Operational amplifier is a high gain electronic voltage amplifier having a differential input and usually one output. The output voltage can exceed the voltage difference at the inputs by hundreds or even thousands of times.

Operational amplifiers have their origins in analog computers, where they were used in many linear, nonlinear, and frequency-dependent circuits. The parameters of operational amplifier circuits are determined only by external components, as well as small temperature dependence or variation in parameters during their production, which makes operational amplifiers very popular elements in the design of electronic circuits.

Operational amplifiers are the most popular devices among modern electronic components; they are used in consumer electronics, industry and scientific instruments. Many standard op-amp ICs cost only a few cents. But some low-volume hybrid or integrated op-amps with special features can cost more than a hundred dollars. Operational amplifiers are usually produced as separate components, but they can also be elements of more complex electronic circuits.

An operational amplifier is a type of differential amplifier. Other types of differential amplifier are:

1. Fully differential amplifier (this device is similar in principle to an operational amplifier, but has two outputs);
2. Instrumentation amplifier (this usually consists of three operational amplifiers);
3. Isolated amplifier (this amplifier is similar to an instrumentation amplifier, but it can withstand high voltages that can destroy a regular op-amp);
4. Negative feedback amplifier (usually contains one or two operational amplifiers and a resistive feedback network).

The supply voltage terminals (V S+ and V S-) may be designated differently. Despite the different designations, their function remains the same - providing additional energy to amplify the signal. Often these conclusions are not shown on diagrams so as not to clutter the drawing, and their presence is either indicated separately or should be clear from the diagram.

Symbols on the diagram

Operating principle

An amplifier's differential inputs consist of two terminals - V+ and V-, an ideal op-amp amplifies only the voltage difference between these two inputs, this difference is called the input differential voltage. The voltage at the output of the operational amplifier is determined by the formula

V out = A OL (V + - V -)

where V + is the voltage at the non-inverting (direct) input, V - is the voltage at the inverting (inverse) input, and A OL is the gain of the amplifier with an open feedback loop (that is, there is no feedback from the output to the input).

Operational amplifier without negative feedback (comparator)

The gain value of operational amplifier chips is usually large - 100,000 or more, therefore a fairly small voltage difference between the V + and V - inputs will result in a voltage almost equal to the supply voltage appearing at the output of the amplifier. It is called saturation amplifier The value of the gain A OL has a technological variation, so you should not use one operational amplifier as a differential amplifier; it is recommended to use a circuit of three amplifiers. Without negative feedback, and possibly with positive feedback, the op-amp will act as a comparator. If the inverting input is connected to the common wire (zero potential) directly or through a resistor, and the voltage V in applied to the non-inverting input is positive, then the output voltage will be maximum positive. If you apply a negative voltage V in to the input, then the output voltage will be as negative as possible. Since there is no feedback from the output to the inputs, such an open-loop feedback circuit will work as a comparator, the gain of the circuit will be equal to the gain of the operational amplifier A OL.

Op-amp with negative feedback (non-inverting amplifier)

In order for the operation of the operational amplifier to be predictable, negative feedback is used, which is established by applying part of the voltage from the output of the amplifier to its inverting input. This closed feedback loop significantly reduces the amplifier's gain. When negative feedback is used, the overall gain of the circuit depends much more on the parameters of the feedback network than on the parameters of the op-amp. If the feedback circuit contains components with relatively stable parameters, then changes in the operational amplifier parameters will not significantly affect the characteristics of the circuit. The transfer characteristic of an op-amp circuit is determined mathematically by the transfer function. Designing circuits with a given transfer function with operational amplifiers belongs to the field of radio electronics. The transfer function is an important factor in most circuits that use op-amps, such as those found in analog computers. High input impedance of the inputs and low output impedance of the output is also a useful feature of operational amplifiers.

For example, if negative feedback is added to a non-inverting amplifier (see figure on the right) using a voltage divider Rf, Rg, this will lead to a decrease in the circuit gain. Equilibrium will be restored when the voltage at the output V out becomes sufficient to change the voltage at the inverting input to voltage V in. The gain of the entire circuit is determined by the formula 1 + R f /R g. For example, if the voltage V in = 1 volt, and the resistances R f and R g are the same (R f = R g), then a voltage of 2 volts will be present at the output V out, the value of this voltage is just sufficient for the inverting input V - a voltage of 1 volt was supplied. Since resistors R f and R g form a feedback circuit connected from the output to the input, a circuit with a closed feedback loop is obtained. The overall gain of the circuit V out / V in is called the closed loop gain A CL . Since the feedback is negative, in this case A CL< A OL .

We can look at this from another angle by making two assumptions:
First, when an op-amp operates in linear mode, the voltage difference between its non-inverting (+) and inverting (-) terminals is so small that it can be neglected.
Secondly, we will consider the input impedances of both inputs (+) and (-) to be very high (several megaohms for modern operational amplifiers).
Thus, when the circuit shown in the figure to the right is operated as a non-inverting linear amplifier, the voltage V in appearing at the (+) and (-) inputs will result in the appearance of a current i, flowing through the resistor R g, with a value of V in /R g. According to Kirchhoff's law, which states that the sum of the currents flowing into a node is equal to the sum of the currents flowing out of that node, and since the input resistance (-) is almost infinite, it can be assumed that almost all the current i, flowing through the resistor R f, creates an output voltage equal to V in + i * R f. By substituting the terms into the formula, you can easily determine the gain of this type of circuit.

i = V in / R g

V out = V in + i * R f = V in + (V in / R g * R f) = V in + (V in * R f) / R g =V in * (1+ R f / R g )

G = V out / V in

G = 1 + R f / R g

Operational Amplifier Characteristics

Ideal op amp

An equivalent circuit of an operational amplifier in which some non-ideal resistive parameters are simulated

An ideal operational amplifier can operate at any input voltage and has the following properties:

• The gain with an open feedback loop is equal to infinity (in theoretical analysis, the gain with an open feedback loop A OL is assumed to tend to infinity).
• The range of output voltages V out is equal to infinity (in practice, the range of output voltages is limited by the value of the supply voltage V s+ and V s-).
• Infinitely wide bandwidth (i.e. the amplitude-frequency response is perfectly flat with zero phase shift).
• Infinitely large input resistance (R in = ∞, current does not flow from V + to V -).
• Zero input current (i.e. assumes no leakage or bias currents).
• Zero offset voltage, i.e. when the inputs are connected to each other V + = V -, then there is a virtual zero at the output (V out = 0).
• Infinitely high slew rate (i.e., the rate of change of output voltage is not limited) and infinitely high power throughput (voltage and current are not limited at all frequencies).
• Zero output resistance (R out = 0, so the output voltage does not change when the output current changes).
• No inherent noise.
• Infinitely high degree of common mode rejection.
• Infinitely high degree of suppression of supply voltage ripple.

These properties come down to two “golden rules”:

1. The output of the operational amplifier tends to make the difference between the input voltages equal to zero.
2. Both op amp inputs consume no current.

The first rule applies to an operational amplifier connected to a circuit with a closed negative feedback loop. These rules are generally applied to the analysis and design of op-amp circuits as a first approximation.

In practice, none of the ideal properties can be fully achieved, so various compromises must be made. Depending on the desired parameters, when simulating a real op-amp, some non-idealities are taken into account by using equivalent networks of resistors and capacitors in its model. The designer can incorporate these undesirable but real effects into the overall characteristics of the designed circuit. The influence of some parameters may be negligible, while other parameters may impose limitations on General characteristics scheme.

Real operational amplifier

Unlike an ideal one, a real operational amplifier has imperfections in various parameters.

Non-ideal DC parameters

Final gain An ideal op-amp with an open feedback loop has infinite gain, unlike a real amplifier, which has finite gain. Typical open loop DC current values ​​for this parameter range from 100,000 to over a million. Because this gain is very large, the gain of the circuit will be determined solely by the negative feedback gain (i.e., the gain of the circuit will not depend on the gain of the op-amp when the feedback loop is open). If the gain of the circuit with a closed feedback loop is required to be very large, then for this the feedback gain must be very small, so in this case the operational amplifier will no longer behave ideally. Final input impedance The differential input resistance of an op-amp is defined as the resistance between its two inputs; Common mode input resistance is the resistance between any of the inputs and ground. Op amps with FET inputs often have protective circuits at their inputs to prevent the input voltage from exceeding a certain threshold, so in some tests the input impedance of such devices may be very low. But since these op-amps are typically used in deep feedback circuits, these protection circuits are left unused. Bias voltage and leakage current, described below, are much more important parameters when designing op-amp circuits. Non-zero output impedance Low output impedance is very important for low-impedance loads, since the voltage drop across the output impedance can be significant. Consequently, the output impedance of the amplifier limits the maximum achievable output power. In circuits with negative voltage feedback, the output impedance of the amplifier decreases. Thus, when using operational amplifiers in linear circuits, very low output impedance can be obtained. However, negative feedback cannot reduce the limitations imposed by R load and R out on the possible maximum and minimum output voltages - it can only reduce errors in that voltage range. Low output impedance typically requires high quiescent currents for the op-amp output stages, which increases power dissipation, so low output impedance must be deliberately sacrificed in low-power designs. Input current Due to the presence of bias or leakage currents, a small current (typically ≈ 10 nanoamps for op amps with bipolar transistors in the input stages, tens of picoamps for FET input stages, and a few picoamps for MOS input stages) flows into the inputs. When a circuit uses resistors or high-impedance signal sources, a small amount of current can create a fairly large voltage drop. If the input currents are the same, and the resistances connected to both inputs are the same, then in this case the voltages at the inputs will be the same. Since the voltage difference between the inputs is important for the operation of the op-amp, these identical voltages at the inputs will not affect the operation of the circuit (unless, of course, the op-amp has good common-mode rejection). But usually these input currents (or the input resistances at the inputs) are slightly mismatched, so a small offset voltage is generated (but not the offset voltage described in the paragraph below). This offset voltage can create offset or drift in the op amp. Often, the circuit uses control elements to compensate for it. Some operational amplifiers have pins for connecting an external trimming resistor, which can be used to balance the inputs and thereby remove this offset. Some op amps can automatically compensate for offset voltage. Input offset voltage This voltage required at the inputs of the op amp to set the output voltage to zero is due to the mismatch of the input bias currents. An ideal amplifier has no input offset voltage. But in real operational amplifiers this voltage is present, since most amplifiers have an imperfect differential stage at the input. Input offset voltage creates two problems: first, due to the high voltage gain, the amplifier's output is almost guaranteed to saturate when operated without negative feedback, even if both inputs are connected to each other. Second, with a closed negative feedback loop, the input offset voltage will increase along with the signal and this can cause problems for high-precision DC amplifiers or if the input signal is very weak. Common Mode Boost An ideal op-amp amplifies only the voltage difference between the inputs, completely suppressing all voltages common to both inputs. However, the differential input stage of real op amps is never ideal, resulting in some amplification of the same voltages applied to both inputs. The magnitude of this disadvantage is measured by the common mode rejection ratio. Minimizing common mode gain is usually important in high gain non-inverting amplifier designs. Output Sink Current The output sink current is the maximum allowable sink current for the output stage. Some manufacturers display the output voltage versus the incoming current on a graph, which allows you to get an idea of ​​the output voltage when there is current from an external source flowing into the amplifier's output stage. Temperature dependence All parameters change with temperature changes. Thermal drift of the input offset voltage is a particularly important parameter. Suppression of supply voltage ripple The output of an ideal op-amp will be completely independent of the supply voltage ripple at its power pins. Each real operational amplifier has a certain supply voltage ripple suppression ratio, which shows how much these ripples are suppressed. The use of power supply blocking capacitors can improve this parameter for many devices, including operational amplifiers. Drifting Real op amp parameters change slowly over time, temperature, etc. Noises Even in the absence of a signal at the input, the amplifiers chaotically change the output voltage. This may be due to thermal noise or flicker noise inherent in the device. When used in high gain or wide bandwidth applications, noise level becomes a very important factor to take into account.

Non-ideal parameters for alternating current

Op-amp gain calculated at DC is not applicable for high frequencies. When designing op amp circuits that are designed to operate at high frequencies, more complex considerations must be made.

