Integrated Circuit Design with the BJT

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Integrated CircuitDesign with the BJT

10.1 Integrated CircuitBiasing with CurrentMirrors

10.2 High-Gain Stages UsingActive Loads

10.3 Amplifier ConfigurationsIn BJT IntegratedCircuits

As mentioned in Chapter 8, design of electronic circuits on a chip can be considerablydifferent from discrete circuit design. Some analog circuits do not require high componentdensities, whereas others may pack a great deal of circuitry into a small chip space. Forlow-density circuits, more resistors and small capacitors may be used, but for high-densitycircuits, these elements must be minimized.

This chapter will consider circuits that replace resistors and capacitors with additionalBJTs, just as Chapter 9 considered replacing these elements with additional MOSFETs.The organization of this chapter is similar to that of Chapter 9. The BJT current mirror,which is quite popular in biasing of IC amplifiers, will be discussed first. The chapterwill then proceed to active load amplifier stages and other single-stage amplifier config-urations in order to lay a foundation for the important op amp chip to be discussed inChapter 11.

D E M O N S T R A T I O N P R O B L E M

A typical problem that uses the principles appearing in this chapter is shown in the amplifiercircuit. For all devices β = 80, |VBE(on)| = 0.7 V, and |VA| = 62 V (Early voltage). Assume thatCµ = 2 pF, Cπ = 20 pF, and Ccs = 2 pF for all devices. The dc voltage at the output is 4 V.Calculate the overall midband voltage gain and upper corner frequency of the amplifier.

vout

vin

V1

Q1

Q2

Q3Q4

8 V

10 kΩ

1 kΩ

Rg

12 kΩ

BJT amplifier for DemonstrationProblem.

307



308 C H A P T E R 1 0 I N T E G R A T E D C I R C U I T D E S I G N W I T H T H E B J T

In order to solve this problem, the following questions must be answered.

1. What determines the output current of a current mirror?

2. What determines the voltage gain when the load consists of the output stage of a currentmirror?

3. What determines the upper corner frequencies of a common-emitter stage and an emitterfollower?

These questions will be answered in general terms throughout this chapter.

10.1 Integrated Circuit Biasingwith Current Mirrors

I M P O R T A N T Concepts

1. The simple current mirror is often used on integrated circuit chips to provide biascurrent for amplifier stages.

2. The output impedance of current mirrors can be increased by certainmodifications. A higher output impedance leads to a better approximation of atrue current source.

The popular emitter-bias scheme of Fig. 7.16 for discrete BJT stages often uses a largeemitter bypass capacitor to achieve high ac gain. Discrete amplifier stages may also userelatively large interstage coupling capacitors. The unavailability of large capacitors andinductors in IC designs requires that special techniques be used to establish bias currents forintegrated amplifiers. Differential stages and complex feedback circuits are often used toobtain the correct bias in the IC amplifier. Although differential amplifiers will be discussedin the next chapter, a significant bias scheme used in differential BJT and other IC amplifierstages will be considered in the following paragraphs.

Io

Q1 Q2

VCC

RIin

Figure 10.1Current mirror bias stage.

10.1.1 THE SIMPLE CURRENT MIRRORThe simple current mirror of Fig. 10.1 represents a popular method of creating a constantcurrent bias for differential stages. The concept of the current mirror was developed specif-ically for analog integrated circuit biasing and is a good example of a circuit that takesadvantage of the excellent matching characteristics that are possible in integrated circuits.In the circuit of Fig. 10.1, the current Io is intended to be equal to Iin. Although not shownin the figure, the external circuit through which Io flows connects to the collector of Q2.

In Chapter 9 we discussed the specific operation of the MOSFET current mirror. Thefollowing material will expand on the use of current mirrors and apply this material tothe BJT version of this circuit. It is useful to discuss the more generalized concept of acurrent mirror and to introduce some appropriate terminology. Figure 10.2 illustrates ablock diagram representation of a current mirror where the input or reference current andoutput currents are shown. Current mirrors can be designed to serve as sinks or sources, asindicated in the figure.

The general function of the current mirror is to reproduce or mirror the input or referencecurrent to the output while allowing the output voltage to assume any value within somespecified range. The current mirror can also be designed to generate an output current that



S E C T I O N 1 0 . 1 I N T E G R A T E D C I R C U I T B I A S I N G W I T H C U R R E N T M I R R O R S 309

IoIin

Sink Source

(a)

—V

+V

In Out

In Out

IoIin

(b)

Figure 10.2Block diagrams of currentmirrors: (a) current sink,(b) current source.

equals the input current multiplied by a scale factor K . The output current can be expressedas a function of input current as

Io = K Iin (10.1)

where K can be equal to, less than, or greater than unity. This constant can be establishedaccurately and will not vary with temperature.

IC

A

I

BB

R

A

(b)(a)

VB

VE

Q1

Figure 10.3Current sink circuits:(a) ideal sink, (b) practical sink.

Current Source Operating Voltage Range Figure 10.3(a) shows an ideal ortheoretical current sink with a practical sink indicated in Fig. 10.3(b). The voltage at node Ain the theoretical sink can be tied to any voltage above or below ground without affecting thevalue of I . On the other hand, the practical circuit of Fig. 10.3(b) requires that the transistorremain in the active region to provide an output current of

I = IC = α IE = αVE

R= α

VB − VBE

R(10.2)

The collector voltage must exceed the voltage VB at all times for active region operation.The upper limit on collector voltage is determined by the breakdown voltage of the transistor.The output voltage must then satisfy

VB < VC < (VE + BVCE) = (VB − 0.7 + BVCE) (10.3)

where BVCE is the breakdown voltage from collector to emitter of the transistor. The voltagerange over which the current source operates within a prescribed accuracy is called the outputvoltage compliance range or the output compliance.

Current Mirror Analysis The current mirror is again shown in Fig. 10.4. If devicesQ1 and Q2 are assumed to be matched devices, we can write

IE1 = IE2 = IEOeVBE /VT (10.4)

VBE

Q1 Q2

VC2

IC1

IC2 = Io

Iin

IB2IB1

Figure 10.4Circuit for current mirroranalysis.




where VT = kT/q, IEO = AJEO, A is the emitter area of the two devices, and JEO is thecurrent density of the emitters. The base currents of the two devices will also be identicaland can be expressed as

IB1 = IB2 = IEO

β + 1eVBE /VT (10.5)

Device Q1 operates in the active region, but near saturation by virtue of the collector-base connection. This configuration is called a diode-connected transistor. The collectorcurrent of Q1 is β times the base current or

IC1 = β IB1 = β

β + 1IEOeVBE /VT (10.6)

Whereas device Q1 is constrained so that VCE = VB E(on) by the connection between baseand collector, device Q2 does not have this constraint. The collector voltage for Q2 will bedetermined by the external circuit that connects to this collector.

