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    Operational amplifier


    DonPetru

    1. The generalities

    Necessity of the miniaturization of electronic circuits has led to the inclusion in a single capsule of several discrete components, such as: transistors, diodes, resistors, etc. In this way, the integrated circuits have been achieved, where most of the components of a circuit are included in a single capsule. If in this capsule we transpose the scheme with discrete components of an operational amplifier then we can say that the integrated circuit is an operational amplifier (fig. 1).

    1181878504_AODIP8.png.7944910025a0b9dabd1dcb9e9a7b9506.png

    Operational amplifiers (AOs) are high-amplitude direct current amplifiers initially designed to perform certain mathematical operations, having differential inputs and, usually, a single output. Although an operational amplifier is an ideal amplifier, with infinite amplification, infinite band and perfectly flat frequency response, infinite input impedance and output impedance 0, without temperature drift, in practice, the operational amplifier has the following characteristics:
    - impedance large entrance;
    - low output impedance;
    - very high profit (over 50 000);
    - very large band and very flat frequency response;
    - drift with very low temperature.

    1738269878_thesymbolofoperationalamplifiers.png.d6df43281576eeaa151b009a3b4eb0d0.png

    Constructively, an operational amplifier consists of: two inputs (inverters and non-inverters), one output and the power terminals, as shown in fig.2. There are many applications of the operational amplifier, including the inverter, the non-inverting amplifier, the voltage repeater, the summing amplifier, the integrating amplifier, the differential amplifier and the compiler. To determine the specific application, different external components are connected to the operational amplifier.

    2. Brief history

    1941 - The first electronic tube operational amplifier. The first operational amplifier was found in the US patent no. 2401779 "Additive Amplifier", recorded in 1941 by Karl D. Swartzel Jr. from Bell laboratories. This design used three electronic vacuum tubes to achieve a gain of 90dB and operated at a symmetrical voltage of ± 350V. The circuit had a single non-inverting input quite similar to the differential inverting and non-inverting inputs of the present operational amplifiers. During the Second World War Swartzel's invention proved very valuable, being used in the control of the M9 artillery, in a system designed by Bell laboratories. This artillery control system worked with the SCR584 radar system to improve the target range, reaching almost 90%,


    1763231528_Historyofoperationalamplifiers.png.0366832064fdae4ba95d05ad32db6a18.png

    1947 - The first operational amplifier with inverting and non-inverting inputs
    In 1947, the operational amplifier was for the first time formally defined and named in a paper by Professor John R. Ragazzini of Columbia University. In this paper a footnote mentions that the operational amplifier was designed by a student whose work proved to be important. This operational amplifier, designed by Loebe Julie, has been superior in several respects. He had two major innovations. In the input circuit he used a triode to reduce the drift of the output circuit and, more importantly, it was the first operational amplifier that had two inputs (inverters and non-inverters). Differential inputs have made a whole host of new features possible.

    1948 - The first stabilizing chopper with operational amplifier
    In 1949, Edwin A. Goldberg designed the stabilizer chopper with AO. It is composed of a common operational amplifier and an ac amplifier that operates in parallel with the AO. The chopper picks up the AC signal by switching the DC voltage between rated and ground, at a fast rate (60Hz or 400Hz). This signal is then amplified, rectified, filtered and feeds the non-inverting input of the operational amplifiers. This has greatly improved the gain of the operational amplifiers by significantly reducing the thermal drift and the dc offset. Unfortunately, any AO that was used with the chopper could not use the non-inverting input for any other purpose. However, the much improved features of the AO stabilizer chopper increased the use rate of operational amplifiers. Techniques that will usually use non-inverting input will not be very popular until the 1960s when operational amplifier integrated circuits appear. In 1953, operational amplifier electronic tubes became commercially available with the launch of George A. K2-W, Philbrick Researches, Incorporated.

    1961 - The first operational amplifier integrated circuit
    Once the transistor was born in 1947 and the silicon transistor in 1954, the concept of integrated circuit became a reality. The introduction of the planar process in 1959 made transistors and integrated circuits stable and cheap enough to be marketed. By 1961, the first integrated circuits of operational amplifiers were produced. These AOs were actually small circuit boards with edge connectors. Usually, they allowed manual selection of resistors, in order to improve certain things, such as offset voltage and temperature drift. In 1961, the P45 could be powered at ± 15 V and had a gain of 94dB and could accept input signals within ± 10V.

    1962 - The first modularized AOs 
    By 1962, several companies produced modular plates that could be introduced into printed circuits. These packages were extremely important leading to the inclusion in a single capsule of the operational amplifier. Once this is done, the operational amplifiers could very easily be included in different schemes, resulting in smaller circuits.

