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History

One owes the term of operational amplifier ( Operational Amplifier in English) in John R. Ragazzini in 1947. The operational amplifiers were initially developed at the era of the electron tubes, they were then used in the analog computers. Currently, the operational amplifiers are available in the form of integrated circuits, although versions in the form of discrete components are used for specific applications.

The first AOP available in great series was the K2-W of company GAP/R in January 1953. At the time, the K2-W was sold for a score of US dollars. Although offering performances similar to those of its main competitor the LM101 of National Semiconductor, the μA741 became a standard because it had in-house a capacity of compensation thus making the μA741 simpler to use than the LM101. Thus, into six years, the price of the AOP was divided by more than one hundred while they are increasingly powerful, robust and simple of use.

The μA741 is still nowadays manufactured and it became omnipresent in electronics. Several manufacturers produce a version improved of this AOP, recognizable thanks to the “741” present in their denomination. Since, more powerful circuits were developed, certain based on JFET (end of the year 1970), or on MOSFET (beginning of the year 1980). The majority of these modern AOP can replace a μA741, in a circuit of old design, in order to improve the performances of them.

The operational amplifiers are available under formats, stitchings, and levels of voltages supply standardized. With some external components, they can carry out a large variety of useful functionalities in Treatment of the signal. The majority of the standard AOP cost only a few tens of centimes of euro, but a AOP discrete or integrated with characteristics not-standard and of low volume of production can cost more than 100 euros part.

The principal manufacturers of operational amplifiers are: Analog Devices, Linear Technology, Maxim, National Semiconductor, STMicroelectronics and Texas Instruments.

Stitching

A AOP has typically two entries, two pins feed and an exit. The noted entry E ₊ is known as non-inverseuse while the entry E _- is known as inverseuse, this because of their respective role in the relations input/output of the amplifier. The potential difference between these two entries is called differential tension of entry.

The pin of located positive food $V_ \ mathrm {CC+}$ is sometimes also called $V_ \ mathrm {DD}$ , $V_ \ mathrm {DC}$ , or V _S+. The pin of located negative food $V_ \ mathrm {DC}$ is sometimes also called $V_ \ mathrm {S}$ , $V_ \ mathrm {EE}$ , or V _S−. The doubled character which is in index of the letter V refers in the name of the pin of the transistor to which this food will be generally connected. Thus, names $V_ \ mathrm {DC}$ and $V_ \ mathrm {EE}$ are generally reserved for the bipolar AOP (C for Collecteur and E for Émetteur) while names $V_ \ mathrm {DD}$ and $V_ \ mathrm {S}$ are generally reserved for the AOP with field effect (D for Drain and S for Source).

According to the applications, the AOP can also be equipped with two pins for the compensation of offset as of a pin for the adjustment of the frequential compensation.

There exist AOP having a differential exit. Such amplifiers have two pins of exits like four pins of food in order to be able to carry out a galvanic Isolation between the entry and the exit. These amplifiers are also called “amplifiers of insulation”.

Perfect operational amplifier

The concept of perfect or ideal operational amplifier makes it possible to reason on the theoretical operation of the operational amplifier while being freed from the parasitic phenomena and the limitations inherent in the technological reality of the components. The progress made since the first AOP tends, by the constant improvement of the performances, to approach the model of the perfect AOP.

The perfect operational amplifier has an impedance of entry, a profit in differential mode, a scanning rate and a band-width infinite, its profit of common mode and its resistance of exit are null. Moreover, it does not have a tension of offset nor of current of polarization. Actually the differential profit of an operational amplifier strongly varying according to the frequency, it is current to regard it as infinite in order to simplifying calculations in order to approach the real behavior of the amplifier.

These characteristics translate the fact that the perfect operational amplifier does not disturb the signal which it will amplify and which its output voltage depends only on the difference in tension between its two entries.

The presence of an infinite differential profit implies that the least potential difference between the two entries of the amplifier will lead it to saturate. If one does not wish that the output voltage of the amplifier is only limited to ± V_sat according to the sign of the potential difference between the two entries of the amplifier, the use of a negative negative feedback is obligatory.