Finite Bandwidth All amplifiers have a finite frequency range. To a first approximation, an operational amplifier has the amplitude-frequency response of an integrator with gain. That is, the gain of a typical op-amp is inversely proportional to frequency, characterized by the gain multiplied by the bandwidth fT. For example, an op-amp with fT = 1 mHz may have a gain of five times at 200 kHz, and a gain of unity at frequency 1 MHz The operational amplifier's frequency response, together with a very high DC gain, produces a frequency response similar to that of a first-order low-pass filter with high DC gain and low cutoff frequency (f T divided by the gain). The finite bandwidth of an op amp can be the source of several problems, including:

• Stability. The phase difference between the input and output signal is associated with bandwidth limitation, so that in some feedback circuits it can lead to self-excitation. For example, if the sinusoidal output signal, which should add out of phase with the input signal, is delayed by 180°, then it will add in phase with the input signal, i.e. positive feedback is formed. In these cases, the feedback loop can be stabilized by using a frequency compensation circuit that increases the gain or phase shift when the feedback loop is open. This compensation can be implemented using external components. This compensation can also be implemented inside the operational amplifier by adding a dominant pole, which sufficiently attenuates the gain at high frequencies. The location of this pole can be set internally by the chip manufacturer, or can be adjusted using op-amp-specific methods. Typically the dominant pole further reduces the op amp's bandwidth. When high closed-loop gain is required, frequency compensation is often not needed because the required open-loop gain is quite low. Therefore, high-gain closed-loop circuits can use op-amps with wider bandwidth.
• Noise, distortion, and other effects. Reducing the bandwidth also leads to a decrease in the transmission coefficient of the feedback circuit at high frequencies, which leads to an increase in distortion, noise, output impedance, and also reduces the linearity of the output signal phase with increasing frequency.

Input capacitance Input capacitance is an important parameter when operating at high frequencies, as it reduces the amplifier's open-loop gain. Common Mode Boost Cm. .

Nonlinear parameters

Saturation The operational amplifier's output voltage swing is limited to values ​​close to the supply voltages. When the output voltage reaches these values, the amplifier saturates, this happens due to the following reasons:

• If bipolar power supply is used, then with a large voltage gain, the signal must be amplified so much that its amplitude would have to exceed the positive supply voltage or be less than the negative supply voltage, which is not feasible, since the output voltage cannot go beyond these limits.
• When using a single-supply supply, either the same thing can happen as when using a bi-supply supply, or the input signal may have such a low voltage relative to ground that the amplifier's gain is insufficient to raise it above the lower threshold.

Limited slew rate The rate of change of voltage at the amplifier's output is finite, usually measured in volts per microsecond. When the maximum possible slew rate of the signal at the input is reached, the slew rate at the output will stop increasing. The slew rate of the signal is usually limited by the internal capacitances in the op amp, these capacitances being especially large where internal equalization is used. Nonlinear dependence of output voltage on input voltage The output voltage may not be exactly proportional to the voltage difference between the inputs. In practical circuits, this effect is very weak if strong negative feedback is used.

Current and voltage limits

Output current limitation The output current cannot be infinite. In practice, most op amps are designed to limit the output current so that the current does not exceed a certain value, which prevents the op amp and load from failing. Modern models of operational amplifiers are more resistant to current overloads than earlier ones, and some models modern devices allow you to withstand an output short circuit without damage. Dissipation power limitation The op amp's output resistance, through which current flows, dissipates heat. If the op-amp dissipates too much heat, its temperature will rise above a critical value. In this case, the overheating protection may trip or the operational amplifier may fail.

Modern FET and MOSFET op amps come much closer in performance to ideal op amps than BJT models when input impedance and input bias currents are important. Bipolar transistor op amps are best used when lower input offset voltages and often lower inherent noise are required. FET and MOSFET op amps in bandwidth-limited circuits operating at room temperature generally perform better.

Although the design different models While chips from different manufacturers may vary, all operational amplifiers have a basically similar internal structure, which consists of three stages:

1. Differential amplifier - designed to amplify the signal, has a low noise floor, high input impedance and usually a differential output.
2. Voltage amplifier - provides high voltage gain, has a single-pole roll-off frequency response, and usually has a single output.
3. Output Amplifier - Provides high load capacity, low output impedance, current limiting and short circuit protection.

Op-amp chips are typically of moderate complexity. A typical example is the widely used operational amplifier chip 741 (Soviet equivalent - K140UD7), developed by Fairchild Semiconductor after the previous model - LM301. Basic architecture The 741 amplifier is the same as the 301 model.

Input stage

The input stage is a differential amplifier with a complex bias circuit, the active load of which is a current mirror.

Differential amplifier

The differential amplifier is implemented in a two-stage stage, satisfying conflicting requirements. The first stage consists of n-p-n emitter followers on transistors Q1 and Q2, which allows for high input impedance. The second stage is based on pnp transistors Q3 and Q4, connected in a common base circuit, which allows you to get rid of the harmful effects of the Miller effect, shift the voltage level down and provide sufficient voltage gain for the operation of the next stage - a class “A” amplifier. Application of pnp transistors also helps to increase the breakdown voltage V be (the base-emitter junctions of n-p-n transistors Q1 and Q2 have a breakdown voltage of about 7 volts, and the breakdown voltage of p-n-p transistors Q3 and Q4 is about 50 volts).

Bias circuits

The emitters of a classic differential cascade with emitter connections are supplied with a bias voltage from a stable current source. The negative feedback circuit forces the transistors to act as voltage stabilizers, causing them to change the voltage Vbe such that current can flow through the collector-emitter junction. As a result, the quiescent current becomes independent of the DC transfer ratio (β) of the transistors.

Signals from the emitters of transistors Q1, Q2 are supplied to the emitters of transistors Q3, Q4. Their collectors are separate and they cannot be used to supply quiescent current from a stable current source, since they themselves function as current sources. Therefore, quiescent current can only be supplied to the bases by connecting them to a current source. To avoid dependence on the DC transfer coefficient of transistors, negative feedback is used. To do this, the entire quiescent current is reflected by a current mirror made on transistors Q8, Q9, and the negative feedback signal is removed from the collector of transistor Q9. This forces transistors Q1-Q4 to change their base-emitter voltage Vbe so that the required quiescent current flows through them. The result is the same effect as a classic pair of emitter-coupled transistors - the magnitude of the quiescent current becomes independent of the DC transfer coefficient (β) of the transistors. This circuit generates a base current of the required magnitude, depending on β, so that a β-independent collector current can be obtained. To obtain base bias currents, a negative voltage power supply is usually used. These currents flow from the common wire to the bases of the transistors. But to obtain the highest possible input impedance, the base bias loops are not closed internally between the base and the common wire, since these circuits are supposed to be closed through the output impedance of the signal source to ground. So the signal source must be galvanically connected to a common wire so that bias currents can flow through it, and it must also have a sufficiently low resistance (tens or hundreds of kilo-ohms) so that there is no significant voltage drop across it. Otherwise, you can connect resistors between the bases of transistors Q1, Q2 and the common wire.

The quiescent current value is set by a 39 kOhm resistor, which is common to both current mirrors Q12-Q13 and Q10-Q11. This current is used as a reference for other bias currents in the circuit. Transistors Q10, Q11 form, in which a small portion of the collector current I ref of transistor Q10 flows through a 5 kOhm resistor. This small collector current flowing through the collector of transistor Q10 is the base reference current for transistors Q3 and Q4, as well as the collector of transistor Q9. Using negative feedback, the current mirror on transistors Q8 and Q9 attempts to make the collector current of transistor Q9 equal to the collector current of transistors Q3 and Q4. The collector voltage of transistor Q9 will change until the ratio of the base currents of transistors Q3 and Q4 to their collector currents becomes equal to β. Therefore, the total base current of transistors Q3 and Q4 (this current is of the same order as the currents of the chip's inputs) is a small part of the weak current of transistor Q10.

Thus, the quiescent current is set by the current mirror on transistors Q10, Q11 without using negative current feedback. This current feedback only stabilizes the collector voltage of transistor Q9 (and the base of transistors Q3, Q4). In addition, the feedback network also isolates the rest of the circuit from common mode signals by setting the base voltage of transistors Q3, Q4 exactly 2V BE lower than the highest of both input voltages.

The differential amplifier formed by transistors Q1–Q4 is connected to an active load based on an improved current mirror on transistors Q5...Q7, which converts the currents of the input differential signal into voltage, and here both input signals are used to form this voltage, which gives a significant increase in strengthening. This is achieved by adding the input signals using current mirrors, in this case the collector of transistor Q5 is connected to the collector of transistor Q3 (the left output of the differential amplifier), and the output of the current mirror - the collector of transistor Q6 is connected to the right output of the differential amplifier - the collector of transistor Q4. Transistor Q7 increases the accuracy of the current mirror by reducing the current drawn from transistor Q3 to drive the bases of transistors Q5 and Q6.

Operational Amplifier Operation

Differential mode

The voltages of the signal sources supplied to the inputs pass through two “diode” chains formed by the base-emitter junctions of transistors Q1, Q3 and Q2, Q4, to the junction of the bases of transistors Q3, Q4. If the input voltages change slightly (the voltage at one input increases and the other decreases), then the voltage at the bases of transistors Q3, Q4 will hardly change, and the total base current will remain unchanged. There will only be a redistribution of currents between the bases of transistors Q3, Q4, the total quiescent current will remain the same, the collector currents will be redistributed in the same proportions as the base currents.

The current mirror will invert the collector current, the signal will return back to the base of transistor Q4. At the junction of transistors Q4 and Q6, the currents of transistors Q3 and Q4 are subtracted. These currents are out of phase in this case (in the case of a differential signal). Consequently, as a result of subtracting the currents, the currents will add up (ΔI - (-ΔI) = 2ΔI), and the conversion from a two-phase signal to a single-phase one will occur without losses. In a circuit with an open feedback loop, the voltage obtained at the junction point of transistors Q4 and Q6 is determined by the result of the subtraction of currents and the total resistance of the circuit (parallel connected collector resistances of transistors Q4 and Q6). Since these resistances are high for signal currents (transistors Q4 and Q6 behave as current generators), the gain of this stage will be very high when the feedback loop is open.

In other words, you can think of transistor Q6 as a copy of transistor Q3, and the combination of transistors Q4 and Q6 can be thought of as a variable voltage divider consisting of two voltage-controlled resistors. For differential input signals, the resistances of these resistors will vary greatly in opposite directions, but the total resistance of the voltage divider will remain unchanged (like a moving contact potentiometer). As a result, the current does not change, but there is a strong change in voltage at the midpoint. Since the resistances change equally but in opposite directions, the resulting voltage change will be twice as large as the single voltage changes.

The base currents at the inputs are not zero, and therefore the effective input impedance of the 741 op amp is approximately 2 mΩ. The “zero setting” pins can be used to connect external resistors in parallel with internal 1 kOhm resistors (a potentiometer is usually connected here) to balance the currents of transistors Q5, Q6, thus indirectly adjusting the output signal when zero signals are applied to the inputs.

Common Mode Rejection Mode

If the input voltages change synchronously, then negative feedback forces the voltage at the bases of transistors Q3, Q4 to repeat (with an offset equal to twice the voltage drop at the base-emitter junctions of the transistors) the variations in input voltages. The output transistor Q10 of the current mirror Q10, Q11 keeps the total current flowing through transistors Q8, Q9 constant and independent of voltage changes. The collector currents of transistors Q3, Q4 and, accordingly, the output voltage at the midpoint between transistors Q4 and Q6 remain unchanged.

The subsequent negative feedback loop effectively increases the input impedance of the op amp in common mode rejection mode.

Amplifier stage operating in class "A"

The cascade made on transistors Q15, Q19 Q22 operates in class “A”. The current mirror, made on transistors Q12, Q13, supplies this cascade with a stable current, independent over a wide range of variations in the output voltage. The cascade is based on two npn transistors, Q15 and Q19, forming the so-called composite Darlington transistor, in the collector of which a dynamic load in the form of a current source is used to obtain high gain. Transistor Q22 protects the amplifier stage from saturation by shunting the base of transistor Q15, that is, it acts like a Baker circuit.

The 30 pF capacitor in the amplifier stage is a selective feedback circuit for frequency correction, which allows you to stabilize the operational amplifier when operating in closed-loop circuits. This circuit solution is called "Miller compensation", the principle of operation of which is reminiscent of the operation of an integrator on an operational amplifier. This circuit solution is also known as “dominant pole correction”, since a dominant pole is introduced into the frequency response, which suppresses other poles in the amplitude-frequency response with an open feedback loop. The frequency of this pole can be less than 10 Hz in a 741 amplifier, and at this frequency the pole introduces an attenuation equal to -3 dB in the amplitude-frequency response when the feedback loop is open. The use of this internal compensation is necessary to obtain absolute stability of the amplifier when operating with non-reactive negative feedback in the case where the op-amp gain is greater than or equal to unity. Thus, there is no need to use external correction to ensure the same stability under different operating modes, which greatly simplifies the use of the operational amplifier. Those operational amplifiers in which there is no internal correction, for example, K140UD1A, may require the use of external correction or a gain greater than unity with a closed feedback loop.