If we limit the voltage VC2 to small values relative to the Early voltage, IC2 is approxi-mately equal to IC1. For integrated circuit designs, the voltage required at the output of thecurrent mirror is generally small, often making this approximation valid.

The input current to the mirror is slightly larger than the collector current and is expressedas

Iin = IC1 + 2IB (10.7)

Since Io = IC2 = IC1 = β IB , we can write Eq. (10.7) as

Iin = β IB + 2IB = (β + 2)IB (10.8)

Relating Iin to Io results in

Io = β

β + 2Iin (10.9)

For typical values of β these two currents are essentially equal. Thus, a desired bias current,Io, is generated by creating the desired value for Iin.

The current Iin is normally established by connecting a resistance, R1, between a voltagesource VCC and the collector of Q1 to set Iin to

Iin = VCC − VBE

R1(10.10)

Control of collector current for Q2 is then accomplished by choosing proper values of VCC

and R1.If VC2 becomes larger, the Early effect of Eq. (7.11) must be considered. This equation is

IC = β IB

(1 + VCE

VA

)(10.11)



S E C T I O N 1 0 . 1 I N T E G R A T E D C I R C U I T B I A S I N G W I T H C U R R E N T M I R R O R S 311

Q1 Q N + 1

IoNIin

Q3

Io2

Q2

Io1

Figure 10.5Multiple output current mirror.

A more accurate expression for the output current is

IC2 = β(1 + VC2

VA

)2 + β

(1 + VC1

VA

) Iin (10.12)

where VA is the Early voltage. This equation can be used to find the voltage compliancerange of the current mirror.

Figure 10.5 shows a multiple output current mirror. It can be shown that the outputcurrent for each identical device in Fig. 10.5 is

Io = β

β + N + 1Iin (10.13)

where N is the number of output devices.The preceding analysis of the current mirror has assumed equal transistor sizes. The

output currents can be scaled by changing the relative areas of the output BJTs comparedto the diode-connected BJT. The ratio of output current to input current scales directly withthe ratio of emitter-base junction area of the output device to that of the input device.

The current sinks can be turned into current sources by using pnp transistors and a powersupply of opposite polarity. The output devices can also be scaled in area to make Io largeror smaller than Iin. The schematic of Fig. 10.6 indicates a multiple output current mirror

Q8Q7Q6Q5

Q4Q3Q2Q1

Iin

Io5

Io3

Io4

Io2

—VEE

R1

+VCC Figure 10.6Multiple output sources andsinks.




Q1 Q N + 1

+VCC

IoN

Iin

IC1

Q3

Q0

Io2

Q2

Io1

NIB1

(N +1) IB1

IB1

+ 1

Figure 10.7Improved multiple outputcurrent mirror.

that includes both sources and sinks. Although parallel transistors are shown to indicatehigher current output devices, single devices with larger areas would be implemented onthe chip.

10.1.2 A CURRENT MIRROR WITH REDUCED ERRORThe difference between output current in a multiple output current mirror and the inputcurrent can become quite large if N is large. One simple method of avoiding this problemis to use an emitter follower to drive the bases of all devices in the mirror, as shown inFig. 10.7. The emitter follower, Q0, has a current gain from base to collector of β + 1,which reduces the difference between Io and Iin to

Iin − Io = N + 1

β + 1IB (10.14)

The output current for each device is

Io = Iin

1 + N+1β(β+1)

(10.15)

10.1.3 THE WILSON CURRENT MIRRORIn the simple current mirrors discussed, it was assumed that the collector voltage of theoutput stage was small compared to the Early voltage. When this is untrue, the outputcurrent will not remain constant, but will increase as output voltage (VCE) increases. In otherwords, the output compliance range is limited with these circuits. This limitation occursbecause the output impedance of Q2 in Fig. 10.4 is relatively low, falling in the tens of k

range.

P R A C T I C E Problems

10.1 In the current mirror ofFig. 10.1, VCC = 10 V, β =120, VA = 60 V, and IE1 =IE2 = 10−12 eVBE/0.026 mAfor the matched pair. SelectR to create an output currentof 0.9 mA at VC2 = 6 V.Calculate VBE to three-placeaccuracy. Ans: R =11.03k ,VBE = 0.713 V.10.2 Both transistors of asimple current mirror havevalues of β = 120,VB E(on) = 0.68 V, andVA = 62 V. If the outputcurrent is to be within 5% ofthe input current, what is theoutput voltage compliance?Ans: VC2 max = 4.92 V.10.3 If the mirror ofPractice Problem 10.2 is tohave a maximum outputvoltage of 10 V, what mustthe tolerance on outputcurrent be, compared toinput current? Ans: 13%.

An improved current mirror was proposed by Wilson and is illustrated in Fig. 10.8.Q1 Q2

IO

Iin

IC1

Q0

Figure 10.8Wilson current mirror.

The Wilson current mirror is connected such that VCB2 = 0 and VBE1 = VBE2. Thedevice Q1 has a collector-emitter voltage of VCE1 = VBE1 + VBE0, and Q2 has a value ofVCE2 = VBE1. Both Q1 and Q2 now operate with a near-zero collector-emitter bias, eventhough the collector of Q0 might feed into a high voltage point. It can be shown that theoutput impedance of the Wilson mirror is increased by a factor of approximately β/2 overthe simple mirror. This higher impedance translates into a higher output compliance range.



S E C T I O N 1 0 . 2 H I G H - G A I N S T A G E S U S I N G A C T I V E L O A D S 313This circuit also reduces the difference between input and output current as a result of theemitter-follower stage.

P R A C T I C A L Considerations

The following chapter introduces the significant IC op amp. The op amp is a veryhigh gain amplifier that requires several amplifying stages. Each amplifying stagerequires a bias current. This chip then requires multiple bias current sources. Inpractice, these sources can be implemented by a current mirror with multiple outputstages having properly scaled emitter areas. A single resistor along with multiplemirror stages require far less chip real estate than would the use of separate biascircuits for each amplifying element.

10.2 High-Gain Stages UsingActive Loads


1. An active load may consist of the collector-to-emitter circuit of a transistor biasedinto its active region. This device replaces the passive resistor often used in thecollector of a gain stage.

2. The incremental output resistance, looking into the collector terminal of thepassive stage, can be large, leading to a high voltage gain. The dc voltage dropacross the active load is quite low.