    1963 - The first integrated circuit operational amplifier in monolithic technology 
    In 1963 it was designed by Bob Widlar, from Fairchild Semiconductor, the first operational amplifier in monolithic technology. Monolithic integrated circuits consist of only one chip. Unlike the chip there are also discrete circuits, only with pieces (discrete IC) or several free chips connected on a circuit board (hybrid IC). Almost all modern operational amplifiers are monolithic integrated circuits; however, this first integrated circuit was not very successful. Issues such as uneven supply voltage, low gain, and a small dynamic range, could not secure a dominant position among operational amplifiers until 1965, when μA709, designed by Bob Widlar, was launched.

    1968 - Launching μA741 - the most used operational amplifier 
    The popularity of monolithic operations increased even more with the launch of the LM101 operational amplifier integrated circuit in 1967, which solved a variety of issues, but also with the subsequent launch of μA741 in 1968. The uA741 integrated circuit was extremely similar to LM101 except for the fact that it included a 30 pF capacitor for compensation inside the capsule, while LM101 required external compensation. This minor difference made the uA741 one of the most used operational amplifiers, the location of the pins of which later became a reference. This operational one is still in production and has become ubiquitous in electronics, many manufacturers of electronic components making this classic chip, recognized under the simple name of 741.

    1966 - The first operational amplifier "varactor bridge"
    From 741, there were several different directions taken in the design of operational amplifiers. Operators "varactor bridge" began to be produced in the 60's, are characterized by low input currents and are the best operational amplifiers available, having a high power supply noise rejection capacity and can handle hundreds of volts, at their entrances. In the 1970s, high speed, low input currents, could be achieved using FET transistors. These will be largely replaced by MOS transistors in the 1980s. During the 1970s, several operational amplifiers with a single power supply were available.

    With a single power source the input and output voltages can be as low as the negative supply voltage instead of at least two volts above it. The result is that it can work in many applications with the negative power supply pin connected to the ground of the signal source, thus eliminating the need for a separate negative power supply.

    1972 - The first integrated circuit with four AOs included in the capsule
    LM324 was the first integrated quad amplifier operational circuit, later becoming an industrial standard. In addition, the encapsulation of multiple operational amplifiers in the same capsule, led in the 1970s to the birth of operational amplifiers in hybrid capsules. These AOs have generally improved existing versions of monolithic operations. As the supply voltages of the analog circuits decreased (like the digital ones), it was necessary to make the low voltage operational amplifiers, precisely to follow this trend. Thus, symmetrical supply voltages of +/- 5V or only 5V or even lower have been reached.

    3. Characteristic Sizes


    184308627_Polarizationofoperationalamplifiers.png.4c893a53f2f190710e09dcd49cca5b5c.png

    a.  Differential amplification factor (gain) in the open loop
    A0 represents the ratio between the output voltage variation (V0) and the differential input voltage (see Figure 4):

    01.png.b7f5963e7f5c8567c077c623639b336d.png
    b.  The common amplification factor in the open loop
    AMC represents the ratio between the variation of the output voltage and the arithmetic mean of the input voltages:

    02.png.5198304a1d223bee37a677feb68124b6.png

    This parameter results from the fact that, even if the two input voltages, are equal to zero, the voltage is output at the output of the operational amplifier. In the ideal case, of the perfect operational amplifier A MC = 0.

    c.  The offset voltage at the input
    U EI  is the value of the DC voltage applied to one of the inputs of the circuit for which the output is zero: V = 0.

    d.  Input polarization current - iB, where iB is the average value of the input currents:

    03.png.f60418f40177dd2b5dc2b9f6b9441041.png

    e.  Common rejection factor CMR
    It is the ratio between the differential amplification factor A0 and the common amplification factor: A MC .

    04.png.bc1e346e30d03abb047980a6348e776a.png

    According to the above, since in a perfect amplifier A MC = 0, it results in this case: C MR = ∞

    f.  The open loop treadmill
    It is the frequency range (range) in which the amplification decreases to the value of A U / √2 (-3 dB) from the maximum value: a U .

    4. Operation of the operational amplifier 

    4.1 Inverter operational amplifier (fig.5)

    2135539665_AOInversor.png.afd9836712648a0284347361882c47a1.png

    In the case of this type of amplifier, the signal is amplified on the terminal marked with (-), and the terminal (+) is connected to the table (fig. 5). Applying the first theorem of Kirchhoff around the node at the input the relation is obtained:

    05.png.d75afa043462163217df7e266c9054d2.png

    where: - the current given by the voltage V 1 ;
    - the reaction current, which appears through the loop formed by the resistance;
    - the current through the input of the operational amplifier.
    Because:

    06.png.89f8f55cf6169ddcf522595612495e68.png

    But:

    07.png.2579cdc8ec6daa4ef85f098c9f889926.png

    Because:

    08.png.f9126eae6f82c7b15489c2c02cf1861e.png

    And so the gain:

    09.png.5a5dfc72c7580d9105464b5e86efe8a4.png

    The (-) sign is observed indicating that the output voltage is in the phase position as compared to the input voltage. Some properties of the inverter operational amplifier can be deduced from this relation.

