Using = , design the circuit shown in Fig. P6.68 so that

The terminal voltages of various npn transistors are measured during operation in their respective circuits with the following results:In this table, where the entries are in volts, 0 indicates the reference terminal to which the black (negative) probe of the voltmeter is connected. For each case, identify the mode of operation of the transistor.

Two transistors, fabricated with the same technology but having different junction areas, when operated at a baseemitter voltage of 0.75 V, have collector currents of 0.2 mA and 5 mA. Find IS for each device. What are the relative junction areas?

In a particular technology, a small BJT operating at conducts a collector current of 100 A. What is the corresponding saturation current? For a transistor in the same technology but with an emitter junction that is 32 times larger, what is the saturation current? What current will this transistor conduct at ? What is the baseemitter voltage of the latter transistor at iC = 1 mA? Assume active-mode operation in all cases.

Two transistors have EBJ areas as follows: AE1 = AE1 = 400m 400 m and AE2 = 0.4m 0.2 m. If the two transistors are operated in the active mode and conduct equal collector currents, what do you expect the difference in their values to be?

Find the collector currents that you would expect for operation at mV for transistors for which A. For the transistor with the larger EBJ, what is the required to provide a collector current equal to that provided by the smaller transistor at mV? Assume active-mode operation in all cases.

In this problem, we contrast two BJT integrated-circuit fabrication technologies: For the old technology, a typical npn transistor has A, and for the new technology a typical npn transistor has A. These typical devices have vastly different junction areas and base width. For our purpose here we wish to determine the required to establish a collector current of 1 mA in each of the two typical devices. Assume active-mode operation.

Consider an npn transistor whose baseemitter drop is 0.76 V at a collector current of 10 mA. What current will it conduct at vBE = 0.70 V? What is its baseemitter voltage for iC = 10 A?

In a particular BJT, the base current is 10 A, and the collector current is 600 A. Find

Find the values of that correspond to values of 0.5, 0.8, 0.9, 0.95, 0.99, 0.995, and 0.999.

Find the values of that correspond to values of 1, 2, 10, 20, 100, 200, 1000, and 2000.

Show that for a transistor with close to unity, if changes by a small per-unit amount , the corresponding per-unit change in is given approximately

An npn transistor of a type whose is specified to range from 60 to 300 is connected in a circuit with emitter grounded, collector at +9 V, and a current of 20 A injected into the base. Calculate the range of collector and emitter currents that can result. What is the maximum power dissipated in the transistor? (Note: Perhaps you can see why this is a bad way to establish the operating current in the collector of a BJT.)

A BJT is specified to have A and that falls in the range of 50 to 200. If the transistor is operated in the active mode with set to 0.650 V, find the expected range of and

Measurements made on a number of transistors operating in the active mode with mA indicate base currents of 50 A, 10 A, and 25 A. For each device, find and

Measurement of VBE and two terminal currents taken on a number of npn transistors operating in the active mode are tabulated below. For each, calculate the missing current value as well as , , and IS as indicated by the table.

A particular BJT when operated in the active mode conducts a collector current of 10 mA and has vBE = 0.70 V and iB = 100 A. Use these data to create specific transistor models of the form shown in Figs. 6.5(a) to (d).

Using the npn transistor model of Fig. 6.5(b), consider the case of a transistor for which the base is connected to ground, the collector is connected to a 10-V dc source through a 2-k resistor, and a 3-mA current source is connected to the emitter with the polarity so that current is drawn out of the emitter terminal. If = 100 and IS = 1015 A, find the voltages at the emitter and the collector and calculate the base current.

Consider an npn transistor operated in the active mode and represented by the model of Fig. 6.5(d). Let the transistor be connected as indicated by the equivalent circuit shown in Fig. 6.6(b). It is required to calculate the values of and that will establish a collector current of 1 mA and a collector-to-emitter voltage of 1 V. The BJT is specified to have and A.

An npn transistor has a CBJ with an area 150 times that of the EBJ. If A, find the voltage drop across EBJ and across CBJ when each is forward biased and conducting a current of 1 mA. Also find the forward current each junction would conduct when forward biased with 0.5 V.

We wish to investigate the operation of the npn transistor in saturation using the model of Fig. 6.9. Let A, V, and ISC/IS 100. For each of three values of (namely, 0.4 V, 0.3 V, and 0.1 V), find and Also find that results in

Use Eqs. (6.14), (6.15), and (6.16) to show that an npn transistor operated in saturation exhibits a collector-toemitter voltage, given by Use this relationship to evaluate for , 10, 5, and 1 for a transistor with and with a CBJ area 100 times that of the EBJ.

Consider the pnp large-signal model of Fig. 6.11(b) applied to a transistor having IS = 1013 A and = 40. If the emitter is connected to ground, the base is connected to a current source that pulls 20 A out of the base terminal, and the collector is connected to a negative supply of 10 V via a 10-k resistor, find the collector voltage, the emitter current, and the base voltage.

A pnp transistor has vEB = 0.8 V at a collector current of 1 A. What do you expect vEB to become at iC = 10 mA? At iC = 5 A?

A pnp transistor modeled with the circuit in Fig. 6.11 (b) is connected with its base at ground, collector at 1.0 V, and a 10-mA current is injected into its emitter. If the transistor is said to have = 10, what are its base and collector currents? In which direction do they flow? If IS = 1015 A, what voltage results at the emitter? What does the collector current become if a transistor with = 1000 is substituted? (Note: The fact that the collector current changes by less than 10% for a large change of illustrates that this is a good way to establish a specific collector current.)

A pnp power transistor operates with an emitter-tocollector voltage of 5 V, an emitter current of 10 A, and VEB = 0.85 V. For = 15, what base current is required? What is IS for this transistor? Compare the emitterbase junction area of this transistor with that of a small-signal transistor that conducts iC = 1 mA with vEB = 0.70 V. How much larger is it?

While Fig. 6.5 provides four possible large-signal equivalent circuits for the npn transistor, only two equivalent circuits for the pnp transistor are provided in Fig. 6.11. Supply the missing two.

