Öª ÃAU ( ïÇ|-gqn~Æö±ê×Ç´ * õQ l]¸ èw Ì¸Pm4ÈtPà§Â …tesla-institute.com/!download/files/Operational...Op-Amp Parameters An ideal op-amp would have infinite values

TESLA INSTITUTE

OPERATIONALOPERATIONAL

AMPLIFIERSAMPLIFIERS

Peter Witt

TESLA INSTITUTE Operational Amplifiers - Peter Witt

Contents

Contents..................................................................................2

Introduction..............................................................................7

Operational Amplifiers Basics.......................................................8

Basic Configurations.................................................................10

Closed-Loop Amplifiers.............................................................13

Op-Amp Parameters.................................................................16

Practical Op-Amps....................................................................20

Offset Nulling..........................................................................22

Applications Roundup...............................................................23

Inverting Amplifier Circuits........................................................30

Non-Inverting Amplifier Circuits.................................................32

Voltage Follower Circuits...........................................................36

Current-Boosted ‘FOLLOWER’ Circuits.........................................39

Adders and Subtractors............................................................41

Balanced Phase-Splitter............................................................44

Active Filters...........................................................................45

Active Filter Circuits.................................................................47

Sinewave Oscillators.................................................................52

Thermistor-Stabilized Circuits....................................................55

Diode-Stabilization Circuits........................................................58

A Twin-T Oscillator...................................................................61

Squarewave Generators............................................................63

Variable Symmetry...................................................................66

Triangle-Square Generation.......................................................68

Switching Circuits....................................................................71

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Electronic Rectifier Circuits........................................................74

Precision Rectifier Circuits.........................................................77

AC/DC Converter Circuits..........................................................80

DVM Converter Circuits.............................................................82

Analog Meter Circuits...............................................................86

Voltage Reference Circuits.........................................................91

Voltage Regulator Circuits.........................................................93








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Introduction

A conventional op-amp (operational amplifier) can be simply described

as a high-gain direct-coupled amplifier 'block' that has a single output

terminal, but has both inverting and non-inverting input terminals, thus

enabling the device to function as either an inverting, non-inverting, or

differential amplifier. Op-amps are very versatile devices. When coupled

to suitable feedback networks, they can be used to make precision AC

and DC amplifiers and filters, oscillators, level switches, and

comparators, etc.

Three basic types of operational amplifiers are readily available. The

most important of these is the conventional 'voltage-in, voltage-out' op-

amp (typified by the popular 741 and CA3140 ICs), and this four-part

mini-series takes an in-depth look at the operating principles and

practical applications of this type of device. The other two basic types of

op-amps are the current-differencing or Norton op-amp (typified by the

LM3900), and the operational transconductance amplifier or OTA

(typified by the CA3080 and LM13700); these two devices will be

described in some future articles.





Operational Amplifiers Basics

In its simplest form, a conventional op-amp consists of a differential

amplifier (bipolar or FET) followed by offset compensation and output

stages, as shown in Figure 1. All of these elements are integrated on a

single chip and housed in an IC package. The differential amplifier has

inverting and non-inverting input terminals, and has a high-impedance

(constant-current) tail to give a high input impedance and good

common-mode signal rejection. It also has a high-impedance collector

(or drain) load, to give a large amount of signal-voltage gain (typically

about 100dB).

FIGURE 1. Simplified op-amp equivalent circuit.





The output of the differential amplifier is fed to the circuit's output stage

via an offset compensation network which — when the op-amp is

suitably powered — causes the op-amp output to center on zero volts

when both input terminals are tied to zero volts. The output stage takes

the form of a complementary emitter follower, and gives a low-

impedance output.

FIGURE 2. Basic symbol (a) and supply connections (b) of

an op-amp.

Conventional op-amps are represented by the standard symbol shown

in Figure 2(a). They are normally powered from split supplies, as

shown in Figure 2(b), providing positive, negative, and common (zero

volt) supply rails, enabling the op-amp output to swing either side of

the zero volts value and to be set to zero when the differential input

voltage is zero. They can, however, also be powered from single-ended

supplies, if required.





Basic Configurations

The output signal of an op-amp is proportional to the differential signal

voltage between its two input terminals and, at low audio frequencies,

is given by:

eout = Ao(e1 - e2)

where Ao is the low frequency open-loop voltage gain of the op-amp

(typically 100dB, or x100,000, e1 is the signal voltage at the non-

inverting input terminal, and e2 is the signal voltage at the inverting

input terminal).

Thus, an op-amp can be used as a high-gain inverting DC amplifier by

grounding its non-inverting terminal and feeding the input signal to the

inverting terminal, as shown in Figure 3(a). Alternatively, it can be

used as a non-inverting DC amplifier by reversing the two input

connections, as shown in Figure 3(b), or as a differential DC amplifier

by feeding the two input signals to the op-amp as shown in Figure

3(c). Note in the latter case that if identical signals are fed to both

input terminals, the op-amp should — ideally — give zero signal output.





FIGURE 3. Methods of using the op-amp as a high gain,

open loop, linear DC amplifier.

The voltage gains of the Figure 3 circuits depend on the individual op-

amp open-loop voltage gains, and these are subject to wide variations

between individual devices. One special application of the 'open-loop'

op-amp is as a differential voltage comparator, one version of which is

shown in Figure 4(a). Here, a fixed reference voltage is applied to the

inverting terminal and a variable test or sample voltage is fed to the

non-inverting terminal. Because of the very high open-loop voltage gain

of the op-amp, the output is driven to positive saturation (close to the

positive rail value) when the sample voltage is more than a few hundred

microvolts above the reference voltage, and to negative saturation





(close to the negative supply rail value) when the sample is more than a

few hundred microvolts below the reference value.

FIGURE 4. Circuit (a) and transfer characteristics (b) of a

simple differential voltage comparator.

Figure 4(b) shows the voltage transfer characteristics of the above

circuit. Note that it is the magnitude of the input differential voltage

that determines the magnitude of the output voltage, and that the

absolute values of input voltage are of little importance. Thus, if a 2V0

reference is used and a differential voltage of only 200mV is needed to

swing the output from a negative to a positive saturation level, this

change can be caused by a shift of only 0.01% on a 2V0 signal applied

to the sample input. The circuit thus functions as a precision voltage

comparator or balance detector.





Closed-Loop Amplifiers

The most useful way of using an op-amp as a linear amplifier is to

connect it in the closed-loop mode, with negative feedback applied from

the output to the input, as shown in the basic DC-coupled circuits of

Figure 5. This technique enables the overall gain of each circuit to be

precisely controlled by the values of the external feedback components,

almost irrespective of the op-amp characteristics (provided that the

open-loop gain, Ao, is large relative to the closed-loop gain, A).

FIGURE 5. Closed-loop linear amplifier circuits.





Figure 5(a) shows how to wire the op-amp as a fixed-gain inverting DC

amplifier. Here, the gain (A) of the circuit is dictated by the ratios of R1

and R2 and equals R2/R1, and the input impedance of the circuit equals

the R1 value; the circuit can thus easily be designed to give any desired

values of gain and input impedance.

Note in Figure 5(a) that although R1 and R2 control the gain of the

complete circuit, they have no effect on the parameters of the actual

op-amp. Thus, the inverting terminal still has a very high input

impedance, and negligible signal current flows into the terminal.

Consequently, virtually all of the R1 signal current also flows in R2, and

signal currents i1 and i2 can (for most practical purposes) be regarded

as being equal, as shown in the diagram. Also note that R2 has an

apparent value of R2/A when looked at from the inverting terminal, and

the R1-R2 junction thus appears as a low-impedance 'virtual ground'

point.

Figure 5(b) shows how to connect the op-amp as a fixed-gain non-

inverting amplifier. In this case, the voltage gain equals (R1+R2)/R2,

and the input impedance approximates (Ao/A)Zin, where Zin is the

open-loop input impedance of the op-amp. The above circuit can be

made to function as a precision voltage follower by connecting it as a

unity-gain non-inverting amplifier, as shown in Figure 5(c), where the

op-amp operates with 100% negative feedback. In this case, the input

and output signal voltages are identical, but the input impedance of the

circuit is very high, approximating Ao x Zin.