    - Multiplication with a constant, putting the condition:

    10.png.9ca9e3cf61982ef11c77c8fdbfdc6389.png

    so the output voltage reproduces the input voltage, multiplied by k times.

     Sharing with a constant . If:

    11.png.0caf29c85d9a7d9f8f45b255d82599a3.png
    so the output voltage is a fraction of the input voltage.

     Repeater circuit :

    12.png.1573277b0edbc068c7e44e29e13b8d26.png

     Addition circuit :

    787604873_Adderandrepeater.png.fe176967e7d0d9c1d2f92be22315659f.png
    If more voltages are applied to the inverter input, by means of resistors, at the output, a signal is obtained in the phase, proportional to the mode with their sum. Applying the first Kirchhoff theorem (Fig. 6b) the following relations are obtained:

    13-14-15.png.16dd506a2517a5d8136bf85ff364afe2.png

    Example 1:  Determine the gain and the output voltage for an AO inverter with the input voltage V1 = 50mV, R= 1 kOhm , R2 = 2,2 KOhmi. Solution: The gain is: A (-) = - R2 / R1 = -2.2 / 1 = -2.2; and the output signal represents the product between the input signal and the gain = -2,2 x 50mV = -110mV (see relation (9) and fig.5).

    Example 2:  In FIG. 6b if we have only R 1  and R 2  and R = R 1 = R 2 = 5KOhm, then the gain for both inputs will be: 5kOhm / 5kOhm = -1. Given V 1 = + 1V and V 2 = + 2V we obtain at the output a level due to V 1  of 1 x (-1) = - 1V and an output due to V 2  of 2 x (-1) = - 2V. Therefore the total output is V = -1-2 = -3V.

    4.2  Non-inverting operational amplifier

    720377012_non-invertingoperationalamplifier.png.711c31e6752a8d6eec878c1631e4c737.png

    In this case the signal is applied to the terminal (+). To deduce the value of the amplification, it is observed that the voltage between terminal A and ground is obtained from the circuit fed by the output voltage as follows:

    16.png.2319547b6d0290e40a203eee468127ee.png

    Since A = ∞, then V A = V = 0, so V A = V B = V 1  (V 1  represents the input voltage). In this case:

    17.png.0aed214e78500ff8154602f7d09829e5.png

    The gain will be:

    18.png.dc3d6f1c0940dc623760aeade39cfc9e.png

    It is observed that the output signal is in phase with the input signal.
    The properties of this amplifier can be deduced as in the case of the inverter, from the amplification formula. Note that he cannot divide because A +> 1, unless one of the resistors is replaced by a device with negative resistance (tunnel diodes). With ordinary physical elements, he can achieve:

     Multiplication with a constant . The following condition is met :

    19.png.018a52dd9e62338787e35518bac60648.png

    Then:
    20.png.5e85718df107bc3afe3e164a571397fc.png
    1509335967_non-invertingadditiveoperationalamplifier.png.0db232d453a7fd14e100eccb435abd5c.png

     Adder.  Considering the above circuit, the following relations can be established:
    21.png.780cc0c658dbd35657657aabfa360a0a.png

    Around the node applying the first Kirchhoff's theorem, we obtain:
    22.png.ccb415c9362561eacbd91f48b92a5882.png
    in which:
    23.png.1e28a9460cd866e0f026604833f77ff6.png
    Substituting we obtain:
    24.png.816b53d58129d4b60ab8128e30966944.png
    Assuming for simplification: R1 = ... = Rn = R, we obtain:
    25.png.d866110097e0f1ad483e46ff4b403028.png
    but:
    26.png.d7c06e7f2b9b482e89322b4ff04d30f6.png
    so:
    27.png.5ed8dc0d3c1f2c2464ea7b28df27cfcf.png
    If:
    28.png.6c9738a85616b7f9e79def14e8f97ae7.png
    It is observed that at the output the sum of the applied voltages from the input was obtained, in the same phase. In order to operate in the alternative current, the operational amplifier must be equipped with capacitors on the signal circuits or on the reaction circuits, according to the intended purpose. Obtaining a linear amplification requires the judicious choice of the values of the capacitors used.

