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BTEC HNC ELECTRICAL / ELECTRONIC ENGINEERING Digital & Analogue Devices & Circuits OPERATIONAL AMPLIFIER CIRCUITS ElectroTech007 04-01-10

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Operational Amplifier Characteristics

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Page 1: HNC EEE OpAmp ElectroTech007

BTEC HNC ELECTRICAL / ELECTRONIC ENGINEERING

Digital & Analogue Devices & Circuits

OPERATIONAL AMPLIFIER CIRCUITS

ElectroTech007

04-01-10

Page 2: HNC EEE OpAmp ElectroTech007

Task.1

The operational amplifier is a differential amplifier with an extremely high voltage

gain and there are many types available.

By carrying out an investigation write a report documenting the key properties of an

„op-amp‟. The report should include the following points.

(i) History

(ii) Construction

(iii) Common types

(iv) Packaging

(v) Basic operation

(vi) Operational characteristics (ideal & actual)

(vii) Voltage gain & bandwidth

Page 3: HNC EEE OpAmp ElectroTech007

(i) History

The development of the operational amplifier as we know it today began in the late

1800‟s with devices not directly associated with amplification, and since then has

revolutionised the design of electronic signal processing equipment. The solid-state

op amp of today plays the same building block role in analog systems as logic gates

and counters do in modern digital systems.

Shown below is a time-line documenting the developmental history of the operational

amplifier from its early beginnings to the modern day 21st century.

1879 – Thomas Edison invents the filament based lamp (fig.2)

Fig.1 First successful filament lamp Fig.2 T.A Edison electric lamp patent

(Wikipedia)

1904 – J.A. Fleming (fig.4) invents a two element vacuum based diode called the

„Fleming diode‟ (fig.3) although not an amplifier; it layed the ground work for further

investigations.

Fig.3 the Fleming Diode Fig.4 Sir J.A Fleming (www.r-type.org)

Page 4: HNC EEE OpAmp ElectroTech007

1906 – Lee De Forest (fig.6) invents a three element triode vacuum tube known as the

„Audion‟ (fig.5) which was the first active device capable of amplification.

Fig.5 the „Audion‟ Fig.6 Lee De Forest

(www.britannica.com)

1928 – Harold S Black (fig.8) working for the Western Electric Company files a

patent for his work into the application of negative feedback. Black was the first to

develop feedback amplifier principles (fig.7) which he published in the Bell System

Technical Journal in 1934. His patent was received in 1937. Black‟s feedback

principle consisted of the application of a portion of the output back into the input

which had the effect of reducing overall gain, giving enhanced gain stability, greater

bandwidth, lower distortion and modified input and output impedances. This work

forms the basis of all modern advances in operational amplifiers. Others around this

time involved in research on the topic of feedback amplification and stability were

Harry Nyquist and Hendrick Bode.

Fig.7 Block diagram of Black‟s feedback amplifier with forward gain μ and feedback

path β (Op amp history Walt Jung)

Fig.8 Harold S Black (www.wpi.edu)

Page 5: HNC EEE OpAmp ElectroTech007

1941 – Karl D Swartzel of Bell Labs patents the design of the first general purpose,

DC coupled inverting feedback amplifier known as the summing amplifier.

It operated on +/- 350V rails and produced a gain of 90dB by the use of three vacuum

tubes.

1943 – John R Ragazzini (fig.9) produced a paper “Analysis of Problems in Dynamics

by Electronic Circuits”. This paper included the work of George A Philbrick and was

the first instance of the term operational amplifier being used; it was later published

by the I.R.E in 1947. The research paper was closely linked to work carried out as

early as 1940 by the U.S. National Defence Research Council. The paper mentioned

operational amplifier as “a generic term applied to amplifiers whose gain functions

are such to enable them to perform certain useful operations such as summation,

integration, differentiation, or a combination of such operations.”

Fig.9 John R Ragazzini

The following diagram (fig.10) was included showing a direct-current amplifier for

use in electronic computers

Fig.10 Direct-current amplifier for use in electronic computers “Analysis of Problems

in Dynamics by Electronic Circuits” John R Ragazzini - 1947

Page 6: HNC EEE OpAmp ElectroTech007

1947 – Operational amplifiers as now known were being employed in analog

computers to perform mathematical operations hence the name „operational‟. This

was the beginning of the modern electronic age. The photograph below (fig.11) shows

typical laboratory electronic computer arrangement with one set of amplifiers. The

schematic for this system which was an electronic computer for symmetric motions of

an aircraft is also shown (fig.12)

Fig.11 Typical laboratory electronic computer arrangement for aircraft symmetrical

motions system. One set of amplifiers can be seen on the lower left bay

Fig.12 Electronic computer schematic for symmetric motions of an aircraft

Page 7: HNC EEE OpAmp ElectroTech007

1952 – The first vacuum tube non inverting operational amplifier was introduced by

George A Philbrick Researches called the K2-W tube general purpose computing op

amp (fig.13). These first vacuum tube designs were complex, bulky and expensive

and were soon to give way to transistorized solid-state versions.

Fig.13 K2-W general purpose computing op amp shown with and without its bakelite

shell

More construction photographs of the K2-W (embree version) can be seen below (fig

14, 15, 16)

Fig.14 Fig.15

Fig.16 K2-W tube interior (The Philbrick archive - www.philbrickarchive.org)

Page 8: HNC EEE OpAmp ElectroTech007

From fig.16 we see that the interior of the K2-W general purpose computing op amp

looks messy. The construction method was to hay wire everything over a jig and then

carefully solder everything into place manually. The 8 pin base would be plugged into

the user socket and the 9 pin tubes then plugged in at the top. The whole device was

then encased inside 2 Bakelite shells. (Info from electronicdesign.com)

The first K2-W data sheet can be seen below (fig.17a, fig.17b)

Fig.17a Original K2-W datasheet page 1 - overview (www.philbrickarchive.org)

Page 9: HNC EEE OpAmp ElectroTech007

Fig.17b Original K2-W datasheet page 2 - technical specifications

(www.philbrickarchive.org)

Page 10: HNC EEE OpAmp ElectroTech007

The circuit schematic (fig.18) for the K2-W is shown below (taken from datasheet).

Fig.18 K2-W schematic diagram

1958 – Jack Kilby (fig.19) an engineer from Texas Instruments invented the

integrated circuit (fig20). This would be the turning point for designers involve in the

development of op amps as it would be possible to build an op amp on a single IC

chip.