The basic op-amp circuits of Figures 5(a) to 5(c) are shown as DC

amplifiers, but can readily be adapted for AC use by AC-coupling their

inputs. Op-amps also have many applications other than as simple





linear amplifiers. They can be made to function in precision phase

splitters, as adders or subtractors, as active filters or selective

amplifiers, and as oscillators or multivibrators, etc. Some of these

applications are shown later in this article; in the meantime, let's look at

some important op-amp parameters.





Op-Amp Parameters

An ideal op-amp would have infinite values of input impedance, gain,

and bandwidth, and have zero output impedance and give perfect

tracking between input and output. Practical op-amps fall short of all of

these ideals. Consequently, various performance parameters are

detailed in op-amp data sheets, and indicate the measure of 'goodness'

of a particular device. The most important of these parameters are

detailed below.

1. Ao (open-loop voltage gain). This is the low-frequency voltage

gain occurring between the input and output terminals of the op-

amp, and may be expressed in direct terms or in terms of dB.

Typical figures are x100,000, or 100dB.

2. ZIN (input impedance). This is the resistive impedance looking

directly into the input terminals of the op-amp when used open-

loop. Typical values are 1M0 for op-amps with bipolar input

stages, and a million megohms for FET-input op-amps.

3. Zo (output impedance). This is the resistive output impedance

of the basic op-amp when used open-loop. Values of a few

hundred ohms are typical of most op-amps.

4. Ib (input bias current). The input terminals of all op-amps sink

or source finite currents when biased for linear operation. The

magnitude of this current is denoted by Ib, and is typically a

fraction of a microamp in bipolar op-amps, and a few picoamps in

FET types.





5. VS (supply voltage range). Op-amps are usually operated from

split (+ve and -ve) supply rails, which must be within maximum

and minimum limits. If voltages are too high, the op-amp may be

damaged and, if too low, the op-amp will not function correctly.

Typical limits are ±3V to ±15V.

6. Vi(max) (input voltage range). Most op-amps will only operate

correctly if their input terminal voltages are below the supply line

values. Typically, Vi(max) is one or two volts less than VS.

7. Vio (differential input offset voltage). Ideally, an op-amp's

output should be zero when both inputs are grounded, but in

practice, slight imbalances within the op-amp cause it to act as

though a small offset or bias voltage exists on its inputs under this

condition. Typically, this Vio has a value of only a few mV, but

when this voltage is amplified by the gain of the circuit in which

the op-amp is used, it may be sufficient to drive the op-amp

output well away from the 'zero' value. Because of this, most op-

amps have some facility for externally nulling out the effects of

this offset voltage.

8. CMMR (common mode rejection ratio). An op-amp produces

an output proportional to the difference between the signals on its

two input terminals. Ideally, it should give zero output if identical

signals are applied to both inputs simultaneously, i.e., in common

mode. In practice, such signals do not entirely cancel out within

the op-amp, and produce a small output signal. The ability of an

op-amp to reject common mode signals is usually expressed in

terms of CMMR, i.e., the ratio of the op-amp's gain with

differential signals versus the gain with common mode signals.





CMMR values of 90dB are typical of most op-amps.

FIGURE 6. Typical frequency response curve of the 741op-amp.

9. fT (transition frequency). An op-amp typically gives a low-

frequency voltage gain of about 100dB, and in the interest of

stability, its open-loop frequency response is internally tailored so

that the gain falls off at a rate of 6dB/octave (= 20dB/decade),

eventually falling to unity (0dB) at a transition frequency denoted

fT. Figure 6 shows the typical response curve of the type 741 op-

amp, which has an fT value of 1MHz and a low-frequency gain of

106dB. Note that, when the op-amp is used in a closed loop

amplifier circuit, the circuit's bandwidth depends on the closed-

loop gain. Thus, in Figure 6, the circuit has a bandwidth of only

1kHz at a gain of 60dB, or 100kHz at a gain of 20dB. The fT figure





can thus be used to represent a gain-bandwidth product.

FIGURE 7. Effect of slew-rate limiting on the output of an

op-amp fed with a squarewave input.

10.Slew rate. As well as being subject to normal bandwidth

limitations, op-amps are also subject to a phenomenon known as

slew rate limiting, which has the effect of limiting the maximum

rate of change of voltage at the op-amp's output. Figure 7 shows

the effect that slew-rate limiting can have on the output of an op-

amp that is fed with a squarewave input. Slew rate is normally

specified in terms of volts per microsecond, and values in the

range 1V/mS to 10V/mS are usual with most popular types of op-

amp. One effect of slew rate limiting is to make a greater

bandwidth available to small-amplitude output signals than to

large-amplitude output signals.





Practical Op-Amps

Practical op-amps are available in a variety of types of IC construction

(bipolar, MOSFET, JFET, etc.), and in a variety of types of packaging

(plastic DIL, metal-can TO5, etc.). Some of these packages house two

or four op-amps, all sharing common supply line connections. Figure 8

gives parameter and outline details of eight popular 'single' op-amp

types, all of which use eight-pin DIL (DIP) packaging.

FIGURE 8. Parameter and outline details of eight popular 'single'

op-amp types.

The 741 and NE531 are bipolar types. The 741 is a popular general-

purpose op-amp featuring internal frequency compensation and full

overload protection on inputs and outputs. The NE531 is a high-

performance type with very high slew rate capability; an external

compensation capacitor (100pF) — wired between pins 6 and 8 — is





needed for stability, but can be reduced to a very low value (1.8pF) to

give a very wide bandwidth at high gain.

The CA3130 and CA3140 are MOSFET-input type op-amps that can

operate from single or dual power supplies, can sense inputs down to

the negative supply rail value, have ultra-high input impedances, and

have outputs that can be strobed; the CA3130 has a CMOS output

stage, and an external compensation capacitor (typically 47pF) between

pins 1 and 8 permits adjustment of bandwidth characteristics; the

CA3140 has a bipolar output stage and is internally compensated.

The LF351, LF411, TL081, and TL061 JFET types can be used as direct

replacements for the 741 in most applications; the TL061 is a low-

power version of the TL081.





Offset Nulling

All of the above op-amps are provided with an offset nulling facility, to

enable the output to be set to precisely zero with zero input, and this is

usually achieved by wiring a 10k pot between pins 1 and 5 and

connecting the pot slider (either directly or via a 4k7 range-limiting

resistor) to the negative supply rail (pin 4), as shown in Figure 9. In

the case of the CA3130, a 100k offset nulling pot must be used.

FIGURE 9. Typical offset nulling system.





Applications Roundup

Operational amplifiers are very versatile devices, and can be used in an

almost infinite variety of linear and switching applications. Figures 10

to 22 show a small selection of basic 'applications' circuits that can be

used, and which will be looked at in greater detail in the remaining

three episodes of this 'Op-Amp' mini-series. In most of these diagrams,

the supply line connections have been omitted for clarity.

FIGURE 10. Basic inverting (a) and non-inverting (b) AC

amplifier circuits.

Figure 10 shows basic ways of using op-amps to make fixed-gain

inverting or non-inverting AC amplifiers. In both cases, the gain and the

input impedance of the circuit can be precisely controlled by suitable

component value selection.

Figure 11 shows how to make a differential or difference amplifier with

a gain equal to R2/R1; if R1 and R2 have equal values, the circuit acts

as an analog subtractor.





FIGURE 11. Differential amplifier or analog subtractor.

FIGURE 12. Inverting analog adder or audio mixer.

Figure 12 shows the circuit of an inverting 'adder' or audio mixer; if R1

and R2 have equal values, the inverting output is equal to the sum of

the input voltages.





FIGURE 13. High-pass (a) and low-pass (b)

second-order active filters.

Op-amps can be made to act as precision active filters by wiring

suitable filters into their feedback networks. Figure 13 shows the basic

connections for making second-order high-pass and low-pass filters;

these circuits give roll-offs of 12dB/octave. Next month's episode of this

mini-series will show more sophisticated versions of these basic circuits.

FIGURE 14. Supply-line splitter.