    4.3  The integrating operational amplifier
    960422949_AOIntegrator.png.fa2cb4f5b944029ee51d134b29a518f2.png

    In order to obtain a type I AO, the resistance in the reaction circuit will be replaced by a capacity resulting from the diagram in fig.9. It is considered that the voltage u C2 , at the capacitance terminals has the value:
    29.png.977134cbd903fd76f8995a163e127b5c.png

    Respectively, considering u1i≈0 is obtained:
    30.png.18f27b253b1f7dff92bcb583e24f6e61.png

    Between the voltage u C2  at the capacitance terminals C 2  and the current I 2  passing through the respective capacitance there are the relations:
    31.png.17c611fff58112d932700343c4674aa9.png

    Substituting in the expression (31 ) the value of u C2  from the relation (30) results:
    32.png.bb2c9f23fcfd42564244ba5e50ec3c11.png

    For the current I 1 the  relation I 1 is preserved * К 1 = u 1 -u1i  and taking into account u 1i ≈0 is obtained: By

    33.png.0a482e6d3fc7472e2f4bace0a9d5266b.png

    replacing the expressions (32), (33) in the relation I 1 and 2  we obtain:

    34.png.0983a96ebdcceffefb5ee232be488c7e.png

    From the relation (34) it is found that the operational amplifier from the schematic fig.9 makes a law of type I, since the expression (34) corresponds to the definition relation of a law I of the form:
    35.png.37344d5aa9cbb87c7986868ccbd1ed7b.png

    From the expressions (33) and (34) it results for the considered scheme:
    36.png.10df971d980a4191d12536dc382e87b3.png

    4.4  The operational amplifier of type PI
    78364870_PIoperationalamplifier.png.965eb8b06aa4c18838c9f3832fc495f7.png

    In order to obtain an AO of PI type, in the negative reaction circuit of fig.5 we must introduce, in series with the resistance, the capacity. Thus, the scheme of Fig. 10, which represents an AO of type PI or by analogy in automatic results, we can say that the diagram of Fig. 10 represents a PI type controller with operational amplifier.

    In this case the voltage u C2  at the capacitance terminals C 2  is similar to the one shown in the expression (31). And if the voltage u R2  on the resistance R 2  has the expression:

    37.png.d466e146a8e0db7b6e4f1dc32363316e.png

    Then summing the voltages u C2  and u R2 the  difference of the voltages from the reaction circuit terminals is obtained, respectively:

    38.png.bc5fe5ab9092fe8462b2af2261884e66.png

    And considering u 1i≈0, results:

    39.png.7bbf8a91311b72c6e62cc8da7dbd5579.png

    For the current I 1 the  value in the expression (33) is preserved, since in the input circuit the same resistance R 1 is found , as in figures 5 and 9, it results:

    40.png.57d3ed3c9d1a46f817c92f9fd074e4d4.png

    Substituting in (40) is obtained:

    41.png.70d54c91c1b953de906f1bb039e62368.png

    The expression (41) ) attests that the diagram in figure 10 makes a regulation of type IP, since, ignoring the sign (-), which is taken into account when making electrical connections at the output of the regulator, this corresponds to the relation that defines the law of type PI:
    42.png.f68bfb46362abe63c933efe4da09f630.png

    If we want to change the parameters K R  and T i  of the regulator with AO, then the resistors R 1  and R 2 will have to be adjustable. From relations (41) and (41) it can be seen that if the value of the resistance is modified to obtain a variation of the value, then an undesirable change of the value is obtained, so an interdependence of granting the parameters of the regulator occurs.

    From the relations 41 and 42, it is shown for the diagram in fig. 10:

    43.png.1e35abe9614b80fad7d58df9dcd936e3.png

    4.5  Proportional - derivative (PD)
    1405243592_PDoperationalamplifier.png.9340ecc10366331216ebec23e37008f8.png

    operational amplifier In order to obtain a PD-type operational amplifier, which is characterized by the proportional derivative law, in the input circuit must be let us introduce in parallel a resistance and a capacity, as shown in Figure 11.
    In this scheme the current I 1 , which enters the node M, is equal to the sum of the currents I 1R and I 1C  by the resistance R 1  and the capacity C 1 . For the current I 1C the  expression results:

    44.png.85a44d7d5ac332c713ae4728d8956118.png

    Because u 1C = u 1 + u 1i  and considering the relation u 1i ≈0 results:
    45.png.f8e57ba770e5d825fa3fe0fde904713c.png

    For the current I R1  and I 1  we obtain:

    46.png.9836a6144e916ee27c724ce9c1f56c71.png

    For the current I 2  we have: I 2 = (u 1i -u 3 ) / R 2  and considering: u 2i ≈u 1i  is obtained:
    47.png.7883ec4e35aeb2c480a39c2f87a659e3.png

    Replacing the expressions of currents I 1  and I 2 it is obtained:
    48.png.b245fc8c7a2cefc3913e867110e64535.png

    This expression attests to the fact that the scheme in fig. 11 makes a PD regulation law, since this expression corresponds to the relation that defines the PD law:

    49.png.f408263a6005ac253634ff79d8106b29.png

    Result:

    50.png.f56736d15d6e6dae5b45565fd4b16290.png

    4.6  PID type operational amplifier
    1302470212_PIDoperationalamplifier.png.0d3e722633f87f280f9b9eb8eb171d81.png

    In order to obtain a PID type operational amplifier, the input circuit it must have the aspect shown in Figure 12.