Fig.19 Jack Kilby Fig.20 First working IC

Page 11: HNC EEE OpAmp ElectroTech007

1962 – The first solid-state monolithic op amps introduced by Burr-Brown Research

Corporation and G.A. Philbrick Researched Inc. One of the first packages was the

PP65 (fig.21), a square outlined potted 7 pin op amp; five pins on one side controlled

the output, power and offset while the other two pins were input pins.

Fig.21 G.A Phil brick‟s PP65 design

(Op amp applications handbook – Walter G Jung)

1963 – The first solid state monolithic op amp; the UA702 (fig.23) was introduced to

the public. Designed by Bob Widlar (fig.22) and manufactured by Fairchild

Semiconductor.

Fig.22 Bob Widlar (www.national.com)

Fig.23 UA702 the first op amp designed by Bob Widlar

Page 12: HNC EEE OpAmp ElectroTech007

1965 – The UA709 (fig.24) was introduced by Fairchild semiconductor; this was due

to further development work by Bob Widlar. The UA709 had a higher gain (45000 or

94 dB), larger bandwidth, low input current and more user friendly supply voltages of

+/-15V. The UA709 was a complete success and demand for the product resulted in

dramatic price decreases from $70 dollars per unit when first released to around $2 a

unit at its peak.

Fig.24 UA709 op amp schematic designed by Bob Widlar

Fig.25 UA709 op amp dual in line package (DIL)

Page 13: HNC EEE OpAmp ElectroTech007

1966 – Bob Widlar left Fairchild Semiconductor to join the young National

Semiconductor.

1967 – National Semiconductor introduces the LM101 (fig.25), designed again by

Bob Widlar. The LM101 boasts an increased gain of 160k and a wider operating

range. Also included is short circuit protection which was achieved by placing

external capacitors between specific pins. This was later achieved internally in the

form of the LH101 which was basically the LM101 with an internal capacitor in a

single packaged IC.

Fig.25 LM101 op amp designed by Bob Widlar

1968 – Competition commenced between Fairchild Semiconductor and National

Semiconductor in the battle between National‟s LH101 and Fairchild‟s new UA741

which were essentially the same in that frequency compensation on both chips is

achieved with internal capacitors, the only differences are that the 741 achieves offset

null by adjustment of currents in input stage emitters where the 101 achieves this by

adjustment of currents in the input stage collectors.

Later in 1968 National Semiconductor released the LM101A which provided greater

input control over temperature and lower offset currents, and following this the

LM107 which had a frequency compensation capacitor built into the chip. Fairchild

then produced the UA748 which had external frequency compensation.

1973 – Analog Devices produce the AD741 a high precision model 741 type op amp.

Page 14: HNC EEE OpAmp ElectroTech007

1974 – Raytheon Semiconductor produced the first dual package op amp the RC4558.

The RC4558 (fig.26) had characteristics similar to Fairchild‟s 741 but used NPN

transistors at its input.

Fig.26 RC4558 op amp schematic (2 on each IC)

Later in 1974 National Semiconductor released its LM324 quad op amp package

(fig.27, 28) which had four op amps on one chip. The LM324 was similar in operation

to the UA741 but had low power consumption.

Fig.27 LM324 op amp schematic (4 on each IC)

Page 15: HNC EEE OpAmp ElectroTech007

Fig.28 LM324 quad DIL package

1975 – RCA produced the first FET input op amp the CA3130 (fig.29) with extremely

low input current and a wide operating range of +5 - +15 V.

Fig.29 CA3130 FET input op amp schematic

Page 16: HNC EEE OpAmp ElectroTech007

In the same year National Semiconductor produced the LF355 (fig.30), the first J-FET

type created using ion implantation method.

Fig.30 LF355 JFET input op amp schematic

1976 – Texas Instruments produce the TL084 (fig.31), a quad J-FET type op amp

using the same ion implantation manufacturing method as National‟s LF355. It boasts

low bias current and high speed operation.

Fig.31 TLO84 Quad JFET op amp schematic (4 on one IC)

1976 – Present

Since 1976 the pace at which new op amps have been developed has increased

tenfold. New advances in manufacturing technology and processes has brought a

range of opportunities for advanced op amp technology which has resulted in the

range of op amps available today to suit almost any purpose. High speed, high

frequency, and low noise op amps are just a few areas that show these technological

advances in full.

Page 17: HNC EEE OpAmp ElectroTech007

(ii) Construction

As operational amplifier technology has advanced through out the years so to have the

methods used for construction. From the earliest vacuum tube technology which was

large and bulky to the tiny modern semiconductor IC‟s, we have seen that

miniaturisation has been the key objective. With semiconductor manufacturers

advancing their processes into the nanoscale (at present as far as 45nm) this trend will

continue.

Although op amp construction techniques have changed dramatically over the years

with advances in semiconductor materials and techniques, the original circuits have

remained almost untouched, with the main catalyst for change being advancing

transistor technology such as, FET‟s, JFET‟s, MOSFET‟s etc.

In the following part of this report we examine the construction, both internally and

externally of the uA741 general purpose op amp as originally designed by Fairchild

Semiconductor in the 1960‟s, and which continues to be manufactured today by

many semiconductor manufacturing companies.

What type of op amp is the 741?

The 741 op amp is a monolithic general purpose operational amplifier with the

following features:

Large input voltage range +/- 15V

Wide supply voltage +/- 22V

Low internal power dissipation 500mW

Offset voltage null capability (using external potentiometer)

This allows the output to be set to zero when unwanted noise is present on the

input.

High open-loop gain (250,000)

Short circuit protection

Internal frequency compensation (using internal capacitor)

Excellent temperature stability

(3 models available with 0 - 70˚C, -40 - 85˚C, -55 - 125˚C ranges)

High CMMR range

The uA741 can be used for a range of analog applications such as:

Summing amplifier

Voltage follower

Integrator

Active Filter

Function generators

Page 18: HNC EEE OpAmp ElectroTech007

What’s inside the uA741?

Internally the uA741 operational amplifier consists of 20 BJT transistors, 11 resistors

(ranging from 25R to 39k) and a capacitor (30pF) as shown in fig.32.

Fig.32 Internal circuitry of a uA741 operational amplifier

How does the internal circuitry work?

In the input stage transistors Q1 and Q2 make a differential amplifier which works

with Q3 and Q4 to form a long tailed pair. Q5, Q6 and Q7 are the loads of the long

tailed pair. The transistor pairs Q8, Q9 and Q10 and Q11 form what are known as

current mirror circuits. Current mirror circuitry is used as a current source to ensure

that identical currents flow in balanced amplifier circuitry. If the collector current in

Q8 changes; the corresponding current in Q9 will change also. Q14 and Q20 form a

class AB output stage with crossover distortion removed by the VBE multiplier Q18.

