure 2. Like the photodiode, the photocell is a light-controlled variable resistor. Flowever, a typical light-to-dark resistance ratio for a photo- cell is 1: This means that its resistance could range from ohms in the light to kilohms in the dark, or from ohms in the light to kilohms in the dark, and so forth.

Of course, other ratios are also available. Photocells are used in various types of control and timing circuits as, for example, the automatic street light controllers in most cities. The symbol for a photocell is shown in Figure 2. Symbol for photocell A solar cell is another device that converts light energy into electrical energy. A solar cell acts much like a battery when exposed to light and produces about 0. As with batteries, solar cells may be connected in series or parallel to produce higher voltages and currents.

The device is finding widespread appli- cation in communications satellites and solar-powered homes. The symbol for a solar cell is shown in Figure 2. The latter name is derived from the fact that it provides isolation between the input and output. It consists of an LED and a photodiode and each of these devices are isolated from each other.

Isolation between the input and output is desirable because it reduces electromagnetic interfer- ence. Their most important application is in fiber optic communications links. A free electron is one which has escaped from its valence orbit and the vacancy it has created is called a hole. The area between the P-type and N-type materials is referred to as the depletion region. When a junction diode is forward-biased, conventional current will flow in the direction of the arrow on the diode symbol.

Commercially available diodes are provided with a given rating volts, watts by the manufacturer, and if these ratings are exceeded, the diode will burn-out in either the forward-biased or the reverse- biased direction. A bias point, denoted as Q , is established at the intersection of a load line and the linear region. A filter is used at the output to obtain a relatively constant out- put with a small ripple. Clipper circuits are used in applications where it is neces- sary to limit the input to another circuit so that the latter would not be damaged.

In its basic form is a series circuit with a voltage source, a capacitor, and a diode, and the output is the voltage across the diode. Voltage tri- plers and voltage quadruplers are also possible with additional diodes and capacitors. A Zener diode is always connected as a reverse-biased diode and its voltage rating V z and the maximum power it can absorb are given by the manufacturer.

Their most important applica- tion is in voltage regulation. The junction of a doped semiconductor - usually n-type - with a special metal elec- trode can produce a very fast switching diode which is mainly used in high up to 5 MHz fre- quency circuits or high speed digital circuits. Schottky diodes find wide application as rectifiers for high frequency signals and also are used in the design of galliun arsenide GaAs circuits. The negative resistance characteristic makes the tunnel diode useful in oscillators and microwave amplifiers.

It is used as a rectifier and in circuits with small amplitude waveforms. A varactor diode uses a PN junction in reverse bias and has a structure such that the capacitance of the diode varies with the reverse voltage. Varactors have now replaced the old variable capacitor tuning circuits as in television tuners. Photodiodes respond quickly to changes in light intensity, and for this reason are extremely useful in digital applications such as photographic light meters and optical scanning equipment. A solar cell acts much like a battery when exposed to light and as with batteries, solar cells may be connected in series or parallel to produce higher voltages and currents.

Solar cells find widespread applica- tion in communications satellites and solar-powered homes. Isolation between the input and output is desirable because it reduces electromagnetic interference. Show that for a decade factor 10 change in current i D of a forward-biased junction diode the voltage v D changes by a factor of 2. Suggest an experiment that will enable one to compute the numerical value of n. At what temperature will I r double in value? What conclusion can we draw from the result?

Find: a. For the circuit below, find the value of V out assuming that all three diodes are ideal. Compare your answer with that of Example 2. Make any reasonable assumptions. It is also known that the voltage across each diode changes by 0. For the peak rectifier shown below, find the value of the capacitor so that the peak-to-peak ripple will be 1 volt. A circuit and its input waveform are shown below. Compute and sketch the waveform for the output v out. C out Shown below is a resistor R , referred to as a tunnel resistor, placed in parallel with the tunnel diode.

Determine the value of this resistor so that this parallel circuit will exhibit no nega- tive resistance region. A typical solar cell for converting the energy of sunlight into electrical energy in the form of heat is shown in the Figure a below. The terminal voltage characteristics are shown in Fig- ure b below. Determine the approximate operating point that yields the maximum power. What is the value of the maximum power output? What should the value of the resistor be to absorb maximum power from the solar cell? We assume that the voltmeter internal resistance is very high and thus all current produced by V s flows through the diode.

However, for bet- ter accuracy, we can adjust V s to obtain the values of several pairs, plot these on semilog paper and find the best straight line that fits these values. We assume that diode D 3 and the resistor are connected first. Therefore, the current through the four diodes decreases by 1. From 2. Then, 0 - sin -1 0. The conduction angle is d. Therefore, the last rela- tion above reduces to 2 V?