FIGURE 15. Adjustable-voltage reference.

FIGURE 16. Adjustable-voltage DC power supply.

Figures 14 to 16 show some useful applications of the basic voltage

follower or unity-gain non-inverting DC amplifier. The Figure 14 circuit

acts as a supply line splitter, and is useful for generating split DC

supplies from single-ended ones. Figure 15 acts as a semi-precision

variable voltage reference, and Figure 16 shows how the output

current drive can be boosted so that the circuit acts as a variable

voltage supply.





FIGURE 17. Bridge-balancing detector/switch.

Figure 17 shows the basic circuit of a DC bridge-balancing detector, in

which the output swings high when the inverting pin voltage is above

that of the non-inverting pin, and vice versa. This circuit can be made to

function as a precision opto- or thermo-switch by replacing one of the

bridge resistors with an LDR or thermistor.

FIGURE 18. Precision half-wave rectifier.





FIGURE 19. Precision half-wave AD/DC converter.

Figures 18 and 19 show how to make precision half-wave rectifiers

and AC/DC converters. These are very useful instrumentation circuits.

FIGURE 20. Wien-bridge sinewave generator.





FIGURE 21. Free-running multivibrator.

FIGURE 22. Sine/square function generator.

Finally, to complete this opening episode, Figures 20 to 22 show some

useful waveform generator circuits. The Figure 20 design uses a Wien

bridge network to generate a good sinewave; amplitude stabilization is

obtained via a low-current lamp (or thermistor). Figure 21 is a very

useful squarewave generator circuit, in which the frequency can be

controlled via any one of the passive component values. The frequency

of the Figure 22 function generator circuit can also be controlled via

any one of its passive component values, but this particular design

generates both square and triangle output waveforms.





Inverting Amplifier Circuits

Figure 23 shows the practical circuit of an inverting DC amplifier with

an overall voltage gain (A) of x10 (= 20dB), and with an offset nulling

facility that enables the output to be set to precisely zero with zero

applied input. The voltage gain and input impedance are determined by

the R1 and R2 values, and can be altered to suit individual needs. The

gain can be made variable — if required — by using a series

combination of a fixed and a variable resistor in place of R2. For

optimum biasing stability, R3 should have a value equal to the parallel

values of R1 and R2.

FIGURE 23. Inverting DC amplifier with offset-

nulling facility and x10 voltage gain.





Note that the Figure 23 circuit will continue to function if the RV1

offset-nulling network is removed, but its output may offset by an

amount equal to the op-amp’s input offset voltage (typically 1mV in a

741) multiplied by the closed-loop voltage gain (A) of the circuit, e.g., if

the circuit has a gain of x100, the output may be offset by 100mV with

zero input applied.

Also note that the circuit’s bandwidth equals the fT value (typically 1MHz

in a 741) divided by the ‘A’ value, e.g., the Figure 23 circuit gives a

bandwidth of 100kHz with a gain of x10, or 10kHz with a gain of x100.

FIGURE 24. Inverting AC amplifier with x10 gain.

The Figure 23 circuit can be adapted for use as an AC amplifier by

simply wiring a blocking capacitor in series with the input terminal, as

shown in Figure 24. Note in this case that no offset nulling facility is

needed, and that (for optimum biasing) R3 is given a value equal to R2.





Non-Inverting Amplifier Circuits

An op-amp can be used as a non-inverting DC amplifier with offset

compensation by using the connections shown in Figure 25, which

shows an x10 amplifier. The voltage gain is determined by the ratios of

R1 and R2, as indicated. If R1 is given a value of zero, the gain falls to

unity; alternatively, if R2 is given a value of zero, the gain equals the

open-loop gain of the op-amp. The gain can thus be made variable by

replacing R1 with a pot and connecting its slider to the inverting

terminal of the op-amp, as shown in the circuit in Figure 26, in which

the gain can be varied over the range x1 to x101 via RV2.

FIGURE 25. Non-inverting DC amplifier

with offset-nulling facility and x10 gain.





FIGURE 26. Non-inverting variable

gain (x1 to x101) DC amplifier.

Note that — for correct operation — the input (non-inverting) terminal

of each of these circuits must be provided with a DC path to the

common or zero-volts rail; this path is provided by the DC input signal.

In Figure 25, the parallel values of R1 and R2 should ideally (for

optimum biasing) have a value equal to the source resistance of the

input signal.

A major feature of the non-inverting op-amp circuit is that it gives a

very high input impedance. In theory, this impedance is equal to the

open-loop input resistance (typically 1M0 in a bipolar 741) multiplied by

AO/A. In practice, input impedance values of hundreds of megohms can

easily be obtained in DC circuits such as those in Figures 25 and 26.

Figure 27 shows how the Figure 25 circuit can be modified for use as





an x10 non-inverting AC amplifier by removing the offset biasing

network, connecting the non-inverting terminal to ground via biasing

resistor R3, and connecting the input signal via a blocking capacitor.

Note that gain-control resistors R1-R2 are isolated from ground via

blocking capacitor C2, which has negligible impedance at practical

operating frequencies; the voltage gain is thus determined by the ratios

of R1 and R2, but the op-amp’s inverting terminal is subjected to

virtually 100% DC negative feedback, thus giving the circuit excellent

DC stability. For optimum biasing, R3 should have the same value as

R1.

FIGURE 27. Non-inverting x10 AC amplifier with

100k input impedance.





FIGURE 28. Non-inverting x10 AC amplifier with

50M input impedance.

Note that the input impedance of the Figure 27 circuit equals the R3

value, and is limited to a few megohms by practical considerations.

Figure 28 shows how the basic circuit can be modified to give a very

high input impedance (typically 50 megohms).

Here, the positions of C2 and R2 are transposed, and the low end of R3

is tied to the C2-R2 junction. As a consequence, near-identical

operating (AC) signal voltages appear at both ends of R3, which thus

passes negligible signal current and has an apparent impedance that is

massively increased by this ‘bootstrap’ action.

In practice, the circuit’s input impedance is typically limited to about 50

megohms by leakage impedances of the op-amp’s socket and the PCB

to which it is wired. Note that — for optimum DC biasing — the sum of

the R2 and R3 values should equal R1. In practice, the R3 value can

differ from this ideal by up to 30%, and an actual value of 100k can be

used in the Figure 28 circui, if desired.





Voltage Follower Circuits

A voltage follower circuit produces an output voltage that is identical to

that of the input signal, but has a very high input impedance and a very

low output impedance. The circuit actually functions as a unity-gain

non-inverting amplifier with 100% negative feedback. Figure 29 shows

the idealized design of a precision voltage follower with offset biasing.

Note that — for optimum biasing — feedback resistor R1 should have a

value equal to the source resistance of the input signal.

In practice, the basic Figure 29 circuit can often be greatly simplified.

Eliminating the offset biasing network, for example, adds an error of

only a few mV to the output of the op-amp. Again, the value of

feedback resistor R1 can be varied from zero to 100k without greatly

influencing the circuit’s accuracy.

FIGURE 29. Precision DC voltage

follower with offset null facility.





FIGURE 30. AC voltage follower with

100k input impedance.

If an op-amp with a low fT value (such as the 741) is used, the R1 value

can usually be reduced to zero. Note, however, that many ‘high fT’ op-

amps tend towards instability when used in the unity-gain mode and, in

such cases, R1 should be given a value of 1k0 or greater to effectively

reduce the circuit’s bandwidth and thus enhance stability.

Figure 30 shows an AC version of the voltage follower. In this case, the

input signal is DC-blocked via C1, and the op-amp’s non-inverting

terminal is tied to ground via R1, which determined the circuit’s input

impedance. Ideally, feedback resistor R2 should have the same value as

R1. If R2 has a high value, however, it may significantly reduce the

circuit’s bandwidth. This problem can be overcome by shunting R2 with

C2, as shown dotted. If the latter technique is used with a ‘high fT’ op-

amp, resistor R3 can be connected as shown to ensure circuit stability.