By analogy to the npn case shown in Fig. 6.9, give the equivalent circuit of a pnp transistor in saturation.

For the circuits in Fig. P6.28, assume that the transistors have very large . Some measurements have been made on these circuits, with the results indicated in the figure. Find the values of the other labeled voltages and currents.

Measurements on the circuits of Fig. P6.29 produce labeled voltages as indicated. Find the value of for each transistor.

A very simple circuit for measuring of an npn transistor is shown in Fig. P6.30. In a particular design, is provided by a 9-V battery; M is a current meter with a 50-A full scale and relatively low resistance that you can neglect for our purposes here. Assuming that the transistor has V at mA, what value of R would establish a resistor current of 1 mA? Now, to what value of does a meter reading of full scale correspond? What is if the meter reading is 1/5 of full scale? 1/10 of full scale?

Repeat Exercise 6.13 for the situation in which the power supplies are reduced to V.

Examination of the table of standard values for resistors with 5% tolerance in Appendix G reveals that the closest values to those found in the design of Example 6.20 are 5.1 k and 6.8 k. For these values use approximate calculations (e.g., VBE  0.7 V and  1) to determine the values of collector current and collector voltage that are likely to result.

Examination of the table of standard values for resistors with 5% tolerance in Appendix G reveals that the closest values to those found in the design of Example 6.20 are 5.1 k and 6.8 k. For these values use approximate calculations (e.g., VBE  0.7 V and  1) to determine the values of collector current and collector voltage that are likely to result.

Design the circuit in Fig. P6.34 to establish mA and V. The transistor exhibits of 0.8 V at mA, and .

For each of the circuits shown in Fig. P6.35, find the emitter, base, and collector voltages and currents. Use = 50, but assume independent of current level.

The current ICBO of a small transistor is measured to be 10 nA at 25C. If the temperature of the device is raised to 125C, what do you expect ICBO to become?

Augment the model of the npn BJT shown in Fig. 6.18(a) by a current source representing ICBO. Assume that ro is very large and thus can be neglected. In terms of this addition, what do the terminal currents iB, iC, and iE become? If the base lead is open-circuited while the emitter is connected to ground, and the collector is connected to a positive supply, find the emitter and collector currents.

A BJT whose emitter current is fixed at 1 mA has a baseemitter voltage of 0.69 V at 25C. What baseemitter voltage would you expect at 0C? At 100C?

A particular pnp transistor operating at an emitter current of 0.5 mA at 20C has an emitterbase voltage of 692 mV. (a) What does vEB become if the junction temperature rises to 50C? (b) If the transistor is operated at a fixed emitterbase voltage of 700 mV, what emitter current flows at 20C? At 50C?

Consider a transistor for which the baseemitter voltage drop is 0.7 V at 10 mA. What current flows for vBE = 0.5 V? Evaluate the ratio of the slopes of the iCvBE curve at vBE = 700 mV and at vBE = 500 mV. The large ratio confirms the point that the BJT has an apparent threshold at .

In Problem 6.40, the stated voltages are measured at 25C. What values correspond at 25C? At 125C?

Use Eq. (6.18) to plot iC versus vCE for an npn transistor having IS = 1015 A and VA = 100 V. Provide curves for vBE = 0.65, 0.70, 0.72, 0.73, and 0.74 volts. Show the characteristics for vCE up to 15 V.

In the circuit shown in Fig. P6.43, current source I is 1.1mA, and at 25 C mV at mA. At 25 C with , what currents flow in and ? What voltage would you expect at node E? Noting that the temperature coefficient of for constant is mV/ C, what is the TC of ? For an ambient temperature of 75 C, what voltage would you expect at node E? Clearly state any simplifying assumptions you make.

For a particular npn transistor operating at a vBE of 670 mV and IC = 2 mA, the iCvCE characteristic has a slope of 2 . To what value of output resistance does this correspond? What is the value of the Early voltage for this transistor? For operation at 20 mA, what would the output resistance become?

For a BJT having an Early voltage of 150 V, what is its output resistance at 1 mA? At 100 A?

Measurements of the iCvCE characteristic of a smallsignal transistor operating at vBE = 720 mV show that iC = 1.8 mA at vCE = 2 V and that iC = 2.4 mA at vCE = 14 V. What is the corresponding value of iC near saturation? At what value of vCE is iC = 2.0 mA? What is the value of the Early voltage for this transistor? What is the output resistance that corresponds to operation at vBE = 720 mV?

Give the pnp equivalent circuit models that correspond to those shown in Fig. 6.18 for the npn case.

A BJT operating at iB = 8 A and iC = 1.2 mA undergoes a reduction in base current of 0.8 A. It is found that when vCE is held constant, the corresponding reduction in collector current is 0.1 mA. What are the values of and the incremental or ac that apply? If the base current is increased from 8 A to 10 A and vCE is increased from 8 V to 10 V, what collector current results? Assume VA = 100 V.

For the circuit in Fig. P6.49 let V, k and k The BJT has Find the value of that results in the transistor operating (a) in the active mode with V; (b) at the edge of saturation; (c) deep in saturation with

Consider the circuit of Fig. P6.49 for the case . If the BJT is saturated, use the equivalent circuit of Fig. 6.20 to derive an expression for in terms of and . Also derive an expression for the total power dissipated in the circuit. For V, design the circuit to obtain operation at a forced as close to 10 as possible while limiting the power dissipation to no larger than 20 mW. Use 1% resistors (see Appendix G).

The pnp transistor in the circuit in Fig. P6.51 has . Show that the BJT is operating in the saturation mode and find and To what value should be increased in order for the transistor to operate at the edge of saturation?

The transistor in the circuit of Fig. P6.52 has a very high

The transistor in the circuit of Fig. P6.52 has a very high . Find the highest value of VB for which the transistor still operates in the active mode. Also, find the value of VB for which the transistor operates in saturation with a forced

Consider the operation of the circuit shown in Fig. P6.54 for VB at 1 V, 0 V, and +1 V. Assume that is very high. What values of VE and VC result? At what value of VB does the emitter current reduce to one-tenth of its value for VB = 0 V? For what value of VB is the transistor just at the edge of conduction? What values of VE and VC correspond? For what value of VB does the transistor reach the edge of saturation? What values of VC and VE correspond? Find the value of VB for which the transistor operates in saturation with a forced of 2.