Output stage bias circuit

Transistor Q16, together with two resistors, form a level bias circuit, also known as a rubber diode, a transistor zener diode, or a base-emitter junction voltage multiplier (V BE). In this circuit, transistor Q16 acts as a voltage regulator, since it provides a constant voltage drop across its collector-emitter junction for any current flowing through this stage. This is achieved by introducing negative feedback between the collector and the base in the form of a two-resistor voltage divider with a division coefficient β = 7.5 kOhm / (4.5 kOhm + 7.5 kOhm) = 0.625. Assuming the transistor's base current is zero, the negative feedback forces the transistor to increase its collector-emitter voltage to about one volt until the base-emitter voltage reaches the typical bipolar transistor voltage of 0.6 volts. This circuit is used to bias the output transistors, thereby reducing harmonic distortion. In the circuits of some low-frequency amplifiers, a pair of series-connected diodes is used for this.

This bias circuit can be thought of as a negative feedback amplifier with a constant input voltage of 0.625 volts and a feedback factor of β = 0.625 (respectively, the gain would be 1/β = 1.6). The same circuit, but with β = 1, is used to set the operating current in the classical current mirror circuit using bipolar transistors.

Output stage

The output stage (transistors Q14, Q17, Q20) is a push-pull emitter follower operating in class "AB", the bias of this stage is set by a level bias circuit made on transistor Q16 and two resistors connected to the base of this transistor. The signal to the output transistors Q14, Q20 is supplied from the collectors of transistors Q13 and Q19. Variations in bias voltage due to temperature changes or transistor variations can cause non-linear distortion and change the op-amp's quiescent current. The amplifier's output voltage ranges approximately one volt less than the supply voltages (i.e., V - +1 to V + -1), determined in part by the base-emitter voltage of output transistors Q14 and Q20.

The 25 ohm resistor in the output stage acts as a current sensor to provide maximum current limit for that stage, and in the 741 op amp this resistor limits the output current of emitter follower Q14 to 25 mA. The current limitation for the lower emitter follower in the circuit is implemented using a 50 Ohm resistor installed in the emitter circuit of transistor Q19; using transistor Q22, the voltage at the base of transistor Q15 is reduced as the voltage drop across the resistor increases above the critical value. Later 741 op amp models may use a slightly different method of limiting the output current.

Unlike an ideal operational amplifier, the Model 741 amplifier has a non-zero output impedance, but uses negative feedback on the low frequencies it becomes almost zero.

Some thoughts on the 741 op amp

Note: Historically, the 741 op amp was used in audio and other high sensitivity circuits, but is rarely used anymore due to its lower noise level modern models operational amplifiers. Except loud noise, 741 and other older models may have poor common-mode rejection and often receive line pickup and other interference.

A Model 741 op amp often refers to some kind of generic op amp (such as the μA741, LM301, 558, LM324, TBA221, or more recent models such as the TL071). The description of the 741 amplifier's output stage is almost the same for many other models (which may have completely different input stages), with the exception of:

• Some operational amplifier models, such as μA748, LM301, LM308, do not have internal correction and require the installation of an external correction capacitor when operating in closed-loop and low-gain circuits.
• For some modern models of operational amplifiers, the output voltage can vary in the range from almost negative to positive supply voltage.

Classification of operational amplifiers

Operational amplifiers can be classified by their type of design:

• Discrete - created from individual transistors or vacuum tubes;
• Microcircuit - integrated operational amplifiers are the most common;
• Hybrid - created on the basis of hybrid microcircuits with a low degree of integration;

Integrated operational amplifiers can be classified according to various parameters, including:

• Division into microcircuits of military, industrial or commercial design, characterized by reliability and resistance to external factors (temperature, pressure, radiation), and therefore price. Example: LM301 general op amp is the commercial version of LM101, and LM201 is the industrial version.
• Classification by case type - models of operational amplifiers in different types of cases (plastic, metal, ceramic) also have different resistance to external factors. In addition, packages come in DIP and surface mount (SMD) types.
• Classification according to the presence or absence of internal correction circuits. Operational amplifiers can operate unstable in some circuits with negative feedback; to avoid this, use a small capacitor to correct the amplitude-frequency response. An operational amplifier with such a built-in capacitor is called an internally corrected operational amplifier.
• One chip package can contain one, two or four operational amplifiers.
• The range of input (and/or output) voltages from negative to positive supply voltage - the operational amplifier can operate with signals whose values ​​are close to the supply voltage values.
• CMOS FET op amps (such as the AD8603) provide very high input impedance, higher than conventional FET op amps, which in turn have higher input impedance than BJT op amps.
• There are so-called “programmable” operational amplifiers, in which a number of parameters can be set using an external resistor, such as quiescent current, gain, and bandwidth.
• Manufacturers often categorize op amps by application type, such as low noise, preamp, wide range, etc.

Applications of operational amplifiers

Use in electronic system designs

Model 741 Op-Amp Pin Assignment

Using operational amplifiers as blocks simplifies the design of circuits and makes them easier to read than using discrete components (transistors, resistors, capacitors). When designing circuits, as a first approximation, operational amplifiers are considered as ideal differential components, and only in subsequent steps are all imperfections and limitations of these devices taken into account.

For all circuits, the circuit design remains the same. The specification indicates the purpose of the circuit and the requirements for it with the corresponding tolerances. For example, a gain of 1000 times with a tolerance of 10% and a drift of 2% in a given temperature range is required, an input impedance of at least 2 mOhm, etc.

Design often involves modeling circuits on a computer, such as with the circuit modeling program LTSpice, which contains some models of commercial op-amps and other components. If, as a result of modeling, it turns out that some parameters of the designed circuit cannot be implemented, then in this case it is necessary to adjust the specification.

After computer modeling They assemble a prototype of the circuit and test it, making changes to the circuit if necessary to improve it or to ensure that the circuit meets the specification. The circuit is also optimized to reduce its cost and improve functionality.

The use of operational amplifiers in circuits without feedback

Voltage comparator on a 741 operational amplifier in a single-supply circuit. V ref = 6.6 V, input signal amplitude V in = 8 V. Capacitor C1 serves to suppress noise coming through the power circuit.

In this case, the operational amplifier is used as a voltage comparator. A circuit designed primarily to act as a comparator is used when high speed or a wide range of input voltages is needed, since the amplifier can quickly recover from saturation.

If a reference voltage V ref is applied to one of the inputs of the operational amplifier, then a signal level detector circuit will be obtained, that is, the operational amplifier will detect a positive signal level. If the detected signal is applied to the direct input, you will get a non-inverting level detector circuit - when the input voltage is higher than the reference voltage, the maximum positive voltage will be established at the output. If the detected signal and the reference voltage are swapped, then a voltage close to the negative supply voltage will be established at the output of the operational amplifier - an inverting level detector circuit will be obtained.

If the standard non-voltage at the amplifier input is V ref = 0 V, then you get a zero detector that can convert, for example, a sinusoidal signal into a rectangular one.

The use of operational amplifiers in circuits using positive feedback

Rectangular signal generator based on an operational amplifier with positive (R1, R3) and negative (R2, C1) feedback circuits. The positive feedback circuit surrounding the amplifier turns it into a Schmitt trigger. Operating frequency is approximately 150 Hz.

Operational amplifiers are also used in circuits with positive feedback, when part of the output signal is supplied to a non-inverting input. One typical circuit that uses this configuration is a comparator circuit with hysteresis, this is the so-called Schmitt trigger. Some circuits can use two types of feedback simultaneously, both positive and negative, across the same amplifier, a configuration often used in ramp voltage generator circuits and active filter circuits.

Due to the low slew rate of the signal and the absence of positive feedback, the amplitude-frequency response of the open-loop zero detector and signal level detector described above will be relatively low-frequency, that is, the circuits will be relatively low-frequency. You can try to cover the circuit with positive feedback, but this will significantly affect the accuracy of the operation when detecting the moment the input signal crosses zero. If you use a conventional 741 op amp, the sine wave to square wave converter will most likely have an operating frequency of no more than 100 Hz.

To increase the rate of signal rise in specialized comparator circuits, positive feedback is introduced into the output stages, therefore it is recommended that level detector circuits be implemented not on operational amplifiers, but on comparator microcircuits.

Using an operational amplifier in a negative feedback circuit

In a non-inverting amplifier circuit, the output voltage changes in the same direction (decreases or increases) as the input.

The equation that determines the gain of an op amp is written as

V out = A OL (V + - V -)

In this circuit, the parameter V - is a function of V out, since resistors R1 and R2 form a negative feedback circuit. In addition, these resistors are a voltage divider, and since it is connected to the V - input, which is high-resistance, the voltage divider is practically unloaded. Hence:

V - = β * V out

Where β = R1 / (R1 + R2)

Substituting this expression into the op-amp gain equation, we get:

V out = A OL (V in - β * V out)

Transforming the resulting expression relative to V out, we get:

V out = V in * (1 / (β + 1/A OL))

If A OL is very large, then the equation simplifies:

V out ≈ V in / β = V in / (R1 / (R1 + R2)) = V in * (1 + R2/R1)

Please note that the signal to the direct input of the operational amplifier is applied relative to the common wire. If for some reason the signal source cannot be connected to the common wire, or it must be connected to a load with a certain resistance, then an additional resistor will need to be installed between the direct input of the operational amplifier and the common wire. In any case, the value of the resistances of the feedback resistors R1 and R2 should be approximately equal to the input resistance, taking into account the load resistor at the direct input of the operational amplifier, while the resistances R1 and R2 should be considered as connected in parallel. That is, if R1 = R2 = 10 kOhm, the signal source has a high resistance, then the additional resistor between the direct input and the common wire should have a value of 5 kOhm, in this case the bias voltage at the inputs will be minimal.

When the operational amplifier is turned on using an inverting circuit, the voltage at its output will change in antiphase with the input voltage.

Let's find the equation that describes the gain when the operational amplifier is turned on inversely:

V out = A OL (V + - V -)

This equation is exactly the same as the equation for a non-inverting amplifier. But in this case the parameter V- will depend simultaneously on the output voltage V out and input V in, this is caused by the fact that the voltage divider formed by series-connected resistors Rf And R in connected between the input signal and the output of the amplifier. The inverting input has high resistance and does not load the divider, therefore:

V - = 1/(R f + R in) * (R f V in + R in V out)

Substituting the resulting equality into the gain equation, we find V out:

V out = -V in * A OL R f / (R f + R in + A OL R in)

If the value A OL is very large, then the expression simplifies:

V out ≈ V in * R f / R in

Often a resistor of such a size is placed between the non-inverting input and the common wire that both inputs remove voltage from the same resistances. The use of this resistor reduces the offset voltage, and in some models of operational amplifiers reduces the amount of nonlinear distortion.

If there is no need to amplify the DC voltage, then in series with the input resistor R in A decoupling capacitor can be installed to block the passage of DC voltage from the signal source to the input of the operational amplifier.

Operational amplifier audio amplifier

In conclusion, let's look at a practical audio amplifier circuit made using a non-inverting circuit with single-polar power supply. The use of a non-inverting circuit provides a high input impedance of the amplifier, which is determined by the values ​​of resistances R2 and R3, as well as the input impedance of the direct input of the operational amplifier (it is very high and can be neglected). In calculations, resistors R2, R3 are considered as connected in parallel, hence the input impedance amplifier will be equal to 100 kOhm.

The voltage gain of the amplifier is determined by the formula R4/R1+1, in this case 49/1+1 = 50 times. The capacitance of capacitor C1 should be such that its reactance at the lowest operating frequencies would be at least ten times less than the total resistance of series-connected resistors R1, R4. Capacitors C2, C3 are DC isolating capacitors; their parameters depend on the resistance of the signal source and load. Capacitor C4 blocks ripple in the power supply circuit.

The amplifier load can be high-impedance headphones of the TON-2 type, with a resistance of at least 1.5 kOhm. To connect low-impedance headphones or a dynamic head to the circuit, you will need to add a cascade of emitter followers on transistors KT502 and KT503.

To reduce nonlinear distortions, resistors R6, R7 were added to the circuit, which set the quiescent current of transistors VT1, VT2. You can use another circuit for connecting transistors, for example, described, which has a lower level of nonlinear distortion.