Rearranging 2. The waveform for the output voltage is as shown below. Tunnel diode For the region of negative resistance the slope m is and thus 1 - 10 To eliminate the negative resistance region, we must have Electronic Devices and Amplifier Circuits with. With this value, the slope of the total current i versus the voltage v across the parallel circuit will be zero. For a positive slope greater than zero we should choose a resistor with a smaller value. Light a. The NPN and PNP transistors are defined and their application as amplifiers is well illustrated with numerous examples.

The small and large signal equivalent circuits along with the h-parameter and T-equivalent circuits are presented, and the Ebers-Moll model is discussed in detail. The three terminals of a transistor, whether it is an NPN or PNP transistor, are identified as the emitter, the base, and the collector. Can a transistor be used just as a diode?

The answer is yes, and Figure 3. Transistors configured as diodes Transistors are used either as amplifiers or more commonly as electronic switches. We will dis- cuss these topics on the next section. Briefly, a typical NPN transistor will act as a closed switch when the voltage V BE between its base and emitter terminals is greater than 0. The transistor will act as an open switch when the voltage V BE is less than 0. Figure 3. NPN transistor as electronic closed switch - inverts 5 V to 0 V Like junction diodes, most transistors are made of silicon.

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Gallium Arsenide GaAs technology has been under development for several years and its advantage over silicon is its speed, about six times faster than silicon, and lower power consumption. The disadvantages of GaAs over silicon is that arsenic, being a deadly poison, requires very special manufacturing processes and, in addi- tion, it requires special handling since it is extremely brittle. For these reasons, GaAs is much more expensive than silicon and it is usually used only in superfast computers.

The difference in these bias voltages is necessary to cause current flow from the collector to the emitter in an NPN tran- sistor and from the emitter to collector in a PNP transistor. Since a tran- sistor is a 3-terminal device, there are three currents, the base current, denoted as i B , the collec- Electronic Devices and Amplifier Circuits with.

They are shown in Figures 3. A very useful parameter in transistors is the common-emitter gain [1 , a constant whose value typi- cally ranges from 75 to Its value is specified by the manufacturer. Please refer to Section 3.

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## Course Outline - Basic Electronics

Find the P range corresponding to this a range. To illustrate, let us draw an equivalent circuit using relations 3. NPN transistor equivalent circuit model for relations 3. Example 3. Find the numerical values of the parameters shown in Figure 3. PNP transistor equivalent circuit model for relations 3. Solution: Since the transistor is to operate at the common base configuration, after connecting the resistors and the bias voltages, our circuit is as shown in Figure 3.

Transistor circuit for Example 3. We find V BE from the ratio 1. Circuit for Example 3. Ideally, this resistance should be infinite and we can connect any passive load to the current source. However, most integrated circuits use transistors as loads instead of resistors R c , and when active loads transistors are used, we should consider the finite output resistance that is in parallel with the collector. This resistance is in the order of 1 00 KQ or greater. Before we consider the next example, let us illustrate a transistor in the common-emitter mode with the resistive circuit shown in Figure 3.

B Figure 3. Representing a transistor as a resistive circuit with a potentiometer When the potentiometer resistance is decreased the wiper moves upwards the current through the collector resistor R c increases and the voltage drop across R c increases. This voltage drop subtracts from the supply voltage V cc and the larger the voltage drop, the smaller the voltage V c at the collector. Conversely, when the potentiometer resistance is increased the wiper moves downwards the current through the collector resistor R c decreases and the voltage drop across R c decreases.

This voltage drop subtracts from the supply voltage V cc and the smaller the volt- age drop, the larger the voltage V c at the collector. We recall also that a resistor serves as a current limiter and it develops a voltage drop when cur- rent flows through it. A transistor is a current-in, current-out device.

We supply current to the base of the transistor and current appears at its collector. The current into the base of the transis- tor is in the order of a few microamps while the current at the collector is in the order of a few mil- E lectronic Devices and Amplifier Circuits with. The transistor circuit and the waveforms shown in Figure 3. Transistor operation in the common-emitter mode For the circuit of Figure 3. A further increase in the supply voltage v s has no effect on v BE which remains fairly constant at 0.

As v s decreases, less current flows into the base and the collector current decreases also causing the voltage drop across the resistor R c to decrease, and consequently the collector voltage v c increases. The base to emitter voltage V BE is held constant at 0. Do you expect a linear relationship between I c and V CE?

Solution: Relations 3. The plot is shown in Figure 3. OOe- 8. OOe- 9. OOe- Generally, the i c versus v CE relation in the active region, and non-linear when it operates in the cutoff and saturation regions. Table 3. Plot for Example 3. Find V E , I E , I c , V c , and determine whether this circuit with the indicated values operates in the active, saturation, or cutoff mode.

