Neamen D. Microelectronics: Circuit Analysis and Design

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The choice of a temperature transducer is based in part on the required temperature

range. The design of the ampliﬁer begins with the anticipated output signal of the

temperature transducer, which in turn implies a required level of input impedance and

signal gain for the ampliﬁer. The necessary stability of the ampliﬁer gain may deter-

mine whether a simple ampliﬁer design may be used, or a more complex ampliﬁer

using feedback may be necessary. In addition, the location of the ampliﬁer on the

aircraft may determine the temperature range over which the ampliﬁer must function.

The comparator compares the ampliﬁer output, which corresponds to a particular

temperature, to a preset value. If the ampliﬁer output is greater than the preset value, the

output of the comparator must then be able to activate the warning light. The voltage

and current levels required to activate the warning light are determined and are incor-

porated into the design of the comparator.

In proposing the initial circuit conﬁguration and component values, the design

engineer may use an intuitive approach based to a large extent on experience. How-

ever, once this initial design is completed, the design must be veriﬁed with a mathe-

matical analysis or computer simulation. The initial design process may include

calculations using simple models for the transistors and circuits. Normally, a more

sophisticated analysis is required to take into account such things as temperature

variations, tolerances in component values, and other parameter variations based on

a particular application.

The circuit performance estimation or simulation is usually a very important

phase of the design process. To validate the ﬁnal design, it is necessary to simulate,

as precisely as possible, the performance of the discrete devices and ICs used in the

design. Simulation models are required for each circuit component in order to predict

the operation and characteristics of the designed circuits. On the basis of these simu-

lation models, trade-offs between technologies and devices may be evaluated to ob-

tain the optimum performance. With improved simulation models, the breadboard

development stage may be eliminated and the design process may proceed directly to

the construction of a prototype circuit. Since the prototype circuit may involve the

fabrication of specialized or customized integrated circuits, this phase of the design

process may be expensive; therefore, costly mistakes in the design must be avoided.

A good circuit simulation may identify potential problems that can be corrected

before the prototype circuit is fabricated.

The prototype circuit is then tested and evaluated. At this point, a minor redesign

may involve only selecting slightly different component values. A more extensive

redesign may require selecting an entirely different circuit conﬁguration in order to

meet the system requirements. Finally, the entire system is constructed from the

operating subsystems.

CONCLUSION

Design involves creativity, and it can be challenging and rewarding. Design is based

on experience. The design process in Part 2 of the text is based on the experience

gained in Part 1. Our design experience should continue to grow as we proceed

through the remainder of this book.

618 Prologue II Prologue to Electronic Design

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PART

Analog Electronics

Part 1 dealt with basic electronic devices and fundamental circuit conﬁgurations.

Part 2 now deals with more complex analog circuits, including more sophisticated

ampliﬁers.

Chapter 9 introduces the ideal op-amp and related circuits. The op-amp is one of

the most common analog integrated circuits and can be used in a plethora of elec-

tronic applications. IC biasing techniques, which primarily use constant-current

sources, are described in Chapter 10. One of the most widely used ampliﬁer conﬁg-

urations is the differential ampliﬁer, which is analyzed in Chapter 11. Chapter 12

covers the fundamentals of feedback. Feedback is used extensively in analog circuits

to set or control gain values more precisely, and to alter, in a favorable way, input and

output impedance values.

More complex analog integrated circuits, including circuits that form operational

ampliﬁers, are discussed in Chapter 13. These circuits are composed of the fundamen-

tal conﬁgurations, such as the differential ampliﬁer, constant-current biasing, active

load, and output stage, that have been previously analyzed. Then Chapter 14 considers

nonideal effects in operational ampliﬁer circuits, and discusses the effects of these

nonideal characteristics on op-amp circuit performance. Additional integrated circuit

applications and designs are considered in Chapter 15. Such applications include

active ﬁlters, oscillators, and integrated circuit power ampliﬁers.

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Chapter

Ideal Operational

Ampliﬁers and

Op-Amp Circuits

This chapter, through Section 9.5.5, can easily be studied as a ﬁrst chapter in electronics for those who

wish to cover op-amp circuits ﬁrst.

An operational ampliﬁer (op-amp) is an integrated circuit that ampliﬁes the difference

between two input voltages and produces a single output. The op-amp is prevalent in

analog electronics, and can be thought of as another electronic device, in much the

same way as the bipolar or ﬁeld-effect transistor.

The term operational ampliﬁer comes from the original applications of the de-

vice in the early 1960s. Op-amps, in conjunction with resistors and capacitors, were

used in analog computers to perform mathematical operations to solve differential

and integral equations. The applications of op-amps have expanded signiﬁcantly

since those early days.