An operational amplifier (op-amp) is a direct current amplifier with a differential input, the characteristics of which are close to the characteristics of the so-called “ideal amplifier”. The op-amp has a large voltage gain K>>1 (K = 10 4 - 10 6), a large input (R input = 0.1-100 MOhm) and low output (R input = 10-100 Ohm) resistance.

In linear amplifiers, op-amps are used only with negative feedback circuits (NFC), which reduces the voltage gain K to 1-10 3, but at the same time reduces the dependence of K on temperature and supply voltage, increases R input ac and decreases R output .us. The use of op-amps in amplifiers without feedback circuits is unacceptable, since the danger of violating the stability of the op-amp increases and the circuits for correcting the frequency response over a wide frequency band become more complicated.

The op-amp (Fig. 15.1.) contains a differential amplifier as the first stage. A differential amplifier has a high gain for the difference between input signals U 2 - U 1 and a low gain for common mode signals, i.e. identical signals applied simultaneously to both inputs. This makes it possible to reduce sensitivity to common-mode signals (external noise) and the offset voltage, determined by the non-identity of the op-amp arms.

Fig. 15.1. Internal structure of an operational amplifier.

The input stage is followed by one or more intermediate stages; they provide the necessary voltage and current gain.

The complementary output stage must provide a low op-amp output impedance and sufficient current to power the expected loads. The output stage is usually a simple or complementary emitter follower.

To reduce the circuit's sensitivity to common mode signals and increase the input resistance, the emitter current of the first differential stage is set using a stable current source.

Basic parameters of operational amplifiers

1. K - own gain of the op-amp (without feedback).

2. U shift - Output shift voltage. A small voltage arising due to the asymmetry of the op-amp arms at zero voltage at both inputs. Typically Usdv has a value of 10 - 100 mV.

3. I cm - Input bias current. The current at the amplifier inputs required to operate the input stage of the operational amplifier.

4. I shift - Input shift current (). The bias current difference appears due to inaccurate matching of the input transistors. .

5. Rin - Input resistance. As a rule, Rin has a value of up to 1-10 megaohms.

6. R out - Output resistance. Usually Rout does not exceed hundreds of ohms.

7. Koss - Common mode signal attenuation coefficient. Characterizes the ability to attenuate signals applied to both inputs simultaneously.

8. Current consumption. The quiescent current consumed by the operational amplifier.

9. Power consumption. Power dissipated by the op-amp.

10. Maximum slew rate of output voltage (V/µs).

11. U power - Supply voltage.

12. Transition response. The signal at the amplifier output when a voltage surge is applied to its input.

The op-amp has several options for switching circuits, which differ significantly in their characteristics.

For performance analysis and performance calculations various schemes switching on the op-amp, you must further remember that, based on the properties of the remote control:

1. The voltage difference between the inputs of the op-amp is very small and can be taken equal to zero.

2. The operational amplifier has a high input impedance, so it consumes very little input current (up to 10 nA).

Basic switching circuits for op-amps

IN inverting amplifier(Fig. 15.2.), the input and output signals are phase shifted by 180º. If U in is positive, then the voltage at point A, and therefore U d, will also become positive, and U out will decrease, which will lead to a decrease at the inverting input to the value U d = U out / K ≈ 0.

Point A is often called virtual earth, because its potential is almost equal to the potential of the earth, since U d is, as a rule, very small

Rice. 15.2. Op amp inverting amplifier

To obtain an expression for the feedback gain, we take into account that , since R input of the amplifier is very large. Because And , That .

Assuming U d = 0 (since K → ∞), we obtain . The feedback gain of the circuit under consideration is equal to

. (15.1)

The output voltage is inverted, as evidenced by the negative value of K os.

Since, thanks to feedback, approximately zero potential is maintained at point A, the input resistance of the inverting amplifier circuit is equal to R 1 .. Resistance R 1 should be chosen so as not to load the input signal source, and, naturally, R os should be large enough so as not to overload the op-amp.

Non-inverting amplifier can also be implemented on an op-amp (Fig. 15.3) with a high input impedance, the voltage gain of which can also be set using resistances R 1 and R os.

As before, we assume that since R in → ∞.

The voltage at the inverting input of the amplifier is equal, so

.

15.3. Non-inverting op-amp amplifier

Hence, .

Since U out = U d · K and U d =U out / K, with K → ∞ and U d ≈ 0, we can write that . Solving the equation, we obtain an expression for the closed-loop gain K os , (15.3)

which is valid under the condition K » K ​​os.

In the scheme voltage follower on op-amp(Fig. 15.4) U out feedback comes from the amplifier output to the inverting input. Since the voltage difference at the inputs of the op-amp increases - U d, you can see that the voltage at the output of the amplifier is U out = U d K.

Fig. 15.4. Voltage follower on op-amp

The output voltage of the op-amp is U out = U in + U d. Since U out = U d · K, we obtain that U d = U out / K. Hence, . Since K is large (K → ∞), then U out / K tends to zero, and as a result we obtain the equality U in = U out.

The input voltage is connected to ground only through the amplifier's input impedance, which is very high, so the repeater can serve as a good matching stage.

Amplifier with differential input has two inputs, and the inverting and non-inverting inputs are under the same voltage, in this case equal to Uoc, since the voltage difference between the inverting and non-inverting inputs is very small (usually less than 1 mV).

Rice. 15.5. Amplifier with differential input

If we set U 1 equal to zero and apply an input signal to the input U 2, then the amplifier will act as a non-inverting amplifier, in which the input voltage is removed from the divider formed by resistors R 2 and R? os. If both voltages U 1 and U 2 are supplied to the corresponding inputs simultaneously, then the signal at the inverting input will cause such a change in the output voltage that the voltage at the connection point of resistors R 1 and R oc becomes equal to U os, where .

Due to the fact that the amplifier has a very high input impedance,

we have .

Solving the resulting equation for U out, we have:

Substituting the expression for Uoc, we get:

If we put R 1 = R 2 and R oc = R´ oc (the situation that most often occurs), we get . The polarity of the output voltage is determined by the larger of the voltages U 1 and U 2 .

Obviously, if U 2 in Fig. 15.5 is equal to zero, then the amplifier will act in relation to U 1 as an inverting amplifier.

Op-amp circuit input impedance can be determined as follows. A voltage is applied to the differential input resistance of the op-amp r d. U d. Due to the presence of feedback, this voltage is small.

U d = U out /K U = U 1 /(1 + K U b), (15.6)

where b = R 1 /(R 1 + R 2) is the transmission coefficient of the divider in the feedback circuit. Thus, only a current equal to U 1 /r d (1 + K U b) flows through this resistance. Therefore, the differential input resistance, due to the action of feedback, is multiplied by a factor of 1 + K U b.

According to Fig. 12, for the resulting input resistance of the circuit we have:

R in = r d (1 + K U b)||r in

This value, even for operational amplifiers with bipolar transistors at the inputs, exceeds 10 9 Ohms. It should be remembered, however, that we are talking exclusively about differential value; this means that changes in the input current are small, while the average value of the input current can take on incomparably larger values.

Rice. 15.6. Circuit of a non-inverting amplifier taking into account the op-amp's own resistances.

Op-amp output impedance an operational amplifier not covered by feedback is given by:

(15.7)

When a load is connected, a slight decrease in the output voltage of the circuit occurs, caused by a voltage drop across rout, which is transmitted to the input of the amplifier through a voltage divider R 1, R 2. The resulting increase in differential voltage compensates for the change in output voltage.

In general, the output resistance can have a fairly high value (in some cases from 100 to 1000 Ohms. Connecting the OS circuit allows you to reduce the output resistance.

For an amplifier covered by feedback, this formula takes the form:

(15.8)

In this case, the value of U d does not remain constant, but changes by the amount

dU d = - dU n = -bdU out

For an amplifier with a linear transfer characteristic, the change in output voltage is

dU out = K U dU d - r out dI out

The magnitude of the current branching into the feedback voltage divider in this case can be neglected. Substituting the value dU d into the last expression, we obtain the desired result:

(15.9)

If, for example, b = 0.1, which corresponds to amplification of the input signal by 10 times, and K U = 10 5, then the output impedance of the amplifier will decrease from 1 kOhm to 0.1 Ohm. The above is generally true within the amplifier bandwidth f p, Hz. At higher frequencies, the output impedance of the feedback op amp will increase because value |K U | with increasing frequency it will decrease at a rate of 20 dB per decade (see Fig. 3). In this case, it acquires an inductive character and at frequencies above f t it becomes equal to the value of the output impedance of the amplifier without feedback.

Dynamic parameters of the op-amp, characterizing the performance of the op-amp can be divided into parameters for small and large signals. The first group of dynamic parameters includes the bandwidth f p, the unity gain frequency f t and the settling time t y. These parameters are called small-signal, because they are measured in the linear mode of operation of the op-amp stages (DU out< 1В).

The second group includes the rate of rise of the output voltage r and the power bandwidth f p. These parameters are measured with a large differential op-amp input signal (more than 50 mV). Some of these parameters are discussed above. The establishment time is counted from the moment the input voltage step is applied to the input of the op-amp until the moment when the equality |U out.set - U out(t) | = d, where Uout.set is the steady-state value of the output voltage, d is the permissible error.

Operating frequency band or bandwidth The op-amp is determined by the type of amplitude-frequency characteristic taken at the maximum possible amplitude of the undistorted output signal. First, at low frequencies, the amplitude of the signal from the harmonic oscillation generator is set such that the amplitude of the output signal U out.max slightly does not reach the saturation limits of the amplifier. Then the frequency of the input signal is increased. The power bandwidth f p corresponds to a value of U out.max equal to 0.707 of the original value. The magnitude of the power passband decreases as the capacitance of the correction capacitor increases.

Operating Parameters The op-amp determines the permissible operating modes of its input and output circuits and the requirements for power supplies, as well as the temperature range of the amplifier. Limitations on operational parameters are determined by the finite values ​​of breakdown voltages and permissible currents through the op-amp transistors. The main operational parameters include: the nominal value of the supply voltage U p; permissible range of supply voltages; current consumed from source I pot; maximum output current I output max; maximum output voltage values ​​at rated power supply; maximum permissible values ​​of common-mode and differential input voltages

Amplitude-frequency response operational amplifier is an important factor on which the stability of real circuits with such an amplifier depends. In most operational amplifiers, individual stages are connected to each other via DC galvanic couplings, so these amplifiers do not have a gain roll-off in the low-frequency region and it is necessary to analyze the gain roll-off with increasing frequency.

Fig.15.7 . Operational amplifier frequency response

In Fig. 15.7. shows a typical op-amp frequency response.

Rice. 15.8. Simplified equivalent op-amp circuit

As the frequency increases, the capacitance decreases, which leads to a decrease in the time constant τ = R n* C. Obviously, there must be a frequency above which the voltage at the output U out will be less than KU d.

Expression for gain K at any frequency:

looks like , where K is the gain without feedback at low frequencies; f - operating frequency; f 1 - cut-off frequency or frequency at 3 dB, i.e. the frequency at which K(f) is 3 dB lower than K, or equal to 0.707 A.

If, as is usually the case, Rn » Rout, then .

Usually the amplitude-frequency response is given in general form. How:

. (15.10)

where f is the frequency we are interested in, while f 1 is a fixed frequency, which is called cutoff frequency and is a characteristic of a particular amplifier. As the frequency increases, the voltage gain decreases. In addition, from the expression for θ it is clear that when the frequency changes, the phase of the output signal shifts relative to the phase of the input; - the output signal lags in phase from the input.

Adding negative feedback, such as is done in inverting or non-inverting amplifiers, increases the effective bandwidth of the op-amp.

To see this, consider the expression for the open-loop gain of an amplifier with a roll-off of 6 dB/octave (at twice the frequency):

, where K(f) is the open-loop gain at frequency f; A is the gain without feedback at low frequencies; f 1 - coupling frequency. Substituting this relationship into the expression for the gain in the presence of feedback , we get

. (15.11)

This expression can be rewritten as , where f 1 oc = f 1 (1 + Aβ); K 1 - gain with closed feedback at low frequencies; f 1oc - cutoff frequency in the presence of feedback.

The cutoff frequency with feedback is equal to the cutoff frequency without feedback multiplied by (1 + Kβ) > 1, so the effective bandwidth actually increases when feedback is used. This phenomenon is shown in Fig. 8, where f 1oc > f 1 for an amplifier with a gain of 40 dB.