3. The active load often takes the form of a current source.

In order to achieve high voltage gains and eliminate load resistors, active loads are usedin BJT IC amplifiers just as they are in MOSFET stages. In a conventional common-emitterstage, the gain is limited by the size of the collector resistance. The midband voltage gainof a common-emitter stage is given by

AMB = − αRC

(re + RE )

It would be possible to increase this voltage gain by increasing RC ; however, makingRC large can lead to some serious problems. A large collector load requires a low quiescentcollector current to result in proper bias. This situation may lead to lower values of β, sincecurrent gain in a silicon transistor typically falls at low levels of emitter current. In orderto achieve a voltage gain of 1000 V/V, a collector load of perhaps 100–200 k might berequired. The low collector current needed for proper bias, perhaps a few microamps, wouldlead to a low value of β and a very high value of re. The desired high voltage gain may notbe achievable under these conditions.

A solution to this problem would result if the collector load presented a low resistanceto dc signals but presented a high incremental resistance. This combination of impedancescan result in a stable operating point along with a high gain. An ideal element to use for




the collector load of a transistor is another transistor. This device present a low dc and highincremental impedance, and it is a simple element to implement on a chip.

10.2.1 A CURRENT SOURCE LOADThe circuit of Fig. 10.9 demonstrates one type of BJT active load. The transistor Q1 is theamplifying element with Q2 acting as the load. Transistor Q1 looks into the collector ofQ2. The incremental output impedance at the collector of a transistor having an emitterresistance in the low k range can easily exceed 500 k. With such a high impedance, thistransistor approximates a current source.

vin

V1

Q1

Q2

vout

+VCC

IB2

RE2

Rg

Figure 10.9A transistor stage with an activeload.

The dc collector currents of both transistors are equal in magnitude. This magnitudecan be set to a value that leads to a reasonable value of β. Since Q2 has a very high outputimpedance, the midband voltage gain will be determined primarily by the collector-to-emitter resistance of Q1 and can be calculated from

AMB = −β1rce1

Rg + rπ1(10.16)

where rce1 is the output impedance of Q1. If the generator resistance, Rg is negligible, thisequation reduces to

AMB = −rce1

re1= − (VA + VCQ1)/IC

VT /IE≈ − VA + VCQ1

VT(10.17)

For an Early voltage of VA = 80 V and VT = 0.026 V, a small-signal voltage gainexceeding −3000 V/V could result. In a normal application, this stage would drive a secondstage. The input impedance of the second stage will load the output impedance of thefirst stage, further lowering the gain. Depending on the input impedance of the secondstage and the impedance of the active load stage, the gain magnitude may still exceed1000 V/V.

The concept of an active load that presents a large incremental resistance while allowinga large dc quiescent current is important in integrated circuit design. It can be extended toFET amplifiers or hybrid bi-FET amplifiers with an FET amplifying stage and an activeBJT load.

In addition to the current source load just considered, the current mirror stage can alsobe used to provide the active load of a differential stage. This topic is discussed in the nextsubsection.

E X A M P L E 10.1

Assume that the active load in the circuit of Fig. 10.10 has an infinite output impedance,VCQ1 = 4 V, and VEB2 = 0.7 V. The Early voltage of the amplifying device is 68 V andβ = 150. Calculate the midband voltage gain of this stage.

SOLUTION In order to apply Eq. (10.16), the output impedance and rπ for Q1 must befound. The quiescent emitter current of Q2 is determined by the base-emitter circuit of Q2.The emitter voltage of Q2 is 0.7 V higher than the base voltage or 8.7 V. The emitter current



S E C T I O N 1 0 . 2 H I G H - G A I N S T A G E S U S I N G A C T I V E L O A D S 315

vin

V1

Q1

Q2

600 Ω

+12 V

+8 V

2 kΩ

RL100 kΩ

vout

Figure 10.10An active load amplifier.

is then

IE2 = 12 − 8.7

2= 1.65 mA

The emitter current of Q1 will be very near to that of Q2. Since IC1 ≈ IE1, the outputimpedance can be found from Eq. (7.13) to be

rout1 = rce1 = VA + VCQ1

IC1= 68 + 4

1.65= 43.6 k

The value of rπ1 is

rπ1 = (β + 1)re = 151 × 26

1.65= 2.38 k

The load impedance consists of rce1 in parallel with 100 k or Rout = 30.4 k. The voltagegain is

AMB = −β Rout

Rg + rπ1= −150 × 30.4

0.6 + 2.38= − 1530 V/V


Another component that can be used to create a collector load with high incrementalor ac impedance and low dc impedance is a transformer. This element generally hasonly a few ohms of dc primary resistance while presenting an ac primary resistanceof n2 RL , where n is the turns ratio from primary to secondary and RL is the resistiveload connected across the secondary terminals.

For example, if n = 5 and RL = 8 , the ac primary resistance is 25 × 8 = 200 .The dc resistance of the primary may be 3 ; thus, the ac resistance is much greaterthan the dc resistance.

Although transformers are used in high-power amplifiers, they cannot be fabri-cated by standard IC processes. Thus the active load developed by a biased tran-sistor remains the most popular load device for IC processes.

P R A C T I C E Problems

10.4 Assume that the activeload in the circuit ofFig. 10.10 is replaced by asimple current mirror withan output current of1.65 mA. The output stageof the current mirror has anEarly voltage of VA = 60 V.Calculate the midbandvoltage gain of the amplifier.Approximate rce2 as VA/IC .Ans: −833 V/V.10.5 Repeat PracticeProblem 10.4 if the 100-k

load is removed from thecircuit. Ans: −999 V/V.




10.3 Amplifier Configurations In BJTIntegrated Circuits


1. A simple pnp current mirror (source) can act as the active load for an npncommon-emitter stage. The load resistance equals the parallel combination ofoutput resistances of the mirror stage and the gain stage.

2. An npn current mirror stage (sink) can also act as a load for an npn emitterfollower stage.

3. The cascode stage minimizes Miller effect capacitance at the input terminal,thereby improving frequency response.

The current mirror serves as an active load for several important BJT IC amplifier stagesto be considered in the following paragraphs.

10.3.1 THE CURRENT MIRROR LOADA rather simple configuration for an amplifying stage is shown in Fig. 10.11. In this stage,the output impedance of the current mirror is not large enough to be negligible as it was inthe circuit of Fig. 10.9. Thus, the analysis will have to account for this element.

vin

V1

Q1R1

Q2Q3

10 kΩ

+10 V

vout

Figure 10.11A common-emitter stage withcurrent mirror active load.