For the transistor shown in Fig. P6.55, assume  1 and vBE = 0.5 V at the edge of conduction. What are the values of VE and VC for VB = 0 V? For what value of VB does the transistor cut off? Saturate? In each case, what values of VE and VC result?

Consider the circuit in Fig. P6.52 with the base voltage VB obtained using a voltage divider across the 3-V supply. Assuming the transistor to be very large (i.e., ignoring the base current), design the voltage divider to obtain VB = 1.5 V. Design for a 0.1-mA current in the voltage divider. Now, if the BJT = 100, analyze the circuit to determine the collector current and the collector voltage.

A single measurement indicates the emitter voltage of the transistor in the circuit of Fig. P5.57 to be 1.2 V. Under the assumption that = 0.7 V, what are VB, IB, IE, IC, VC, , and ? (Note: Isnt it surprising what a little measurement can lead to?)

Design a circuit using a pnp transistor for which  1 using two resistors connected appropriately to 5 V so that IE = 2 mA and VBC = 2.5 V. What exact values of RE and RC would be needed? Now, consult a table of standard 5% resistor values (e.g., that provided in Appendix G) to select suitable practical values. What values of resistors have you chosen? What are the values of IE and VBC that result?

In the circuit shown in Fig. P6.59, the transistor has = 50. Find the values of VB, VE, and VC. If RB is raised to 100 k, what voltages result? With RB = 100 k, what value of would return the voltages to the values first calculated?

In the circuit shown in Fig. P6.59, the transistor has = 50. Find the values of VB, VE, and VC, and verify that the transistor is operating in the active mode. What is the largest value that RC can have while the transistor remains in the active mode?

For the circuit in Fig. P6.61, find VB, VE, and VC for RB = 100 k, 10 k, and 1 k. Let

For the circuits in Fig. P6.62, find values for the labeled node voltages and branch currents. Assume to be very high.

Repeat the analysis of the circuits in Problem 6.62 using = 100. Find all the labeled node voltages and branch currents.

It is required to design the circuit in Fig. P6.64 so that a current of 1 mA is established in the emitter and a voltage of 5 V appears at the collector. The transistor type used has a nominal of 100. However, the value can be as low as 50 and as high as 150. Your design should ensure that the specified emitter current is obtained when = 100 and that at the extreme values of the emitter current does not change by more than 10% of its nominal value. Also, design for as large a value for RB as possible. Give the values of RB, RE, and RC to the nearest kilohm. What is the expected range of collector current and collector voltage corresponding to the full range of

The pnp transistor in the circuit of Fig. P6.65 has = 50. Find the value for RC to obtain VC = +3 V. What happens if the transistor is replaced with another having = 100?

Consider the circuit shown in Fig. P6.66. It resembles that in Fig. 6.29 but includes other features. First, note diodes D1 and D2 are included to make design (and analysis) easier and to provide temperature compensation for the emitterbase voltages of Q1 and Q2. Second, note resistor R whose purpose is to provide negative feedback (more on this later in the book!). Using and VD = 0.7 V independent of current and = , find the voltages VB1, VE1, VC1, VB2, VE2, and VC2, initially with R open-circuited and then with R connected. Repeat for = 100, initially with R open-circuited then connected.

For the circuit shown in Fig. P6.67, find the labeled node voltages for: (a) = (b) = 100

Using = , design the circuit shown in Fig. P6.68 so that the bias currents in Q1, Q2, and Q3 are 1 mA, 1 mA, and 2 mA, respectively, and V3 = 0, V5 = 2 V, and V7 = 1 V. For each resistor, select the nearest standard value utilizing the table of standard values for 5% resistors in Appendix G. Now, for = 100, find the values of V3, V4, V5, V6,and V7.

For the circuit in Fig. P6.69, find VB and VE for vI = 0V, +2V, 2.5 V, and 5 V. The BJTs have

Find approximate values for the collector voltages in the circuits of Fig. P6.70. Also, calculate forced for each of the transistors. (Hint: Initially, assume all transistors are operating in saturation, and verify the assumption.

A BJT amplifier circuit such as that in Fig. 6.33(a) is operated with VCC = +5 V and is biased at VCE = +1 V. Find the voltage gain, the maximum allowed output negative swing without the transistor entering saturation, and the corresponding maximum input signal permitted.

For the amplifier circuit in Fig. 6.33(a) with VCC = +5V and RC = 1 k, find VCE and the voltage gain at the following dc collector bias currents: 0.5 mA, 1 mA, 2.5 mA, 4 mA, and 4.5 mA. For each, give the maximum possible positive- and negative-output signal swing as determined by the need to keep the transistor in the active region. Present your results in a table.

Consider the CE amplifier circuit of Fig. 6.33(a) when operated with a dc supply VCC = +5 V. It is required to find the point at which the transistor should be biased; that is, find the value of VCE so that the output sine-wave signal vce resulting from an input sine-wave signal vbe of 5-mV peak amplitude has the maximum possible magnitude. What is the peak amplitude of the output sine wave and the value of the gain obtained? Assume linear operation around the bias point. (Hint: To obtain the maximum possible output amplitude for a given input, you need to bias the transistor as close to the edge of saturation as possible without entering saturation at any time, that is, without vCE decreasing below 0.3 V.)

A designer considers a number of low-voltage BJT amplifier designs utilizing power supplies with voltage of 1.0, 1.5, 2.0, or 3.0 V. For transistors that saturate at V, what is the largest possible voltage gain achievable with each of these supply voltages? If in each case biasing is adjusted so that , what gains are achieved? If a negative-going output signal swing of 0.4V is required, at what should the transistor be biased to obtain maximum gain? What is the gain achieved with each of the supply voltages? Notice that all of these gains are independent of the value of chosen!)