If the amplifier roll-off rate is 6 dB/octave, the product of the gain and the bandwidth is constant: Kf 1 = const. To see this, let's multiply the ideal gain at low frequencies by the upper cutoff frequency of the same amplifier in the presence of feedback.

Then we get the product of gain and bandwidth:

, where K is the open-loop gain at low frequencies.

Whereas previously it was shown that to increase bandwidth using feedback, the gain must be reduced, now the derived relationship makes it possible to find out how much of the gain must be sacrificed to obtain the desired bandwidth.

Operational amplifier equivalent circuit allows you to take into account the influence of amplifier imperfections on the characteristics of the circuit. To do this, it is convenient to imagine the amplifier as a complete equivalent circuit containing significant elements of non-ideality. A complete op-amp equivalent circuit for small slow signal changes is shown in Fig. 15.9.

Rice. 15.9.. Operational amplifier equivalent circuit for small signals

For operational amplifiers with bipolar transistors at the input, the input resistance for the differential signal r d is several megaohms, and the input resistance for the common-mode signal r in is several giga ohms. The input currents determined by these resistances are on the order of several nanoamperes. Direct currents flowing through the inputs of the operational amplifier and determined by the bias of the differential stage transistors have significantly larger values. For universal op-amps, input currents range from 10 nA to 2 μA, and for amplifiers with field-effect transistor input stages, they amount to fractions of nanoamps.

Operational Amplifier Parameters

Since the op-amp is a universal device, a large number of parameters are used to describe its properties.

1. The gain K is equal to the ratio of the output voltage to the differential input signal that caused this increment in the absence of feedback (amounts to 10 3-10 7) and is determined when idling at the exit. TO = U out / U in.d.

2. The zero offset voltage U cm shows what voltage must be applied to the input of the op-amp in order to obtain U out = 0 at the output (amounts to 0.5-0.15 mV). This is a consequence of inaccurate matching of the emitter-base voltages of the input transistors.

3. The input current Iin is determined by the normal operating mode of the input differential stage on bipolar transistors. This is the base current of the remote control input transistor. If field-effect transistors are used in the differential stage, then these are leakage currents.

When connecting signal sources with different internal resistances to the op-amp inputs, different voltage drops are created across these resistances by bias currents. The resulting differential signal changes the input voltage. To reduce it, the resistances of the signal sources must be the same.

4. The difference in input currents DI in is equal to the difference in the values ​​of currents flowing through the inputs of the op-amp, at a given value of the output voltage, is 0.1-200 nA.

5. Input resistance R bx (resistance between input pins) is equal to the ratio of the input voltage increment to the input current increment at a given signal frequency. R bx is determined for the low frequency region. Depending on the nature of the applied signal, the input impedance can be differential (for a differential signal) or common mode (for a common-mode signal).

Differential input resistance is the total input resistance from any input, when the other input is connected to the common terminal, amounts to tens of kOhms - hundreds of MOhms. Such a large R bx is obtained due to the input remote control and a stable constant voltage source. Common mode input resistance is the resistance between the shorted input pins and ground. It is characterized by a change in the average input current when a common-mode signal is applied to the inputs and is several orders of magnitude higher than Rin differential.

6. Common-mode signal attenuation coefficient K osl sf is defined as the ratio of the common-mode signal voltage supplied to both inputs to the differential input voltage, which causes the same output voltage value. The attenuation coefficient shows how many times the gain of the differential signal is greater than the gain of the common-mode input signal and is 60-120 dB:

. (15.16)

As the common-mode signal rejection ratio increases, the differential input signal can be more accurately distinguished from the background of common-mode interference, and the quality of the op-amp improves. Measurements are carried out in the low frequency range.

7. Output resistance Rout is determined by the ratio of the increment in the output voltage to the increment in the active component of the output current at a given value of the signal frequency and is from units to hundreds of Ohms.

8. Temperature drift of the bias voltage is equal to the ratio of the maximum change in bias voltage to the temperature change that caused it and is estimated in µV/deg .

Temperature drifts in bias voltage and input currents cause thermal errors in op-amp devices.

9. The coefficient of influence of power supply instability on the output voltage shows the change in the output voltage when the supply voltage changes by 1 V and is estimated in µV/V.

10. The maximum output voltage U out max is determined by the limiting value of the op-amp output voltage at a given load resistance and input signal voltage, ensuring stable operation of the op-amp and distortion not exceeding the specified value. U out max 1-5 V below the supply voltage.

11. The maximum output current Iout max is limited by the permissible collector current of the op-amp output stage.

12. Power consumption - power dissipated by the op-amp when the load is off.

13. The unity gain frequency f 1 is the frequency of the input signal at which the op-amp gain is 1: |K(f 1)| = l. For integrated op-amps, the unity gain frequency has a limit value of 1000 MHz. The output voltage at this frequency is approximately 30 times lower than for direct current.

14. Cutoff frequency f c op-amp - the frequency at which the gain decreases by a factor. It estimates the op-amp bandwidth and is tens of MHz.

15. The maximum rate of rise of the output voltage V max is determined by the highest rate of change of the output voltage of the op-amp when a rectangular pulse with an amplitude equal to the maximum value of the input voltage is applied to the input and lies in the range of 0.1-100 V/µs. When exposed to the maximum input voltage, the output stage of the op-amp falls into the saturation region in both polarities. This parameter is specified for wideband and pulsed op-amp based devices and results in the presence of output signal edges with finite duration values. V max characterizes the performance of the op-amp in large-signal mode.

16. Settling time of the output voltage t yc t (decay time of the transient process) is the time required for the amplifier to return from the output saturation state to the linear mode.

The settling time is the time during which, after a jump in the input voltage, the output voltage differs from the steady-state value by the amount of the permissible relative error dU out. During the establishment time, the output voltage of the op-amp, when exposed to a rectangular input voltage, changes from a level of 0.1 to a level of 0.9 of the steady-state value.

17. The noise voltage referred to the input is determined by the effective voltage value at the amplifier output at zero input signal and zero signal source resistance divided by the op-amp gain. The noise spectral density is estimated as the square root of the square of the reduced noise voltage divided by the frequency band over which the noise voltage is measured. The dimension of this parameter. In op-amp specifications, noise figure (dB) is sometimes specified, defined as the ratio of the reduced noise power of an amplifier operating from a source with internal resistance R g to the noise power of active resistance

, (15.17)

, (15.18)

where U sh - reduced noise voltage at R g =0;

4kTR g - spectral density of thermal noise of the resistor.

The requirements for the parameters of the op-amp depend on the functions it performs. It is desirable in all practical cases to reduce the error of the operations performed, increase reliability and speed. Simultaneous improvement of all parameters puts forward conflicting requirements for the circuit and its manufacture. All this is explained by the wide variety of op amps, in which only specific parameters are optimized at the expense of others.

Thus, measuring equipment uses precision op-amps that have a high gain, high input impedance, low zero offset voltage and low noise. And high-speed op-amps must have high speed output voltage rise, large bandwidth and short settling time of the output voltage. Such op-amps have found application in pulsed and wideband amplifier devices and in analog-to-digital converter devices.

To create comparators that serve to compare the instantaneous values ​​of two voltages, high-speed op-amps operating in switching mode are used.

5.4.1. General information about operational amplifiers

In classical electronics, an operational amplifier is usually called a linear converter, with the help of which you can perform various mathematical operations - summation, subtraction, integration, differentiation, etc. This determined the name of such amplifiers - operational (decisive), on the basis of which, by introducing feedback, you can carry out mathematical operations. Integrated op-amps are designed not only to perform mathematical operations, but also to carry out signal conversion (amplification, processing, signal generation).

Conditional graphic image and the functional designation of the op-amp is shown in Fig. 5.5.

Modern op-amps are built according to a direct amplification circuit with differential inputs equal in electrical parameters (inverse input “○” or “−” and non-inverse input - without designation or “+”) and a push-pull bipolar (in terms of signal amplitude) output. The main element of the op-amp is the input stage, built according to a differential amplifier (DA) circuit, the purpose of which is to amplify the signal difference observed between its inputs (Fig. 5.6a). The remote control has two transistors VT1 and VT2 with collector load resistors R K. The emitter currents of these transistors are formed using a stable current generator (GCT) I 0 made on transistors VT3 and VT4. If the parameters of transistors VT1 and VT2 are identical, the collector resistors are equal and the condition is that the input signals U − = U + = 0, the difference between the output signals of the remote control will be equal to zero, since for an ideal remote control the emitter current I 0 is divided in half between transistors VT1 and VT2.

From the theory of differential amplifiers it is known that in balance mode the potential of each output has a common-mode voltage level relative to ground: .

The balance mode corresponds to the diagram (Fig. 5.6, b) up to the point in time t1. When appearing at the moment t1 signal U − transistor VT1 receives more bias current and its collector current I K 1 increases, and the current of transistor VT2 decreases, since

I K 1 + I K 2 = I 0. Thus, as the input voltage U − increases, the output voltage at the output of the first transistor decreases (signal increment is inverted in phase). At the other output of the remote control the voltage will increase (the signal increment is not phase inverted). The total differential output signal between the remote control outputs is determined by the relation:

The change in output signals stops when all the current I 0 begins to flow through transistor VT1. At time t2, transistor VT2 goes into cutoff mode. Since the input resistance of the remote control is inversely proportional to the value of its operating current I0, this current is usually set small (tens of microamps), and this in turn determines the low gain of the remote control:

where is the transconductance of the bipolar transistor. Therefore, integrated op amps use subsequent amplification stages to achieve high voltage gain. In general, the voltage gain of the op-amp is equal to the product of the gain factors of all its stages: .

Absolute values ​​of input voltages U − , U + And U OUT limited by op-amp supply voltage +U pit And −U pit− (≤ ± 15 V). A typical property of the transfer characteristic of an op-amp is that it is sensitive to the difference in input voltages and does not depend on their absolute values. From this property follows the introduction of two concepts: common-mode input voltage U SINF for the common voltage component at both their inputs, which must be suppressed by the amplifier, and the differential input voltage U D, to which the amplifier responds:

, ,

Where K = 1/2 or 0.

To simplify the determination of op-amp parameters, it is usually assumed TO= 0, then U SINF =U + .

Integrated op amps typically consist of a differential input stage, gain stages, a stage that converts the two-phase output of the differential amplifier to single-phase, and a stage for level shifting. At the output of the amplifier, an emitter follower on complementary transistors is used, which ensures the transmission of signals of both positive and negative polarity. In modern op-amps K 0 reaches a value of the order of 1*10 5 or more.

When considering and analyzing circuit designs based on operational amplifiers and deriving basic relationships, the concept is often used ideal operational amplifier. In an ideal op-amp it is considered that:

· the operational amplifier has an infinitely large input and zero output resistance;

· op-amp inputs are symmetrical and do not consume current;

· the voltage between the inputs of the op-amp is zero;

· the voltage gain of the op-amp tends to infinity, and the output voltage is zero in the absence of input signals.

5.4.2. Amplitude-frequency response of the operational amplifier

The amplitude-frequency response (AFC) of the op-amp is the dependence of the voltage gain on frequency. Any multi-channel amplifier at high frequencies can be represented by an equivalent circuit (Fig. 5.7), in which the signal generator K 0 U VX is loaded onto a number of integrating RC chains, the number of which is equal to the number of op-amp stages (R and C are, respectively, the own transfer conductivity and load capacitance cascade).

Voltage transfer coefficient of one RC chain:

Where - circular cutoff frequency.

Accordingly, the cutoff frequency is . The frequency response module of the RC chain is determined by the relation:

The type of frequency response for a two-stage op-amp in accordance with the equivalent circuit is shown in Fig. 5.8 (curve 1), where the frequency and gain are plotted on a logarithmic scale. Gain is measured in decibels (1 dB = 20lg K). Changing the frequency ten times (per decade), we obtain a decrease in gain by the same ten times (a gain drop of 20 dB). As can be seen from the figure, at low frequencies TO asymptotically approaches the open-loop gain value K 0. As the frequency increases beyond the cutoff frequency f cp1, on which TO decreases to the value 0.707 K 0 (by 3 dB), the high-frequency roll-off rate is uniform and amounts to 20 dB/dec. In a multistage amplifier, each stage has its own transfer conductivity and load capacitance, therefore at frequency f cp2 for the second stage the high-frequency roll-off rate will be 40 dB/dec. Modern operational amplifiers have a corrected frequency response, which for an op-amp without feedback has the form of curve 2. As the frequency increases, the gain drops and the graph crosses the zero decibel line at frequency unity gain f t. This frequency determines the active frequency band of the op-amp, in which the gain K≥ 1. Product of input signal frequency and open-loop gain TO equal to unity gain band f t = K f VX. To eliminate amplitude-phase distortions in a given frequency band, it is necessary to ensure uniformity of the amplitude characteristics in this band. This is achieved by introducing negative feedback (NFB) into the op-amp. As the OOS depth increases (the op-amp gain decreases), the frequency band of the uniform amplitude characteristic expands (curve 3). Frequency range from zero to upper limit frequency f b is called the small-signal passband, which is related to the unity gain band of the op-amp with the feedback ratio f b = f t K OS, Where TO OS- feedback gain.