Is the circuit operating in the active mode? Solution: The circuit is as shown in Figure 3. Is the transistor operating in the active mode? V 'cc Figure 3. The circuit in Figure 3. However, it is not practical to use a separate emitter-base bias voltage V BE. This is because conventional batteries are not available for 0. For this reason we use resistors in the order of kilohms to form voltage dividers with desired values. In addition to eliminating the battery, some of these biasing methods compensate for slight variations in transistor characteristics and changes in transistor conduction resulting from temperature irregularities.

Conventional current flows from V cc through R B to the base then to the grounded emitter. Since the current in the base circuit is very small a few hun- dred microamperes and the forward resistance of the transistor is low, only a few tenths of a volt of positive bias will be felt on the base of the transistor. Flowever, this is enough voltage on the base, along with ground on the emitter and the large positive voltage on the collector to properly bias the transistor. The basic NPN transistor amplifier biased with a resistive network With the transistor properly biased, direct current flows continuously, with or without an input signal, throughout the entire circuit.

The direct current flowing through the circuit develops more than just base bias; it also develops the collector voltage V c as it flows from V cc through resistor R c and, as we can see on the output graph, the output signal starts at the V c level and either increases or decreases. These DC voltages and currents that exist in the circuit before the applica- tion of a signal are known as quiescent voltages and currents the quiescent state of the circuit. We will discuss the Q point in detail in a later section.

The collector resistor R c is placed in the circuit to keep the full effect of the collector supply volt- age off the collector. This permits the collector voltage V c to change with an input signal, which in turn allows the transistor to amplify voltage. Without R c in the circuit, the voltage on the col- lector would always be equal to V cc. The coupling capacitor C is used to pass the ac input signal and block the dc voltage from the pre- ceding circuit.

This prevents DC in the circuitry on the left of the coupling capacitor from affect- ing the bias on the transistor. The coupling capacitor also blocks the bias of the transistor from reaching the input signal source. The input to the amplifier is a sine wave that varies a few millivolts above and below zero. It is introduced into the circuit by the coupling capacitor and is applied between the base and emitter. This in effect increases forward bias, which causes base current to increase at the same rate as that of the input sine wave.

Collector and emitter currents also increase but much more than the base current. With an increase in collector current, more voltage is developed across R c. Since the voltage across R c and the voltage across the transistor collector to emitter must add up to V cc , an increase in voltage across R c results in an equal decrease in voltage across the transistor. Therefore, the output voltage from the amplifier, taken at the collector of the transis- tor with respect to the emitter, is a negative alternation of voltage that is larger than the input, but has the same sine wave characteristics.

During the negative alternation of the input, the input signal opposes the forward bias. This action decreases base current, which results in a decrease in both collector and emitter currents. The decrease in current through R c decreases its voltage drop and causes the voltage across the transistor to rise along with the output voltage. Therefore, the output for the negative alterna- tion of the input is a positive alternation of voltage that is larger than the input but has the same sine wave characteristics. By examining both input and output signals for one complete alternation of the input, we can see that the output of the amplifier is an exact reproduction of the input except for the reversal in polarity and the increased amplitude a few millivolts as compared to a few volts.

With a negative V cc , the PNP base voltage is slightly negative with respect to ground, which provides the neces- sary forward bias condition between the emitter and base. When the PNP input signal goes positive, it opposes the forward bias of the transistor. This action cancels some of the negative voltage across the emitter-base junction, which reduces the current through the transistor.

Since V cc is negative, the voltage on the collector V c goes in a negative direction toward V cc.

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Thus, the output is a negative alternation of voltage that varies at the same rate as the sine wave input, but it is opposite in polarity and has a much larger amplitude. During the negative alternation of the input signal, the transistor current increases because the input voltage aids the forward bias. Therefore, the voltage across R c increases, and consequently, the voltage across the transistor decreases or goes in a positive direction. This action results in a positive output voltage, which has the same characteristics as the input except that it has been amplified and the polarity is reversed.

In summary, the input signals in the preceding circuits were amplified because the small change in base current caused a large change in collector current. And, by placing resistor R c in series with the collector, voltage amplification was achieved. Even though with modern technology transistors are components parts of integrated circuits, or ICs, some are used as single devices. To bias a transistor properly, one must establish a constant DC current in the emitter so that it will not be very sensitive to temperature variations and large variations in the value of [1 among transistors of the same type.

Also, the Q point must be chosen so that it will allow maximum signal swing from positive to negative values. Therefore, let us now derive an expression for I E. From Figure 3. It is often said that the emitter resistor R E provides a negative feedback action which stabilizes the bias current.