    In the diagram of Fig. 11, the current I 1  is determined by the expression (46), since the input circuits are identical in Figures 10 and 11. On the other hand, for the scheme of Fig. 11, the expression (39) remains valid because the reaction circuits in the figures 10 and 12 are identical.

    From the relation (46) we obtain:

    51.png.f312afaf38f7fc821500ec2cb6f262bb.png

    and by replacing this expression of the current I 2  (39) it results:

    52.png.11860d40d565aa06969e3b0aaac875ac.png

    The expression (51) attests that the scheme in figure 12 makes a PID-type regulation law, since this expression corresponds to the relation that defines the PID law. :
    53.png.443a06f9bd8955110c820cb8980204a0.png

    5. The influence of the negative reaction on the amplifier parameters

    • 5.1 The influence of the negative reaction on the operational amplifier (fig.13)

    151807757_Theinfluenceofthenegativereaction.png.779145e4ac65d8ba9527e4aaa9d68d1c.png

    The negative reaction decreases the amplification but increases its stability. Indeed let us consider that for some reason (eg temperature variation) a variation ΔA << A of the unreacted amplifier occurred. In this case, in the relation A ' = A / (1-β · A), which represents the relation of the amplifier with reaction, A becomes A + ΔA and A '  becomes A ' + ΔA ' :

    54.png.eba0bf415ddc9ab3dbd402e3b129ae50.png

    subtracting the two relations is obtained:

    55.png.707d608a5a34c7143e9edc78ed74c357.png

    Dividing by A 'and taking into account that the

    56.png.d1d963321b16203695a6c23a5ef39fac.png

    reports ΔA / A and respectively ΔA ' / A ' are obtained ,  they give stability to the amplification without reaction, respectively with reaction. In the case of the negative reaction K> 1, so ΔA ' / A '<ΔA / A, stability improves.

    • 5.2 The influence of the negative reaction on the amplitude-frequency characteristics

    In the case of a negative reaction, the frequency characteristic is modified as shown in Figure 13, resulting in a broadening of the frequency band. It can be shown that the upper and lower boundary frequencies become:
    57.png.3242988c4496ca8cdcf32a7da76c9b43.png

    • 5.3 The influence of the negative reaction on the linear distortions

    Suppose that at the input of the amplifier a sinusoidal signal is applied, and at the output due to the non-linear characteristic of the transistor, the signal appears distorted. Through the negative feedback circuit, it is applied again to the phase opposition input, so with a deformation contrary to the output one. Consequently the resulting signal will be less deformed by compensation. The distortion factor in the case of the amplifier with negative reaction, is given by the formula:

    58.png.e9ca2167e48f4cfd9998d16d943f753f.png

    • 5.4 The influence of the negative reaction on the input and output impedances of the amplifier

    In the case of the amplifier with serial reaction, the input impedance increases with respect to the case of the amplifier without reaction. Indeed starting from the formulas:

    59.png.795a62fe227ee1134b6e173294a1d6a9.png

    and using the relation β = U 1 / U 2  regarding the reaction coefficient β and the input voltage in the reaction amplifier and the fact that I 1 = I 1 '  results:

    60.png.46d139557b13e250b7242d0bc549ed37.png

    It can be shown that the output impedance decreases when using the negative reaction, according to the formula:

    61.png.53abec896760a608eab2e302b1f0fec6.png

    In general, if a very strong negative reaction is used 1- βA >> 1, replacing A ' = A / (1-β · A) results in A '= -1 / β, that is, the amplification with reaction becomes independent of the amplifier parameters, thus obtaining high stability amplifiers.
    These consequences of applying the negative reaction in the amplifiers are justified for the simple reason that it is absent from the amplifiers.

    6 Measures to protect and balance the operational amplifiers

    The correct and safe operation of the operational amplifiers depends on the compliance with the maximum permissible data indicated by the manufacturing company. The protective measures to be taken refer to the supply voltages, the surges that may occur at the input and output of the amplifier and the current supplied by the load amplifier. By balancing the amplifiers, it is usually understood to compensate for offset or offset currents and voltages.