5.4.3. Operational amplifier circuits

The number of op-amp circuits is continuously increasing as the element base develops and new op-amps appear, so it is especially important to know the principles of construction and analysis of the so-called typical (basic) op-amp switching circuits. There are three basic circuits for connecting operational amplifiers:

Inverting switching of op-amp;

Non-inverting switching of op-amp;

Differential switching on of the op-amp.

These circuits are the basis for building other operational amplifier circuits and calculating their parameters. When analyzing basic circuits and simplifying the calculation of their parameters, the concept of an ideal operational amplifier is often used. Let's consider the basic circuits for connecting an op-amp.

5.5.3.1. Inverting switching of op-amp

The equivalent circuit of the inverting connection of the op-amp is shown in Fig. 5.9. In this circuit, the input signal and feedback signal are supplied to the inverse input of the op-amp. The introduction of OOS leads to the fact that the circuit now has a feedback gain TO OS. Let's determine the value TO OS based on the properties of an ideal op-amp.

We consider the voltage between the inputs to be zero. Then the potential of the non-inverse input and the potential of the inverse input, and therefore the potential of point A (current summation point) is also zero. Provided that the input impedance of the op-amp R BX is large enough, we can assume that the current from the signal source i C = U C / R1 flows only through the feedback resistor R OS, creating a voltage drop across it:

Voltage drop across resistor R OS with great accuracy equal to the output voltage U OUT, since the potential of the left output of the resistor R OS(point A) is equal to zero (artificial zero potential of the circuit). Therefore, we can write:

Closed-loop voltage gain:

The minus sign in expression (4.4) shows that the voltage at the op-amp output is out of phase with the input voltage. In a real op-amp, taking into account the limited gain value K 0 expression for TO OS has the form:

. (5.5)

The input resistance when the op-amp is switched on inverting can be calculated approximately R ВХ ≈ R1. Output impedance

Where ROUT.0- output impedance of the op-amp without feedback.

Note. The resistance R C in this circuit further serves to reduce the bias currents I CM in operational amplifier circuits.

5.4.3.2. Non-inverting op-amp switching

The equivalent circuit of a non-inverting op-amp connection is shown in Fig. 5.10.

In this circuit, the feedback voltage is created by a divider R1 – R OS :

Assuming that the voltage between the inputs of the op-amp is close to zero, we can write that UOC= U C, whence the voltage gain:

The input resistance when the op-amp is turned on non-inverting is large and is approximately determined by the relation:

Output resistance where β =R1/R OC .

5.4.3.3. Differential switching of op-amp

The equivalent circuit of the differential connection of the op-amp is shown in Fig. 5.11. It is a combination of inverting and non-inverting switching circuits and makes it possible to obtain the difference between two input signals with a given gain.

For
To obtain the voltage gain of this circuit, we still assume that the voltage difference at the inputs of the op-amp is zero, and the signal currents do not branch to its inputs. Let's create a system of equations for the voltages at the inverse and non-inverse inputs:

- inverse input:

, where does the voltage at the inverse input come from? (5.8)

- non-inverse input:

Considering that for an ideal op-amp the voltage between the inputs is zero, solving jointly (9.7) and (9.8) we obtain the expression for

output voltage:

Where n =R OC /R ВХ = nR/R– gain of the feedback amplifier. If the resistances in the circuit are different, then the output voltage can be determined:

5.4.3.4. Adder

By analogy with op-amp switching circuits, inverting and non-inverting adders are distinguished. The circuit of the inverting adder is shown in Fig. 5.12. Based on the principle of superposition, the voltage at the output of the inverting adder can be determined by the relation:

, Where K OC i =R OC /R i– transmission coefficient of the i-th input signal at the inverting input. In a non-inverting adder circuit, the input voltages are applied to the non-inverting input, and all resistors except the feedback resistance ROC, make them the same. The voltage at the output of such an adder is determined by the relation:

5.4.3.5. Comparators

A comparator (from English Compare) is a device that compares the signal voltage at one of the inputs with the reference voltage at the other input. When used as an op-amp comparator, a positive or negative saturation voltage will be set at its output ±U us. Typically, in an op-amp, the saturation voltage and supply voltage are related by the relation: ±U us = ± 0.9 U power Comparators are used in many devices and circuits, for example:

In a Schmitt trigger or circuit that converts an arbitrary waveform into a square wave or pulse signal;

In the zero detector - a circuit indicating the moment and direction of passage of the input signal through 0 V;

In a level detector - a circuit that indicates the moment the input voltage reaches a given reference voltage level,

In a triangular or rectangular waveform generator, etc.

A distinctive feature of comparators is the lack of environmental feedback, i.e. The voltage gain is determined by the intrinsic gain K 0 OU.

In Fig. 5.13. shows a comparator circuit that is sensitive to input voltage (−). In this circuit, the input signal is supplied to the inverse input, and the non-inverse input is used to set the reference voltage U op. Since both inputs are involved in the comparator circuit, to analyze its operation and the behavior of the output voltage, one should use

introduce the third basic switching circuit - differential switching of the op-amp and relation (5.10).

In the case when U op = 0, the comparator circuit works as a zero detector (Fig. 5.13.b). In the case when U VX positive (during the first half-cycle), U OUT equals − U US, since the input potential (+) is less than the input potential (−) (see Fig. 5.13. b). During the second half period, when U VX negative, U OUT will be equal to + U US, since the input potential (+) is greater than the input potential (−). Thus, U OUT shows when U VX positive or negative with respect to the zero reference voltage.

When U op > 0 The comparator circuit works as a level detector (Fig. 5.13. c). On the interval M – N U OUT equals − U US, since the input potential (+) is less than the input potential (−) ( U op< U ВХ ). At U VX< U оп (interval N – K) U OUT equals + U US.

If you swap the inputs for supplying the input voltage and generating the reference, you can get a comparator circuit that is sensitive to the voltage at the input (+).

In practice, in some cases the input voltage may fluctuate around the reference level. Such oscillations are more than likely due to the inevitable interference on the wires approaching the input terminals of the op-amp (noise voltage). In this case the voltage U OUT will fluctuate from one saturation level to another, which may lead to false alarms, measurement devices or actuators. In order to prevent the output voltage from reacting to false crossings of the reference level, positive feedback (POF) is introduced into the comparators. Such comparators are called comparators with PIC or regenerative comparators, Schmitt triggers. PIC is carried out by applying a certain part of the output voltage to the non-inverse input U OUT using a resistive divider R3 - R4 (Fig. 5.14). The voltage generated by the resistive divider will have different values ​​because it depends on the sign U OUT. It called upper or lower threshold voltage and in comparators with PIC it is installed automatically:

. (5.12)

Positive feedback creates a trigger effect, speeding up shifting U OUT from one state to another. As soon as

U OUT begins to change, regenerative feedback arises, forcing U OUT change even faster. At a time equal to zero (Fig. 5.14. a, b), U VX negative, so the output voltage is + U US and a threshold will be set at the non-inverse input U P.V.. At a moment in time t1 voltage U IN > +U US and the comparator switches to voltage output − U US. In this case, a threshold will be set at the non-inverse input U P.N.. The next switching of the comparator will occur at the moment t2, When U VX will become more negative than the voltage − U US.If the threshold voltages exceed the noise amplitude, then the PIC will not allow false positives at the output (Fig. 5.14. a, b). Voltage range − U US ≤ U ≤ +U US is called “Hysteresis” or “Dead Zone”.

An operational amplifier (op-amp) is usually called an integrated DC amplifier with a differential input and a push-pull output, designed to work with feedback circuits. The name of the amplifier is due to its original area of ​​application - performing various operations on analog signals (addition, subtraction, integration, etc.). Currently, op-amps serve as multifunctional units in the implementation of a variety of electronic devices for various purposes. They are used for amplification, limiting, multiplication, frequency filtering, generation, stabilization, etc. signals in continuous and pulsed devices.

It should be noted that modern monolithic op-amps differ slightly in size and price from individual discrete elements, for example, transistors. Therefore, the implementation of various devices on an op-amp is often much simpler than on discrete elements or on amplification ICs.

An ideal op-amp has an infinitely large voltage gain ( K and op-amp=∞), infinitely large input impedance, infinitely small output impedance, infinitely large CMRR and infinitely wide operating frequency band. Naturally, in practice, none of these properties can be fully realized, but they can be approached to a degree sufficient for many areas.

Figure 6.1 shows two versions of op-amp symbols - simplified (a) and with additional terminals for connecting power circuits and frequency correction circuits (b).

Figure 6.1. OS symbols

Based on the requirements for the characteristics of an ideal op-amp, it is possible to synthesize its internal structure, presented in Figure 6.2.

Figure 6.2. Block diagram of the op-amp

Simplified electrical diagram simple op-amp that implements block diagram Figure 6.2 is shown in Figure 6.3.

Figure 6.3. Simple op-amp circuit

This circuit contains an input remote control (VT 1 and VT 2) with a current mirror (VT 3 and VT 4), intermediate stages with OK (VT 5) and with OE (VT 6), and an output current booster on transistors VT 7 and VT 8 . The op-amp may contain frequency correction circuits (Ccor), power supply and thermal stabilization circuits (VD 1, VD 2, etc.), IST, etc. Bipolar power supply allows for galvanic communication between the stages of the op-amp and zero potentials at its inputs and output in the absence of a signal. In order to obtain a high input impedance, the input remote control can be performed on a DC. It should be noted that there is a wide variety of op-amp circuit solutions, but the basic principles of their construction are quite fully illustrated in Figure 6.3.

6.2. Main parameters and characteristics of the op-amp

The main parameter of the op-amp is the voltage gain without feedback K u op-amp, also called total voltage gain. In the bass and midrange regions it is sometimes designated K u Op-amp 0 and can reach several tens and hundreds of thousands.

Important parameters The op-amp is its precision parameters determined by the input differential stage. Since the accuracy parameters of the remote control were discussed in subsection 5.5, here we limit ourselves to listing them:

◆ zero offset voltage U cm;

◆ temperature sensitivity of zero offset voltage dU cm/dT;

◆ bias current Δ I input;

◆ average input current I input wed.

The input and output circuits of the op-amp are represented by the input R input and weekends R out of the op amp resistances given for op-amps without OOS circuits. For the output circuit, parameters such as maximum output current are also given I output OU and minimum load resistance R n min and sometimes the maximum load capacity. The input circuit of the op amp may include capacitance between the inputs and the common bus. Simplified equivalent circuits of the input and output circuits of the op-amp are presented in Figure 6.4.

Figure 6.4. A simple linear macromodel of an op-amp

Among the parameters of the op-amp, it is worth noting the CMRR and the coefficient of attenuation of the influence of instability of the power source KOVNP=20lg·(Δ E/Δ U in). Both of these parameters in modern op-amps have their values ​​within (60...120) dB.

The energy parameters of the op-amp include the voltage of the power supplies ±E, the current consumption (quiescent) I P and power consumption. Usually, I P amounts to tenths - tens of milliamps, and the power consumption is uniquely determined I P, units - tens of milliwatts.

K maximum acceptable parameters OUs include:

◆ maximum possible (undistorted) output signal voltage U out max (usually slightly less than E);

◆ maximum permissible power dissipation;

◆ operating temperature range;

◆ maximum supply voltage;

◆ maximum input differential voltage, etc.

Frequency parameters include absolute cut-off frequency or unity gain frequency f T (F 1), i.e. frequency at which K u op-amp=1. Sometimes the concept of slew rate and settling time of the output voltage is used, determined by the response of the op-amp to the impact of a voltage surge at its input. For some op amps, additional parameters are also provided that reflect their specific area of ​​application.

The amplitude (transfer) characteristics of the op-amp are presented in Figure 6.5 in the form of two dependencies U out=f(U in) for inverting and non-inverting inputs.