The amplification stage is driven by Q16 and Q17 in the form of a Darlington pair.

The Darlington pair is a pair of transistors joined together in common collector mode

with the emitter of the first transistor joined to the base of the second, the result of this

is that it acts like a single transistor with a current gain equal to the product of the hfe

values of the two transistors. Output overload protection is provided by Q15 and Q22

which sense the voltage drop across the sense resistors R9 and R11.

(Referenced to ‘Higher Electronics’ by Mike James ISBN 0-7506-4169-X, and

„Practical Electronics Handbook‟ by Ian R. Sinclair and John Dunton ISBN 10: 0-75-

068071-7)

Page 19: HNC EEE OpAmp ElectroTech007

How is the internal circuitry fabricated on a semiconductor IC?

The circuit itself is fabricated onto an IC chip using a method called ion implantation

using a planar epitaxial process, which is a process that uses photographic masks and

surface oxidisation to build up a variety of layers. This fabrication process is

summarised below:

A copy of the circuit (photomask) is created on a piece of glass plate coated with

metallic film. This is used to later transcribe the design onto a silicon wafer.

A thin circular piece of semiconductor material is created from a piece of single

crystal silicon. This material is then used as the substrate onto which the circuit will

be created. The circular slice of material is known as a wafer.

The wafer is then placed through a process of diffusion where various oxidisation

layers are built up which are later used for the insulation of transistor gates etc and

circuit wiring. The methods used to achieve these layers are thermal oxidation,

chemical vapour deposition (CVD), and physical vapour deposition (PVD).

A 1μm layer of a chemical called photo resist is then deposited on the wafer.

The photomask is then placed on top of the photo resist coated wafer and blasted with

ultraviolet light thus transcribing the circuit design onto the wafer. This design is

duplicated over the entire wafer surface. This process is termed masking and

exposure.

An alkaline based developer is then used to dissolve photo resist not masked during

the exposure stage; the remaining photo resist is left on the wafer surface in the shape

of the mask pattern and is called the resist pattern.

Etching of oxide films and metallic films now occur using the resist pattern as a mask.

Etching is a process of removal of these layers by chemical or physical means. The

oxide films are etched away using liquid chemicals (wet etching method), and

metallic layers are etched away using gas (dry etching method).

After etching, any remaining photo resist is removed and the wafer is then rinsed with

an acidic solution to remove any impurities. The circuit pattern is now visible on the

wafer and is ready for the next stage, device insulation layer formation, where oxides

are formed around active regions on the pattern to create components. This is known

as ion implantation. This is followed by transistor formation and metallization.

The wafer is now ready to be cut into individual IC chips in a process known as

dicing.

Once the IC chips have been separated they are ready to be mounted to a platform

called a lead frame. This consists of an island for the IC to rest on and connections for

the chips terminals (leads). The chip is fixed to the island by using a silver paste resin.

Page 20: HNC EEE OpAmp ElectroTech007

The chips terminals are then attached to the lead frame by a process known as

bonding, where the terminals are bonded directly with thin gold wire using a ball or

wedge bonding machine.

The IC chips and lead frame are now encapsulated in a plastic resin with only the

leads left protruding. Once the resin is cured we have the finished package depending

on how many leads there are and its physical dimensions (footprint). The IC is then

packed into trays or magazines ready for despatch. A cutaway view of an IC can be

seen below in fig.33 showing the internal IC chip the lead frame and the external

plastic packaging.

(Referenced from NEC Electronics Corporation)

Fig.33 Cutaway view of an IC

There are various IC packages available. Now that we know how they are

manufactured, we shall continue to have a further look at some of the common 741

packages.

Page 21: HNC EEE OpAmp ElectroTech007

(iii) Packaging

How is the uA741 packaged?

The standard through-hole IC package in use for the uA741 operational amplifier is

the 8 pin dual in line package (DIL) for a single 741 op amp, as shown in fig.34.

Fig.34 3D visualisation of 8 pin DIL package / PCB footprint, pin numbering and

functional diagram produced with ARES layout software (Proteus) / uA741 Datasheet

Note the small notch or dot on the package; this indicates the end from which to start

counting the pin numbers which go anticlockwise. This is common practice on all

IC‟s for orientation and identification purposes.

When designing op amp circuits the internal circuitry of the op amp is not so much

taken into account but instead the op amp is given a standard circuit symbol, the

symbol used for the uA741 is shown in fig.35. The pins on this symbol correspond to

the leads on the physical IC as shown in fig.36.

Fig.35 Standard 741 circuit symbol (ISIS) Fig.36 uA741 pin assignments

Each numbered pin is assigned a task within the IC, and these tasks are as follows:

1 & 5 offset null terminals

These allow the output to be set to zero when unwanted noise is present on the input.

2 & 3 Inverting and non-inverting inputs

The inverting input creates an inversion of the input signal at the output, and non-

inverting input creates a non inverted version of the input signal at the output.

Page 22: HNC EEE OpAmp ElectroTech007

4 & 7 Vcc- and Vcc+

Rail to rail power supply pins +/-15V for the 741 op amp

6 Signal output

This is where the inputted signal whether amplified, inverted or non-inverted

eventually leaves the IC.

8 NC (not connected)

The only unused pin on the 741 op amp

The internal physical circuit layout is shown below (fig.37) with the bonding areas

that correspond to the numbered leads in fig.36. The schematic symbol in fig.35 is

used to represent this physical circuit for design purposes.

Fig.37 Internal uA741 circuitry with bonding pad assignments (uA741 datasheet)

Page 23: HNC EEE OpAmp ElectroTech007

Various other packages exist for op amps, an example is the 14 pin DIL package used

for quad op amps such as the LM324, where 4 devices are located on one IC. This

package is also in use for the dual 741 op amp commonly known as the 747. These

packages can be found in fig.38.

Fig.38 3D visualisation of 14 pin DIL package / PCB foot print produced with ARES

layout software (Proteus), and dual/quad op amp functional diagrams

An alternative is the surface mount version; the 8 and 14 pin DIP which is available

for printed circuit boards where pads are used instead of through holes, as shown

below in fig.39.