In Chapter 7, the high-frequency response of a discrete circuit was considered. Typically,this value was determined by the input circuit, including the Miller effect capacitance. Thecollector load resistance in a discrete stage is usually small enough that the output circuitdoes not affect the upper corner frequency. In the circuit of Fig. 10.11, as in most IC amplifierstages, the output impedance is very high compared to the discrete stage. For this circuit,the output impedance of the amplifier consists of the output impedance of Q2 in parallelwith that of Q1. This value will generally be several tens of k.

The equivalent circuit of the amplifier of Fig. 10.11 is indicated in Fig. 10.12. The valueof Rout is

Rout = ro1 ‖ ro2 = rce1 ‖ rce2 (10.18)

The capacitance in parallel with Rout is approximately

Cout = Cµ1 + Cµ2 + Ccs1 + Ccs2 (10.19)

In this equation, Cµ1 and Cµ2 are the collector-to-base junction capacitances, and Ccs1

and Ccs2 are the collector-to-substrate capacitances of the respective transistors. If no gen-erator resistance is present, Cµ1 will also appear in parallel with the output terminal andground. When Rg is present, we will still approximate the output capacitance with the same

vin

rx1

e

vout

Coutr1

v1

c1

gm1v1

cb’b

RoutC1

Figure 10.12Equivalent circuit of theamplifier in Fig. 10.11.



S E C T I O N 1 0 . 3 A M P L I F I E R C O N F I G U R A T I O N S I N B J T I N T E G R A T E D C I R C U I T S 317equation, although feedback effects between the output and the bases of Q1 and Q2 actuallymodify the value slightly.

The midband gain is easy to evaluate as

AMB = −β1 Rout

rx1 + rπ1(10.20)

The upper corner frequency is now more difficult to evaluate than that of the discretecircuit, which often has a low value of collector load resistance. In the discrete circuit, theinput loop generally determines the overall upper corner frequency of the circuit. Althoughthe Miller effect will be much larger in the IC stage, lowering the upper corner frequencyof the input loop, the corner frequency of the output loop will also be smaller due to thelarge value of Rout. Both frequencies may influence the overall upper corner frequency ofthe amplifier.

The calculation of upper corner frequency begins by reflecting the bridging capacitance,Cµ, to both the input and the output. The value reflected to the input side, across terminalsb′ and e, is

(1 − Ab′c1)Cµ1 (10.21)

as in the discrete circuit amplifier. Thus, the total input capacitance in parallel with rπ1 is

Cin = Cπ1 + (1 − Ab′c1)Cµ1 (10.22)

The upper corner frequency resulting from the input circuit of this stage is

fin−high = 1

2πCin Req(10.23)

where Req = rx1 ‖ rπ1.The upper corner frequency resulting from the output side of the stage is

fout−high = 1

2πCout Rout(10.24)

The actual overall upper corner frequency, f2o, must be found using the method ofChapter 3 for a two-pole response. An example will demonstrate these points.

E X A M P L E 10.2

Assume that the circuit of Fig. 10.11 is biased so that the collector currents of Q1 and Q2have a magnitude of 1.14 mA. The parameters for Q1 are β = 160, rx1 = 10 , rce1 =68 k, Cπ1 = 20 pF, and Cµ1 = 2.1 pF. For device Q2, the necessary parameters arerce2 = 21 k and Cµ2 = 3.1 pF. Each device has a value of Ccs1 = Ccs2 = 2.5 pF. In thiscircuit, the power supply is 10 V and R1 = 10 k.

Calculate the midband voltage gain and the upper corner frequency for this amplifierstage. Do a Spice simulation using 2N3904 (npn) and 2N3905 (pnp) transistors.




0.668 V

V2

V1

Q1

vout

vin = 0.005 sin t

R1

Q2Q3

10 kΩ

10 V V3

3

5

4

2

1

Figure 10.13Schematic for Windows Spicesimulation.

SOLUTION The midband voltage gain can be calculated from Eq. (10.20) after evaluatingrπ1 and Rout. These resistances are

rπ1 = (β + 1)re1 = 161 × 26

1.14= 3672

and

Rout = rce1 ‖ rce2 = 68 ‖ 21 = 16 k

The midband gain is then

AMB = − β Rout

rx1 + rπ1= −160 × 16,000

10 + 3672= −695 V/V

The upper corner frequency is found from a consideration of the two poles caused bythe input circuit and the output circuit. The corner frequency of the input circuit is

fin−high = 1

2πCin Req= 1

2π (Cπ1 + [1 − Ab′c]Cµ1)(rx1 ‖ rπ1)

= 1

2π × 1481 × 10−12 × 10= 10.7 MHz

Since rπ1 rx1, the value of 10 was used for Req. In addition, the midband gain was usedto approximate Ab′c.

The corner frequency of the output circuit is

fout−high = 1

2πCout Rout= 1

2π × (2.1 + 3.1 + 2.5 + 2.5) × 10−12 × 16,000= 975 kHz

Table 10.1 SpiceNetlist File for Example10.2

EX10-2.CIR

R1 0 4 10K

V1 1 0 0.668V

V2 2 1 AC 0.005V

V3 5 0 10V

Q1 3 20 0 Q2N3904

Q2 3 4 5 5 Q2N3905

Q3 4 4 5 5 Q2N3905

.AC DEC 100 100 1G

.OP

.PROBE

.LIB BIPOLAR.LIB

.END

The input corner frequency is much higher than the output corner frequency; conse-quently, the latter value approximates the overall corner frequency. The result is a value off2o = 975 kHz.

The schematic for a Windows Spice simulation is shown in Fig. 10.13 with node andelement numbers added. The Spice netlist file used to simulate this circuit is shown inTable 10.1.

Note that the connections for the BJT correspond to collector node, base node, emitternode, and substrate node. Normally, the substrate for a pnp device connects to the positive



S E C T I O N 1 0 . 3 A M P L I F I E R C O N F I G U R A T I O N S I N B J T I N T E G R A T E D C I R C U I T S 319power supply voltage. The substrate for the npn device connects to the most negative powersupply rail, which is often the ground terminal.

The results of the simulation are AMBsim = −685 V/V and f2o−sim = 900 kHz. Thecalculated and simulated values of midband voltage gain agree within 2%, and the uppercorner frequency values are within 10%.