If a very high input impedance is required from an AC voltage follower,

it can be obtained by using the basic configuration shown in Figure 31,





in which R1 is ‘bootstrapped’ from the op-amp output via C2, thus

raising its impedance to near-infinity. In practice, this circuit can easily

give an input impedance of 50 megohms from a 741 op-amp; this limit

being set by the leakage impedance of the op-amp’s IC socket and the

PCB.

FIGURE 31. AC voltage follower with 50M input impedance

without the guard ring, or 500M with the guard ring.

If an even greater input impedance is needed, the area of PCB

surrounding the op-amp input pin should be provided with a printed

‘guard ring’ that is driven from the op-amp output, as shown, so that

the leakage impedances of the PCB, etc., are themselves bootstrapped

and raised to near-infinite values. In this case, the Figure 33 circuit

gives an input impedance of about 500 megohms when used with a 741

op-amp, or even greater if an FET-input op-amp is used.





Current-Boosted ‘FOLLOWER’ Circuits

Most op-amps can provide maximum output currents of only a few

milliamps, and this is the current-driving limit of the voltage follower

circuits in Figures 29 to 31. The current-driving capacity of a voltage

follower can easily be increased, however, by wiring a simple or a

complementary emitter follower current booster stage between the op-

amp output and the final output terminal of the circuit, as shown in the

basic designs in Figures 32 and 33. Note that the base-emitter

junctions of the transistors are wired into the negative feedback loop of

the op-amp, to minimize the effects of junction non-linearity.

FIGURE 32. Unidirectional DC voltage

follower with boosted output-current drive.





FIGURE 33. Bidirectional DC voltage follower

with boosted output-current drive.

The Figure 33 circuit is able to source large currents (via Q1), but can

sink only relatively small ones (via R1). This circuit can thus be

regarded as a unidirectional, positive-only, DC voltage follower.

The Figure 33 circuit can both source (via Q1) and sink (via Q2) large

output currents, and can be regarded as a bidirectional (positive and

negative) voltage follower. In the simple form shown in the diagram, the

circuit produces significant cross-over distortion as the output moves

around the zero volts value. This distortion can be eliminated by

suitably biasing Q1 and Q2.

In practice, the Figure 32 and 33 circuits have maximum current-drive

capacities of about 50mA, this figure being dictated by the low power

ratings of the specified transistors. Greater drive capacity can be

obtained by using alternative transistors.





Adders and Subtractors

Figure 34 shows the circuit of a unity-gain analog DC voltage adder,

which gives an inverted output voltage equal to the sum of the three

input voltages. Input resistors R1 to R3 and feedback resistor R4 have

identical values, so the circuit acts as a unity-gain inverting DC amplifier

between each input terminal and the output. The current flowing in R4

is equal to the sum of the R1 to R3 currents, and the inverted output

voltage is thus equal to the sum of the input voltages. In high-precision

applications, the circuit can be provided with an offset nulling facility.

FIGURE 34. Unity-gain inverting DC adder.





FIGURE 35. Unity-gain audio mixer.

The Figure 34 circuit is shown with three input connections, but can, in

fact, be given any number of inputs (each with a value equal to R1), but

in this case, the R5 value should (for optimum biasing) be altered to

equal the parallel values of all other resistors. If required, the circuit can

be made to give a voltage gain greater than unity by simply increasing

the value of feedback resistor R4. The circuit can be used as a multi-

input ‘audio mixer’ by AC-coupling the input signals and giving R5 the

same value as the feedback resistor, as shown in the four-input circuit

in Figure 35.





FIGURE 36. Unity-gain DC differential

amplifier, or subtractor.

Figure 36 shows the circuit of a unity-gain DC differential amplifier, or

analog subtractor, in which the output equals the difference between the

two input signal voltages, i.e., equals e2 - e1. In this type of circuit, the

component values are chosen such that R1/R2 = R3/R4, in which case,

the voltage gain, A, equals R2/R1. When — in Figure 36 — R1 and R2

have equal values, the circuit gives unity overall gain, and thus acts as

an analog subtractor.





Balanced Phase-Splitter

A phase-splitter has a pair of output terminals, which produce outputs

that are identical in amplitude and form, but with one output phase-

shifted by 180° (i.e., inverted) relative to the other. Figure 37 shows

an easy way of making a unity-gain balanced DC phase-splitter, using a

pair of 741 op-amps.

FIGURE 37. Unity-gain balanced DC phase-splitter.

Here, IC1 acts as a unity-gain non-inverting amplifier or voltage

follower, and provides a buffered output signal that is identical to that of

the input.

This output also provides the input drive to IC2, which acts as a unity-

gain inverting amplifier, and provides the second output, which is

inverted but is otherwise identical to the original input signal.





Active Filters

Filter circuits are used to reject unwanted frequencies and pass only

those wanted by the designer. A simple R-C low-pass filter (Figure

38(a)) passes low-frequency signals, but rejects high-frequency ones.

The output falls by 3dB at a ‘break’ or ‘cross-over’ frequency (fC) of

1/2πRC), and then falls at a rate of 6dB/octave (= 20dB/decade) as the

frequency is increased (see Figure 38(b)). Thus, a simple 1kHz filter

gives roughly 12dB of rejection to a 4kHz signal, and 20dB to a 10kHz

one.

FIGURE 38. Circuit and response curves of

simple 1st-order R-C filters.





A simple R-C high-pass filter (Figure 38(c)) passes high-frequency

signals, but rejects low-frequency ones. The output is 3dB down at a

break frequency of 1/2πRC), and then falls at a 6dB/octave rate as the

frequency is decreased below this value (Figure 38(d)). Thus, a simple

1kHz filter gives roughly 12dB of rejection to a 250Hz signal, or 20dB to

a 100Hz signal.

Each of the above two filter circuits uses a single R-C stage, and is

known as a ‘1st order’ filter. If a number (n) of similar filters are

effectively cascaded, the resulting circuit is known as an ‘nth order’

filter and has an output slope, beyond fC, of (n x 6dB)/octave.

Thus, a 4th order 1kHz low-pass filter has a slope of 24dB/octave, and

gives 48dB of rejection to a 4kHz signal, and 80dB to a 10kHz signal.

One way of effectively cascading such filters is to wire them into the

feedback networks of suitable op-amp amplifiers; such circuits are

known as ‘active filters,’ and Figures 39 to 45 show practical examples

of some of them.





Active Filter Circuits

Figure 39 shows the practical circuit and formula of a maximally-flat

(Butterworth) unity-gain 2nd-order low-pass filter with a 10kHz break

frequency. Its output falls off at a 12dB/octave rate beyond 10kHz, and

is about 40dB down at 100kHz, and so on. To change the break

frequency, simply change either the R or the C value in proportion to

the frequency ratio relative to Figure 39; reduce the values by this

ratio to increase the frequency, or increase them to reduce it. Thus, for

4kHz operation, increase the R values by a ratio of 10kHz/4kHz, or 2.5

times.

FIGURE 39. Unity-gain 2nd-order 10kHz

low-pass active filter.





FIGURE 40. ‘Equal components’ version of

2nd-order 10kHz low-pass active filter.

A minor snag with the Figure 39 circuit is that one of its C values must

be twice the value of the other, and this may demand odd component

values. Figure 40 shows an alternative 2nd-order 10kHz low-pass filter

circuit that overcomes this snag and uses equal component values. Note

here that the op-amp is designed to give a voltage gain (4.1dB in this

case) via R1 and R2, which must have the values shown

FIGURE 41. 4th-order 10kHz low-pass filter.





Figure 41 shows how two of these ‘equal component’ filters can be

cascaded to make a 4th-order low-pass filter with a slope of

24dB/octave. Note in this case that gain-determining resistors R1/R2

have a ratio of 6.644, and R3/R4 have a ratio of 0.805, giving an overall

voltage gain of 8.3dB. The odd values of R2 and R4 can be made up by

series-connecting 5% resistors.

FIGURE 42. Unity-gain 2nd-order 100Hz high-pass filter.

FIGURE 43. ‘Equal components’ version of

2nd-order 100Hz high-pass filter.