The negative feedback on the inverseuse entry (or negative negative feedback) of a AOP makes it possible to withdraw part of the output signal from the entry signal of the amplifier. Thanks to this subtraction, the negative negative feedback makes it possible to keep a null potential difference in entry of the amplifier. One speaks then about linear mode because one can vary the output voltage between + and - V_sat following the tension applied in entry of the amplifier. The absence of negative feedback or a negative feedback on the non-inverseuse entry (or positive reaction) of the AOP will bring the amplifier in positive or negative saturation according to the signal applied in entry. One speaks then about comparator mode (or saturated).

Linear mode - Application to an amplifier not-reverser

See also: basic Assemblies of the amplifier opérationnel#Circuits in linear mode, Circuits in linear mode

For this study, one will consider that the operational amplifier used is perfect, and that it functions in linear mode because it uses a Contre-réaction on the inverseuse entry of the AOP. The negative feedback on the inverseuse entry makes it possible to carry out a negative negative feedback: any increase in the output voltage will decrease the differential tension of entry of the AOP. Thus, the difference in tension between the two entries of the amplifier is maintained to zero. Moreover, the impedance of entry being infinite, no current circulates in these entries. One thus finds the V_e tension at exit of the tension divider bridge noncharged formed by R₂ and R₁.

One obtains then:

$V_ {E} = V_ {S} \ times {R_ {1} \ over {R_ {1} + R_ {2}}}$

and thus:

$V_ \ mathrm {S} = V_ \ mathrm {E} \ left (1 + {R_2 \ over R_1} \ right)$

Saturated mode - Application to a comparator with two thresholds not-reverser

See also: basic Assemblies of the amplifier opérationnel#Circuits in non-linear mode, Circuits in non-linear mode

For this study, one will consider that the operational amplifier used is perfect, and that it functions in “comparator mode” because it uses a negative feedback on the non-inverseuse entry of the AOP. The negative feedback on the non-inverseuse entry makes it possible to carry out a positive negative feedback: any increase in the output voltage will increase the differential tension of entry of the AOP. The differential profit of the amplifier being infinite, the output voltage V_s can be worth only +V_cc or - V_cc following the sign of the differential tension V_diff.

$V_ {diff} =V_ {e^+} - V_ {e^-} =V_ {e^+} =V_e \ cdot \ frac {R_2} {R_1+R_2} + V_s \ cdot \ frac {R_1} {R_1+R_2}$ The V_e tension, cancelling the differential tension V_diff, is thus worth:

$V_e =-V_s \cdot \frac{R_1}{R_2}$

According to the sign of V_s, one can define a tension of positive swing V_T⁺ making pass the V_s exit of - V_cc with +V_cc, and a tension of negative swing V_T^- making pass V_s of +V_cc to - V_cc:

Tension of positive swing: $V_ \ mathrm {T^+} = V_ \ mathrm {DC} \ left ({R_1 \ over R_2} \ right)$
Tension of negative swing: $V_ \ mathrm {T^-} = - V_ \ mathrm {DC} \ left ({R_1 \ over R_2} \ right)$
T for threshold , meaning threshold.

Real operational amplifier

Although the perfect model of the AOP makes it possible to calculate the Transfer function transfer and to include/understand the majority of the assemblies containing AOP, the real AOP have a certain number of limitations compared to this model.

The AOP presents the following defects: presence of an offset in entry, influence of the tension of common mode (mean arithmetic of the tensions of the two entries) on the output voltage, nonnull impedance at exit, noninfinite impedance in entry and variation of the profit according to the frequency. Moreover, the output voltage can be influenced by variations of supply voltage and has a Scanning rate finished.

Differential profit and of common mode

The differential profit G_diff of a real AOP is finished and varies according to the frequency. For a compensated AOP, the variation in frequency of the differential profit can be comparable with that of a system low-pass first order whose product busy profit-band is constant:

$G_ {diff} = \ frac {G_0} {1+j \ frac {F} {f_1}}$

With G₀ continuous profit and f₁, the frequency cut-off with 3 dB. The G₀ profit is generally worth between 100 and 130 dB for a AO of precision and between 60 and 70 dB for a fast AO.