Table 10.2 Summary of Results for the Common-Emitter Current-SourceLoad Stage

CL, pF Rg, kΩ AMB cal, V/V AMB sim, V/V f2o−cal, kHz f2o−sim, kHz

0 0 −696 −685 975 90010 0 −696 −685 480 493

0 10 −187 −186 40 3910 10 −187 −186 39 38

In order to evaluate the effects of a signal generator resistance and a larger capacitiveload, a 10-k resistance was inserted in the base lead of Q1, which led to a simulatedmidband gain of −186 V/V and an upper corner frequency of 39 kHz. If a 10-pF capacitoris placed across the output and no generator resistance is used, the voltage gain returnsto the value of −685 V/V, but the upper corner frequency is lowered to 480 kHz. Addingthe generator resistance while the capacitor loads the output gives AMB = −186 V/V andf2o = 37.8 kHz. The comparison of calculated and simulated values for the different loadingconditions is given in Table 10.2.

The calculated results are designated AM Bcal and f2o−cal, and the simulated values aredesignated AMBsim and f2o−sim. The task of calculating values for Table 10.2 is left to thestudent. Note that adding a 10-k generator resistance lowers the upper corner frequency bya large factor, approximately 25, whereas adding 10 pF to the output lowers this frequencyby a factor of about two.


For a BJT with a high value of current gain-bandwidth product, ft , the current sourceload stage has a relatively low upper corner frequency. In Example 10.2, the value offt for these BJTs is 300–400 MHz. The resulting upper corner frequency is just 975kHz. It should be recognized that this type of stage is used in op amp chips that willultimately have a very low upper corner frequency. When used in an amplifier, the opamp chip will use feedback to improve the overall upper corner frequency. Thus, thelow value of f2o for an individual gain stage is not significant in these applications.

P R A C T I C E Problem

10.6 Calculate the value ofRg that lowers the uppercorner frequency of thecircuit in Example 10.2 to100 kHz. Assume a 10-pFload capacitance. Calculatethe midband voltage gain.Ans: Rg = 1.43 k,AMB = −501 V/V.

Q2Q3

vout

vin

Q1

R14 kΩ

5 V

V1

1

Figure 10.14An emitter follower.

10.3.2 THE EMITTER FOLLOWERA stage that can be used to minimize the adverse effect on frequency response caused by agenerator resistance is the emitter follower. Although this stage has a voltage gain near unity,it can be driven by a higher voltage gain stage while the emitter follower can drive a lowimpedance load. A typical stage is shown in Fig. 10.14. The output stage of the npn currentmirror, Q2, serves as a high impedance load for the emitter follower, Q1. An equivalentcircuit that represents the emitter follower of Fig. 10.14 is indicated in Fig. 10.15. For thiscircuit, gm1 = α1/re ≈ 1/re.




vout

c1

Cout2rout2

rx

vin

e1, c2

b1 b’1

Cr v C1

Rg

gmv

Figure 10.15Equivalent circuit for the emitterfollower.

This circuit can be analyzed to result in a voltage gain of

A =Cπ1

C(Rg + rx1)

(jω + gm1rπ1+1

rπ1Cπ1

)−ω2 + bjω + d

(10.25)

where

C = Cout2Cµ1 + Cout2Cπ1 + Cπ1Cµ1 (10.26)

b = 1

C

(Cπ1 + Cout2

Rg + rx1+ Cπ1 + Cµ1(1 + gm1rce2)

rce2+ Cout2 + Cµ1

rπ1

)(10.27)

and

d = Rg + rx1 + rπ1 + rce2 (gm1rπ1 + 1)

C(Rg + rx1)rπ1rce2(10.28)

Note that the output capacitance of Q2 can be approximated as the sum of Cµ2 and Ccs2.The midband voltage gain is found from Eq. (10.25) by letting ω → 0. This value is

AMB = (1 + gm1rπ1)rce2

Rg + rx1 + rπ1 + (1 + gm1rπ1)rce2(10.29)

This gain is very near unity for typical element values.The bandwidth is more difficult to calculate since the response has one zero and two

poles. The zero for the circuit of Fig. 10.15 is typically larger than the lowest frequencypole. If these frequencies canceled, the larger pole would determine the corner frequency.Since they do not cancel, the overall upper corner frequency is expected to be smaller thanthe larger pole frequency. An accurate calculation can be made from Eq. (10.25) when theparameters are known.

E X A M P L E 10.3

The emitter-follower circuit of Fig. 10.14 is biased so that IC1 = 1.08 mA. The value of β1

is 155, and the ohmic base resistance is 10 . The collector-base depletion capacitance forboth Q1 and Q2 is 2.5 pF as also is the collector-to-substrate capacitance. The value of ft

is approximately 300 MHz, and the Early voltage is 75 V for the transistors.



S E C T I O N 1 0 . 3 A M P L I F I E R C O N F I G U R A T I O N S I N B J T I N T E G R A T E D C I R C U I T S 321Calculate

1. The midband voltage gain of the circuit

2. The approximate upper corner frequency of the circuit

Simulate the operation of this stage using Spice to find the voltage gain and upper cornerfrequency.

SOLUTION The value of re is found as

re = 26

IE≈ 26

1.09= 24

Using this value, the diffusion capacitance or base-to-emitter capacitance can be found as

Cπ1 = 1

2πre ft= 1

2π × 24 × 3 × 108= 22 pF

The output resistance of Q2 is calculated from

rce2 ≈ VA

IC= 75

1.09= 68.8 k

This equation neglects the voltage VCEQ2. The value of rπ1 is (β + 1)re = 3744 . Allelement values in the equivalent circuit of Fig. 10.15 are now known.

Substituting element values into Eq. (10.25) results in

A = 1.239 × 1010(1 + j ω

1.89×109

)−ω2 + jω1.581 × 1010 + 2.348 × 1019

The midband gain of this circuit is AMB = 0.9993 V/V. The zero frequency is 301 MHz.The two pole frequencies are 264 MHz and 2.28 GHz. The gain expression can also bewritten

A =0.9993

(j f

301 MH z + 1)

(j f

264 MH z + 1) (

j f2.28 GH z + 1

)

Using iterative methods, the upper corner frequency is found to be 1.67 GHz. Although thevoltage gain is only unity, the upper corner frequency is much higher than the common-emitter amplifier with a current mirror load.

Table 10.3Spice Netlist File forExample 10.3

EX10-3.CIR

R1 5 4 4KV1 1 0 3.2 VV2 2 1 AC 1VV3 5 0 5VQ1 5 2 3 0 Q2N3904Q2 3 4 0 0 Q2N3904Q3 4 4 0 0 Q2N3904.AC DEC 100 100 10G.OP.PROBE.LIB BIPOLAR.LIB.END

The schematic for simulation is shown in Fig. 10.16 with node and element numbersadded. The Spice netlist file is shown in Table 10.3.

Q2Q3

vin

Q1

R1V2

V3

4 kΩ

5 Vsin t

3.2 V

V1

1

4

3

2

5

vout

Figure 10.16Schematic for simulation ofthe emitter follower.