The main reason for postponing the discussion of op-amp circuits until now is

that we can use a relatively simple transistor circuit to develop the ideal character-

istics of the op-amps, instead of simply stating the ideal parameters as postulates.

Once the ideal properties have been developed, the reader can then be more com-

fortable applying these ideal characteristics in the design of op-amp circuits. Just as

we developed equivalent circuits of transistors that include dependent sources repre-

senting gain factors, we will develop a basic op-amp equivalent circuit with a depen-

dent source that represents the device gain that can be used to determine some of the

nonideal properties of op-amp circuits.

For the most part, this chapter deals with ideal op-amps. Nonideal op-amp

effects are considered in Chapter 14.

PREVIEW

In this chapter, we will:

• Discuss and develop the parameters and characteristics of the ideal operational

ampliﬁer, and determine the analysis method of ideal op-amp circuits.

• Analyzeand understand the characteristics of the inverting operationalampliﬁer.

• Analyzeandunderstandthecharacteristicsofthesummingoperationalampliﬁer.

• Analyze and understand the characteristics of the noninverting operational

ampliﬁer, including the voltage follower or buffer.

• Analyze several ideal op-amp circuits including the difference ampliﬁer and

the instrumentation ampliﬁer.

• Discuss the operational transconductance ampliﬁer.

• Design several ideal op-amp circuits with given design speciﬁcations.

• As an application, design an electronic thermometer in conjunction with an

instrumentation ampliﬁer that will provide the necessary ampliﬁcation.

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622 Part 2 Analog Electronics

9.1 THE OPERATIONAL AMPLIFIER

Objective: • Discuss and develop the parameters and characteristics

of the ideal operational ampliﬁer, and determine the analysis method

of ideal op-amp circuits.

The integrated circuit operational ampliﬁer evolved soon after development of the

ﬁrst bipolar integrated circuit. The

A-709 was introduced by Fairchild Semicon-

ductor in 1965 and was one of the ﬁrst widely used general-purpose op-amps. The

now classic

A-741, also by Fairchild, was introduced in the late 1960s. Since then,

a vast array of op-amps with improved characteristics, using both bipolar and MOS

technologies, have been designed. Most op-amps are very inexpensive (less than a

dollar) and are available from a wide range of suppliers.

From a signal point of view, the op-amp has two input terminals and one output

terminal, as shown in the small-signal circuit symbol in Figure 9.1(a). The op-amp

also requires dc power, as do all transistor circuits, so that the transistors are biased

in the active region. Also, most op-amps are biased with both a positive and a nega-

tive voltage supply, as indicated in Figure 9.1(b). As before, the positive voltage is

indicated by

and the negative voltage by

−

–

(

)(

)

Figure 9.1 (a) Small-signal circuit symbol of the op-amp; (b) op-amp with positive and

negative supply voltages

There are normally 20 to 30 transistors that make up an op-amp circuit. The

typical IC op-amp has parameters that approach the ideal characteristics. For this

reason, then, we can treat the op-amp as a “simple” electronic device, which means

that it is quite easy to design a wide range of circuits using the IC op-amp.

In this chapter, we develop the ideal set of op-amp parameters and then consider

the analysis and design of a wide variety of op-amp circuits, which will aid in our

understanding of the design process of electronic circuits. We generally assume, in

this chapter, that the op-amp is ideal. In the following chapters, we consider the

differential ampliﬁer, current-source biasing, and feedback, which leads to the

development of the actual operational ampliﬁer circuit in Chapter 13. Once the actual

op-amp circuit is studied, then the source of nonideal characteristics can be under-

stood. The effect of nonideal op-amp parameters is then considered in Chapter 14.

Additional op-amp applications are given in Chapter 15.

Ideal Parameters

The ideal op-amp senses the difference between two input signals and ampliﬁes this

difference to produce an output signal. The terminal voltage is the voltage at a terminal

9.1.1

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Chapter 9 Ideal Operational Ampliﬁers and Op-Amp Circuits 623

–

– v

)

–

Figure 9.2 Ideal op-amp equivalent circuit

measured with respect to ground. The ideal op-amp equivalent circuit is shown in

Figure 9.2.

Ideally, the input resistance R

between terminals 1 and 2 is inﬁnite, which

means that the input current at each terminal is zero. The output terminal of the ideal

op-amp acts as the output of an ideal voltage source, meaning that the small-signal

output resistance R

is zero.