    6.1  Supply voltages

    1449685959_Reversevoltageprotection.png.951a23daf9b41382d223bfbedefb19c6.png

    In the catalog data, it is usually indicated the maximum values of the supply voltages, values greater than the nominal values. Although the operational amplifiers can work at voltages lower than indicated, the characteristics of the amplifiers change. The supply voltages may vary when connecting and disconnecting loads, as well as the variation of the mains voltage. The application of the voltages with the indicated polarity is obligatory, the change of the polarity could lead to the destruction of the amplifier. A good role for the proper functioning of the amplifier is played by the internal resistance of the sources that must be as small as possible. Since the voltage amplification is very high even at high frequencies, it is recommended to connect in parallel with the power sources some decoupling capacitors with values between 10 ... 100nF.

    6.2  Protection against overcurrent and overvoltage
    For operational amplifiers that do not have internal protection, it is recommended that the output resistance R be equal to the internal resistance of the amplifier. This resistance is especially indicated when the load is capacitive in nature. If the load is inductive, dangerous voltages may occur when switching on and off. The protection against overvoltages can be done with the circuits presented in fig.15.

    1278965910_Protectionforinductiveloads.png.1c52782a9f71edc9372048acd2a92bf4.png

    6.3  Limiting input voltage and output
    voltage Differential voltage V D = V 1 + -V 1 - may not exceed certain values indicated by the manufacturer. To limit the input voltage to small values (+/- 0.6V) use the mounting in figure 16a. If the operational amplifier supports higher voltages, Zener diodes mounted in opposition as in figure 16b are used.

    1748951384_Limitinginputvoltages.png.ed3668e09e35ece2c5d58282e38fd705.png

    584216589_Limitingtheoutputvoltage.png.5b22be29da4ad6eef33a411daffcb84a.png

    In order to limit the output voltage, the circuits shown in figure 17 can be used between points A and B of the operational amplifier (fig.17g). These circuits are individualized by a non-linear character, entering into action only when the output voltage exceeds a certain value. For example, the circuit in Fig. 17a limits the asymmetric voltage according to the characteristic of the Zener diode. Obviously, the diode can be connected and vice versa, it being parallel to the RN resistance (fig.17g). In the case of the circuit in Fig. 17b, the output voltage is symmetrically limited to values slightly higher than the voltages of the Zener diodes. In Fig. 17c, the voltage is symmetrically limited to approx. +/- 0.6V; high-value R resistor with the role of allowing residual currents to flow. The circuits of FIG. 17e and 17f allow depending on the choice of resistors or diodes, symmetrical or asymmetrical limitations of the output voltage. For example, in Fig. 17d, the limit voltage value for each alternation is calculated using the formulas:

    62.png.eddbf4c583d940e5ae504a2a9b5d193e.png

    6.4  Balancing operational amplifiers. Generally, by balancing the operational amplifiers is meant the compensation of the offset voltage, the resting current and the offset current.

    To compensate for the offset voltage, there are two possibilities:
    - the operational amplifier has special terminals, in which case the information in the catalog must be respected;
    - the operational amplifier does not have such terminals. In this case the voltage compensation is made according to the circuit.

    Figure 18a shows a circuit for offset voltage compensation on an inverter amplifier, and in Figure 18b a circuit for offset voltage compensation on a non-inverting amplifier.

    97483371_Offsetvoltagecompensation.png.df008e35bb9bd19f111f7879d7b6eaa5.png

    In both circuits, the input terminal (u1 = 0) is connected to the ground and the semi-regulator (or potentiometer) is operated until the output voltage is canceled. The internal resistance of the compensation circuit depends on the position of the  semi-regulator and appears connected in parallel with the resistance R P (fig.18a) or R  (fig.18b). In the case of the circuit of figure 18b, with the modification of the resistance R 1 there  is also a modification of the amplification. In order for the amplification modification to be as small as possible it is necessary that the resistance R be adopted much higher than R 1 .

    Although the offset current and voltage can be compensated, the compensation is effective only for a temperature range and only for a certain operating mode. For this reason, in the case of more complex circuits from which the last drop of performance is squeezed, specialized circuits are introduced in the offset cancellation in stationary and dynamic operating regime.

    The offset current drift is kept relatively small if the circuit is sized so that the resistors are low value. The resting currents although charging the signal sources are necessary for the operation of the amplifier, they constitute polarization currents of the transistors in the input circuit of the operational amplifier. In the ideal case, the input currents on the inverter and non-inverting terminals are equal. In fact, due to the voltage drops on the input resistors, these currents are not equal, which leads to the emergence of a differential voltage between the inverting and non-inverting terminals, which voltage is amplified and appears at the output. In order to compensate for the influence of currents, the resistors are chosen so that the voltage drops on them are equal.