Moreover, there exists in parallel of each one of these resistances a condenser whose value can vary some PF to 25 PF, the effect of the impedance of entry of a AOP, supplied with a source of low resistance, on the system can generally be neglected.

For the AOP using a negative feedback while running, the impedance of the non-inverseuse entry can it also be modelled by a resistance ranging between 10⁵ and 10⁹ Ω in parallel with a condenser.

The output impedance, noted R_S, of a AOP is not null. It is worth between 50 Ω and 200 Ω. This output impedance does not represent a fall of the output voltage as the charging current increases. In an assembly using a negative feedback, the output impedance is divided by the profit of the loop of negative feedback what makes it possible to bring back it to a value close to the zero ideal.

Offset

When an operational amplifier does not receive any signal on its entries (when its entries are both joined together to zero), there generally remains a continuous tension of shift of the output voltage with respect to zero. This shift comes from two phenomena: tension of offset clean with the internal circuits of the AOP on the one hand, and influences it currents of polarization of the differential pair of the transistors of entry on the external circuit on the other hand.

The tension of offset represents the difference in tension which it would be necessary to apply between the two entries of a AOP in open loop, when one connected one of the entries to the zero, to have a zero output voltage. This tension of offset can be represented in series with the non-inverseuse or inverseuse entry. This defect of offset comes from the technological imperfections of the operational amplifier. They result in an imbalance in tension, related for example to dissymmetries of V of the transistors of the differential stage of entry in a AOP with bipolar transistors. It is about the “tension of offset”. Other imperfections, like dissymmetries of profit and internal components are added to the causes of this imbalance. For the standard AOP, the tension of offset is worth between 50 and 500 µV, but it varies between 1 µV for the amplifiers of the type chopper to 50 mV for the least good AO CMOS.

The currents crossing each entry of the AOP when no signal is applied to him come from the currents from polarization from the transistors from entry. One defines a current of polarization which is the average between the currents of polarization crossing the two entries and a displacement current says “current of offset” which is the difference between the currents in polarization crossing the two entries. The current of polarization can vary from 60 F to several µA. The current of offset is him also depend on the temperature. It can vary few tens of nA/°C to some pA/°C, even of the still lower values.

Scanning rate

The Scanning rate (or slew spleen ) represents the speed of maximum variation of tension which an amplifier can produce. When the speed of variation of the output signal of an amplifier should be higher at its scanning rate, its output voltage is a line of slope

\ mathrm {SR}

$\ mathrm {SR} = \ max \ left (\ frac {dv_s (T)}{dt} \ right)$ .

The scanning rate is expressed in V/µs.

In a AOP, the slew-spleen generally depends on the maximum current which can provide the differential stage. The differential stage provides on the floor amplification of tension a current proportional to the difference in tension between the two entries. This current is mainly used to charge the capacity with compensation interns C present in the stage of amplification in tension. The relation running/tension is then that of a condenser: $i=C\frac{dV_c}{dt}$ The maximum current that the stage of entry can provide being equal to twice the current of I_C0 polarization crossing the collector of one of the transistors of entry, the slew-spleen can be obtained in the following way:

$\ mathrm {SR} = \ frac {2I_ {C0}} {C}$

For a µA741 one ad interim _C0=10 µA and C=30 PF what gives us a scanning rate of 0,67 V/ΜS which is in agreement with what can be measured. If the AOP does not have of capacity of compensation, the slew-spleen is determined by the internal stray capacities with the AOP. Such AOP have a slew-spleen and a band-width more important than the compensated AOP, but they are not stable during a use as a follower!! BiFET
(TL081)!! Bimos
(CA3140)!! Cmos
(LMC6035) |- | colspan=" 6" height=" 3" bgcolor=" #BED4EA" | |- align=" center" | align=" left" |Profit G_diff ||> 10⁵ ||||||~20 Hz|| |- align=" center" | align=" left" |Leakage currents I+ , I ||< 500 Na||80 Na||30 Pa||10 Pa||0,02 Pa |- align=" center" | align=" left" |Tension of offset Voff (mV)||< 10||1||3||8||0,5 |- align=" center" | align=" left" | TRMC G_diff/G_mc (dB)||> 70|| || ||18||40||27 |- | colspan=" 6" height=" 3" bgcolor=" #EDEDED" | |}