To understand how this is done, let us assume that the emitter current I E increases. But the base voltage being determined by the voltage division provided by resistors R[ and R 2 will remain relatively con- stant and according to KVL, the base-to-emitter voltage V BE will decrease. Obviously, this is a contradiction to our original assumption increase in I E and thus we say that the emitter resistor R E provides a negative feedback action. Let us consider the transistor circuit in Figure 3.

For convenience, we will denote the sum of R[ and R 2 as R eq. Find the values of the four resistors for appro- priate fixed biasing. The Thevenin equiva- lent is shown just to indicate the value of V BB which will be used in the calculations. The transistor circuit in Example 3.

If the tempera- ture of the transistor rises for any reason due to a rise in ambient temperature or due to current flow through it , the collector current will increase. This increase in current also causes the DC quiescent point to move away from its desired position level. This reaction to temperature is undesirable because it affects amplifier gain the number of times of amplification and could result in distortion, as we will see later in this chapter.

A better method of biasing, known as self- bias is obtained by inserting the bias resistor directly between the base and collector, as shown in Figure 3. NPN transistor amplifier with self-bias By tying the collector to the base in this manner, feedback voltage can be fed from the collector to the base to develop forward bias. Now, if an increase of temperature causes an increase in col- lector current, the collector voltage V c will fall because of the increase of voltage produced across the collector resistor R L.

This drop in V c will be fed back to the base and will result in a decrease in the base current. The decrease in base current will oppose the original increase in collector current and tend to stabilize it. The exact opposite effect is produced when the collector current decreases.

Find the values of R c and R B to meet these specifications. This is not always the case with all types of amplifiers. It may be desir- able to have the transistor conducting for only a portion of the input signal. The portion of the input for which there is an output determines the class of operation of the amplifier.

There are four classes of amplifier operations. Before discussing the different classes of amplifiers, we should remember that every amplifier has some unavoidable limitations on its performance. For each amplifier there is an upper frequency beyond which it finds it impossible to amplify signals. All electronic devices tend to add some random noise to the signals passing through them, hence degrading the SNR signal to noise ratio.

This, in turn, limits the accuracy of any measurement or communication. A given amplifier cannot output signals above a particular level; there is always a finite limit to the output signal size. The actual signal pattern will be altered due non-linearities in the amplifier. This also reduces the accuracy of measurements and communications. A given amplifier may have a high gain, but this gain cannot normally be infinite so may not be large enough for a given purpose.

This is why we often use multiple amplifiers or stages to achieve a desired overall gain. Let us first discuss the limits to signal size. We denote this variable resistor, i. These conditions are shown in Fig- ures 3. Simple amplifier with resistive load Application of the voltage division expression for the circuit in Figure 3. Thevenin equivalent for the circuit in Figure 3. Since there is no current through the load, this current will flow through the transistor and the emitter resistor and into the negative power supply. This is indeed a very large amount of power and thus this amplifier is obviously very inefficient.

For a comparison of output signals for the different amplifier classes of operation, please refer to Figure 3. Output signals for Class A, Class B, Class AB, and Class C amplifiers We should remember that the circuits presented in our subsequent discussion are only the output stages of an amplifier to provide the necessary drive to the load. In a PNP transistor, for example, if the base becomes positive with respect to the emitter, holes will be repelled at the PN junction and no current can flow in the collector circuit.

This condition is known as cutoff. Saturation occurs when the base becomes so negative with respect to the emitter that changes in the signal are not reflected in collector-current flow. Biasing an amplifier in this manner places the DC operating point between cutoff and saturation and allows collector current to flow during the complete cycle degrees of the input signal, thus providing an output which is a replica of the input.

Although the output from this amplifier is degrees out-of-phase with the input, the output current still flows for the complete duration of the input. Class A amplifiers are used as amplifiers in radio, radar, and sound systems. The output stages of Class A amplifiers carry a fairly large current. This current is referred to a qui- escent current and it is defined as the current in the amplifier when the output voltage is zero. However, a Class A amplifier can be made more efficient if we employ a push-pull arrangement as shown in Figure 3.

It is convenient to set the quiescent current, denoted as I Q , to one-half the maximum current drawn by the load. Then, we can adjust the currents ij and i, to be equal and opposite. Compute the power absorbed by the circuit if we want to apply up to 24 V to the 8 Q load. This consists also of a push-pull arrangement but the bases inputs are tied by two diodes. The current in the diodes is supplied by two current sources denoted as I bjas. I I Figure 3. Output stage in a typical Class B amplifier When v in goes positive, the upper transistor conducts and the lower transistor is cutoff.