    CAUTION! In the case of inverter mounting, the introduction of an offset current can also be done by adding a resistance to the non-inverting input connected to the ground. For optimal operating conditions, the value of this resistance, which I will note with R, will have to respect the relation:  R = R 2 R 1 / (R 2 + R 1 ) , where R 2  and R  are the resistors in figure 5 For this reason, in different electronic schemes with AO, only certain values of the external electronic components are used, the performances are no longer 100% the same, if the type of the operational amplifier is changed.

    7 Operational amplifier applications

    7.1 Ideal voltage controlled current
    source The ideal voltage controlled current source is very useful in all applications that require ideal voltage sources with linear variation as a function of time and with controlled slope (this is the case with analog digital converters, multipliers, of triangular function generators ramp etc.). One of the efficient possibilities for realizing such a current source is shown in figure 19.
    If the condition of equality between the absolute values applied to the two inputs is set, that is:: | U 1 | = | -U 2 | = U and if I choose the resistors so that R 5  << R 4  and R 4 / R 2 = R 3/ R 1 , then I R << I 5  and I E = I E '+ I R  ≈ I E ' ≈ U E '/ R 5  and:

    63.png.d7a281a7b6aec82a7a5b582eeaee79b1.png

    1817810029_Powersource-impedanceconverter.png.5e2fcfce4a8ca184eaec052995e582cc.png

    7.2 Negative impedance converter (CIN)
    Figure 20 shows the diagram of a active dipole, with differential operational amplifier, capable of converting a Z impedance (connected as the amplifier load) to a "negative" impedance: Z  = KZ. This circuit is used, in particular, for the synthesis of active RC filters.

    7.3 Active RC filters
    The combination of operational amplifiers with passive RC filters leads to the realization of active RC filters with transfer functions of the most diverse, suitable for certain applications, and of very good quality (efficiency). Active RC filters are used, in the case of electronic measurements, in distortion meters, audio filters, in the low frequency selective voltmeters (5 Hz to 1 MHz), in the interferential oscillators in the signal generators, etc. With the help of active filters you can obtain a wide class of frequency characteristics required in practice (such as the characteristics of the TJ, TB and TS filters) with the minimization of the active and passive elements.

    7.4 Simulated inductances

    508918098_Inductancesimulatedwithoperationalamplifier.png.84ca2641d09d3e1b5fc425c51edc2d8e.png

    At low frequencies, where the coils would be too large, or in the case of integrated circuits (where the coils that is, those circuit components having the inductance circuit parameter L cannot be physically realized), the inductances (inductances) L must be "simulated" ", an operation that can be carried out with floors often called and rotating. In the drawing in Fig. 21a is shown a rotator with operational amplifier whose equivalent scheme (Fig. 21b) is that of a coil LS with the inductance CR 1 R 2  and with the losses given by the resistance series R 1 + R 2 .

    7.5 The Comparator
    comparator is a floor which is attacked by two different signals (for example two voltages U 1  and U2 ) provides an answer when there is a certain relationship (eg equality) between the two input signals.

    911194323_comparatorwithoperationalamplifier.png.3a0456edaa37017ec9cad456c10ef5c2.png

    Figure 22 shows a comparator with hysteresis. The presence of hysteresis is useful if it is desired that the two stresses are not affected by the disturbances. The two levels of voltage or comparison determine the output state: U eP  or U eN .
    The hysteresis effect is given by the relation:

    64.png.8796e727bff03471fdd8b92c70062769.png

    The error of comparison, expressed as a deviation from the value U 1 , with which compares U 2 = const., Is:

    65.png.99f29db0000d22032d2e643b2177ed2b.png

    where u d1 is the voltage gap related to the input, the second term of the relationship the area of uncertainty, and the third term of the relationship, the signal on the incomplete common node rejected.

    2023209078_DumperOp-Amp.png.10036c27ba0c02ad7ac440c2610fda65.png

    7.6 Self-propelled amplifiers at output with modulation in duration
    With the help of operational amplifiers, simple rectangular signal generators can be made, with a constant period, but with a duration of 1 + t 2  of the positive impulse (see fig. 23) adjustable so with a filling factor t 1 / t 1 + t 2  that can be adjusted between 0 and 1 ie a self-propelled amplifier with the output voltage modulated in duration. Thus, the presence of the positive reaction introduced by the circuit R 3  R4 , causes the voltage at the output of the amplifier to take only one of the limit values + U e  or U e .