Compensation of the offset of entry

Current of polarization

The currents of polarization (noted I_e- and I_e+ on the figure opposite) create a voltage drop at the boundaries of the circuit components, thus creating a tension of offset. It is possible to reduce this tension of offset while inserting between the zero and the non-inverseuse entry of the same a R3 resistance value than the equivalent resistance of the circuit seen of the inverseuse entry. In this way, one creates an equivalent voltage drop between the two entries of the AOP.

Tension of offset

The tension of offset is directly amplified by the assembly. Thus, a AOP having an offset of 10 mV which is used in an assembly having a profit in tension of 100, will have an offset of 1 V at exit. On the AOP having an adjustment of zero, one can cancel this offset by connecting a potentiometer to the suitable pins. If the AO is not equipped with rigging pins of the zero (case of the cases integrating several AOP, in particular), it is then necessary to pass by an external assembly in order to cancel this offset. This way of doing also makes it possible to be freed from the differences in mode of adjustment of the offset envisaged by the manufacturers according to the types of AOP, and thus to improve the interchangeability.

Whatever the method of compensation of offset chosen, it is necessary to keep in mind that the offset of a AOP varies with the temperature of this one and that certain methods can increase this variation, even to cancel it.

Frequential compensation

Each stage of an amplifier has a resistance of exit and a capacity in entry. Thus, each stage of an amplifier behaves like a low-pass Filtre first order for its predecessor. It is what explains the variations of profit and phase according to the frequency in a AOP. AOP being generally composed of at least three stages of amplification. Before this date, all the amplifiers used a negative feedback in tension. The use of a negative feedback while running makes it possible to carry out faster AOP and generating less distortions. The principal defect of the negative-feedback amplifiers while running is that they have a tension of offset more important than their counterparts with negative feedback in tension. This defect returns them less adapted to the manufacture of amplifiers with strong amplifying profit or of instrumentation.

The AOP using a negative feedback while running are all of the bipolar amplifiers. Of share their design, they have a strong impedance of entry for the non-inverseuse entry and a low impedance for the inverseuse entry (that used mainly as entry of the signal in the amplifying assemblies). For the amplifiers with negative feedback while running, the profit in open loop is measured in ohms and either in V/V as for the standard AOP. Low impedance of the non-inverseuse entry also rises a great immunity with respect to unwanted noise in the amplifying assemblies.

Inner working

The AO generally consist of at least three stages: a differential stage (in yellow on the figure), one or more stages of amplification of the tension (out of orange) and a buffer of tension (in blue). The differential stage of entry generally consists of a differential pair. It provides differential amplification between the two entries as well as the high impedance of entry. The differential stage can comprise a compensation system of the currents of polarization. In this case, the base of each transistor of entry is connected to the collector of a transistor which then provides the current necessary to the polarization of the differential pair of entry. The stage of amplification is generally an amplifier of strong profit and of class has. The capacity present in the stage of amplification of tension makes it possible to carry out the frequential compensation. The buffer of tension which is used as stage of exit, has a profit in tension of one. It makes it possible the amplifier to provide important currents in exit with a low output impedance. It includes also the limitations of current as well as protections against the short-circuits.

Internal example of diagram: 741

In blue the differential stage of entry, in red mirrors of current, cyan the stage of exit, magenta the stage of amplification in tension and green the device of polarization of the stage of exit.

Power sources

The three sections of the diagram ringed of red are mirrors of current. A mirror of current is an electronic assembly made up of two transistors. The term of mirror of current comes owing to the fact that each one of these two transistors is traversed by the same one running whatever the tension on its terminals.