Accordingly, it appears that this arrangement has perfect efficiency. Flowever, this ideal condition is never achieved because no two diodes or two transistors are exactly identi- cal. There exists a range where both transistors are cutoff when the input signal changes polarity and this results in crossover distortion as shown in Figure 3. This distortion is due to the non-lin- earities in transistor devices where the output does not vary linearly with the input. Crossover distortion Figure 3. Crossover distortion in Class B amplifier The efficiency of a typical Class B amplifier varies between 65 to 75 percent.

Class AB amplifiers combine the advantages of Class A and Class B amplifiers while they minimize the problems associated with them. Two possible arrangements for the output stage of a typical Class AB amplifier are shown in Figure 3. In Figure 3. But for larger signals, one transistor will con- duct and supply the current required by the load, while the other will be cutoff.

In other words, for large signals the circuit of Figure 3. Then, 3. The adjustable resistor R ad j is set to a position to yield the desired value of the quiescent current I bias. From the above discussion, we have seen that the Class AB amplifier maintains current flow at all times so that the output devices can begin operation nearly instantly without the crossover distor- tion in Class B amplifiers. Flowever, complete current is not allowed to flow at any one time thus avoiding much of the inefficiency of the Class A amplifier. Class AB designs are about 50 percent efficient half of the power supply is power is turned into output to drive speakers compared to Class A designs at 20 percent efficiency.

Class AB amplifiers are the most commonly used amplifier designs due to their attractive combi- nation of good efficiency and high-quality output low distortion and high linearity close to but not equal to Class A amplifiers. How- ever, Class C amplifiers cannot be used with amplitude modulation AM because of the high dis- tortion. A typical Class C output stage is shown in Figure 3. I - Load Figure 3. The load can be thought of as an antenna. During the negative half-cycle the transistor behaves like an open switch, the magnetic field in the inductor collapses and the current i L will flow through the capacitor and the load.

Other classes of amplifiers such as Class D, Class E, and others have been developed by some manufacturers. These are for special applications and will not be discussed in this text. For more information on these, the interested reader may find information on the Internet.

We will use the cir- cuit in Figure 3. Circuit showing the variables used in the graphs in Figures 3. This equation and the curve of equation 3. Plot showing the intersection of Equations 3. Next, we refer to the family of curves of the collector current i c versus collector-emitter voltage v CE for different values of i B as shown in Figure 3. Obviously, the value of the collector resistor R c must be chosen such that the load line is neither a nearly horizontal nor a nearly vertical line.

Graphical representation of V CE and i c when the input voltage v in is a sinusoid 3. We will represent average DC values with upper case letters and upper case subscripts. We will use lower case letters with upper case subscripts for the sum of the instantaneous and average values. Let us consider the circuit of Figure 3. A transistor model In Figure 3. An alternative transistor model. The transistor models shown in Figures 3. An improved transistor model is shown in Figure 3. B C Figure 3. The model in Figure 3. It applies also to PNP transistors provided that the diodes, voltage polarities, and current directions are reversed.

The transistor amplifier in Figure 3. The piece-wise linear model in Figure 3. Piecewise linear model for the circuit in figure 3. The current I cs represents the collector saturation current. When this occurs, there is no voltage drop across either diode, all three terminals of the transistor are at ground potential, and the current in the collector diode D c is zero.

When this occurs, there is no current in either diode, and the base terminal is at ground potential. The resistor Rj provides a suitable current to sustain the breakdown condition of the Zener diode. Any change in supply voltage causes a compensating change in the voltage drop across the transistor from collector to emitter and the load voltage v load is thereby held constant in spite of changes in the input voltage or load resistance R load.

Find the values of the load voltage v load , the collect-to-emitter voltage v CE , and the power P c absorbed by the transistor. The piece— wise linear model for the transistor in Figure 3. This occurs because the collector can be represented as an ideal current source pi B. However, if the supply voltage falls below the Zener voltage of 25 V, the collector-base junction will no longer be reverse-biased, and the voltage regulation action of the transistor will fail. Also, when this occurs, the breakdown state will not be sustained in the Zener diode. However, the base-to-emitter voltage cannot be neglected when only the increments of voltage and currents is considered.

Also, when calculating increments of current and voltage, it is often necessary to account for the small effects of variations in collector voltage on both the input and output circuits. For these reasons the incremental model for the transistor provides a better approximation than the piece-wise linear approximation. The base-to-emitter voltage v BE and the collector current i c are functions of the base current i B and collector-to-emitter voltage v CE.

It is also conve- nient to denote these derivatives in lower case letters with lower case subscripts.

## Steven T. Karris-Electronic Devices and Amplifier Circuits With MATLAB Applications_1250

It is referred to as hybrid model because of the mixed set of voltages and currents as indicated by the expressions of 3. The hybrid incremental model for a transistor in the common— emitter configuration The input resistance r n is the slope of the input voltage and current characteristics and it accounts for the voltage drop across the base-emitter junction. Likewise, the output conduc- tance g 0 is the slope of the output current and voltage characteristics.