    7.7 Sinusoidal oscillators

    With the use of operational amplifiers, sinusoidal self-oscillators can also be obtained, if a reaction assembly such as the one in figure 24 is performed, which contains a selective circuit on the positive feedback loop and a negative reaction through two resistors R 3  and R 4 . Noting with β (ω) = U N / U E  the transfer function (attenuation) of the positive reaction block (network), the maintenance condition of the oscillations at the tuning pulse ω0. So, the self-oscillation condition is:
    Image posted
    In order to ensure the functioning of the auto-oscillator (sinusoidal oscillations maintained) it is necessary that, in addition to satisfying the above condition, the equality of the attenuations of the two reaction networks is maintained, which means achieving equal gains in the two reaction loops.

    1887814933_Sinusoidaloscillators.png.45bdd2586fd550baa81551f4146b465f.png

    7.8 Amplitude detectors
    Amplitude detectors are electronic floors that convert a variable voltage into a continuous voltage (this being the case of the type mutator: alternator continuous converter) or a low frequency voltage (the case of the type mutator: tire converter, used for signals). harmonics with amplitude modulation). Amplitude detectors are used in alternating current electronic voltmeters (which basically consist of an amplitude detector floor, followed by a direct current electronic voltmeter), in signal generators, in electronic blocks to determine the level or modulation degree (in modulometers) etc.

    1326731112_Amplitudedetectors.png.a610711439a434cf31523de127afa094.png
    1676817649_Peakdetectors.png.5b8288f5ca80eb037a5f06ff843a9133.png

    There are two types of amplitude detectors, named: medium value detectors (fig. 25) and peak detectors (fig. 26). If the diodes are reversed in Fig. 26, a peak detector is obtained for the negative values of the input voltages U1.

    7.9 Phase and frequency
    discriminators There is a wide variety of phase discriminators, depending on the purpose of their use. An example of a purpose is that of phase measurement, which can be done by the so-called phase sensitive detector.
    Frequency discriminators are used to measure the frequency deviation in the case of frequency modulated signals or for analog frequency measurement (in analog electronic frequency meters, these discriminators produce a continuous voltage proportional to the frequency of the signal to be measured, so that in fact these discriminators frequency are numerical-analogical converters of frequency-voltage). Frequency discriminators are also used in AC generators for automatic frequency adjustment, in which case they also function as a frequency converter.

    7.10 Electronic multipliers
    Electronic multipliers are stages that have a voltage proportional to the output of two analog voltages applied to the inputs. Floors with electronic multiplier function are used in many devices used in electronic measurements, including: effective value electronic voltmeters, electronic wattmeters, electronic meters (active and reactive energy), modulometers, amplitude modulated generators, interference oscillators, synthesizers frequency, synchronous detectors, electronic phasemeters, as well as in the phase shift circuits, in the circuits for the automatic amplification control, in the analogical calculation circuits, in the circuits for obtaining voltage-controlled (adjustable) impedances and many more.

    With the help of operational amplifiers, the synthesis of networks or signals in the field of frequencies or time with minimal errors can also be realized, many of them with applications being found in electronic measuring devices, such as: negative impedance converter, active filters, RC, comparator circuits with or without hysteresis, simulated inductors, analog splitters, peak detectors, mean value detectors, frequency discriminators, phase discriminators, self-tapping amplifiers, correlation analyzers, Fourier transformer samd.

    8. Practical schematics with operational amplifiers

    Figure 27 shows a simple mounting with operational amplifier type 741 in DIP-8 capsule. For other types of capsules it is recommended to study the datasheets of the integrated circuits, in order to identify the functions of the pins. There are also two operational amplifiers in the DIP-8 capsule (see NE5532). The RS  resistance represents the load resistance of the operational amplifier.

    1061405728_AO741.png.ad7b98a5c9f49f14fe2bfebde8be6b48.png

    Fig. 28 shows a Baxandall audio tone controller made with the operational amplifier OPA134:

    60371340_BaxandallOPA134.png.5156821a3210c33a1e94df1c94f67f72.png

    Bibliography :

    • [1]  http://elearning.algonquincollege.com
    • [2]  HANDBOOK OF OPERATIONAL AMPLIFIER APPLICATIONS - Texas Instruments
    • [3]  Edmond Nicoalu, Beliş Mariana - Electrical and electronic measurements "- Didactic and Pedagogical Publishing House, Bucharest 1984
    • [4]  Theodor Dănilă, Monica Ionescu-Vlad - Electronic components and circuits "- Didactic and Pedagogical Publishing House, Bucharest 1984
    • [5]  G. Vasilescu, Ș. Lungu - Electronic "- Didactic and Pedagogical Publishing House, Bucharest 1981
    • [6]  Miron C. - Introduction to electronic circuits " Dacia Publishing House, Cluj Napoca, 1983.

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