Fig.39 3D visualisation of 4 main uA741 packages, SMT compared to THT produced

with ARES (Proteus)

8/14 pin Dip SMT

Page 24: HNC EEE OpAmp ElectroTech007

Another package found commonly amongst the uA741 is the metal can package i.e.

the TO77 shown below in fig.40.

Fig.40 3D visualisation and Actual TO77 metal can package

Shown below is the PCB footprint for the TO77 package (fig 41), and the pin

assignments (fig.42). Note that a tab at pin 8 is now used for orientation purposes with

pin numbers moving in the anti-clockwise direction.

Fig.41 PCB foot print / pin numbering Fig.42 uA741 (T077) pin assignments

Pin assignments 1 – 8 are listed below:

1. Offset Null

2. Inverting Input

3. Non-Inverting Input

4. Vcc – and case

5. Offset Null

6. Output

7. Vcc +

8. Tab

The tin can package also comes in a dual op amp format as shown below in fig.43.

Fig.43 Dual TO package

Page 25: HNC EEE OpAmp ElectroTech007

(iv) Common Operational Amplifier Types

There are many types of op amp available. These op amps can be divided into various

family groupings as described below:

General Purpose Op Amps

Devices designed for a wide range of operations. These op amps have limited

bandwidth but as a consequence frequency compensation results in good stability.

Non frequency compensated op amps have a much wider bandwidth but tend to

oscillate.

Voltage Comparator Op Amps

These are devices that have no negative feedback networks and therefore saturate with

very low input signal voltages (μV), they are normally used to compare input signal

levels.

Low Noise Op Amps

These are devices optimised to reduce internal noise, normally used in the first stages

of amplification circuits.

Low Input Current Op Amps

Devices with extremely low input current typically Pico-amps, compared to μA or

mA currents found in other devices.

Low Power Op Amps

Devices optimised for low power consumption. These devices can run with extremely

low power supply voltages i.e. ±1.5V or ± 3V.

Low Drift Op Amps

These are devices that have internal compensation which minimises drift caused by

temperature fluctuations. They can be found in instrumentation circuits with low level

signals.

Wide Bandwidth Op Amps

These are devices with very large gain bandwidth product (GB) i.e. around 100 MHz

compared with for example 741 type op amps at 0.3 – 1.2 MHz. They are commonly

used in video circuits.

Single D.C. Supply Op Amps

These are devices that run from a monopolar D.C. power supply voltage i.e. + 5V /

GND

Page 26: HNC EEE OpAmp ElectroTech007

High Voltage Op Amps

These are devices that run at high D.C. supply voltages i.e. ± 44V.

Multiple Device Op Amps

These are devices that have more than one op amp on one device i.e. dual or quad

packages.

Instrumentation Op Amps

These are D.C. differential Op Amps made with 2 -3 internal op amps. Voltage gain

in these devices is set with external resistors.

The table below (fig.44) gives a good overview of the Op Amp families and some of

the particular devices within them.

Fig.44 Operational Amplifier Family Groupings (taken from ‘Designers Handbook of

Instrumentation and Control Circuits’ by J.J. Carr)

Page 27: HNC EEE OpAmp ElectroTech007

(v) Basic Op Amp Operation

In its simplest form an op amp is a differential amplifier with an extremely high

voltage gain. It has one output and two Inputs (fig.45). The op amp was originally

intended for use in analogue computers to perform mathematical operations such as

summing multiplication, and integration.

Fig.45 Basic Op Amp Symbol

The output from the op amp will be an amplified version of the difference between

the two inputs, and is given by the equation:

O/P = A (I/P 1 – I/P 2) where A = Gain

Most op amps are voltage devices therefore from the above

VO/P = Av (V1 – V2)

The op amp has two inputs (fig.46), one inverting (-), and one non-inverting (+).

These input pins allow two modes of operation to be achieved, known as either

inverting or non-inverting.

Fig.46 Basic op amp symbol

Page 28: HNC EEE OpAmp ElectroTech007

Inverting operation

If a positive polarised voltage enters the inverting input (-) of the op amp, that positive

input voltage will be inverted, and become a negative voltage at the output, hence the

name inverting amplifier.

Non-inverting operation

If a positive voltage enters the non-inverting input (+) of the op amp, that positive

input voltage will remain positive at the output, hence the name non-inverting

amplifier

To enable operation in either non-inverting mode (fig.47) or inverting mode (fig.48)

one of the inputs should be connected to the signal earth or ground line. Fig 47 and 48

show the two types of circuit operation. The only instance in which both inputs are

used together would be in the case of a comparator circuit.

Fig.47 Non-inverting mode (note output waveform is amplified version of input)

Fig.48. Inverting mode (note output waveform is inverted amplified version of input)

The detail in this section refers only to the basic operations of the operational

amplifier; further sections cover in more detail the operational characteristics and way

in which external circuitry effects the operation of the op amp and will cover topics

such as feedback etc.

Page 29: HNC EEE OpAmp ElectroTech007

(vi) Operational Characteristics

There are certain characteristics of op amp devices both ideal and actual that indicate

the devices theoretical or real performance.

An ideal op amp is characterised by seven open loop properties which can be used for

the purpose of analysing op amp circuits. These idealised properties are:

Infinite open loop gain voltage

Open loop gain (Av) is the gain of the op amp without positive or negative feed back.

In an ideal circuit Av is infinite, in reality however the open gain voltage is in the

range of 20,000 to 250,000.

Infinite input impedance

Input impedance is the ratio of input voltage V to input current I, therefore

Z in = Vin / Iin (Ω)

When Zin is infinite the input current is zero. In reality input impedance is around

1MΩ

Zero output impedance

An ideal op amp acts like an ideal voltage source (i.e. a battery) with no internal

resistance. In reality the internal resistance is in series with the load which reduces the

output voltage available to the load. An actual op amp has an output resistance of

around 75Ω (741). An example of this theory can be seen in fig.49. According to the

formula the higher the resistance the lower the voltage available to the load, therefore

output voltage is reduced.

Fig.49 Theoretical diagram of output voltage reduction caused by impedance.

Page 30: HNC EEE OpAmp ElectroTech007

Zero noise contribution

In an ideal op amp zero noise is produced internally, this would imply that any noise

at the output was at the input and therefore was externally produced. In reality though;

op amps produce internal in the form of Johnson or thermal noise.

Zero output offset

The output offset is the output voltage of an amplifier when both inputs are grounded

(fig.50). The ideal op amp has zero output offset but in reality some op amps have a

certain amount of output offset voltage normally caused by manufacturing processes.