Figures 42 and 43 show unity-gain and ‘equal component’ versions

respectively of 2nd-order 100Hz high-pass filters, and Figure 44 shows

a 4th-order 100Hz high-pass filter. The operating frequencies of these

circuits, and those of Figures 41 and 42, can be altered in exactly the

same way as in Figure 39, i.e., by increasing the R or C values to

reduce the break frequency, or vice versa.

FIGURE 44. 4th-order 100Hz high-pass filter.

Finally, to complete this installment of the series, Figure 45 shows how

the Figure 43 high-pass and Figure 40 low-pass filters can be wired in

series to make (with suitable component value changes) a 300Hz to

3.4kHz speech filter that gives 12dB/octave rejection to all signals

outside of this range.





FIGURE 45. 300Hz to 3.4kHz speech filter with

2nd-order response.

In the case of the high-pass filter, the C values in Figure 43 are

reduced by a factor of three, to raise the break frequency from 100Hz

to 300Hz and, in the case of the low-pass filter, the R values in Figure

40 are increased by a factor of 2.94, to reduce the break frequency

from 10kHz to 3.4kHz.





Sinewave Oscillators

An op-amp can be made to act as a sinewave oscillator by connecting it

as a linear amplifier in the basic configuration shown in Figure 46, in

which the amplifier output is fed back to the input via a frequency-

selective network, and the overall gain of the amplifier is controlled via

a level-sensing system.

Figure 46. Conditions for stable sinewave oscillation.

For optimum sinewave generation, the feedback network must provide

an overall phase shift of zero degrees and a gain of unity at the desired

frequency. If the overall gain is less than unity, the circuit will not

oscillate and, if it is greater than unity, the output waveform will be

distorted.





Figure 47. Basic Wien Bridge sinewave oscillator.

One way of implementing the above principle is to connect a Wien

Bridge network and an op-amp in the basic configuration shown in

Figure 47. Here, the frequency-sensitive Wien Bridge network is

constructed from R1-C1 and R2-C2. Normally, the network is

symmetrical, so that C1 = C2 = C, and R1 = R2 = R. The main feature

of the Wien network is that the phase relationship of its output-to-input

signals varies from -90° to +90°, and is precisely 0° at a center

frequency (fO) of 1/2πpCR. At this center frequency, the symmetrical

network has a voltage gain of 0.33.

Thus, in Figure 47, the Wien network is connected between the output

and the non-inverting input of the op-amp, so that the circuit gives zero

overall phase shift at fO, and the actual amplifier is given a voltage gain

of x3 via feedback network R3-R4, to give the total system an overall

gain of unity.

The circuit thus provides the basic requirements of sinewave oscillation.

In practice, however, the ratios of R3-R4 must be carefully adjusted to

give overall voltage gain of precise unity that is necessary for low-

distortion sinewave generation.





The basic Figure 47 circuit can easily be modified to give automatic

gain adjustment and amplitude stability by replacing the passive R3-R4

gain-determining network with an active gain-control network that is

sensitive to the amplitude of the output signal, so that gain decreases

as the mean output amplitude increases, and vice versa. Figures 48 to

52 show some practical versions of Wien Bridge oscillators with

automatic amplitude stabilization.





Thermistor-Stabilized Circuits

Figure 48 shows the basic circuit of a 1kHz thermistor-stabilized Wien

bridge oscillator of the type that has been popular in the UK and other

European countries for many years. The thermistor used here is a

rather expensive and delicate RA53 (or similar) negative-temperature-

coefficient (ntc) type. The thermistor (TH1) and RV1 form a gain-

determining network.

Figure 48. Thermistor stabilized 1kHz

Wien Bridge oscillator.

The thermistor is heated by the mean output power of the op-amp, and

at the desired output signal level has a resistance value double that of

RV1, thus giving the op-amp a gain of x3 and the overall circuit a gain

of unity. If the oscillator output starts to rise, TH1 heats up and reduces

its resistance, thereby automatically reducing the circuit’s gain and

stabilizing the amplitude of the output signal.





Figure 49. 150Hz-1.5kHz lamp-stabilized Wien

Bridge oscillator.

An alternative method of thermistor stabilization is shown in Figure 49;

this circuit variant is very popular in the USA. In this circuit, a low-

current filament lamp is used as a positive-temperature-coefficient (ptc)

thermistor, and is placed in the lower part of the gain-determining

feedback network.

Thus, if the output amplitude increases, the lamp heats up and

increases its resistance, thereby reducing the circuit gain and providing

automatic amplitude stabilization. This circuit also shows how the Wien

network can be modified by using a twin-gang pot to make the oscillator

frequency variable over the range 150Hz to 1.5kHz, and how the

sinewave output amplitude can be made variable via RV3.

Note in the Figure 48 and 49 circuits that the pre-set pot should be

adjusted to set the maximum mean output signal level to about 2V

RMS, and that under this condition, the sinewave has a typical total

harmonic distortion (THD) level of about 0.1%.





If the circuit’s thermistor is a low-resistance type, it may be necessary

to interpose a bidirectional current-booster stage between the op-amp

output and the input of the amplitude control network, to give it

adequate drive.

Finally, a slightly annoying feature of thermistor-stabilized circuits is

that, in variable-frequency applications, the sinewave’s output

amplitude tends to judder or ‘bounce’ as the frequency control pot is

swept up and down its range.





Diode-Stabilization Circuits

Figure 50. Diode-regulated 150Hz-1.5kHz

Wien Bridge oscillator.

The amplitude ‘bounce’ problem of variable-frequency circuits can be

minimized by using the basic circuits in Figures 50 or 51, which rely

on the onset of diode or zener conduction for automatic gain control. In

essence, RV2 is set so that the circuit gain is slightly greater than unity

when the output is close to zero, causing the circuit to oscillate, but as

each half-cycle nears the desired peak value, one or other of the diodes

starts to conduct and thus reduces the circuit gain, automatically

stabilizing the peak amplitude of the output signal.





Figure 51. Zener-regulated 150Hz-1.5kHz Wien

Bridge oscillator.

This ‘limiting’ technique typically results in the generation of 1% to 2%

THD on the sinewave output when RV2 is set so that oscillation is

maintained over the whole frequency band. The maximum peak-to-peak

output of each circuit is roughly double the breakdown voltage of its

diode regulator element. In the Figure 50 circuit, the diodes start to

conduct at 500mV, so the circuit gives a peak-to-peak output of about

1V0; in the Figure 51 circuit, the zener diodes are connected back-to-

back and may have values as high as 5V6, giving a pk-to-pk output of

about 12V.





Figure 52. Three-decade (15Hz-15kHz) Wien Bridge oscillator.

The frequency ranges of the above circuits can be altered by changing

the C1 and C2 values; increasing the values by a decade reduces the

frequency by a decade. Figure 52 shows the circuit of a variable-

frequency Wien oscillator that covers the range 15Hz to 15kHz in three

switched decade ranges. The circuit uses zener diode amplitude

stabilization; its output amplitude is variable via both switched and

fully-variable attenuators. Note that the maximum useful operating

frequency of this type of circuit is restricted by the slew-rate limitations

of the op-amp. The limit is about 25kHz with a 741 op-amp, or about

70kHz with a CA3140.





A Twin-T Oscillator

Another way of making a sinewave oscillator is to wire a Twin-T network

between the output and input of an inverting op-amp, as shown in the

diode-regulated 1kHz oscillator circuit in Figure 53. The Twin-T network

comprises R1-R2-R3-RV1 and C1-C2-C3, and in a ‘balanced’ circuit;

these components are in the ratios R1 = R2 = 2 (R3 + RV1), and C1 =

C2 = C3/2.

When the network is perfectly balanced, it acts as a frequency-

dependent attenuator that gives zero output at a center frequency (fO)

of 1/2 π R1.C1, and a finite output at all other frequencies. When the

network is imperfectly balanced, it gives a minimal but finite output at

fO, and the phase of this output depends on the direction of the

imbalance: if the imbalance is caused by (R3 + RV1) being too low in

value, the output phase is inverted relative to the input.

Figure 53. Diode-regulated 1kHz Twin-T oscillator.





In Figure 53, the 1kHz Twin-T network is wired between the output and

the inverting input of the op-amp, and RV1 is critically adjusted so that

the Twin-T gives a small inverted output at fO; under this condition zero

overall phase inversion occurs around the feedback loop, and the circuit

oscillates at the 1kHz center frequency.