When at both inputs of the op-amp U in=0, then an error voltage will be present at the output U osh, determined by the precision parameters of the op-amp (in Figure 6.5 U osh not shown due to its small size).

Figure 6.5. AH OU

The frequency properties of an op-amp are represented by its frequency response, performed on a logarithmic scale, K u op-amp=φ(log f). This frequency response is called logarithmic (LAFC), its typical form is shown in Figure 6.6 (for the K140UD10 op amp).

Figure 6.6. LFC and LFCH OU K140UD10

Frequency dependence K u op-amp can be represented as:

Here τ V time constant of the op-amp, which at M in=3 dB determines the coupling (cutoff) frequency of the op-amp (see Figure 6.6);

ω V= 1/τ V= 2π f in.

Replacing in the expression for K u op-amp τ V by 1/ω V, we get the entry LACHH:

On bass and midrange K u Op-amp=20lg K u Op-amp 0, i.e. The LFC is a straight line parallel to the frequency axis. With some approximation, we can assume that in the HF region the decrease K u Op-amp occurs at a rate of 20 dB per decade (6 dB per octave). Then for ω>>ω V you can simplify the expression for LAC:

K u op-amp= 20lg K u Op-amp 0 – 20log(ω/ω V).

Thus, the LFC in the HF region is represented by a straight line with a slope to the frequency axis of 20 dB/dec. The intersection point of the considered straight lines representing the LFC corresponds to the conjugation frequency ω V (f in). The difference between the real and ideal LFC at frequency f in is about 3 dB (see Figure 6.6), however, for the convenience of analysis this is tolerated, and such graphs are usually called Bode diagrams .

It should be noted that the LFC decay rate of 20 dB/dec is typical for corrected op-amps with external or internal correction, the basic principles of which will be discussed below.

Figure 6.6 also shows the logarithmic phase response (LPFC), which is the dependence of the phase shift j of the output signal relative to the input signal on frequency. The real LFFC differs from the presented one by no more than 6°. Note that for a real op-amp j=45° at frequency f in, and at frequency f T- 90°. Thus, the intrinsic phase shift of the working signal in the corrected op-amp in the HF region can reach 90°.

The parameters and characteristics of the op-amp discussed above describe it in the absence of OOS circuits. However, as noted, op-amps are almost always used with OOS circuits, which significantly affect all of its indicators.

6.3. Inverting amplifier

Op-amps are most often used in inverting and non-inverting amplifiers. Simplified circuit diagram an inverting amplifier using an op-amp is shown in Figure 6.7.

Figure 6.7. Op amp inverting amplifier

Resistor R 1 represents the internal resistance of the signal source E g, by means of R os the OU is covered by ∥OOSN.

With an ideal op-amp, the voltage difference at the input terminals tends to zero, and since the non-inverting input is connected to the common bus through resistor R2, the potential at the point a must also be null (“virtual zero”, “apparent ground”). As a result, we can write: I g=I os, i.e. E g/R 1 =–U out/R os. From here we get:

K U inv = U out/E g = –R os/R 1 ,

those. with ideal op amp K U inv is determined by the ratio of the values ​​of external resistors and does not depend on the op-amp itself.

For a real op-amp, it is necessary to take into account its input current I input, i.e. I g=I os+I input or ( E g–U in)/R 1 =(U in–U out)/R os+U in/U input, Where U in- signal voltage at the inverting input of the op-amp, i.e. at the point a. Then for a real op-amp we get:

It is easy to show that when the OOS depth is more than 10, i.e. K u op-amp/K U inv=F>10, calculation error K U inv for the case of an ideal op-amp, it does not exceed 10%, which is quite sufficient for most practical cases.

Resistor values ​​in op-amp devices should not exceed units of megohms, otherwise it is possible unstable work amplifier due to leakage currents, op-amp input currents, etc. If, as a result of the calculation, the value R os exceeds the maximum recommended value, then it is advisable to use a T-shaped OOS chain, which, with moderate resistor values, allows it to perform the function of an equivalent high-resistance R os(Figure 6.7b) . In this case, you can write:

In practice it is often believed that R OS 1 =R OS 2 >>R OS 3 and the value R 1 is usually given, so R OS 3 is determined quite simply.

Op-amp inverting amplifier input impedance R input inv has a relatively small value determined by parallel OOS:

R input inv = R 1 +(R os/K u op-amp + 1)∥R input≈ R 1 ,

those. at large K u op-amp input resistance is determined by the value R 1 .

Inverting amplifier output impedance R out inv in a real op-amp it is different from zero and is defined as R out op amp, and the depth of environmental protection F. For F>10, we can write:

R out inv = R out op amp/F = R out op amp/K U inv/K u op-amp.

Using the LFC of the op-amp, you can represent the frequency range of the inverting amplifier (see Figure 6.6), and

f OC = f T/K U inv.

In the limit you can get K U inv=1, i.e. get an inverting follower. In this case, we obtain the minimum output impedance of the op-amp amplifier:

R out = R out op amp/K u op-amp.

In an amplifier using a real op-amp at the output of the amplifier at U in=0 error voltage will always be present U osh, generated U cm and Δ I input. In order to reduce U osh strive to equalize the equivalent resistors connected to the inputs of the op-amp, i.e. take R 2 =R 1 ∥R os(See Figure 6.7a). If this condition is met for K U inv>10 can be written:

U osh ≈ U cm K U inv + Δ I in R os.

Decrease U osh possible by applying additional bias to the non-inverting input (using an additional divider) and reducing the values ​​of the resistors used.

Based on the considered inverting UPT, it is possible to create an AC amplifier by connecting separating capacitors to the input and output, the ratings of which are determined based on a given frequency distortion factor M n(see subsection 2.5).

6.4. Non-inverting amplifier

A simplified circuit diagram of a non-inverting op-amp amplifier is shown in Figure 6.8.

Figure 6.8. Non-inverting op-amp amplifier

It is easy to show that in a non-inverting amplifier the op-amp is covered by the POSN. Because the U in And U os are supplied to different inputs, then for an ideal op-amp we can write:

U in = U out R 1 /(R 1 + R os),

whence the voltage gain of the non-inverting amplifier:

K U noninv = 1 + R os/R 1 ,

K U noninv = 1 + |K U inv|.

For a non-inverting amplifier based on a real op-amp, the obtained expressions are valid at a feedback depth of F>10.

Input impedance of a non-inverting amplifier R input noninv is large and is determined by deep consistent OOS and high value R input:

R input noninv = R input· F = R input· K U OU/K U noninv.

The output impedance of a non-inverting op-amp amplifier is determined as for an inverting amplifier, because in both cases, the voltage protection system applies:

R out non-inv = R out of the op amp/F = R out of the op amp/K U noninv/K U OU.

The expansion of the operating frequency band in a non-inverting amplifier is achieved in the same way as in an inverting amplifier, i.e.

f OC = f T/K U noninv.

To reduce the current error in a non-inverting amplifier, similar to an inverting amplifier, the following condition must be met:

R g = R 1 ∥R os.

A non-inverting amplifier is often used for large R g(which is possible due to the large R input noninv), therefore, fulfilling this condition is not always possible due to restrictions on the value of resistor values.

The presence of a common-mode signal at the inverting input (transmitted through the circuit: non-inverting op-amp input ⇒ op-amp output ⇒ R os⇒ inverting input of the op-amp) leads to an increase U osh, which is a disadvantage of the amplifier in question.

By increasing the depth of environmental protection, it is possible to achieve K U noninv=1, i.e. obtaining a non-inverting repeater, the circuit of which is shown in Figure 6.9.

Figure 6.9. Non-inverting op-amp follower

Here, 100% POSN is achieved, so this repeater has the highest input and minimum output impedance and is used, like any repeater, as a matching stage. For a non-inverting follower, you can write:

U osh ≈ U cm + I in sr R g ≈ I in sr R g,

those. The error voltage can reach quite large values.

Based on the considered non-inverting UPT, it is also possible to create an AC amplifier by connecting separating capacitors to the input and output, the ratings of which are determined based on a given frequency distortion factor M n(see subsection 2.5).

In addition to inverting and non-inverting amplifiers based on op-amps, various op-amp options are available, some of which will be discussed below.

6.5. Types of control units on the op amp

difference (differential) amplifier , the diagram of which is shown in Figure 6.10.

Figure 6.10. Op-amp difference amplifier

An op-amp difference amplifier can be considered as a combination of inverting and non-inverting amplifier options. For U out difference amplifier can be written:

U out = K U inv U in 1 +K U noninv U in 2 R 3 /(R 2 + R 3).

Usually, R 1 =R 2 and R 3 =R os, hence, R 3 /R 2 =R os/R 1 =m. Expanding the values ​​of the gain factors, we get:

U out = m(U in 2 – U in 1),

For the special case when R 2 =R 3 we get:

U out = U in 2 – U in 1 .

The last expression clearly explains the origin of the name and purpose of the amplifier in question.

In a difference amplifier based on an op-amp, with the same polarity of input voltages, a common-mode signal occurs, which increases the amplifier error. Therefore, in a difference amplifier it is desirable to use an op-amp with a large CMRR. The disadvantages of the considered difference amplifier include different values ​​of input resistances and difficulty in adjusting the gain. These difficulties are eliminated in devices using several op-amps, for example, in a difference amplifier with two repeaters (Figure 6.11).

Figure 6.11. Repeater difference amplifier

This circuit is symmetrical and is characterized by the same input resistances and low error voltage, but only works for a symmetrical load.

Based on the op-amp it can be performed logarithmic amplifier , the schematic diagram of which is shown in Figure 6.12.

Figure 6.12 Logarithmic op-amp amplifier

The P-n junction of the VD diode is forward biased. Assuming the op-amp is ideal, we can equate the currents I 1 and I 2. Using the expression for the current-voltage characteristic p-n junction {I=I 0 ), it is easy to write:

U in/R= I 0 ·,

from where after transformations we get:

U out = φ T ln( U in/I 0 R) = φ T(ln U in–ln I 0 R),

from which it follows that the output voltage is proportional to the logarithm of the input, and the term ln I 0 R represents the logarithm error. It should be noted that this expression uses voltages normalized to one volt.

When replacing diode VD and resistor R, we get antilog amplifier .

Inverting and non-inverting adders on op-amps, also called summing amplifiers or analog adders. Figure 6.13 shows a schematic diagram of an inverting adder with three inputs. This device is a type of inverting amplifier, many of the properties of which are also manifested in the inverting adder.

Figure 6.13. Op-amp inverting adder

U in 1 /R 1 + U in 2 /R 2 + U in 3 /R 3 = –U out/R os,

From the resulting expression it follows that the output voltage of the device is the sum of the input voltages multiplied by the gain K U inv. At R os=R 1 =R 2 =R 3 K U inv=1 and U out=U in 1 +U in 2 +U in 3 .

When the condition is met R 4 =R os∥R 1 ∥R 2 ∥R 3, the current error is small and can be calculated using the formula U osh=U cm(K U osh+1), where K U osh=R os/(R 1 ∥R 2 ∥R 3) - error signal amplification factor, which has a greater value than K U inv.

Non-inverting adder is implemented in the same way as an inverting adder, but it should use the non-inverting input of the op-amp by analogy with a non-inverting amplifier.

When replacing resistor Roc with capacitor C (Figure 6.14), we obtain a device called analog integrator or just an integrator.

Figure 6.14. Analog integrator on op-amp

With an ideal op-amp, the currents can be equated I 1 and I 2, from which it follows:

The higher the integration accuracy, the greater K u op-amp.

In addition to the considered control units, op amps are used in a number of continuous devices, which will be discussed below.

6.6. Frequency response correction

By correction of frequency characteristics we mean changing the LFC and LPFC to obtain the necessary properties from op-amp devices and, above all, ensuring stable operation. An op-amp is usually used with OOS circuits, however, under certain conditions, due to additional phase shifts in the frequency components of the signal, the OOS can turn into a POS and the amplifier will lose stability. Since the OOS is very deep ( βK U>>1), it is especially important to ensure a phase shift between the input and output signals to ensure that there is no excitation.

Previously, in Figure 6.6, the LFC and LPFC response for the corrected op-amp were shown, in shape equivalent to the LFC and LPFC response of a single amplifier stage, from which it can be seen that the maximum phase shift φ<90° при K u op-amp>1, and the gain decay rate in the HF region is 20 dB/dec. Such an amplifier is stable at any depth of feedback.

If the op-amp consists of several cascades (for example, three), each of which has a decay rate of 20 dB/dec and does not contain correction circuits, then its LFC and LPFC have a more complex shape (Figure 6.15) and contain a region of unstable oscillations.