The voltage amplification factor p is related to the input characteristics caused by a change in v CE , and the current amplification factor p is related to the output characteristics caused by a change in i B. Typical values for the parameters of relations 3. Let us, for example, consider the circuit of Figure 3. Therefore, the negative resistance -pPR eq can be replaced by a short circuit, and assuming that the base current i b is unaffected by this assumption, the volt- ages and currents in the collector side of the circuit are not affected. The second sub- script e indicates that the parameters apply for the transistor operating in the common-emitter mode.

A similar set of symbols with the subscript b replacing the subscript e denotes the hybrid parameters for a transistor operating in the common-base mode, and a set with the subscript c replacing the letter e denotes the hybrid parameters for a transistor operating in the common-col- lector mode. Values for the hybrid parameters at a typical quiescent operating point for the common-emitter mode are provided by the transistor manufacturers.

Please refer to the last section in this chapter. TABLE 3. The incremental model for the transistor circuit in Figure 3. The current gain A c can be found from the relation 3. This relation is derived as follows: From 3. The transconductance g m defined By substitution of 3. Therefore, a transistor can be viewed as an amplifier with a transconductance of 40 millimhos for each milli- ampere of collector current. Figures 3. Alternate forms for the transistor model In Figure 3. From 3. For higher frequencies, the effects of junction capacitances must be taken into account.

The hybrid— n model for the transistor at high frequencies The capacitor C, represents the capacitance that exists across the forward-biased emitter junc- tion while the capacitor C 2 represents a much smaller capacitance that exists across the reverse- biased collector junction. At low frequencies the capacitors act as open circuits and thus do not affect the transistor perfor- mance.

At high frequencies, however, the capacitors present a relatively low impedance and thereby reduce the amplitude of the signal voltage v 'be ' This reduction in v' be causes in turn a reduction in the strength of the controlled source g m v' be and a reduction in the collector current i c. We can derive some useful relations by determining the short-circuit collector current i c when a sinusoidal input current is applied between the base and emitter terminals.

Impedances and admittances are complex quantities but not phasors. The coefficient of I b in 3. Thus, C 0 p serves as a useful measure of the band of fre- quencies over which the short-circuit current amplification remains reasonably constant and nearly equal to its low-frequency value. For this reason, C 0 p is referred to as the p cutoff fre- quency.

Also, from 3. Using the hybrid- 7t model of Fig- ure 3. The circuit has high input impedance and low output impedance. Common-base transistor circuit and its equivalent Electronic Devices and Amplifier Circuits with. The h-parameter equivalent circuit for common-base transistor From Figures 3. This can be shown as follows: From 3. Retaining only the first two terms of this series, by substitution into 3. With these observations, the circuit of Figure 3. Simplified circuit for the computation of voltage gain in a common base transistor From Figure 3. Find the voltage and current gains, and input and output resistances.

Common-emitter transistor circuit and its equivalent The equivalent circuit in Figure 3. Therefore, for simplicity and compact- ness, we can represent the circuit of Figure 3. The h-parameter equivalent circuit in Figure 3. Using the circuit in Figure 3. Therefore, to compute the input and output resis- tances and overall voltage and current gains to a fairly accurate values, we can use the simplified circuit in Figure 3. The simplified common-emitter transistor equivalent circuit From the equivalent circuit in Figure 3.

Then, the voltage drop across the resistor R E will rise and the voltage drop across the resistor r e will decrease to maintain the voltage v be relatively constant. But a decrease in the voltage drop across the resistor r e means a decrease in the emitter current i e and consequently a decrease in the collector current i c. Relation 3. Find the maximum value of the applied signal v s so that v be or v b under the conditions of a and b will not exceed 5 mV.

The emitter-follower is useful in applications where a high-resistance source is to be connected to a low-resistance load. Common-collector or emitter-follower transistor circuit and its equivalent From the equivalent circuit in Figure 3. The simplified common— collector transistor amplifier equivalent circuit From the equivalent circuit in Figure 3. Equivalent circuit for the computation of the output resistance From Figure 3. Emitter— follower transistor amplifier equivalent circuit for Example 3.

With this resistor discon- nected, the input resistance as given by 3. We will refer to it in our subsequent discus- sion to define the cutoff, active, and saturation regions. Transistor circuit for defining the regions of operation 3. With reference to the circuit in Figure 3. In this case p is referred to as the current gain at saturation and it is denoted as P sat.