In practice, RV1 is adjusted so that oscillation is barely sustained and,

under this condition, the sinewave output distortion is less than 1%

THD. Automatic amplitude control is provided via D1, which provides a

feedback signal via RV2; this diode progressively conducts and reduces

the circuit gain when the diode forward voltage exceeds 500mV.

To set up the Figure 53 circuit, first set RV2 slider to the op-amp

output and adjust RV1 so that oscillation is just sustained; under this

condition, the output signal has an amplitude of about 500mV pk-to-pk.

RV2 then enables the output signal to be varied between 170mV and

3V0 RMS. Note that Twin-T circuits make good fixed-frequency sinewave

oscillators, but are not suitable for variable-frequency use, due to the

difficulties of varying three or four network components simultaneously.





Squarewave Generators

Figure 54. Basic relaxation oscillator circuit.

Figure 54 shows a basic op-amp relaxation oscillator or squarewave

generator using dual (split) power supplies. Its circuit action is such that

C1 alternately charges and discharges (via R1) towards an ‘aiming’ or

reference voltage set by R2-R3, and each time C1 reaches this aiming

voltage, a regenerative comparator action occurs and makes the op-

amp output switch state (to positive or negative saturation); this action

produces a symmetrical squarewave at the op-amp’s output and a non-

linear trianglewave across C1.





Figure 55. Simple 500Hz-5kHz

squarewave generator.

The operating frequency can be varied by altering either the R1 or C1

values or the R2-R3 ratios; this circuit is thus quite versatile. A fast op-

amp such as the CA3140 should be used if good output rise and fall

times are needed from the squarewave.

Figure 56. Improved 500Hz-5kHz squarewave generator.





Figure 55 shows the basic circuit adapted to make a practical 500Hz to

5kHz squarewave generator, with frequency variation obtained by

altering the R2-RV1-R3 attenuator ratio. Figure 56 shows the circuit

improved by using RV2 to pre-set the range of the RV1 frequency

control, and by using RV3 as an output amplitude control.

Figure 57. Four-decade, 2Hz-20kHz, squarewave generator.

Figure 57 shows how the above circuit can be modified to make a

general-purpose squarewave generator that covers the 2Hz to 20kHz

range in four switched decade ranges. Pre-set pots RV1 to RV4 are used

to precisely set the minimum frequency of the 2Hz to 20Hz, 20Hz to

200Hz, 20Hz to 2kHz, and 2kHz to 20kHz ranges, respectively.





Variable Symmetry

In the basic Figure 54 circuit, C1 alternately charges and discharges

via R1, and the circuit generates a symmetrical squarewave output. The

circuit can easily be modified to give a variable-symmetry output by

providing C1 with alternate charge and discharge paths, as shown in

Figures 58 and 59.

Figure 58. Squarewave generator with

variable M/S-ratio and frequency.

In the Figure 58 circuit, the mark/space (M/S) ratio of the output

waveform is fully variable from 11:1 to 1:11 via RV1, and the frequency

is variable from 650Hz to 6.5kHz via RV2. The circuit action is such that

C1 alternately charges up via R1-D1 and the left-hand side of RV1, and





discharges via R1-D2 and the right-hand side of RV1, to provide a

variable-symmetry output. In practice, variation of RV1 has negligible

effect on the operating frequency of the circuit.

Figure 59. Variable-frequency narrow-pulse generator.

In the Figure 59 circuit, the mark period is determined by C1-D1-R1,

and the space period by C1-D2-R2; these periods differ by a factor of

100, so the circuit generates a narrow pulse waveform. The pulse

frequency is variable from 300Hz to 3kHz via RV1.





Triangle-Square Generation

Figure 60 shows the basic circuit of a function generator that

simultaneously generates a linear triangle and a square waveform,

using two op-amps. IC1 is wired as an integrator, driven from the

output of IC2, and IC2 is wired as a differential voltage comparator,

driven from the output of IC1 via potential divider R2-R3, which is

connected between the outputs of IC1 and IC2. The squarewave output

of IC2 switches alternately between positive and negative saturation.

The circuit functions as follows.

Suppose initially that the output of IC1 is positive and the output of IC2

has just switched to positive saturation. The inverting input of IC1 is a

virtual earth point, so a current (i) of +Vsat/R1 flows into R1, causing

the output of IC1 to start to swing down linearly at a rate of i/C1 volts

per second. This output is fed — via the R2-R3 divider — to the non-

inverting input of IC2, which has its inverting terminal referenced

directly to ground.

Consequently, the output of IC1 swings linearly to a negative value until

the R2-R3 junction voltage falls to zero, at which point IC2 enters a

regenerative switching phase, in which its output abruptly switches to

negative saturation. This reverses the inputs of IC1 and IC2, so IC1

output starts to rise linearly, until it reaches a positive value at which

the R2-R3 junction voltage reaches the zero volts reference value,

initiating another switching action. The whole process then repeats add

infinitum.





Figure 60. Basic triangle/square function generator.

Important points to note about the Figure 60 circuit are that the pk-to-

pk amplitude of the linear triangle waveform is controlled by the R2-R3

ratio, and that the circuit’s operating frequency can be altered by

changing either the ratios of R2-R3, the values of R1 or C1, or by

feeding R1 from a potential divider connected to the output of IC2

(rather than directly from IC2 output. Figure 61 shows the practical

circuit of a variable-frequency triangle/square generator that uses the

latter technique.

Figure 61. 100Hz-1kHz triangle/square function generator.





In Figure 61, the input current of C1 (obtained from RV2-R2) can be

varied over a 10:1 range via RV1, enabling the frequency to be varied

from 100Hz to 1kHz; RV2 enables the full-scale frequency to be set to

precisely 1kHz. The amplitude of the linear triangle output waveform is

fully variable via RV3, and of the squarewave via RV4.

Figure 62. 100Hz-1kHz ramp/rectangle generator with

variable slope-M/S ratio.

The Figure 61 circuit generates symmetrical output waveforms, since

C1 alternately charges and discharges at equal current values

(determined by RV2-R2, etc.). Figure 62 shows how the circuit can be

modified to make a variable-symmetry ramp/rectangle generator, in

which the slope is variable via RV2. C1 alternately charges via R2-D1

and the upper half of RV2, and discharges via R2-D2 and the lower half

of RV2.





Switching Circuits

Figures 63 to 65 show three ways of using op-amps as simple

regenerative switches. Figure 63 shows the connections for making a

simple manually-triggered bistable circuit. Note here that the inverting

terminal of the op-amp is tied to ground via R1, and the non-inverting

terminal is tied directly to the output. The circuit operates as follows.

Figure 63. Simple manually-triggered bistable.

Normally, SW1 and SW2 are open. If SW1 is briefly closed, the op-amp

inverting terminal is momentarily pulled high and the output is driven to

negative saturation; consequently, when SW1 is released again, the

inverting terminal returns to zero volts, but the output and the non-

inverting terminals remain in negative saturation.





Figure 64. Single-supply manually-triggered bistable.

The output remains in this state until SW2 is briefly closed, at which

point, the op-amp output switches to positive saturation, and locks into

this state until SW1 is again operated. The circuit thus gives a bistable

form of operation. Figure 64 shows how the circuit can be modified for

operation from a single-ended power supply. In this case, the op-amp’s

inverting terminal is biased to half-supply volts via R1 and the R2-R3

potential divider.

Figure 65. Schmitt trigger.





Finally, Figure 65 shows how to connect an op-amp as a Schmitt

trigger, which can (for example), be used to convert a sinewave input

into a squarewave output. The circuit operates as follows.

Suppose initially that the op-amp output is at a positive saturation value

of 8V0. Under this condition, the R1-R2 divider feeds a positive

reference voltage of 8V x (R1+R2)/R2 (= about 80mV in this case) to

the op-amp’s non-inverting pin. Consequently, the output remains in

this state until the input rises to a value equal to this voltage, at which

point the op-amp output switches regeneratively to a negative

saturation level of -8V0, feeding a reference voltage of -80mV to the

non-inverting input.