The mirror of current formed by Q₁₀ and Q₁₁ is a “mirror of current of Widlar”. The presence of the resistance of 5 kΩ makes it possible to decrease the current crossing Q₁₀ compared to that crossing Q₁₁.

The mirrors of current formed by Q₈-Q₉ and Q₁₂-Q₁₃ allow the transistors Q₈ and Q₁₃ to be traversed by a current only related to that crossing the resistance of 39 kΩ and that whatever the tension on their terminals. The current crossing the resistance of 39 kΩ depending only on the supply voltage of the AOP, the Q₈ transistors and Q₁₃ thus behave as power sources with respect to the part of the assembly to which they are attached.

The differential stage

The stage of amplification of this amplifier is surrounded by blue on the figure opposite. The Q₁ transistors in Q₄ form the differential amplifier of entry. The non-inverseuse entry is done on the basis of Q₁ transistor while the inverseuse entry is done on the basis of Q₂ transistor.

The current provided by the Q₈ transistor being independent of the tension on its terminals, it acts like a Power source for the Paire differential formed by the transistors Q₁ and Q₂. The use of a power source like charges with a differential pair, makes it possible to improve the Taux of rejection of the common mode of the assembly.

The transistors Q₅ and Q₆ form a mirror of current. The use of a mirror of current makes it possible to make sure that the two branches of the differential amplifier are traversed by the same current of polarization. The Q₇ transistor makes it possible to increase the performances of the mirror of current by decreasing the taken current with Q₃ to feed the bases of the transistors Q₅ and Q₆.

The stage of amplification in tension

The stage of amplification of this amplifier is surrounded by magenta on the figure above. It is consisted of the Q₁₅ transistors and Q₁₉ assembled in configuration “darlington”. This amplifier functions in class has in order to amplify with less possible distortion the signal coming from the differential stage. The capacity of 30 PF makes it possible to carry out a local negative feedback at the boundaries of the stage of amplification in tension and thus to ensure the frequential compensation of the AOP.

The stage of exit

The stage of power of exit is surrounded by cyan on the figure above. It consists of a push-pull of class AB (Q₁₄ and Q₂₀). The polarization of the push-pull is ensured by the multiplier of V surrounded by green on the figure.

The resistance of 25 Ω is used as probe of current for the output current crossing the Q₁₄ transistor. The terminal voltage of this resistance orders the Q₁₇ transistor directly. Thus, the terminal voltage of the resistance of 25 Ω is limited to the tension base-transmitter “of threshold” of the transistor (approximately 0,6 V with 20 °C). Once this tension reached, the Q₁₇ transistor enters in conduction, thus limiting the basic current of the Q₁₄ transistor and thus, the output current. For a maximum tension base-transmitter of 0,6 V one obtains a limitation of the output current to 25 my. The limitation of the current crossing Q₂₀ takes again the same principle as that of the Q₁₄ transistor. It is done via the tension base-transmitter of the Q₁₄ transistor, of the tension transmitter-collector of the Q₁₆ transistor and the resistance of 50 Ω.

Resistances of 25 Ω and 50 Ω connected to the transmitter of the transistors Q₁₄ and Q₂₀ also make it possible to avoid their thermal runaway. Indeed, more the temperature of a bipolar Transistor increases, more its profit while running β increases. This increase in β results in an increase in the current crossing the transistor and thus an increase in the temperature of the component, which in its turn will amplify the current crossing the transistor and so on until the failure of this one. The assembly describes above allows on the whole avoiding that. The zone of operation or, for example for Q, Q enters in conduction, the final stage behaves like a generator of constant current (25 my in the example), limiting the dissipated power of the transistor of exit. It is the same for Q.

Applications

The AOP is component very present in the analogical assemblies:

realization of active filters: the filters containing AOP make it possible to reach precise details more important than passive filters;
amplification of signals: the AOP is at the base many diagrams allowing the conditioning of the sensors, one speaks then about the field of instrumentation;
realization of analog computations: in spite of progress of the digital processing, the AOP remains used to carry out analog computations: addition/subtraction, profit, multiplication, integration/derivation. It can be used for example in Automatique to carry out controls, Régulateur PID, etc

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