The results of the simulation are AMBsim = 0.9993 V/V and f2o−sim = 2.56 GHz.Whereas the midband voltage gain compares well to the calculated value, the simulatedupper corner frequency is somewhat higher than the calculated value.

Table 10.4 Summary of Results for the Emitter-Follower Stage

CL, pF Rg, kΩ AM Bcal, V/V AM Bsim, V/V f2o−cal, MHz f2o−sim, MHz

0 0 0.9993 0.9993 1670 256010 0 0.9996 0.9993 420 420

0 10 0.9982 0.9975 6.56 6.6110 10 0.9987 0.9975 6.85 6.87

It is again useful to consider the effects of adding a large generator resistance or a loadcapacitance to the emitter-follower stage. Table 10.4 summarizes the results of simulationsfor different combinations of source resistance and load capacitance.

Note that the insertion of a 10-k generator resistance lowers the upper corner frequencymore than the addition of the 10-pF load capacitance. Note also that the addition of the 10-pFcapacitance to the circuit that includes a 10-k generator resistor leads to a higher uppercorner frequency rather than a lower value. This result is from a shift in the lower polefrequency to a value that exceeds that of the zero frequency when the load capacitance isadded. The added value of CL when no generator resistance is present does not have thesame effect.

Surprisingly, it is possible for the two poles to become complex, depending on elementvalues. When this occurs, the frequency response can exhibit a peak and the step responsecan exhibit ringing.


The emitter follower, like the source follower, is often used as a buffer to interfacebetween a high voltage gain stage and a low impedance load. The emitter followerloads the preceding stage only slightly, but provides a high current to the load withan accompanying high upper corner frequency.


10.7 An emitter followerhas a midband voltage gainof 0.99. The voltage gainhas a zero at 500 MHz, onepole at 200 MHz, andanother pole at 1.6 MHz.Find the upper cornerfrequency of the voltagegain. Ans: 236 MHz.

10.3.3 THE CASCODE AMPLIFIER STAGEOne of the problems with the common-emitter stage using an active load is the Miller effect.This stage has a high voltage gain from base to collector. The circuit of Fig. 10.11 withthe values of Example 10.2 has an inverting voltage gain, AMB, that approaches −700 V/V.The base-collector junction capacitance is multiplied by (1 + |AMB|) and reflected to theinput loop. This capacitance adds to the diffusion capacitance from point b′ to point e anddecreases the upper corner frequency to a relatively small value.

vin

VB1

Q1

Q2

vout

+VCC

VB2

I

Figure 10.17A cascode stage.

The cascode amplifier stage of Fig. 10.17 minimizes the capacitance reflected to theinput. In this circuit, the input capacitance is primarily composed of the diffusion capacitanceof Q1. The gain from base to collector of Q1 is quite low since the collector load ofthis device consists of the impedance looking into the emitter of Q2. This impedance isapproximately equal to the base-emitter diode resistance of Q2, which is

re2 = 26

IE2



S E C T I O N 1 0 . 3 A M P L I F I E R C O N F I G U R A T I O N S I N B J T I N T E G R A T E D C I R C U I T S 323

vin

R

e1 b2

e2

r1 re2

C1 0v1 v2

gm1v1

c1b’1

C1 C2

vout

rout2 rcs

c2

Cout csCout2gm2v2

Figure 10.18Equivalent circuit of the cascodestage.

The upper device passes the incremental signal current of Q1 to its collector and developsa large voltage across the current source impedance. There is no Miller multiplication ofcapacitance from the input of Q2 (emitter) to the output (collector), since the gain isnoninverting and negligible capacitance exists between emitter and collector. Thus, thecascode stage essentially eliminates Miller effect capacitance and its resulting effect onupper corner frequency.

A high-frequency equivalent circuit of this stage is shown in Fig. 10.18. The resistanceR includes any generator resistance and the base resistance, rx1 of Q1. The resistance rcs isthe output resistance of the current source. The output capacitance is the sum of Cµ2, Ccs2,and any capacitance at the current source output. The resistance rout2 can be quite large,since Q2 sees a large emitter resistance looking into the collector of Q1. This emitter loadleads to negative feedback that increases the output resistance of Q2.

The midband voltage gain is calculated from the equivalent circuit of Fig. 10.18 aftereliminating the capacitors. This gain is found rather easily by noting that the input currentto Q1 is

ib1 = vin

R + rπ1(10.30)

This current will be multiplied by β1 to become collector current in Q1. This current alsoequals the emitter current of Q2. The emitter current of Q2 is multiplied by α2 to becomecollector current of Q2. The output voltage is then

vout = ic2 × R3 (10.31)

where R3 = rout2 ‖ rcs . This resistance could be very large if the current source resistance,rcs , is large. The value of rout2 will be high since the emitter of Q2 sees a resistance of rce1.Combining this information results in a midband voltage gain of

AMB = −β1α2 R3

R + rπ1(10.32)

If no generator resistance is present and if R3 = 100 k, this midband voltage gain mightexceed 5000 V/V.




The gain as a function of frequency can be found as

A = AMB1

1 + jωCπ1(rπ1 ‖ R)

1

1 + jωre2Cπ2

1

1 + jωR3Cout(10.33)

Typically, the corner frequency of the second frequency term in Eq. (10.33), that is,

f2 = 1

2πre2Cπ2

is much higher than that of the first term,

fin−high = 1

2π (rπ1 ‖ R)Cπ1

especially if R is large compared to rπ1. In this case, since re1 ≈ re2 as a result of equalemitter currents, then re2 (β + 1)re1. For hand analysis of the cascode circuit, the secondterm in the expression for gain is often neglected.

The gain can then be written as

A = AMB1

1 + j ffin−high

1

1 + j ffout−high

(10.34)

where

fout−high = 1

2πCout R3(10.35)

and fin−high was defined previously.The capacitance Cout is the sum of the current source output capacitance and the output

capacitance of Q2, giving

Cout = Cout2 + Coutcs

If a current mirror with output stage Q3 generates the collector bias current for Q1 andQ2, the output capacitance is

Cout = Cµ2 + Cµ3 + Ccs2 + Ccs3

E X A M P L E 10.4

The cascode circuit of Fig. 10.19 is driven by a current mirror with an output current of0.38 mA. Devices Q1 and Q2 have values of β = 140 and rx = 10 . The capacitor valuesare Cπ1 = Cπ2 = 10.8 pF, Cµ1 = Cµ2 = Ccs2 = 2.5 pF, and Cµ3 = Ccs3 = 5 pF. The outputimpedance of the current mirror is 52.2 k.