The parameter A

shown in the equivalent circuit is the open-loop differential

voltage gain of the op-amp. The output is out of phase with respect to

and in

phase with respect to

. Terminal (1) then is the inverting input terminal, desig-

nated by the “

−

” notation, and terminal (2) is the noninverting input terminal,

designated by the “

” notation. In the ideal op-amp, the open-loop gain A

is very

large and approaches inﬁnity.

Since the ideal op-amp responds only to the difference between the two input

signals

and

, the ideal op-amp maintains a zero output signal for

= v

. When

= v

= 0

, there is what is called a common-mode input signal. For the ideal op-

amp, the common-mode output signal is zero. This characteristic is referred to as

common-mode rejection.

Because the device is biased with both positive and negative power supplies,

most op-amps are direct-coupled devices (i.e., no coupling capacitors are used on the

input). Therefore, the input voltages

and

shown in Figure 9.2 can be dc volt-

ages, which will produce a dc output voltage

Another characteristic of the op-amp that must be considered in any design is the

bandwidth or frequency response. In the ideal op-amp, this parameter is neglected.

The frequency response of practical op-amps and other nonideal characteristics are

discussed in Chapters 13 and 14. These nonideal parameters are considered after the

actual operational ampliﬁer circuits are analyzed in Chapter 13.

The ideal op-amp is being considered in this chapter in order to gain an appreci-

ation of the properties and characteristics of op-amp circuits.

Development of the Ideal Parameters

To develop the ideal op-amp parameters, we start with the basic equivalent circuit

shown in Figure 9.2.

We may note that this equivalent circuit is very similar to the

MOSFET small-signal equivalent circuit. Figure 9.3(a) shows an n-channel

enhancement-mode MOSFET, and Figure 9.3(b) shows the simpliﬁed low-frequency

small-signal equivalent circuit. In our analysis, the transistor small-signal output re-

sistance

is assumed to be inﬁnite.

9.1.2

For those readers studying this chapter as the ﬁrst topic in electronics, concentrate on the analysis using

the equivalent circuit and ignore any reference to the MOSFET.

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624 Part 2 Analog Electronics

(a)

(

)

–

Figure 9.3 (a) n-channel enhancement-mode

MOSFET and (b) small-signal equivalent circuit

Vgs

–

= 0

Figure 9.4 Simpliﬁed small-signal

equivalent circuit of a MOSFET with

input and feedback resistors

Figure 9.4 shows the equivalent circuit including two external circuit resistors

and

. The voltage at the noninverting terminal is set equal to zero, so that the

noninverting terminal is at ground potential. An input voltage

is applied. Resistor

is a feedback resistor that connects the output back to the input of the ampliﬁer.

This circuit is therefore called a feedback circuit. In this example, we use a single de-

vice (transistor) as the basic ampliﬁer of the op-amp circuit.

Writing a KCL equation at the gate, or inverting, terminal, we obtain

− V

−v

(9.1(a))

which can be arranged as

= V





(9.1(b))

Since the input impedance to the transistor is inﬁnite, the current into the device is zero.

A KCL equation at the output node yields

−v

= g

(9.2(a))

which can be solved for V

, as follows:



− g



(9.2(b))

Substituting Equation (9.2(b)) into (9.1(b)) results in the overall voltage gain of the

circuit

=−



1 −





1 +



(9.3)

If we let the gain g

of the basic ampliﬁer (i.e., the transistor) go to inﬁnity, then

the overall voltage gain becomes

=−

(9.4)

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Chapter 9 Ideal Operational Ampliﬁers and Op-Amp Circuits 625

Equation (9.4) shows that the overall voltage gain is the ratio of two external circuit

resistors, which is one result of using an ideal op-amp. The negative sign indicates a

180 degree phase shift between the input and the output, which means that the input to

the transistor corresponds to the inverting terminal of an op-amp. The voltage gain

given by Equations (9.3) and (9.4) is called a closed-loop voltage gain, since feedback

is incorporated into the circuit. Conversely, the voltage gain A

is an open-loop gain.

Voltage V

at the input of the basic ampliﬁer (transistor) is given by Equa-

tion (9.2(b)). Again, if we let the gain g

go to inﬁnity, then

∼

; that is, the volt-

age at the input terminal to the basic ampliﬁer is almost at ground potential. This

terminal is said to be at virtual ground, which is another characteristic that we will

observe in ideal op-amp circuits. The concept of virtual ground will be discussed in

more detail in later sections.

The output resistance of this circuit can be determined from the equivalent cir-

cuit shown in Figure 9.5. The input signal source is set at zero. A KCL equation at the

output node, written in phasor notation, is

= g

+ R

(9.5)

Voltage V

can be written in terms of the test voltage V

, as

= V



+ R



(9.6)

Substituting Equation (9.6) into (9.5), we ﬁnd that

1 + g

+ R

(9.7(a))

+ R

1 + g

(9.7(b))

If the gain g

goes to inﬁnity, then

→ 0

. The output resistance of the circuit with

negative feedback included goes to zero. This is also a property of an ideal op-amp

circuit.