Fig.50 Model of ideal output offset voltage.

Infinite Bandwidth

The ideal op amp will amplify all signals from the lowest D.C. to the highest A.C

frequencies. In reality op amp bandwidth is limited by the Gain Bandwidth product

(GB) which is equal to the point where the amplifier gain becomes unity. The 741 op

amp has a bandwidth of up to 1 MHz.

Differential inputs are equal

In an ideal op amp when a voltage appears at one input; that same voltage appears at

the other input.

The properties named above help us to analyse the operation of op amps in theory, but

to help us to see how the device can be applied in actual circuits we must look at it in

terms of a closed loop with two inter-related parameters, the voltage gain (Av) and the

bandwidth (B), which combine to give us the Gain Bandwidth Product (GB) of the

specific op amp.

GB = the numerical value of voltage gain (Av) x bandwidth (B) Hz

Page 31: HNC EEE OpAmp ElectroTech007

(vii) Voltage Gain & Bandwidth

Voltage gain

The 741 op amp has a maximum quoted voltage gain of around 106 dB (200 x 103).

At low frequencies the gain will be high; but as the frequency increases the gain will

decrease until it hits 0dB (unity =1 = 0 dB), it is at this point that the op amp will

provide no further gain.

The voltage gain of a 741 in decibels is given by:

Av (dB) = 20log (numerical voltage gain)

Therefore for the 741 with a maximum open loop voltage gain of 200000:

Av (dB) = 20log (200 x 103) = 106 dB

If we are given the maximum voltage gain in dB we can calculate the numerical

voltage gain

Antilog (20 dB / 20) = voltage gain of 199526 (approx 200 x 103)

* Decibel is the logarithmic unit used when considering amplifier gain.

These calculations become useful when determining the gain needed in an op amp

when working with signals of a certain frequency.

Gain is said to be inversely proportional to frequency. This can be seen in the

frequency response of a 741 op amp (fig.51), where as the frequency increases the

gain decreases.

Fig.51 Graph of gain (Av) vs. Frequency (frequency response) for uA741

Page 32: HNC EEE OpAmp ElectroTech007

At low frequencies the enormous gain is not much use as even the smallest input

signal (around 12μV) will result in the output saturating at the level of the power

supply voltage (+/-15 V, 741). This would result in a switching rather than an

amplification operation.

To operate an op amp effectively as an amplifier it is necessary to apply principles of

negative feed back to reduce the voltage gain to the required level for your

application.

What is negative Feedback?

Feedback is where a proportion of a systems output is fed back into the systems input.

Negative feedback is achieved by taking a portion of the output and feeding it back

into the inverting input of the op amp using a network of resistors. In op amps

negative feedback is used to reduce gain to an adequate level, which gives greater

gain stability with reduced distortion between input and output signal waveforms as

well as wider bandwidth. Feedback and its application shall be covered in greater

detail in further sections, where we shall investigate various op amp circuits.

Bandwidth

The bandwidth is the range of frequencies over which the op amp will operate

satisfactorily. To be more specific it is the frequency range where voltage gain does

not fall below 70% (-3dB) of its maximum gain (mid band value). Fig.52 gives a good

representation of bandwidth. From the graph we see that the gain (Av) drops by 70%

(-3 dB) from its mid point at points f1 and f2. It is the range of frequencies between f1

and f2 that are known as the bandwidth. The op amp should work satisfactorily at any

frequency within this range.

Fig.52 Simplified op amp bandwidth graph

Page 33: HNC EEE OpAmp ElectroTech007

Gain Bandwidth

Copy -Fig.51 Graph of gain (Av) vs. Frequency (frequency response) for uA741

When we look at the frequency response of an op amp as shown in fig.51, it can be

seen that the voltage gain and bandwidth are linked. If the voltage gain (Av) of an op

amp is increased or decreased (using negative feedback) then, the bandwidth will

either increase or decrease. The link between gain and bandwidth is known as the gain

bandwidth product (GB), which is a constant up to a maximum value (1MHz for the

741) given by the large signal voltage gain of the particular device. The open loop

gain at a given frequency is limited by the GB of the device. The GB is given by the

formula:

Gain-bandwidth product (GB) = Numerical value of voltage gain (Av) x Bandwidth (B) in Hz

(GB = Av x B) (Hz)

Given this, if we know the GB for an amplifier then we can determine the voltage

gain or bandwidth.

To show an example of this we will look at the 741. If we reduce the gain to 40dB

with the application of a negative feedback network then to find the band width we:

1. Convert the 40dB gain to its numerical equivalent.

Av = 40dB therefore antilog (40/20) = 100

2. We know that for a 741 the GB = 1MHz = 1000000 Hz = 1 x 106 Hz

Therefore

GB = Av x B

1 x 106 = 100 x B

Transposing for B gives

B = (1 x 106 / 100) = 10000 Hz

= 10 kHz

Page 34: HNC EEE OpAmp ElectroTech007

From this we know that for a 741 with a gain of 40 dB the maximum bandwidth

would be 10 kHz.

The GB formula is a useful aid when analysing op amps for a specific specification,

for example when an amplifier is needed for an input signal of a certain frequency.

For example, if using a 741 and a bandwidth of 100 kHz is required, and we need to

know the gain needed that would enable us to design the negative feedback network

for this purpose we would use the formula:

GB = Av x B (Hz)

1 x 106 = Av x 100 x 103

Transposing for Av gives

Av = 1 x 106 = 10

100 x 103

We then convert the numerical voltage gain to dB

Av = 20log (10) = 20 dB

From this we can say that the gain needed would be 20 dB, which would enable us to

go on to ascertain values needed for the negative feedback network.

On the graph below we can see clearly the open loop response of a 741 and the closed

loop response we calculated above for a bandwidth of 100 kHz using the GB.

Fig.52 Frequency response (Closed loop) for uA741 at 100 kHz

From this we can conclude that if we know the open loop response of an op amp, then

by using the gain bandwidth product we can determine the gain needed at any

particular bandwidth frequency thus determining the closed loop response.

Open Loop Response

Closed Loop Response

Page 35: HNC EEE OpAmp ElectroTech007

Task.2

With reference to op amp datasheets compare and explain at least three specifications

quoted for 2 op amps.