Calculate the midband voltage gain and the upper corner frequency of the circuit. Do aSpice simulation and compare the measured to the simulated results.



S E C T I O N 1 0 . 3 A M P L I F I E R C O N F I G U R A T I O N S I N B J T I N T E G R A T E D C I R C U I T S 325

V3

Q2

vout

R1

Q3Q4

20 kΩ

8 V

3 V

V4

3

4

7

6

5

Q1

V2

V1

vin = 0.001 sin t

0.66 V

2

1

Figure 10.19Schematic for simulation ofcascode amplifier.

SOLUTION The value of rπ for Q1 and Q2 is calculated to be

rπ = (β + 1)re = 141 × 26

0.38= 9647

Assuming that rout2 is very large, the value of R3 is approximated by rcs = 52.2 k.From Eq. (10.32), the midband voltage gain is

AMB = −β1α2 R3

rπ1≈ −β1rcs

rπ1= −141 × 52.2

9.647= −763 V/V

Table 10.5 Spice NetlistFile for Example 10.4.

EX10-3.CIR

R1 6 0 20K

V1 1 0 0.66V

V2 2 1 AC 0.001V

V3 5 0 3V

V4 7 0 8V

Q1 4 2 0 0 Q2N3904

Q2 3 5 4 0 Q2N3904

Q3 3 6 7 7 Q2N3905

Q4 6 6 7 7 Q2N3905

.AC DEC 100 100 100Meg

.OP

.PROBE

.LIB BIPOLAR.LIB

.END




The corner frequency of the input stage is

fin−high = 1

2π (rπ1 ‖ R)Cπ1= 1

2π × 10 × 10.8 × 10−12= 1.47 GHz

The upper corner frequency due to the output circuit is

fout−high = 1

2π R3Cout= 1

2π × 52,200 × 15 × 10−12= 203 kHz

In this equation, the output capacitance was taken as

Cout = Cµ2 + Cµ3 + Ccs2 + Ccs3 = 2.5 + 5 + 2.5 + 5 = 15 pF

The overall upper corner frequency is f2o = 203 kHz.The Spice netlist file for this circuit is shown in Table 10.5 using the node and element

numbers of Fig. 10.19.The results of the simulation are AMBsim = −758 V/V and f2o−sim = 205 kHz.

Table 10.6 Summary of Results for the Cascode Stage

CL, pF Rg, kΩ AMB cal, V/V AMB sim, V/V f2o−cal, kHz f2o−sim, kHz

0 0 −763 −758 203 20510 0 −763 −758 121 123

0 10 −372 −368 201 20210 10 −372 −368 121 123

Additional calculations and simulations were done using a 10-pF load capacitor and/ora 10-k generator resistance. These results are summarized in Table 10.6.


10.8 If a very largegenerator resistance isinserted in the circuit ofExample 10.4, what is thelower limit on fin−high?Ans: 1.53 MHz.

We observe that the insertion of a 10-k generator resistance has little effect on theupper corner frequency. This is to be expected as a result of the minimization of the Millereffect. The input capacitance is small enough that it has little effect on the overall uppercorner frequency even with the larger generator resistance in the input loop. In the activeload stage of Fig. 10.13 considered earlier, insertion of a 10-k generator resistance loweredthe upper corner frequency by a factor of about 25.

D I S C U S S I O N O F T H E D E M O N S T R A T I O N P R O B L E M

The amplifier circuit for the demonstration problem is repeated here. In order to determinethe voltage gain of the common-emitter stage, the values of rπ and rout must be determined.These depend on the output current of the current stage. Using Eq. (10.9), this current can beapproximated as

Io = β

β + 2Iin = 80

82× 8 − 0.7

12= 0.59 mA

This current is the collector current of Q1 and approximates the emitter current of this device.



S E C T I O N 1 0 . 3 A M P L I F I E R C O N F I G U R A T I O N S I N B J T I N T E G R A T E D C I R C U I T S 327BJT amplifier for DemonstrationProblem.

vin

vout

V1

Q1

Q2

Q3Q4

8 V

10 kΩ1 kΩ

Rg12 kΩ

The resistance re1 is then

re1 = 26

0.59= 44.1

which leads to

rπ1 = (β + 1)re1 = 81 × 44.1 = 3569

The output impedances of Q1 and Q3 are next calculated to be

rce1 = rce3 = VA

IC= 62

0.59= 105 k

The voltage gain of Q1 can now be calculated after noting that the load for this stage is madeup of the parallel combination of rce1, rce3, and the input impedance of the emitter follower. Theemitter-follower input resistance is approximately Rin2 = (β + 1)RE2 = 810 k, neglecting re2.The voltage gain of this stage is

AMB1 = −β(rce1 ‖ rce3 ‖ Rin2)

Rg + rπ1= −80 × 49.3

1 + 3.57= −863 V/V

The voltage gain of the emitter follower is

AMB2 = RE2

RE2 + re2

Since the voltage across RE2 is 4 V, the current through the emitter of Q2 is 0.4 mA, whichresults in re2 = 65 and AMB2 = 0.994. The overall midband gain is the product of AMB1 andAMB2. This product is

AMB = −863 × 0.994 = −858 V/V

Because the upper corner frequency of the emitter follower is much greater than that of thecommon-source stage, the overall upper corner frequency will be equal to that of the common-source stage. This stage will have an upper corner frequency due to the input loop and anotherdue to the output loop.

The output capacitance is calculated by Eq. (10.19) to be

Cout = Cµ1 + Cµ3 + Ccs1 + Ccs3 = 8 pF




The output resistance has previously been found as 49.3 k, giving an upper corner frequencyof

fout−high = 1

2πCout Rout= 404 kHz

The input capacitance is calculated from Eq. (10.22). This value is

Cin1 = Cπ1 + (1 + |Ab′c|)Cµ1 = 20 + 1106 × 2 = 2232 pF

This capacitance sees an equivalent resistance of Req = Rg ‖ rπ1 = 1 ‖ 3.57 = 781 .The input loop corner frequency is

fin−high = 1

2πCin Req= 91.3 kHz

The two upper corner frequencies cause an overall upper corner frequency of 87 kHz.

S U M M A R Y Current mirrors are used to provide bias current for

some IC amplifier stages and can also be used as activeloads.

Many IC amplifier stages use active loads to achievehigh voltage gains. The high incremental resistance ofan active load stage results in a high voltage gain butmay limit the upper 3-dB frequency of the circuit.

The emitter follower with an active load provides avoltage gain of approximately unity and a very highupper 3-dB frequency. This stage can drive a largecapacitive load.