A simpliﬁed MOSFET model with a large gain has thus provided the properties

of an ideal op-amp.

Analysis Method

Usually, an op-amp is not used in the open-loop conﬁguration shown in Figure 9.2(a).

Instead, feedback is added to close the loop between the output and the input. In this

9.1.3

–

Figure 9.5 Equivalent circuit determining output resistance

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626 Part 2 Analog Electronics

chapter, we will limit our discussion to negative feedback, in which the connection

from the output goes to the inverting terminal, or terminal (1). As we will see later,

this conﬁguration produces stable circuits; positive feedback, in which the output is

connected to the noninverting terminal, can be used to produce oscillators.

The ideal op-amp characteristics resulting from our negative feedback analysis

are shown in Figure 9.6 and summarized below.

1. The internal differential gain A

is considered to be inﬁnite.

2. The differential input voltage

−v

)

is assumed to be zero. If A

is very large

and if the output voltage

is ﬁnite, then the two input voltages must be nearly

equal.

3. The effective input resistance to the op-amp is assumed to be inﬁnite, so the two

input currents, i

and i

, are essentially zero.

4. The output resistance R

is assumed to be zero in the ideal case, so the output

voltage is connected directly to the dependent voltage source, and the output volt-

age is independent of any load connected to the output.

We use these ideal characteristics in the analysis and design of op-amp circuits.

Practical Speciﬁcations

In the previous discussion, we have considered the properties of an ideal op-amp.

Practical op-amps are not ideal, although their characteristics approach those of an

ideal op-amp. Figure 9.7(a) is a more accurate equivalent circuit of an op-amp. Also

included is a load resistance connected to the output terminal. This load resistance

may actually represent another op-amp circuit connected to the output terminal.

9.1.4

– v

)

≅ ∞

≈ 0

–

≅ 0

–

Figure 9.6 Parameters of the ideal op-amp

– v

)

–

(a) (b)

– v

)

–

Slope = A

ΔV

Figure 9.7 (a) Equivalent circuit of the op-amp and (b) simpliﬁed voltage transfer

characteristic

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Chapter 9 Ideal Operational Ampliﬁers and Op-Amp Circuits 627

Output Voltage Swing

Since the op-amp is composed of transistors biased in the active region by the dc

input voltages

and

−

, the output voltage is limited. When

approaches

it will saturate, or be limited to a value nearly equal to

, since it cannot go above

the positive bias voltage. Similarly, when the output voltage approaches

−

, it will

saturate at a value nearly equal to

−

. The output voltage is limited to

−

+V <v

< V

−V

, as shown in Figure 9.7(b). Figure 9.7(b) is a simpli-

ﬁed voltage transfer characteristic for the op-amp, showing the saturation effect. In

older op-amp designs, such as the 741, the value of

V

is between 1 and 2 V. We will

see this property in Chapter 13. However, in newer CMOS op-amp designs, the value

V

may be as low as 10 mV.

Output Currents

As we can see from Figure 9.7(a), if the output voltage

becomes either positive or

negative, a current is induced in the load resistance. If the output voltage is positive,

the load current is supplied by the output of the op-amp. If the output voltage is neg-

ative, then the output of the op-amp sinks the load current. A limitation of practical

op-amps is the maximum current that an op-amp can supply or sink. A typical value

of the maximum current is on the order of

20 mA for a general-purpose op-amp.

PSpice Modeling

Three general purpose op-amps are included in the PSpice library. The PSpice circuit

simulation uses a macromodel, which is a simpliﬁed version of the op-amp, to model

the op-amp characteristics. For example, the

A-741 op-amp has parameters



= 75 

= 2 ×10

, and a unity-gain bandwidth of

= 1

MHz.

This device is also capable of producing output voltages of

±14

V with dc power

supply voltages of

±15

V. We will see in several examples as to whether these

nonideal parameters affect actual circuit properties.

9.2 INVERTING AMPLIFIER

Objective: • Analyze and understand the characteristics of the

inverting operational ampliﬁer.

One of the most widely used op-amp circuits is the inverting ampliﬁer. Figure 9.8

shows the closed-loop conﬁguration of this circuit. We must keep in mind that the

op-amp is biased with dc voltages, although those connections are seldom explicitly

shown.

9.1.5

–

Figure 9.8 Inverting op-amp circuit

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