This section of the report details a comparison of three op amp specifications as

quoted on the datasheets of the following op amps:

Fairchild Semiconductor FAN4274

Fairchild Semiconductor FHP3130

The specifications we shall be concerned with for the purpose of this report are:

Gain Bandwidth Product (GB)

Slew Rate

Common mode rejection ratio (CMMR)

Page 36: HNC EEE OpAmp ElectroTech007

Fairchild Semiconductor FAN4274 (datasheet description / features / applications)

Page 37: HNC EEE OpAmp ElectroTech007

Shown below are the absolute maximum ratings and specifications that we are

interested in for the FAN4274 taken directly from the datasheet.

Absolute Maximum Ratings

Specifications of Interest

Gain Bandwidth Product (GB)

Slew Rate

Open Loop Gain

Common mode rejection ratio (CMMR)

Page 38: HNC EEE OpAmp ElectroTech007

Fairchild Semiconductor FHP3130 (datasheet description / features / applications)

Page 39: HNC EEE OpAmp ElectroTech007

Shown below are the absolute maximum ratings and specifications that we are

interested in for the FHP3130 taken directly from the datasheet.

Absolute Maximum Ratings

Specifications of Interest

Gain Bandwidth Product (GB)

Slew Rate

Open Loop Gain

Common Mode Rejection Ratio (CMMR)

Page 40: HNC EEE OpAmp ElectroTech007

The table and graphs below show the specification comparison between the two op

amps in a clear format.

Table.1

Direct Comparison of Op Amp Specifications for the FAN4274 and FHP3130

Specification FAN4274 FHP3130

GBWP (MHz) 4 60

Slew Rate (V/μs) 3 90

CMMR (dB) 65 95

Open loop gain (dB) 98 100

Fig.53 Fig.54

Direct Comparison of Gain Bandwidth

Product (GB)

4

60

0

10

20

30

40

50

60

70

GBWP

(MH

z)

FAN4274

FHP3130

Direct Comparison of Slew Rate

3

90

0

10

20

30

40

50

60

70

80

90

100

(V/u

s)

FAN4274

FHP3130

Fig.55

Direct Comparison of CMMR

65

95

0

10

20

30

40

50

60

70

80

90

100

(dB

) FAN4247

FHP3130

Page 41: HNC EEE OpAmp ElectroTech007

Gain Bandwidth Product (GB)

For an op amp the ideal open loop gain is infinite in magnitude and frequency, in

reality though the open loop gain is extremely large at DC (frequency = 0).

The open loop response of an op amp begins to roll off at 70% below the maximum

gain of the device; this is known as the -3 dB bandwidth. The -3 dB Bandwidth of the

FAN4274 is calculated as follows:

Max open loop gain = 98 dB

Convert this to numerical voltage gain

Antilog (98/20) = 79433

Multiply the numerical gain by 0.707

79433 x 0.707 = 56159

Convert this to dB

20 log (56159) = 95 dB

The -3 dB bandwidth for the FAN4274 is given by

-3 dB Bandwidth = GB (given on datasheet) x numerical gain (Av)

= (4 x 106) / (56159)

= 71 Hz (fig.56 dark blue marker)

This can be checked by looking at the frequency response graph for the FAN4274

below. We draw a line directly across from 95 dB and then directly down, and we

come to 71 Hz thus proving our calculation.

Fig.56 FAN4274 Frequency Response (Open Loop Gain vs. Frequency) (datasheet)

4 MHz (GB) at 0 dB (1)

Unity. No further gain

after this point.

Page 42: HNC EEE OpAmp ElectroTech007

From this we can see that the open loop gain at or near DC is much too large to be

useful and that the bandwidth is much to low to be of any real use.

This is where the use of negative feedback comes into play. If we reduce the gain by

40 dB by designing a negative feedback network we have effectively reduced the gain

from the open loop value of 95 dB (56234) down to 40 i.e. by a factor of 1405.

56234 / 40 = 1405

The corresponding closed loop bandwidth then goes up by this factor:

71 Hz x 1405 = 99755 = 99.8 kHz (fig.56 red marker)

This now leads us on to the gain bandwidth product (GB) of the op amp.

If we consider the original open loop for the FAN4274,

The gain 95 dB (56234) x the bandwidth (71Hz) = 3992614 = 4 MHz

Then our closed loop model using negative feedback

The gain 40 dB (100) x the bandwidth (99.8 kHz) = 3990400 = 4 MHz

We can see that the product of gain and bandwidth for both models is equal to 4 MHz

(as on datasheet), this relationship is known as the gain bandwidth product and holds

true for any value of gain selected for this op amp.

The gain bandwidth product (GB) is used to determine the closed loop bandwidth for

a given closed loop gain or the maximum closed loop gain for a given bandwidth, and

is given by the formula:

Gain-bandwidth product (GB) = Numerical value of voltage gain (Av) x Bandwidth (B) in Hz

When we directly compare the GB product for both the FAN4274 and the FHP3130

on their corresponding data sheets we can see that the FHP3130 has a much higher

gain bandwidth product of 60 MHz compared to the FAN4274 4 MHz. What this

means in reality is that the FHP3130 is a much faster op than the FAN4274.

If a 20 dB gain is applied through negative feedback to each op amp then we can draw

a comparison based on the bandwidth

20 dB = Antilog (20/20) = 10

For the FAN4274 B = GB / Av = (4 x 106) / 10 = 400000 = 400 kHz

For the FHP3130 B = GB / Av = (60 x 106) / 10 = 6000000 = 6 MHz

This show that for the same closed loop gain there is a difference of 5.6 MHz, this

shows the difference in signal speed that the FHP3130 has over the FAN4274, making

it much better for large bandwidth applications such as CCD imaging systems.

Page 43: HNC EEE OpAmp ElectroTech007

Another specification of great importance when considering op amps is the slew rate.

Slew Rate

The slew rate is a measure of how fast an op amps output can change in response to

an input signal, measured in V/μs. It gives an idea of the maximum frequency and

amplitude of a signal that an op amp can handle at its output.

If an op amp is operated at a frequency that exceeds the slew rate the output signal

would be distorted. (The output waveform would change shape and a reduction in

amplitude would occur).

The slew rate for an op amp relates the maximum frequency to the peak output

voltage and is given by the formula

SR = 2πfV / 106 (V/μs)

Where f = maximum frequency and V = peak voltage

To find the maximum frequency for an op amp if we know the slew rate we

Rearrange the formula

f (max) = SR / 2πV

The gain bandwidth product relates the maximum frequency to circuit gain using the

formula

GB = f (max) x Gain

To find the maximum frequency in relation to a closed loop circuit gain we

Rearrange the formula

f (max) = GB / Gain

Page 44: HNC EEE OpAmp ElectroTech007

We shall now compare our op amps using the above formulae with the actual quoted

slew rate for each.