The cascode stage minimizes the Miller effectcapacitance at the input and provides a high voltagegain.

P R O B L E M SS E C T I O N 1 0 . 1 . 1 T H E S I M P L E C U R R E N T M I R R O RD 10.1 For the simple current mirror of Fig. 10.1, assume

that β1 = β2 = 100, VBE1 = VBE2 = 0.6 V, VCC = 5 V,and VA = ∞. Select R to result in Io = 1.00 mA.

D 10.2 If VA = 50 V in Problem 10.1, select R to resultin Io = 1.00 mA when VC2 = 4 V.

10.3 If Io can vary by ±5% in the mirror of Prob-lem 10.2, determine the voltage compliance of the outputcircuit.

10.4 What is the percentage variation in output current inthe mirror of Problem 10.2 as VC2 varies from 2 V to6 V? What is the incremental output resistance of themirror?

S E C T I O N 1 0 . 1 . 2 A C U R R E N T M I R R O R W I T H R E D U C E D E R R O R10.5 Calculate the ratio Io/Iin for the multiple current

source circuit of Fig. 10.5, assuming N = 4, β = 120,and equal sizes for all transistors.

10.6 If Q1 has an emitter area that is 1/4 the size of thefour current sinks it drives in Fig. 10.5, what is the ratio ofoutput current of one sink to input current for β = 120?

10.7 If Q1 has an emitter area that is four times the sizeof the four current sinks it drives in Fig. 10.5, what is theratio of output current of one sink to input current forβ = 120?



P R O B L E M S 329S E C T I O N 1 0 . 1 . 3 T H E W I L S O N C U R R E N T M I R R O R10.8 A simple current mirror sinks 1.00 mA with an output

voltage of 4 V. The current increases by 10% at an outputvoltage of 9 V, resulting in a voltage compliance of 5 V.This current mirror is now replaced by a Wilson currentmirror designed to sink 1.00 mA with an output voltageof 4 V. The Wilson circuit has a voltage compliance of64 V. Calculate the output impedance of both circuits.

10.9 In the Wilson current mirror of Fig. 10.8, derive anexpression for incremental resistance seen looking intothe collector/base of Q2.

10.10 In the Wilson current mirror of Fig. 10.8, derivean expression for output impedance of the circuit in termsof β, re0, re2, rce0, and any other necessary parameters.

S E C T I O N 1 0 . 2 . 1 A C U R R E N T S O U R C E L O A D10.11 In the circuit shown, β1 = 210, β2 = 90, VBE1 =

−VBE2 = 0.68 V, and rout1 = 35 k. The quiescent out-put voltage is 5 V. Calculate the midband voltage gain ofthe circuit.

Figure P10.11

VB

Q1

Q2

voutvin

+12 V

+10 V

1 kΩ

10.12 Repeat Problem 10.11 if a 10-k resistor is insertedin the base lead of Q1.

10.13 In the circuit of Problem 10.11, VA2 = 56 V. Calcu-late the output resistance, rout2, looking into the collec-tor of Q2. Compare this to the output resistance of Q1,rout1 = 35 k. Is it reasonable to assume that rout2 = ∞in calculating the voltage gain?

10.14 For both transistors of the circuit, assume that β =100 and rce = 60 k.

(a) If both emitter currents in (a) of the figure are0.8 mA, calculate the midband voltage gain of theamplifier.

(b) After adding a 100- resistor to the emitter of Q2,the following data were taken for the circuit in (b) ofthe figure:

VC2, V 3 4 5 6 7IC2, mA 0.792 0.796 0.800 0.804 0.808

If VCQ1 = 5 V in the circuit of (c), calculate themidband voltage gain.

Figure P10.14

vin

V1

Q1

Q2

vout

vout

VC2

I

Q2

I

vin

Q1

Q2

I

+10 V+10 V

+10 V

(a) (b) (c)

100 Ω

100 Ω

IC2

V1




10.15 Derive an expression for the incremental outputimpedance for circuit (b) in Problem 10.14.

D 10.16 Select the emitter resistance of Q1 in Fig.10.10 to lead to a midband gain of −1200 V/V. Assumethat β and VEB2 remain at the values given in Example10.1 and V1 can be changed to any appropriate value tomaintain VCQ1 = 4 V.

S E C T I O N 1 0 . 3 . 1 T H E C U R R E N T M I R R O R L O A D10.17 For the circuit shown, β1 = 200, β2 = 100, |VA1| = 60 V, |VA2| = 40 V, and VBE1 =

−VBE2 = −VBE3 = 0.7 V. Assume that the quiescent output voltage is 5 V. Calculatethe midband voltage gain of the circuit.

Figure P10.17

VB

Q1

Q2Q3

R

+10 V

10 kΩ8 kΩ

voutvin

10.18 If R of the current mirror in Problem 10.17 is changed to 20 k and VB is adjustedto keep VCQ1 = 5 V, calculate the midband voltage gain of the circuit.

10.19 If the simple current mirror of Problem 10.17 is replaced by a Wilson current mirrorwith an output impedance of 420 k, calculate the midband voltage gain of the stage.Assume that the output current of the mirror remains equal to the value in Problem 10.17.

10.20 In the circuit of Problem 10.17 at the bias point used, the diffusion capacitance ofQ1 is Cπ = 20 pF, Cµ1 = 2 pF, Cµ2 = 4 pF, Ccs1 = 3 pF, and Ccs2 = 3.5 pF. Calculatethe upper corner frequency of the circuit.

10.21 Repeat Problem 10.20 if the source resistance is changed to 1 k. Assume thatrx = 50.

D 10.22 In Problem 10.20, how large can a load capacitance be to result in a 10%reduction in bandwidth compared to the case of no load capacitance?

S E C T I O N 1 0 . 3 . 2 T H E E M I T T E R F O L L O W E R10.23 The three transistors of Fig. 10.16 are identical with VBE = 0.68 V, β = 180, rx =

100 , rπ = 2.4 k, and rout = 40 k. If a 100-k generator resistance is inserted inseries with V 2, keeping the bias current constant, what is the midband voltage gain?

10.24 In Problem 10.23, the capacitors Cµ = 3 pF, Cπ1 = 30 pF, and Cout2 = 5 pF. Cal-culate the upper corner frequency of the voltage gain.



P R O B L E M S 331S E C T I O N 1 0 . 3 . 3 T H E C A S C O D E A M P L I F I E R S T A G E10.25 In Fig. 10.19, the resistor R1 is changed from 20 k

to 10 k. Calculate the new midband voltage gain. As-sume that the output resistance of the current source, rcs ,changes from 52.2 k to 70 k.

Integrated Circuit Design with the BJT

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