The output remains in this state until the input signal falls to -80mV, at

which point, the op-amp output switches regeneratively back to the

positive saturation level. The process then repeats add infinitum. The

actual switching levels can be altered by changing the R1 value.





Electronic Rectifier Circuits

Simple diodes are poor rectifiers of low-level AC signals, and do not

start to conduct until the applied voltage exceeds a certain ‘knee’ value;

silicon diodes have knee values of about 600mV, and thus give

negligible rectification of signal voltages below this value. This weakness

can be overcome by wiring the diode into the feedback loop of an op-

amp, in such a way that the effective knee voltage is reduced by a

factor equal to the op-amp’s open-loop voltage gain; the combination

then acts as a near-perfect rectifier that can respond to signal inputs as

low as a fraction of a millivolt. Figure 1 shows a simple half-wave

rectifier of this type.

FIGURE 66. Simple half-wave rectifier circuit.

The Figure 66 circuit is wired as a non-inverting amplifier with

feedback applied via silicon diode D1, and with the circuit output taken

from across load resistor R1. When positive input signals are applied to

the circuit, the op-amp output also goes positive; an input of only a few





microvolts is enough to drive the op-amp output to the 600mV ‘knee’

voltage of D1, at which point, D1 becomes forward biased. Negative

feedback through D1 then forces the inverting input (and thus the

circuit’s output) to accurately follow all positive input signals greater

than a few microvolts. The circuit thus acts as a voltage follower to

positive input signals.

When the input signal is negative, the op-amp output swings negative

and reverse biases D1. Under this condition, the reverse leakage

resistance of D1 (typically hundreds of megohms) acts as a potential

divider with R1 and determines the negative voltage gain of the circuit;

typically, with the component values shown, the negative gain is

roughly -60dB. The circuit thus ‘follows’ positive input signals but

rejects negative ones, and hence acts like a near-perfect signal rectifier.

FIGURE 67. Peak detector with buffered output.

Figure 67 shows how the above circuit can be modified to act as a

peak voltage detector by wiring C1 in parallel with R1. This capacitor

charges rapidly, via D1, to the peak positive value of an input signal,

but discharges slowly via R1 when the signal falls below the peak value.





IC2 is used as a voltage-following buffer stage, to ensure that R1 is not

shunted by external loading effects.

Note that the basic Figure 66 and 67 circuits each have a very high

input impedance. In most practical applications, the input signal should

be AC-coupled and pin 3 of the op-amp should be tied to the common

rail via a 100k resistor.





Precision Rectifier Circuits

The Figure 66 rectifier circuit has a rather limited frequency response,

and may produce a slight negative output signal if D1 has poor reverse

resistance characteristics. Figure 68 shows an alternative type of half-

wave rectifier circuit, which has a greatly improved rectifier

performance at the expense of a greatly reduced input impedance.

FIGURE 68. Precision half-wave rectifier.

In Figure 68, the op-amp is wired as an inverting amplifier with a 10k

(= R1) input impedance. When the input signal is negative, the op-amp

output swings positive, forward biasing D1 and developing an output

across R2. Under this condition the voltage gain equals (R2+RD)/R1,

where RD is the active resistance of this diode. Thus, when D1 is

operating below its knee value its resistance is large and the circuit

gives high gain, but when D1 is operating above the knee value its





resistance is very low and the circuit gain equals R2/R1. The circuit thus

acts as an inverting precision rectifier to negative input signals.

When the input signal goes positive, the op-amp output swings

negative, but the negative swing is limited to -600mV via D2, and the

output at the D1-R2 junction does not significantly shift from zero under

this condition. This circuit thus produces a positive-going half-wave

rectified output. The basic circuit can be made to give a negative-going

half-wave rectified output by simply reversing the polarities of the two

diodes.

FIGURE 69. Precision full-wave rectifier.

Figure 69 shows how a negative-output version of the above circuit

can be combined with an inverting ‘adder’ to make a precision full-wave

rectifier. Here, IC2 inverts and gives x2 gain (via R3-R5) to the half-

wave rectified signal of IC1, and inverts and gives unity gain (via R4-

R5) to the original input signal (Ein). Thus, when negative input signals

are applied, the output of IC1 is zero, so the output of IC2 equals +E in.





When positive input signals are applied, IC1 gives a negative output, so

IC2 generates an output of +2Ein via IC1 and -Ein via the original input

signal, thus giving an actual output of +Ein. The output of this circuit is

thus positive, and always has a value equal to the absolute value of the

input signal.





AC/DC Converter Circuits

The Figure 68 and 69 circuits can be made to function as precision

AC/DC converters by first providing them with voltage-gain values

suitable for form-factor correction, and by then integrating their outputs

to give the AC/DC conversion, as shown in Figures 70 and 71,

respectively. Note that these circuits are intended for use with sinewave

input signals only.

FIGURE 70. Precision half-wave AC/DC converter.

In the half-wave AC/DC converter in Figure 70, the circuit gives a

voltage gain of x2.22 via R2/R1, to give form-factor correction, and

integration is accomplished via C1-R2. Note that this circuit has a high

output impedance, and the output must be buffered if it is to be fed to

low-impedance loads.





FIGURE 71. Precision full-wave AC/DC converter.

In the full-wave AC/DC converter in Figure 71, the circuit has a voltage

gain of x1.11 to give form-factor correction, and integration is

accomplished via C1-R5. This circuit has a low-impedance output.





DVM Converter Circuits

Precision 3-1/2 digit Digital Voltmeter (DVM) modules are readily

available at modest cost, and can easily be used as the basis of

individually-built multi-range and multi-function meters. These modules

are usually powered via a 9V battery, and have a basic full-scale

measurement sensitivity of 200mV DC and a near-infinite input

resistance. They can be made to act as multi-range DC voltmeters by

simply feeding the test voltage to the module via a suitable ‘multiplier’

(resistive attenuator) network, or as multi-range DC current meters by

feeding the test current to the module via a switched current shunt.

FIGURE 72. AC/DC converter for use with DVM module.

A DVM module can be used to measure AC voltages by connecting a

suitable AC/DC converter to its input terminals, as shown in Figure 72.

This particular converter has a near-infinite input impedance. The op-





amp is used in the non-inverting mode, with DC feedback applied via R2

and AC feedback applied via C1-C2 and the diode-resistor network.

The converter gain is variable over a limited range (to give form-factor

correction) via RV1, and the circuit’s rectified output is integrated via

R6-C3, to give DC conversion. The COMMON terminal of the DVM

module is internally biased at about 2.8 volts below the VDD (positive

supply terminal) voltage, and the CA3140 op-amp uses the VDD,

COMMON, and VSS terminals of the module as its supply rail points.

FIGURE 73. Five-range AC voltmeter converter for

use with DVM modules.

Figure 73 shows a simple frequency-compensated attenuator network

used in conjunction with the above AC/DC converter to convert a

standard DVM module into a five-range AC voltmeter, and Figure 74

shows how a switched shunt network can be used to convert the

module into a five-range AC current meter.





FIGURE 74. Five-range AC current-meter

converter for use with DVM modules.

FIGURE 75. Five-range ohmmeter converter for use

with DVM modules.

Figure 75 shows a circuit that can be used to convert a DVM module

into a five-range ohmmeter. This circuit actually functions as a multi-

range constant-current generator, in which the constant current feeds





(from Q1 collector) into RX, and the resulting RX volt drop (which is

directly proportional to the RX value) is read by the DVM module.

Here, Q1 and the op-amp are wired as a compound voltage follower, in

which Q1 emitter precisely follows the voltage set on RV1 slider. In

practice, this voltage is set at exactly 1V0 below VDD, and the emitter

and collector (RX) currents of Q1 thus equal 1V0 divided by the R3 to

R7 range-resistor value, e.g., 1mA with R3 in circuit, etc. The actual

DVM module reads full scale when the RX voltage equals 200mV, and

this reading is obtained when RX has a value one-fifth of that of the

range resistor, e.g., 200R on Range 1, or 2M0 on Range 5, etc.