FAN4274 (quoted slew rate 3 V/μs)

(3 x 106) = 2πfV / 106 Therefore f (max) = 3 x 106

2πV

We know that the supply for the op amp is +/-5V and V will be the output swing

voltage which is quoted on the datasheet as 4.9V

Therefore f (max) = 3 x 106 / (2π x 4.9) = 97441.8 Hz = 97.4 kHz

The max frequency is 97.4 kHz

If we have the FAN4274 in a circuit and set the gain to 50 we can then calculate the

maximum closed loop frequency achievable for that gain that can be used without

risking distortion on the output.

We know that the GB = 4 MHz (as quoted on datasheet)

Therefore

F (max) = (4 x 106) / 50 = 80000 = 80 kHz

If the maximum required frequency in the circuit is 80 kHz then the peak output

voltage is

Vpk (at 80 kHz) = SR / 2πf = (3 x 106) / (2π x 80 x 103) = 5.97 V

This exceeds the power supply voltage which would cause distortion at the output;

therefore we would need to lower the peak output voltage by lowering the gain, thus

increasing the maximum frequency.

Page 45: HNC EEE OpAmp ElectroTech007

FHP3130 (quoted slew rate 90 V/μs)

(90 x 106) = 2πfV / 106 Therefore f (max) = 90 x 106

2πV

We know that the supply for the op amp is +/-5V and V will be the output swing

voltage which is quoted on the datasheet as 4.65V

Therefore f (max) = 90 x 106 / (2π x 4.65) = 3080418 Hz = 3.1 MHz

The max frequency is 3.1 MHz

If we have the FHP3130 in a circuit and set the gain to 50 we can then calculate the

maximum closed loop frequency achievable for that gain that can be used without

risking distortion on the output.

We know that the GB = 60 MHz (as quoted on datasheet)

Therefore

F (max) = (60 x 106) / 50 = 1200000 = 1.2 MHz

If the maximum required frequency in the circuit is 1.2 MHz then the peak output

voltage is

Vpk (at 1.2 MHz) = SR / 2πf = (90 x 106) / (2π x 1.2 x 106) = 11.9 V

This exceeds the power supply voltage which would cause distortion at the output;

therefore we would need to lower the peak output voltage by lowering the gain, thus

increasing the maximum frequency.

Ultimately the higher the slew rate the better, as the op amps output can cope with

higher rates of change in input signal thus enabling wider bandwidth to be achieved.

Page 46: HNC EEE OpAmp ElectroTech007

Common Mode Rejection Ratio (CMMR)

Ideally a differential amplifier (fig.57) is designed to amplify the difference between

the its inputs, if the input signals are identical they will be cancelled out producing

zero signal at the output. The cancelling effect is known as Common mode rejection.

The parameter used to measure how well an amplifier rejects common mode signals is

the CMMR, the higher this value the better the op amp is at rejecting common mode

signals.

In reality when both inputs are driven by the same identical signal (Vcm) there will

still be a small output (Vout (cm)) due to component differences within the amplifier,

normally caused during manufacture.

Fig.57 Differential Amplifier Circuit

The CMMR is the logarithmic ratio between the normal differential amplifier gain

and the common mode gain of the device, measured in dB.

The differential gain (Ad) is given by

Ad = Rf/R1

The common mode gain is given by

Acm = Vout (cm) / Vcm

CMMR is then given by

CMMR = 20log (Ad / Acm) dB

For the FAN4274 the quoted CMMR value is 65 dB

For the FHP3130 the quoted CMMR value is 95 dB

The larger the CMMR value; the better the op amp is at rejecting common mode

signals such as unwanted noise, therefore the FHP3130 would be better equipped than

the FAN4274 for an application such as; a differential amplifier for amplifying signals

from sensors that give very small outputs.

Page 47: HNC EEE OpAmp ElectroTech007

Task.3

In practice the op amp is used as a feedback amplifier. Circuit design can be made

simple by treating the device as ideal for the purposes of analysing circuit

performance.

List the appropriate rules and then explain, using diagrams the following op amp

circuits. Derivation of the relationship between input and output voltage should be

included.

(i) Inverting amplifier

(ii) Non-Inverting Amplifier

(iii) Summing Amplifier

(iv) Differential Amplifier

Page 48: HNC EEE OpAmp ElectroTech007

The design of feedback amplifiers can be made simple by treating the op amp as ideal

for purposes of analysing circuit performance.

The following simple rules apply

1. The input current (Ii/p) drawn by the inverting (-) and non-inverting (+)

terminals is zero.

2. The voltage drop across the input terminals (Vd) is zero

3. The open loop gain of the device is infinite

Negative feed back occurs when a portion of the op amps output signal is fed back

into the inverting input for mixing with the original signal. The amplifier will then

have 2 inputs Vi/p and the negative feedback signal, which gives direct control over

the amplifier gain, increased bandwidth, reduced distortion of output waveform, and

improved reproducibility.

From this point we can go on further to discuss the various op amp circuits and their

applications.

Page 49: HNC EEE OpAmp ElectroTech007

(i) Inverting Amplifier

A typical op amp with no negative feedback has an open loop gain of 200000, with

the output being limited by the supply voltage (+/-15V).

Due to this; the signal at the inverting input (-) can not be any larger than +/-15μv or

the op amp will be driven into saturation. The inverting input is therefore treated as

virtual ground (VG) or 0V. Below we can see the inverting amplifier circuit (fig.58)

Fig.58 Inverting Amplifier Circuit

The input signal is shown as Vi. The full input signal is determined by the voltage

drop across Ri. Therefore the input current is

Ii = Vi / Ri

From the diagram you can see that the full output voltage Vo is shown, with the full

output current across the feedback resistor Rf we can determine the feedback current

If

If = Vo / Rf

The circuit‟s impedance (Z) is approximately equal to the value of resistor Ri

Since the signal at the inverting input is small and the input impedance is high the

input current is negligible therefore Ii can become If, thus

If Ii = If then Vi/Ri = -Vo/Rf

The minus sign (-) indicates that one current flows into the node that the other flows

out.

If we transpose the formula for the output voltage we get

Vo = -Vi (Rf/Ri)

The minus sign indicates that the output is the opposite polarity of the input, hence the

amplifier is inverting the input signal

The stage gain (Av) can be given by

Av = Vo/Vi = - (Rf/Ri)

The closed loop gain of an op amp is determined by the resistors used.