A BJT amplifier such as that in Fig. 6.33(a) is to be designed to support relatively undistorted sine-wave output signals of peak amplitudes P volt without the BJT entering saturation or cutoff and to have a voltage gain of V/V. Show that the minimum supply voltage needed is given by Also, find , specified to the nearest 0.5 V, for the following situations: (a) V/V, V (b) V/V, V (c) V/V, V (d) V/V, V (e) V/V, V (f) V/V, V (g) V/V, V

The transistor in the circuit of Fig. P6.76 is biased at a dc collector current of 0.4 mA. What is the voltage gain? (Hint: Use Thvenins theorem to convert the circuit to the form in Fig. 6.33a).

Sketch and label the voltage transfer characteristics of the pnp common-emitter amplifiers shown in Fig. P6.77.

In deriving the expression for small-signal voltage gain Av in Eq. (6.31) we neglected the Early effect. Derive this expression including the Early effect, by substituting in Eq. (6.24) and including the factor in Eq. (6.28). Show that the gain expression changes to For the case VCC = 5 V and VCE = 2.5 V, what is the gain without and with the Early effect taken into account? Let VA = 100 V.

When the amplifier circuit of Fig. 6.33(a) is biased with a certain VBE, the dc voltage at the collector is found to be +2 V. For VCC = +5 V and RC = 1k, find IC and the small-signal voltage gain. For a change vBE = +5 mV, calculate the resulting vO. Calculate it two ways: by finding iC using the transistor exponential characteristic, and approximately using the small-signal voltage gain. Repeat for vBE = 5 mV. Summarize your results in a table.

Consider the amplifier circuit of Fig. 6.33(a) when operated with a supply voltage VCC = +3V. (a) What is the theoretical maximum voltage gain that this amplifier can provide? (b) What value of VCE must this amplifier be biased at to provide a voltage gain of 80 V/V? (c) If the dc collector current IC at the bias point in (b) is to be 0.5 mA, what value of RC should be used? (d) What is the value of VBE required to provide the bias point mentioned above? Assume that the BJT has IS = 1015 A. (e) If a sine-wave signal vbe having a 5-mV peak amplitude is superimposed on VBE, find the corresponding output voltage signal vce that will be superimposed on VCE assuming linear operation around the bias point. (f) Characterize the signal current ic that will be superimposed on the dc bias current IC. (g) What is the value of the dc base current IB at the bias point? Assume = 100. Characterize the signal current ib that will be superimposed on the base current IB. (h) Dividing the amplitude of vbe by the amplitude of ib, evaluate the incremental (or small-signal) input resistance of the amplifier. (i) Sketch and clearly label correlated graphs for vBE, vCE, iC, and iB. Note that each graph consists of a dc or average value and a superimposed sine wave. Be careful of the phase relationships of the sine waves.

The essence of transistor operation is that a change in vBE, vBE, produces a change in iC, iC. By keeping vBE small, iC is approximately linearly related to vBE, iC = gmvBE, where gm is known as the transistor transconductance. By passing iC through RC, an output voltage signal vO is obtained. Use the expression for the small-signal voltage gain in Eq. (6.30) to derive an expression for gm. Find the value of gm for a transistor biased at IC = 1 mA.

The purpose of this problem is to illustrate the application of graphical analysis to the circuit shown in Fig. P6.82. Sketch characteristic curves for the BJT for A, 10 A, 20 A, and 40 A. Assume the lines to be horizontal (i.e., neglect the Early effect), and let . For V and k sketch the load line. What peak-to-peak collector voltage swing will result for varying over the range 10 A to 40 A? If the BJT is biased at find the value of and If at this current V and if k find the required value of .

Sketch the iCvCE characteristics of an npn transistor having = 100 and VA = 100 V. Sketch characteristic curves for iB = 20 A, 50 A, 80 A, and 100 A. For the purpose of this sketch, assume that iC = iB at vCE = 0. Also, sketch the load line obtained for VCC = 10 V and RC = 1 k. If the dc bias current into the base is 50 A, write the equation for the corresponding iCvCE curve. Also, write the equation for the load line, and solve the two equations to obtain VCE and IC. If the input signal causes a sinusoidal signal of 30-A peak amplitude to be superimposed on IB, find the corresponding signal components of iC and vCE.

Consider the operation of the circuit shown in Fig. P6.84 as vB rises slowly from zero. For this transistor, assume = 50, vBE at which the transistor conducts is 0.5 V, vBE when fully conducting is 0.7 V, saturation begins at vBC = 0.4 V, and the transistor is deeply in saturation at vBC = 0.6V. Sketch and label vE and vC versus vB. For what range of vB is iC essentially zero? What are the values of vE, iE, iC, and vC for vB = 1 V and 3 V? For what value of vB does saturation begin? What is iB at this point? For vB = 4 V and 6 V, what are the values of vE, vC, iE, iC, and iB? Augment your sketch by adding a plot of iB.

Consider a transistor biased to operate in the active mode at a dc collector current IC. Calculate the collector signal current as a fraction of IC (i.e., for input signals vbe of +1 mV, 1 mV, +2 mV, 2 mV, +5 mV, 5 mV, +8 mV, 8 mV, +10 mV, 10 mV, +12 mV, and 12 mV. In each case do the calculation two ways: (a) using the exponential characteristic, and (b) using the small-signal approximation. Present your results in the form of a table that includes a column for the error introduced by the small-signal approximation. Comment on the range of validity of the small-signal approximation.

An npn BJT with grounded emitter is operated with VBE = 0.700 V, at which the collector current is 0.5 mA. A 10-k resistor connects the collector to a +10-V supply. What is the resulting collector voltage VC? Now, if a signal applied to thebase raises vBE to 705 mV, find the resulting total collector current iC and total collector voltage vC using the exponential iCvBE relationship. For this situation, what are vbe and vc? Calculate the voltage gain Compare with the value obtained using the small-signal approximation, that is, gmRC.

A transistor with = 120 is biased to operate at a dc collector current of 0.6 mA. Find the values of gm, r , and re. Repeat for a bias current of 60 A.