When a transistor is deeply into saturation, the collector to emitter voltage is denoted as v CE sat and its value is approximately 0. We now can find the value of p at saturation. It is valid in all regions of operation of the bipolar transistor, transitioning between them smoothly. The Ebers-Moll bipolar transistor model expresses each of the terminal currents in terms of a for- ward component I F , which only depends on the base-to-emitter voltage, and a reverse compo- nent I R , which only depends on the base-to-collector voltage.

In this case, the terminal currents are given by I c - I F Figure 3. By using 3. Let I s be the saturation current and V T the thermal voltage. Then for the NPN bipolar transis- tor biased as shown in Figure 3. First, we will find the incremental resistance seen looking into the base terminal of an NPN tran- sistor with the emitter voltage held fixed. Due to the large diffusion capacitance, it takes a considerably long time to drive the transistor out of saturation.

The Schot- tky diode alleviates this problem if connected between the base and the collector as shown in Fig- ure 3. The Schottky diode has the property that it turns on at a lower voltage than the PN junction. Therefore, when a transistor is in the saturation region, the current between the base and the col- lector is carried by the Schottky diode.

The specifications usually cover the items listed below, and the values given are typical. Features, e. Maximum Ratings and Thermal Characteristics, e. Electrical Characteristics, e. Gallium Arsenide GaAs technol- ogy has been under development for several years and its advantage over silicon is its speed, about six times faster than silicon, and lower power consumption.

The disadvantages of GaAs over silicon is that arsenic, being a deadly poison, requires very special manufacturing pro- cesses. In a Class A amplifier the efficiency is very low. Class A amplifiers are used for audio and frequency amplification. Class AB amplifi- ers are normally used as push-pull amplifiers to alleviate the crossover distortion of Class B amplifiers. Class B amplifiers are used in amplifiers requiring high power output. Class C amplifiers have the highest efficiency and are used for radio frequency amplification in transmitters.

Likewise, the output conductance g 0 is the slope of the output current and voltage characteristics. The voltage amplification factor p is related to the input characteristics caused by a change in v CE , and the current amplification factor [S is related to the output characteris- tics caused by a change in i B. Therefore, when a transistor is in the saturation region, the current between the base and the collector is carried by the Schottky diode.

Find the range of changes in v BE at this temperature for the range 0. Find p, a, and Ir- 3. Find the highest voltage to which the base can be set so that the transistor will be in the active mode. Find all indicated volt- ages and currents. Are both the transistors operating in the active mode? What is the total power absorbed by this circuit? What should the values of R c and R E be to achieve this value? Construct a load line, and indicate the current and the voltage at which the load line intersects the axes.

Find the quiescent collector current I c and collector-to-emitter voltage V CE. Sketch the load line on the i c versus v EC coordinates. Show the current and voltage at which the load line intersects the axes, and indicate the quiescent point on this line. It is not necessary to draw the collector characteristics. If the input signal is a sinusoidal current, approximately what is the greatest amplitude that the signal i s can have without waveform distortion at the output? Find the transconductance g m and the base-emitter resistance r be.

Using the hybrid representation for the transistor, draw an incremental model. Find the current amplification A c. Determine whether the PNP transistor shown below is operating in the cutoff, active, or sat- uration region The equations describing the h parameters can be used to represent the network shown below.

This network is a transistor equivalent circuit for the common-emitter configuration and the h parameters given are typical values for such a circuit. EE From Table 3. Under those conditions the transistor behaves like an open switch and thus it is operating in the cutoff mode. Therefore the given circuit is redrawn as shown below. Then, Electronic Devices and Amplifier Circuits with. The load line then intercepts the v CE axis at 20 V and the i c axis at 1 mA. We recall that 4. The chapter includes also a brief discussion on unijunction transistors, and diacs.

Figure 4. These characteristics are similar to those for the junction transistor except that the parameter for this family is the input voltage rather than the input current. Like the old vacuum triode, the FET is a voltage-controlled device. Pictorial representation and output volt-ampere characteristics for a typical JFET The lower terminal in the N material is called the source, and the upper terminal is called the drain; the two regions of P material, which are usually connected together externally, are called gates.

P-N junctions exist between the P and N materials, and in normal operation the voltage applied to the gates biases these junctions in the reverse direction. A potential barrier exists across the junctions, and the electrons carrying the current i D in the N material are forced to flow through the channel between the two gates. If the voltage applied to the gates is changed, the width of the transition region at the junction changes; thus the width of the channel changes, resulting in a change in the resistance between source and drain.

A small potential applied to the gates, 5 to 10 volts, is sufficient to reduce the channel width to zero and to cut off the flow of current in the output circuit. One of the most attractive features of the JFET is the fact that the input resistance, measured between gate and source, can be made very large, from 1 to megohms.