Analog Meter Circuits

An op-amp can easily be used to convert a standard moving coil meter

into a sensitive analog voltage, current, or resistance meter, as shown

in the practical circuits of Figures 76 to 77. All six circuits operate from

dual 9V supplies and are designed around the LF351 JFET op-amp,

which has a very high input impedance and good drift characteristics.

All circuits have an offset nulling facility, to enable the meter readings to

be set to precisely zero with zero input, and are designed to operate

with a moving coil meter with a basic sensitivity of 1mA fsd.

If desired, these circuits can be used in conjunction with the 1mA DC

range of an existing multi-meter, in which case, these circuits function

as ‘range converters.’ Note that each circuit has a 2k7 resistor wired in

series with the output of its op-amp, to limit the available output

current to a couple of milliamps and thus provide the meter with

automatic overload protection.

FIGURE 76. A DC millivoltmeter circuit.





Figure 76 shows a simple way of converting the 1mA meter into a

fixed-range DC millivolt meter with a full-scale sensitivity of 1mV, 10mV,

100mV, or 1V0. The circuit has an input sensitivity of 1M0/volt, and the

table shows the appropriate R1 value for different fsd sensitivities. To

set the circuit up initially, short its input terminals together and adjust

RV1 to give zero deflection on the meter. The circuit is then ready for

use.

FIGURE 77. A DC voltage or current meter.

Figure 77 shows a circuit that can be used to convert a 1mA meter into

either a fixed-range DC voltmeter with any full-scale sensitivity in the

range 100mV to 1000V, or a fixed-range DC current meter with a full-

scale sensitivity in the range 1µA to 1A. The table shows alternative R1

and R2 values for different ranges.





FIGURE 78. Four-range DC millivoltmeter.

Figure 78 shows how the above circuit can be modified to make a four-

range DC millivolt meter with fsd ranges of 1mV, 10mV, 100mV, and

1V0, and Figure 79 shows how it can be modified to make a four-range

DC microammeter with fsd ranges of 1µA, 10µA, 100µA, and 1mA. The

range resistors used in these circuits should have precisions of 2% or

better.

FIGURE 79. Four-range DC microammeter.

Figure 80 shows the circuit of a simple but very useful four-range AC





millivoltmeter. The input impedance of the circuit is equal to R1, and

varies from 1k0 in the 1mV fsd mode to 1M0 in the 1V fsd mode. The

circuit gives a useful performance at frequencies up to about 100kHz

when used in the 1mV to 100mV fsd modes. In the 1V fsd mode, the

frequency response extends up to a few tens of kHz. This good

frequency response is ensured by the LF351 op-amp, which has very

good bandwidth characteristics.

FIGURE 80. Four-range AC millivoltmeter.

Finally, Figure 81 shows the circuit of a five-range linear-scale

ohmmeter, which has full-scale sensitivities ranging from 1k0 to 10M.

Range resistors R5 to R9 determine the measurement accuracy. Q1-ZD1

and the associated components simply apply a fixed 1V0 (nominal) to

the ‘common’ side of the range-resistor network, and the gain of the

op-amp circuit is determined by the ratios of the selected range-resistor

and RX and equals unity when these components have equal values.

The meter reads full-scale under this condition, since it is calibrated to

indicate full-scale when 1V0 (nominal) appears across the RX terminals.





FIGURE 81. Five-range linear-scale ohmmeter.

To initially set up the Figure 81 circuit, set SW1 to the 10k position and

short the RX terminals together. Then adjust the RV1 ‘set zero’ control

to give zero deflection on the meter. Next, remove the short, connect an

accurate 10k resistor in the RX position, and adjust RV2 to give

precisely full-scale deflection on the meter. The circuit is then ready for

use, and should need no further adjustment for several months.





Voltage Reference Circuits

An op-amp can be used as a fixed or variable voltage reference by

wiring it as a voltage follower and applying a suitable reference to its

input. An op-amp has a very high input impedance when used in the

‘follower’ mode and thus draws near-zero current from the input

reference, but has a very low output impedance and can supply several

milliamps of current to an external load. Variations in output loading

cause little change in the output voltage value.

FIGURE 82. Variable positive voltage reference.

Figure 82 shows a practical positive voltage reference with an output

fully variable from +0.2V to +12V via RV1. Zener diode ZD1 generates

a stable 12V, which is applied to the non-inverting input of the op-amp

via RV1. A CA3140 op-amp is used here because its input and output

can track signals to within 200mV of the negative supply rail voltage.





The complete circuit is powered from an unregulated single-ended 18V

supply.

FIGURE 83. Variable negative voltage reference.

Figure 83 shows a negative voltage reference that gives an output fully

variable from -0.5V to -12V via RV1. An LF351 op-amp is used in this

design, because its input and output can track signals to within about

0.5V of the positive supply rail value. Note that the op-amps used in

these two regulator circuits are wide-band devices, and R2 is used to

enhance their circuit stability.





Voltage Regulator Circuits

The basic circuits in Figures 82 and 83 can be made to act as high-

current regulated voltage (power) supply circuits by wiring current-

boosting transistor networks into their outputs.

FIGURE 84. Simple variable-voltage

regulated power supply.

Figure 84 shows how the Figure 82 circuit can be modified to act as a

1V to 12V variable power supply with an output current capability

(limited by Q1’s power rating) of about 100mA. Note that the base-

emitter junction of Q1 is included in the circuit’s negative feedback loop,

to minimize offset effects. The circuit can be made to give an output

that is variable all the way down to zero volts by connecting pin 4 of the

op-amp to a supply that is at least 2V negative.





FIGURE 85. 3V to 15V, 0 to 100 mA stabilized PSU.

Figure 85 shows an alternative type of power supply circuit, in which

the output is variable from 3V to 15V at currents up to 100mA.

In this case, a fixed 3V reference is applied to the non-inverting input

terminal of the 741 op-amp via ZD1 and the R2-C1-R3 network, and the

op-amp plus Q1 are wired as a non-inverting amplifier with gain

variable via RV1.

When RV1 slider is set to the upper position, the circuit gives unity gain

and gives an output of 3V; when RV1 slider is set to the lower position

the circuit gives a gain of x5 and thus gives an output of 15V. The gain

is fully variable between these two values. RV2 enables the maximum

output voltage to be pre-set to precisely 15V.

Figure 86 shows how the above circuit can be modified to act as a 3V

to 30V, 0 to 1A stabilized power supply unit (PSU). Here, the available

output current is boosted by the Darlington-connected Q1-Q2 pair of





FIGURE 86. 3V to 30V, 0 to 1 amp stabilized PSU.

transistors, the circuit gain is fully variable from unity to x10 via RV1,

and the stability of the 3V reference input to the op-amp is enhanced by

the ZD1 pre-regulator network.

FIGURE 87. 3V to 30V stabilized PSU with

overload protection.





Figure 87 shows how the above circuit can be further modified to

incorporate automatic overload protection. Here, R6 senses the

magnitude of the output current and when this exceeds 1A, the

resulting volt drop starts to bias Q3 on, thereby shunting the base-drive

current of Q1 and automatically limiting the circuits output current.

FIGURE 88. Simple center-tapped 0 to 30V PSU.

Finally, Figure 88 shows the circuit of a simple center-tapped 0 to 30V

PSU that can provide maximum output currents of about 50mA. The

PSU has three output terminals, and can provide either 0 to +15V

between the common and +ve terminals and 0 to -15V between the

common and -ve terminals, or 0 to 30V between the -ve and +ve

terminals. The circuit operates as follows: ZD1 and R2-RV1 provide a

regulated 0 to 5V potential to the input of IC1. IC1 and Q1 are wired as

a x3 non-inverting amplifier, and thus generate a fully variable 0 to 15V

on the +ve terminal of the PSU.

This voltage is also applied to the input of the IC2-Q2 circuit, which is

wired as a unity-gain inverting amplifier and thus generates an output





voltage of identical magnitude, but opposite polarity on the -ve terminal

of the PSU.

The output current capability of each terminal is limited to about 50mA

by the power ratings of Q1 and Q2, but can easily be increased by

replacing these components with Darlington (Super-Alpha) power

transistors of appropriate polarity.








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