A pnp BJT is biased to operate at IC = 1.0 mA. What is the associated value of gm? If = 100, what is the value of the small-signal resistance seen looking into the emitter (re)? Into the base (r )? If the collector is connected to a 5-k load, with a signal of 5-mV peak applied between base and emitter, what output signal voltage results?

A designer wishes to create a BJT amplifier with a gm of 25 mA/V and a base input resistance of 3000 or more. What emitter-bias current should he choose? What is the minimum he can tolerate for the transistor used?

A transistor operating with nominal gm of 50 mA/V has a that ranges from 50 to 150. Also, the bias circuit, being less than ideal, allows a 20% variation in IC. What are the extreme values found of the resistance looking into the base?

In the circuit of Fig. 6.36, VBE is adjusted so that VC = 1 V. If VCC = 3 V, RC = 2 k, and a signal vbe = 0.005 sin t volts is applied, find expressions for the total instantaneous quantities iC (t), vC (t), and iB (t). The transistor has = 80. What is the voltage gain?

We wish to design the amplifier circuit of Fig. 6.36 under the constraint that VCC is fixed. Let the input signal vbe = sin t, where is the maximum value for acceptable linearity. For the design that results in the largest signal at the collector, without the BJT leaving the active region, show that and find an expression for the voltage gain obtained. For VCC = 3 V and = 5 mV, find the dc voltage at the collector, the amplitude of the output voltage signal, and the voltage gain.

The table below summarizes some of the basic attributes of a number of BJTs of different types, operating as amplifiers under various conditions. Provide the missing entries. (Note: Isnt it remarkable how much two parameters can reveal?)

A BJT is biased to operate in the active mode at a dc collector current of 0.5 mA. It has a of 100. Give the four small-signal models (Figs. 6.40 and 6.41) of the BJT complete with the values of their parameters.

The transistor amplifier in Fig. P6.95 is biased with a current source I and has a very high . Find the dc voltage at the collector, VC. Also, find the value of gm. Replace the transistor with the simplified hybrid model of Fig. 6.40(a) (note that the dc current source I should be replaced with an open circuit). Hence find the voltage gain

For the conceptual circuit shown in Fig. 6.39, RC = 3k, gm = 50 mA/V, and = 100. If a peak-to-peak output voltage of 1 V is measured at the collector, what are the peak-to-peak values of vbe and ib?

Figure P6.97 shows the circuit of an amplifier fed with a signal source with a source resistance The bias circuitry is not shown. Replace the BJT with its hybrid equivalent circuit of Fig. 6.40(a). Find the input resistance , the voltage transmission from source to amplifier input, and the voltage gain from base to collector, . Use these to show that the overall voltage gain is given by

Figure P6.98 shows a transistor with the collector connected to the base. The bias arrangement is not shown. Since a zero implies operation in the active mode, the BJT can be replaced by one of the small-signal models of Figs. 6.40 and 6.41. Use the model of Fig. 6.41(b) and show that the resulting two-terminal device, known as a diode connected transistor, has a small-signal resistance r equal to

Figure P6.99 shows a particular configuration of BJT amplifiers, known as emitter follower. The bias arrangement is not shown. Replace the BJT with its T equivalentcircuit model of Fig. 6.41(b). Show that

For the circuit shown in Fig. P6.100, draw a complete small-signal equivalent circuit utilizing an appropriate T model for the BJT (use = 0.99). Your circuit should show the values of all components, including the model parameters. What is the input resistance Rin? Calculate the overall voltage gain

In the circuit shown in Fig. P6.101, the transistor has a of 200. What is the dc voltage at the collector? Find the input resistances Rib and Rin and the overall voltage gain For an output signal of 0.4 V, what values of vsig and vb are required?

Consider the augmented hybrid model shown in Fig. 6.47(a). Disregarding how biasing is to be done, what is the largest possible voltage gain available for a signal source connected directly to the base and a very-high-resistance load? Calculate the value of the maximum possible gain for VA = 25 V and VA = 250 V.

Reconsider the amplifier shown in Fig. 6.42 and analyzed in Example 6.14 under the condition that is not well controlled. For what value of does the circuit begin to saturate? We can conclude that large is dangerous in this circuit. Now, consider the effect of reduced , say, to = 25. What values of re, gm, and r result? What is the overall voltage gain? (Note: You can see that this circuit, using base-current control of bias, is very -sensitive and usually not recommended.)

Reconsider the circuit shown in Fig. 6.44(a) under the condition that the signal source has an internal resistance of 100 . What does the overall voltage gain become? What is the largest input signal voltage that can be used without output-signal clipping?

Redesign the circuit of Fig. 6.44 by raising the resistor values by a factor n to increase the resistance seen by the input vi to 75 . What value of voltage gain results? Grounded-base circuits of this kind are used in systems such as cable TV, in which, for highest-quality signaling, load resistances need to be matched to the equivalent resistances of the interconnecting cables.

Design an amplifier using the configuration of Fig. 6.44(a). The power supplies available are 5 V. The input signal source has a resistance of 50 , and it is required that the amplifier input resistance match this value. (Note that Rin = re || RE  re.) The amplifier is to have the greatest possible voltage gain and the largest possible output signal but retain small-signal linear operation (i.e., the signal component across the baseemitter junction should be limited to no more than 10 mV). Find appropriate values for RE and RC. What is the value of voltage gain realized?

The transistor in the circuit shown in Fig. P6.107 is biased to operate in the active mode. Assuming that is very large, find the collector bias current IC. Replace the transistor with the small-signal equivalent circuit model of Fig. 6.41(b) (remember to replace the dc power supply with a short circuit). Analyze the resulting amplifier equivalent circuit to show that Find the values of these voltage gains (for  1). Now, if the terminal labeled vo1 is connected to ground, what does the voltage gain become?

An amplifier with an input resistance of 100 k , an open-circuit voltage gain of 100 V/V, and an output resistance of 100 is connected between a 10-k signal source and a 1-k load. Find the overall voltage gain Also find the current gain, defined as the ratio of the load current to the current drawn from the signal source.