This high input resis- tance results from the fact that the input voltage v G biases the junctions in the reverse direction and consequently is required to deliver only the small leakage current across the junctions. There are many circuits in which a high input resistance is required, and the ordinary junction transis- tor is not suitable for such applications. JFETs have been made with input resistances exceeding 1 megohm, with transconductances in the range of 1 to 5 millimhos, and with the ability to provide a voltage amplification of about 10 at frequencies up to 10 MHz.

The current in a JFET is carried only by majority carriers and for this reason the FET is also known as unipolar transistor, in contrast to the ordinary transistor in which both majority and minority carriers participate in the conduction process, and it is known as bipolar transistor. To better understand the JFET operation, let us review the depletion region which we discussed in Chapter 2. PN junction and depletion region of a typical PN junction The width of the depletion region depends on the applied bias.

Thus, the forward biasing causes the depletion region to decrease resulting in a low resistance at the junction and a relatively large current across it. A high resistance between the terminals is developed, and only a small current flows between the terminals. This is illustrated in Figure 4. Figure This reverse-bias condition cause the depletion region to expand and that reduces the effective cross-sectional area of the channel.

The voltage at the gate which causes the drain-to-source resistance R DS to become infinite, is referred to as the pinch-off volt- age and it is denoted as V p. A P-channel JFET operates similarly except that the voltage polarities are reversed as shown in Figure which also shows the symbols for each. Is this an inverting or a non-inverting amplifier? Find the transconductance using the results of a and b. Plot i DS versus v GS and indicate how the transconductance can be calculated from this plot. Solution: From Figure 4.

Therefore, 'out From the plot of Figure 4. Therefore, out The results of a and b indicate that an increase in the input voltage results in a decrease of the output voltage. Therefore, we conclude that the given JFET circuit is an inverting ampli- fier. A neg- ative gate voltage will then drive electrons out of the channel, increasing the resistance from source to drain. This is termed depletion-mode operation. The JFET also operates in this manner. This is termed enhancement-mode operation. The enhancement mode MOSFET has a lightly doped channel and uses forward bias to enhance the current carriers in the channel.

A MOSFET can be constructed that will operate in either mode depending upon what type of bias is applied, thus allowing a greater range of input signals. Current— voltage characteristics for typical MOSFET The voltage at which the channel is closed is known as the pinch-off voltage V p , and the mini- mum voltage required to form a conducting channel between the drain and source is referred to as the threshold voltage and it is denoted as V T.

Typical values for V T are 2 to 4 volts for high voltage devices with thicker gate oxides, and 1 to 2 volts for lower voltage devices with thinner gate oxides. Then 4. The quadratic triode and saturation regions are as shown in Figure 4. The saturation region starts where for any further increases in v DS there is no increase in the drain current i D.

Figures 4. It is also referred to as the quadratic region. Likewise, the saturation region is sometimes referred to as the pentode region. It increases with increasing v DS due to the so-called channel width modulation caused by reduction of the effective channel length, and since i D is inversely proportional to the channel length, i D increases with v DS and thus 4. Assume that k n , L , and W do not change significantly in this interval. Relation 4. As indicated in the previous chapter, subscripts in upper case represent the sum of the quiescent and small signal parameters, and subscripts in lower case represent just the small signal parame- ters.

If, however we want to decrease the channel conductivity, we can apply a sufficiently negative v GS to deplete the implanted channel, and this mode of operation is referred to as the depletion mode. At this threshold negative voltage V T , the drain current i D is zero although v DS may still be present. Example 4. What would the drain current i D be if the voltage v DS is set to its minimum value to keep the device in the saturation region?

The dotted curve of the i D vs v DS characteristics of Figure 4. Then, with 4. Circuit for the derivation of the voltage gain Figure 4. From Figure 4. The author and publisher shall have neither liability nor responsibility to any person or entity with respect to any loss or damages arising from the information contained in this text. Orchard Publications Visit us on the Internet www. Steven T. Karris is the president and founder of Orchard Publications.

He earned a bachelors degree in electrical engineering at Christian Brothers University, Memphis, Tennessee, a masters degree in electrical engineering at Florida Institute of Technology, Melbourne, Florida, and has done post-master work at the latter. He is a registered professional engineer in California and Florida.

He has over 35 years of professional engineering experience in industry. In addition, he has over 30 years of teaching experience that he acquired Electronic Devices and Amplifier Circuits. This comprehensive text describes just about all semiconductor devices and their industrial applications illustrated with numerous practical examples, and detailed instructions for using MATLAB to obtain accurate and quick solutions.

Chapter 1: Basic Electronic Concepts and Signals. Chapter 2: Introduction to Semiconductor Electronics-Diodes. Chapter 3: Bipolar Junction Transistors. Chapter 5: Operational Amplifiers. Chapter 6: Integrated Circuits.