Page 50: HNC EEE OpAmp ElectroTech007

(ii) Non-Inverting Amplifier

A non inverting amplifier is constructed by using an op amp and a two resistor

potential divider arrangement. (fig.59)

Fig.59 Non-inverting amplifier circuit

The purpose of the non-inverting amplifier is to increase the amplitude of the input

signal without altering the polarity.

The gain of the amplifier is determined by the resistor values in the circuit.

To produce output signals with no distortion the input multiplied by gain must be

below the power supply voltage.

The difference between op amps inverting and non inverting inputs can never be more

than a few microvolt‟s in order to provide a distortion free output signal. As discussed

previously this is due to the open loop gain being so large.

Looking at the non-inverting amplifier circuit (fig.59) the feedback to the inverting

terminal is a voltage produced from the potential divider action of Rf and R1,

therefore

Inverting input voltage (V-) = (R1 / (Rf+R1) ) x Vout

Due to the high gain of the op amp the value at the non-inverting input (V+) is

identical to the value at the inverting input (V-)

The circuits impedance is equal to that of the op amp, which can be around 2MΩ

between + and – terminals.

The input signal (Vin) is connected to the non-inverting input (V+)

Therefore

Vin = V+ which is equal to V – which equals (R1/ (Rf+R1)) x Vout

Transposing for stage gain gives

Av = Vout / Vin = (Rf+R1) / R1 = Rf/R1 + R1/R1 = 1+ Rf/R1

Therefore Vout = (1+(Rf/R1)) x Vin

Page 51: HNC EEE OpAmp ElectroTech007

(iii) Summing Amplifier

The summing amplifier sometimes known as either a mixer or adder performs the

function of summing the voltages at its inputs.

It contains the same circuitry as an inverting amplifier with the addition of multiple

inputs and input resistors. The circuit is shown below (Fig….)

Fig.60 Summing amplifier circuit

The summing amplifier is used to add together the magnitude of the input signals and

will then produce an inverted output of the combined magnitude of the input signal.

Fig.60 shows a summing amplifier with three inputs, in practice any number of input

resistors can be connected to the inverting input, one for each input voltage. Input

voltages can be either negative or positive.

Using Ohms Law the input currents are determined

I1 = V1/R1

I2 = V2/R2

I3 = V3/R3

The junction at which these currents meet (inverting input) is known as the summing

junction, the currents at this point will be added together (Kirchhoff‟s Current Law)

“The total charge flowing into a node must be the same as the the total charge flowing

out of the node.”

Due to the high input impedance of the op amp no current will enter the op amp,

instead the sum of the input currents will now flow out as feedback current If.

Using Kirchhoff‟s current law

I1 + I2 + I3 = -If

Summing Junction

Page 52: HNC EEE OpAmp ElectroTech007

If we use this as our starting point and substitute for each current using ohms law we

get

V1/R1 + V2/R2 + V3/R3 = -Vout/Rf

Transposing for Vout we get

Vout = -Rf ((V1/R1) + (V2/R2) + (V3/R3))

Therefore

Vout = - ((Rf/R1 x V1) + (Rf/R2 x V2) + (Rf/R3 x V3)

From this we can see that the output voltage will be the sum of the three input

voltages inverted with each input voltage multiplied by its own coefficient. By

using this formula we can now determine the input resistor values.

Note - the summing amplifier can be configured to allow some inputs to have more

influence on the output than others. This is achieved by using a smaller input resistor

on a particular input which gives a larger input current thus giving greater weighting

to the particular input with regards output.

How do we choose resistor values?

We first decide on a resistor value for Rf such as 10kΩ, this is then used to calculate

the input resistance values. The feedback resistor Rf is constant for all calculations

and is normally chosen before performing any calculations.

The inverting input is effectively at 0V due to the virtual ground on the amplifier,

therefore no current is flowing through R2 and R3 so these can be ignored.

To calculate the resistor value for R1, we set V2 and V3 to zero

Vout = - ((Rf/R1 x V1) + (Rf/R2 x 0) + (Rf/R3 x 0)

Vout is set to the output voltage required with only V1 applied, and the input resistor

is now calculated using the formula:

Vout = - (Rf/R1) x V1

Therefore if we know the output signal wanted (-5V) when V1 = 1V and Rf is 10 kΩ

We get

-5 = - ((10 x 103) / R1) x 1

Transposing for R1 gives

R1 = ((10 x 103)/5) x 1) = 2000 = 2 kΩ

We would then repeat the process for R2 and R3. This provides a useful tool for

circuit analysis.

Page 53: HNC EEE OpAmp ElectroTech007

(iv) Differential Amplifier

The differential amplifier (subtractor) as the name suggests was designed to produce

an amplified version of the difference between the inputs. Fig 61 shows the

differential amplifier circuit.

Fig.61 Differential amplifier circuit

The differential amplifier is in effect a combination of the inverting and non-inverting

amplifier covered previously.

For the inverting input with V2 connected to ground and an input applied to V1:

Vo (-) = - (Rf/R1) x V1

For the non-inverting input (+) with an input V1 connected to ground (0V) and an

input applied to V2:

Voltage at (+) input: V (+) = (R3/(R2+R3)) x V2

Vo = (1+ (Rf/R1) x V (+)) Therefore Vo (+) = (1+ (Rf/R1)) (R3/ (R2+R3)) x

V2

We then consider each input in turn and take the other to 0V:

Vo (-) = -(Rf/R1) x V1

Vo (+) = (1+(Rf/R1))(R3/(R2+R3)) x V2

Then finally with both inputs used at the same time in differential mode

Vo = Vo(+) + Vo(-) = (1+(Rf/R1)) (R3/(R2+R3)) x V2 + -(Rf/R1) V1

Therefore

Vo = (1+ (Rf/R1)) (R3/ (R2+R3) x V2 – (Rf/R1) x V1

Page 54: HNC EEE OpAmp ElectroTech007

Reference

Notes

„The operational amplifier‟

„Introduction to Operational Amplifiers‟

„Inverting voltage amplifiers‟

„Non-inverting voltage amplifiers‟

„Summing amplifier‟

„Advanced op amps‟

„Decibels and noise‟

Books

Circuits, Devices, and Systems Ralf J. Smith

Higher Electronics Mike James

Designers Handbook of Instrumentation and Control Circuits J.J. Carr

Practical Electronics Handbook Ian Sinclair

Websites

IEEE Explore

NEC

Wikipedia

www.philbrickarchive.org

National Semiconductor

Fairchild Semiconductor