Specify the parameters and of an amplifier that is to be connected between a 100-k source and a 2-k load. The amplifier is required to meet the following specifications: (a) No more than 10% of the signal strength is lost in the connection to the amplifier input. (b) If the load resistance changes from the nominal value of 2 k to a low value of 1 k , the change in output voltage is limited to 10% of nominal value. (c) The nominal overall voltage gain is 10 V/V.

Figure P6.110 shows an alternative equivalent circuit representation of an amplifier. If this circuit is to be equivalent to that in Fig. 6.50(b) show that Also convince yourself that the transconductance is defined as and hence is known as the short-circuit transconductance. Now if the amplifier is fed with a signal source and is connected to a load resistance , show that the gain of the amplifier proper is given by and the overall voltage gain is given by

An alternative equivalent circuit of an amplifier fed with a signal source and connected to a load is shown in Fig. P6.111. Here is the open-circuit overall voltage gain, and is the output resistance with set to zero. This is different from Show that where . Also show that the overall voltage gain

Most practical amplifiers have internal feedback that make them nonunilateral. In such a case, depends on To illustrate this point we show in Fig. P6.112 the equivalent circuit of an amplifier in which a feedback resistance models the internal feedback mechanism that is present in this amplifier. It is that makes the amplifier nonunilateral. Show that Evaluate and for the case k M mA/V, and k Which of the amplifier characteristic parameters is most affected by (i.e., relative to the case with )? For k , determine the overall voltage gain, with and without present.

A CE amplifier utilizes a BJT with and V, biased at mA; it has a collector resistance k Assume . Find and If the amplifier is fed with a signal source having a resistance of 10 k and a load resistance k is connected to the output terminal, find the resulting and . If the peak voltage of the sine wave appearing between base and emitter is to be limited to 5 mV, what is allowed, and what output voltage signal appears across the load?

In this problem we investigate the effect of the inevitable variability of on the realized gain of the CE amplifier. For this purpose, use the overall gain expression in Eq. (6.79). Assume is sufficiently large to be negligible and thus show that where . Consider the case k and k and let the BJT be biased at mA. The BJT has a nominal of 100. (a) What is the nominal value of ? (b) If can be anywhere between 50 and 150, what is the corresponding range of ? (c) If in a particular design, it is required to maintain within % of its nominal value, what is the maximum allowable range of ? (d) If it is not possible to restrict to the range found in (c), and the designer has to contend with in the range 50 to 150, what value of bias current would result in falling in a range of % of a new nominal value? What is the nominal value of in this case?

In this problem, we investigate the effect of changing the bias current on the overall voltage gain of a CE amplifier. Consider the situation of a CE amplifier operating with a signal source having k and having k The BJT is specified to have and V. Use Eq. (6.79) to find at mA, 0.2 mA, 0.5 mA, 1.0 mA, and 1.25 mA. Observe the effect of on limiting as is increased. Find the value of that results in V/V.

Two identical CE amplifiers are connected in cascade. The first stage is fed with a source having a resistance k A load resistance k is connected to the collector of the second stage. Each BJT is biased at mA and has and a very large Each stage utilizes a collector resistance k (a) Sketch the equivalent circuit of the two-stage amplifier. (b) Calculate the voltage transmission from the signal source to the input of the first stage. (c) Calculate the voltage gain of the first stage, . (d) Calculate the voltage gain of the second stage, (e) Find the overall voltage gain,

A CE amplifier utilizes a BJT with biased at mA and has a collector resistance k and a resistance connected in the emitter. Find and If the amplifier is fed with a signal source having a resistance of 10 k , and a load resistance k is connected to the output terminal, find the resulting and If the peak voltage of the sine wave appearing between base and emitter is to be limited to 5 mV, what is allowed, and what output voltage signal appears across the load?

Design a CE amplifier with a resistance in the emitter to meet the following specifications: (i) Input resistance k (ii) When fed from a signal source with a peak amplitude of 0.1 V and a source resistance of 20 k , the peak amplitude of is 5 mV. Specify and the bias current . The BJT has If the total resistance in the collector is 5 k , find the overall voltage gain and the peak amplitude of the output signal D

Inclusion of an emitter resistance reduces the variability of the gain due to the inevitable wide variance in the value of . Consider a CE amplifier operating between a signal source with k and a total collector resistance of 10 k . The BJT is biased at mA and its is specified to be nominally 100 but can lie in the range of 50 to 150. First determine the nominal value and the range of without resistance Then select a value for that will ensure that be within % of its new nominal value. Specify the value of , the new nominal value of , and the expected range of

A CB amplifier is operating with k k and At what current should the transistor be biased for the input resistance to equal that of the signal source? What is the resulting overall voltage gain? Assume

For the circuit in Fig. P6.121, let and . Find

A CB amplifier is biased at mA with k and is driven by a signal source with k Find the overall voltage gain If the maximum signal amplitude of the voltage between base and emitter is limited to 10 mV, what are the corresponding amplitudes of and Assume

An emitter follower is required to deliver a -V peak sinusoid to a -k load. If the peak amplitude of is to be limited to 5 mV, what is the lowest value of at which the BJT can be biased? At this bias current, what are the maximum and minimum currents that the BJT will be conducting (at the positive and negative peaks of the output sine wave)? If the resistance of the signal source is 200 k what value of is obtained? Thus determine the required amplitude of .

An emitter follower with a BJT biased at mA and having is connected between a source with k and a load k (a) Find and (b) If the signal amplitude across the baseemitter junction is to be limited to 10 mV, what is the corresponding amplitude of and (c) Find the open-circuit voltage gain and the output resistance Use these values first to verify the value of obtained in (a), then to find the value of obtained with reduced to 500

An emitter follower is operating at a collector bias current of 0.25 mA and is used to connect a -k source to a 1-k load. If the nominal value of is 100, what output resistance and overall voltage gain result? Now if transistor is specified to lie in the range 50 to 150, find the corresponding range of

An emitter follower, when driven from a 10-k source, was found to have an output resistance of 200 . The output resistance increased to 300 when the source resistance was increased to 20 k . Find the overall voltage gain when the follower is driven by a 30-k source and loaded by a 1-k resistor.

For the general amplifier circuit shown in Fig. P6.127 neglect the Early effect. (a) Find expressions for and (b) If is disconnected from node X, node X is grounded, and node Y is disconnected from ground and connected to find the new expression for

For the circuit in Fig. 6.59(a), neglect the base current IB in comparison with the current in the voltage divider. It is required to bias the transistor at IC = 1 mA, which requires selecting RB1 and RB2 so that VBE = 0.690 V. If VCC = 3 V, what must the ratio be? Now, if RB1 and RB2 are 1% resistors, that is, each can be in the range of 0.99 to 1.01 of its nominal value, what is the range obtained for VBE? What is the corresponding range of IC? If RC = 2 k, what is the range obtained for VCE? Comment on the efficacy of this biasing arrangement.

It is required to bias the transistor in the circuit of Fig. 6.59(b) at IC = 1 mA. The transistor is specified to be nominally 100, but it can fall in the range of 50 to 150. For VCC = +3 V and RC = 2 k, find the required value of RB to achieve IC = 1 mA for the nominal transistor. What is the expected range for IC and VCE? Comment on the efficacy of this bias design.

Consider the single-supply bias network shown in Fig. 6.60(a). Provide a design using a 9-V supply in which the supply voltage is equally split between RC, VCE, and RE with a collector current of 0.6 mA. The transistor is specified to have a minimum value of 90. Use a voltage divider current of or slightly higher. Since a reasonable design should operate for the best transistors for which is very high, do your initial design with = . Then choose suitable 5% resistors (see Appendix H), making the choice in a way that will result in a VBB that is slightly higher than the ideal value. Specify the values you have chosen for RE, RC, R1, and R2. Now, find VB, VE, VC, and IC for your final design using

Repeat Problem 6.130, but use a voltage divider current that is Check your design at = 90. If you have the data available, find how low can be while the value of IC does not fall below that obtained with the design of Problem 6.130 for

It is required to design the bias circuit of Fig. 6.60 for a BJT whose nominal = 100. (a) Find the largest ratio that will guarantee IE remain within 10% of its nominal value for as low as 50 and as high as 150.(b) If the resistance ratio found in (a) is used, find an expression for the voltage that will result in a voltage drop of across RE. (c) For VCC = 5 V, find the required values of R1, R2, and RE to obtain IE = 0.5 mA and to satisfy the requirement for stability of IE in (a). (d) Find RC so that VCE = 1.5 V for equal to its nominal value. Check your design by evaluating the resulting range of IE.

Consider the two-supply bias arrangement shown in Fig. 6.61 using 3-V supplies. It is required to design the circuit so that IC = 0.6 mA and VC is placed midway between VCC and VE. (a) For = , what values of RE and RC are required? (b) If the BJT is specified to have a minimum of 90, find the largest value for RB consistent with the need to limit the voltage drop across it to one-tenth the voltage drop across RE. (c) What standard 5% resistor values (see Appendix H) would you use for RB, RE, and RC? In making your selection, use somewhat lower values in order to compensate for the low effects. (d) For the values you selected in (c), find IC, VB, VE, and VC for

Utilizing 3-V power supplies, it is required to design a version of the circuit in Fig. 6.61 in which the signal will be coupled to the emitter and thus RB can be set to zero. Find values for RE and RC so that a dc emitter current of 0.5 mA is obtained and so that the gain is maximized while allowing 1 V of signal swing at the collector. If temperature increases from the nominal value of 25C to 125C, estimate the percentage change in collector bias current. In addition to the 2 mV/C change in VBE, assume that the transistor changes over this temperature range from 50 to 150.

Using a 3-V power supply, design a version of the circuit of Fig. 6.62 to provide a dc emitter current of 0.5 mA and to allow a 1-V signal swing at the collector. The BJT has a nominal = 100. Use standard 5% resistor values (see Appendix H). If the actual BJT used has = 50, what emitter current is obtained? Also, what is the allowable signal swing at the collector? Repeat for

(a) Using a 3-V power supply, design the feedback bias circuit of Fig. 6.62 to provide IC = 3 mA and for = 90. (b) Select standard 5% resistor values, and reevaluate VC and IC for = 90. (c) Find VC and IC for = . (d) To improve the situation that obtains when high transistors are used, we have to arrange for an additional current to flow through RB. This can be achieved by connecting a resistor between base and emitter, as shown in Fig. P6.136. Design this circuit for = 90. Use a current through RB2 equal to the base current. Now, what values of VC and IC result with = ?

A circuit that can provide a very large voltage gain for a high-resistance load is shown in Fig. P6.137. Find the values of I and RB to bias the BJT at IC = 1 mA and VC = 1.5 V. Let

The circuit in Fig. P6.138 provides a constant current IO as long as the circuit to which the collector is connected maintains the BJT in the active mode. Show that

The current-source biasing circuit shown in Fig. P6.139 provides a bias current to that is determined by the current source formed by , and The bias current is independent of and nearly independent of (as long as both and operate in the active mode). It is required to design the circuit using -V dc supplies to establish mA and V, in the ideal situation of infinite and In designing the current source, use 2-V dc voltage drop across and impose the requirement that remain within 5% of its ideal value for as low as 50. In selecting a value for ensure that for the lowest value of is 2.5 V. Use standard 5% resistor values (see Appendix H). What values for , and do you choose? What values of and result for 100, and 200

For the circuit in Fig. P6.140, assuming all transistors to be identical with infinite, derive an expression for the output current IO, and show that by selecting and keeping the current in each junction the same, the current IO will be which is independent of VBE. What must the relationship of RE to R1 and R2 be? For VCC = 10 V and VBE = 0.7 V, design the circuit to obtain an output current of 0.5 mA. What is the lowest voltage that can be applied to the collector of Q3?

For the circuit in Fig. P6.141 find the value of R that will result in IO  1 mA. What is the largest voltage that can be applied to the collector? Assume = 0.7 V.

For the common-emitter amplifier shown in Fig.P6.142, let VCC = 15 V, R1 = 27 k, R2 = 15 k, RE = 2.4k, and RC = 3.9 k. The transistor has = 100. Calculate the dc bias current IC. If the amplifier operates between a source for which Rsig = 2 k and a load of 2 k, replace the transistor with its hybrid model, and find the values of Rin, and the overall voltage gain

Using the topology of Fig. P6.142, design an amplifier to operate between a 2-k source and a 2-k load with a gain of 40 V/V. The power supply available is 15 V. Use an emitter current of approximately 2 mA and a current of about one-tenth of that in the voltage divider that feeds the base, with the dc voltage at the base about onethird of the supply. The transistor available has = 100. Use standard 5% resistor (see Appendix H).

A designer, having examined the situation described in Problem 6.142 and estimating the available gain to be approximately 36.6 V/V, wants to explore the possibility of improvement by reducing the loading of the source by the amplifier input. As an experiment, the designer varies the resistance levels by a factor of approximately 3: R1 to 82 k, R2 to 47 k, RE to 7.2 k, and RC to 12 k (standard values of 5%-tolerance resistors). With VCC = 15 V, Rsig =2 k, RL = 2 k, and = 100, what does the gain become? Comment.

Consider the CE amplifier circuit of Fig. 6.65(a). It is required to design the circuit (i.e., find values for I, RB, and RC) to meet the following specifications: (a) Rin  5 k.(b) The dc voltage drop across RB is approximately 0.2 V. (c) The open-circuit voltage gain from base to collector is the maximum possible, consistent with the requirement that the collector voltage never falls by more than approximately 0.4 V below the base voltage with the signal between base and emitter being as high as 5 mV. Assume that vsig is a sinusoidal source, the available supply VCC = 3 V, and the transistor has = 100. Use standard 5% resistance values, and specify the value of I to one significant digit. What base-to-collector open-circuit voltage gain does your design provide? If Rsig = RL = 10 k, what is the overall voltage gain?

In the circuit of Fig. P6.146, vsig is a small sinewave signal with zero average. The transistor is 100. (a) Find the value of RE to establish a dc emitter current of about 0.5 mA. (b) Find RC to establish a dc collector voltage of about +1 V. (c) For RL = 10 k, draw the small-signal equivalent circuit of the amplifier and determine its overall voltage gain.

The amplifier of Fig. P6.147 consists of two identical common-emitter amplifiers connected in cascade. Observe that the input resistance of the second stage, Rin2, constitutes the load resistance of the first stage. (a) For VCC = 9 V, R1 = 100 k, R2 = 47 k, RE = 3.9 k, RC = 6.8 k, and = 100, determine the dc collector current and dc collector voltage of each transistor. (b) Draw the small-signal equivalent circuit of the entire amplifier and give the values of all its components. (c) Find Rin1 and for Rsig = 5 k. (d) Find Rin2 and (e) For RL = 2 k, find (f) Find the overall voltage gain

In the circuit of Fig. P6.148, vsig is a small sinewave signal. Find Rin and the gain Assume = 100. If the amplitude of the signal vbe is to be limited to 5 mV, what is the largest signal at the input? What is the corresponding signal at the output?

The BJT in the circuit of Fig. P6.149 has = 100. (a) Find the dc collector current and the dc voltage at the collector. (b) Replacing the transistor by its T model, draw the smallsignal equivalent circuit of the amplifier. Analyze the resulting circuit to determine the voltage gain

Consider the CB amplifier of Fig. 6.67(a) with the collector voltage signal coupled to a 1-k load resistance through a large capacitor. Let the power supplies be 3 V. The source has a resistance of 50 . Design the circuit so that the amplifier input resistance is matched to that of the source and the output signal swing is as large as possible with relatively low distortion (vbe limited to 10 mV). Find I and RC and calculate the overall voltage gain obtained and the output signal swing. Assume

For the circuit in Fig. P6.151, find the input resistance Rin and the voltage gain Assume that the source provides a small signal vsig and that

For the emitter-follower circuit shown in Fig. P6.152, the BJT used is specified to have values in the range of 50 to 200 (a distressing situation for the circuit designer). For the two extreme values of ( = 50 and = 200), find: (a) IE, VE, and VB. (b) the input resistance Rin. (c) the voltage gain

For the emitter follower in Fig. P6.153, the signal source is directly coupled to the transistor base. If the dc component of vsig is zero, find the dc emitter current. Assume = 100. Neglecting ro, find Rin, the voltage gain the current gain and the output resistance

For the circuit in Fig. P6.154, called a bootstrapped follower: (a) Find the dc emitter current and gm, re, and r . Use = 100. (b) Replace the BJT with its T model (neglecting ro), and analyze the circuit to determine the input resistance Rin and the voltage gain (c) Repeat (b) for the case when capacitor CB is open-circuited. Compare the results with those obtained in (b) to find the advantages of bootstrapping.

For the follower circuit in Fig. P6.155, let transistor Q1 have = 50 and transistor Q2 have = 100, and neglect the effect of ro. Use VBE = 0.7 V. (a) Find the dc emitter currents of Q1 and Q2. Also, find the dc voltages VB1 and VB2. (b) If a load resistance RL = 1 k is connected to the output terminal, find the voltage gain from the base to the emitter of Q2, and find the input resistance Rib2 looking into the base of Q2. (Hint: Consider Q2 as an emitter follower fed by a voltage vb2 at its base.) (c) Replacing Q2 with its input resistance Rib2 found in (b), analyze the circuit of emitter follower Q1 to determine its input resistance Rin, and the gain from its base to its emitter,(d) If the circuit is fed with a source having a 100-k resistance, find the transmission to the base of Q1, (e) Find the overall voltage gain

A CE amplifier has a midband voltage gain of V/V, a lower 3-dB frequency of Hz, and a higher 3-dB frequency MHz. In Chapter 9 we will learn that connecting a resistance in the emitter of the BJT results in lowering and raising by the factor If the BJT is biased at mA, find that will result in at least equal to 5 MHz. What will the new values of and be?