Figure 6.15. LFC and LPFC of uncorrected op-amp

To ensure stable operation of op-amp devices, internal and external correction circuits are used, with the help of which they achieve a total phase shift with an open feedback loop of less than 135° at the maximum operating frequency. In this case, it automatically turns out that the decline K u op-amp is about 20dB/dec.

It is convenient to use as a criterion for the stability of op-amp devices Bode criterion , formulated as follows: “An amplifier with a feedback circuit is stable if the straight line of its gain in decibels crosses the LFC in a section with a roll-off of 20 dB/dec.” Thus, we can conclude that the frequency correction circuits in the op-amp must provide the decay rate K U inv(K U noninv) at HF ​​about 20 dB/dec.

Frequency correction circuits can be either built into the semiconductor crystal or created by external elements. The simplest frequency correction circuit is carried out by connecting a capacitor C cor of a sufficiently large value to the output of the op-amp. It is necessary that the time constant τ core=R out C cor was greater than 1/2π f in. In this case, high-frequency signals at the output of the op-amp will be shunted C core and the operating frequency band will narrow, most of them quite significantly, which is a significant drawback of this type of correction. The LFC obtained in this case is shown in Figure 6.16.

Figure 6.16. Frequency correction with external capacitor

Recession K u op-amp here it will not exceed 20 dB/dec, and the op-amp itself will be stable with the introduction of OOS, since φ will never exceed 135°.

Corrective circuits of integrating (lag correction) and differentiating (advanced correction) types are more advanced. In general, an integrating type correction manifests itself similarly to the action of a corrective (load) capacitance. The correcting RC circuit is connected between the op-amp stages (Figure 6.17).

Figure 6.17. Integrating type frequency correction

Resistor R 1 is the input resistance of the op-amp stage, and the correction circuit itself contains R core and C core. The time constant of this circuit must be greater than the time constant of any of the op-amp stages. Since the correction circuit is the simplest single-link RC circuit, its LFC slope is 20 dB/dec, which guarantees stable operation of the amplifier. And in this case, the correction circuit narrows the operating frequency band of the amplifier, but a wide band still does not give anything if the amplifier is unstable.

Stable operation of the op-amp with a relatively wide band is ensured by differential-type correction. The essence of this method of correcting LFC and LPFC is that RF signals pass inside the op-amp, bypassing part of the cascades (or elements) that provide maximum K u Op-amp 0, they are not amplified or delayed in phase. As a result, RF signals will be amplified less, but their small phase shift will not lead to loss of amplifier stability. To implement differential-type correction, a correction capacitor is connected to the special terminals of the op-amp (Figure 6.18).

Figure 6.18. Differential type frequency correction

In addition to the corrective circuits considered, others are known (see, for example). When choosing correction schemes and the values ​​of their elements, you should refer to reference literature (for example,).

5.4.1. General information about operational amplifiers

In classical electronics, an operational amplifier is usually called a linear converter, with the help of which you can perform various mathematical operations - summation, subtraction, integration, differentiation, etc. This determined the name of such amplifiers - operational (decisive), on the basis of which, by introducing feedback, you can carry out mathematical operations. Integrated op-amps are designed not only to perform mathematical operations, but also to carry out signal conversion (amplification, processing, signal generation).

A conventional graphical representation and functional designation of the op-amp is shown in Fig. 5.5.

Modern op-amps are built according to a direct amplification circuit with differential inputs equal in electrical parameters (inverse input “○” or “−” and non-inverse input - without designation or “+”) and a push-pull bipolar (in terms of signal amplitude) output. The main element of the op-amp is the input stage, built according to a differential amplifier (DA) circuit, the purpose of which is to amplify the signal difference observed between its inputs (Fig. 5.6a). The remote control has two transistors VT1 and VT2 with collector load resistors R K. The emitter currents of these transistors are formed using a stable current generator (GCT) I 0 made on transistors VT3 and VT4. If the parameters of transistors VT1 and VT2 are identical, the collector resistors are equal, and provided that the input signals U − = U + = 0 , the difference between the output signals of the remote control will be equal to zero, since for an ideal remote control the emitter current I 0 is divided in half between transistors VT1 and VT2.

From the theory of differential amplifiers it is known that in balance mode the potential of each output has a common-mode voltage level relative to ground: .

The balance mode corresponds to the diagram (Fig. 5.6, b) up to the point in time t1 . When appearing at the moment t1 signal U − transistor VT1 receives more bias current and its collector current I K 1 increases, and the current of transistor VT2 decreases, since

I K 1 + I K 2 = I 0 . Thus, as the input voltage U − increases, the output voltage at the output of the first transistor decreases
(signal increment is inverted in phase). At the other output of the remote control the voltage
will increase (the signal increment is not phase inverted). The total differential output signal between the remote control outputs is determined by the relation:

The change in output signals stops when all the current I 0 begins to flow through transistor VT1. At time t2, transistor VT2 goes into cutoff mode. Since the input resistance of the remote control is inversely proportional to the value of its operating current I 0, this current is usually set small (tens of microamps), and this in turn determines the low gain of the remote control:

Where
- transconductance of the bipolar transistor. Therefore, integrated op amps use subsequent amplification stages to achieve high voltage gain. In general, the voltage gain of an op-amp is equal to the product of the gain factors of all its stages:
.

Absolute values ​​of input voltages U − , U + And U EXIT limited by op-amp supply voltage + U Pete And − U Pete− (≤ ± 15 V). A typical property of the transfer characteristic of an op-amp is that it is sensitive to the difference in input voltages and does not depend on their absolute values. From this property follows the introduction of two concepts: common-mode input voltage U SINF for the common voltage component at both their inputs, which must be suppressed by the amplifier, and the differential input voltage U D, to which the amplifier responds:

,
,

Where K = 1/2 or 0.

To simplify the determination of op-amp parameters, it is usually assumed TO= 0, then U SINF = U + .

Integrated op amps typically consist of a differential input stage, gain stages, a stage that converts the two-phase output of the differential amplifier to single-phase, and a stage for level shifting. At the output of the amplifier, an emitter follower on complementary transistors is used, which ensures the transmission of signals of both positive and negative polarity. In modern op-amps TO 0 reaches a value of the order of 1*10 5 or more.

When considering and analyzing circuit designs based on operational amplifiers and deriving basic relationships, the concept is often used ideal operational amplifier. In an ideal op-amp it is considered that:

The operational amplifier has an infinitely large input impedance and zero output impedance;

op-amp inputs are symmetrical and do not consume current;

the voltage between the op-amp inputs is zero;

The voltage gain of the op-amp tends to infinity, and the output voltage is zero in the absence of input signals.

5.4.2. Amplitude-frequency response of the operational amplifier

A amplitude-frequency response (AFC) of the op-amp – dependence of the voltage gain on frequency. Any multi-channel amplifier at high frequencies can be represented by an equivalent circuit (Fig. 5.7), in which the signal generator K 0 U VX is loaded onto a number of integrating RC chains, the number of which is equal to the number of op-amp stages (R and C are, respectively, the own transfer conductivity and load capacitance of the cascade).

Voltage transfer coefficient of one RC chain:

Where
- circular cutoff frequency.

Accordingly, the cutoff frequency
. The frequency response module of the chain is determined by the relation:

IN The frequency response id for a two-stage op-amp in accordance with the equivalent circuit is shown in Fig. 5.8 (curve 1), where the frequency and gain are plotted on a logarithmic scale. Gain is measured in decibels (1 dB = 20lgK). Changing the frequency ten times (per decade), we obtain a decrease in gain by the same ten times (a gain drop of 20 dB). As can be seen from the figure, at low frequencies TO asymptotically approaches the open-loop gain value TO 0 . As the frequency increases beyond the cutoff frequency f sr1, on which TO decreases to the value 0.707 K 0 (by 3 dB), the high-frequency roll-off rate is uniform and amounts to 20 dB/dec. In a multistage amplifier, each stage has its own transfer conductivity and load capacitance, therefore at frequency f sr2 for the second stage the high-frequency roll-off rate will be 40 dB/dec. Modern operational amplifiers have a corrected frequency response, which for an op-amp without feedback has the form of curve 2. As the frequency increases, the gain drops and the graph crosses the zero decibel line at frequency unity gainf t. This frequency determines the active frequency band of the op-amp, in which the gain K≥ 1. Product of input signal frequency and open-loop gain TO equal to unity gain band f t = Kf VX. To eliminate amplitude-phase distortions in a given frequency band, it is necessary to ensure uniformity of the amplitude characteristics in this band. This is achieved by introducing negative feedback (NFB) into the op-amp. As the OOS depth increases (the op-amp gain decreases), the frequency band of the uniform amplitude characteristic expands (curve 3). Frequency range from zero to upper limit frequency f b is called the small-signal passband, which is related to the unity gain band of the op-amp with the feedback ratio f b = f t TO OS, Where TO OS- feedback gain.

5.4.3. Operational amplifier circuits

The number of op-amp circuits is continuously increasing as the element base develops and new op-amps appear, so it is especially important to know the principles of construction and analysis of the so-called typical (basic) op-amp switching circuits. There are three basic circuits for connecting operational amplifiers:

Inverting switching of op-amp;

Non-inverting switching of op-amp;

Differential switching on of the op-amp.

These circuits are the basis for building other operational amplifier circuits and calculating their parameters. When analyzing basic circuits and simplifying the calculation of their parameters, the concept of an ideal operational amplifier is often used. Let's consider the basic circuits for connecting an op-amp.

5.5.3.1. Inverting switching of op-amp

The equivalent circuit of the inverting connection of the op-amp is shown in Fig. 5.9. In this circuit, the input signal and feedback signal are supplied to the inverse input of the op-amp. The introduction of OOS leads to the fact that the circuit now has a feedback gain TO OS. Let's determine the value TO OS based on the properties of an ideal op-amp.

We consider the voltage between the inputs to be zero. Then the potential of the non-inverse input and the potential of the inverse input, and therefore the potential of point A (current summation point) is also zero. Provided that the input impedance of the op-amp R VX is large enough, we can assume that the current from the signal source i C = U C / R1 flows only through the feedback resistor R OS, creating a voltage drop across it:

Voltage drop across resistor R OS with great accuracy equal to the output voltage U OUT, since the potential of the left output of the resistor R OS(point A) is equal to zero (artificial zero potential of the circuit). Therefore, we can write:

.

Closed-loop voltage gain:

The minus sign in expression (4.4) shows that the voltage at the op-amp output is out of phase with the input voltage. In a real op-amp, taking into account the limited gain value TO 0 expression for TO OS has the form:

. (5.5)

The input resistance when the op-amp is switched on inverting can be calculated approximately R VX ≈ R1. Output impedance

Where R OUT.0- output impedance of the op-amp without feedback.

Note. The resistance R C in this circuit further serves to reduce the bias currents I CM in operational amplifier circuits.

5.4.3.2. Non-inverting op-amp switching

The equivalent circuit of a non-inverting op-amp connection is shown in Fig. 5.10.

In this circuit, the feedback voltage is created by a divider R1 – R OS :

Assuming that the voltage between the inputs of the op-amp is close to zero, we can write that U O.C. =U C , whence the voltage gain:

The input resistance when the op-amp is turned on non-inverting is large and is approximately determined by the relation:

Output resistance where β =R1/ R O.C. .

5.4.3.3. Differential switching of op-amp

The equivalent circuit of the differential connection of the op-amp is shown in Fig. 5.11. It is a combination of inverting and non-inverting switching circuits and makes it possible to obtain the difference between two input signals with a given gain.

For P To obtain the voltage gain of this circuit, we still assume that the voltage difference at the inputs of the op-amp is zero, and the signal currents do not branch to its inputs. Let's create a system of equations for the voltages at the inverse and non-inverse inputs:

- inverse input:

, where is the voltage at the inverse input; (5.8)

- non-inverse input:

Considering that for an ideal op-amp the voltage between the inputs is zero
, solving jointly (9.7) and (9.8) we obtain the expression for

output voltage:

Where n = R O.C. / R VX = nR/ R – gain of the feedback amplifier. If the resistances in the circuit are different, then the output voltage can be determined:

5.4.3.4. Adder

P By analogy with op-amp switching circuits, inverting and non-inverting adders are distinguished. The circuit of the inverting adder is shown in Fig. 5.12. Based on the principle of superposition, the voltage at the output of the inverting adder can be determined by the relation:

, Where K O.C. i = R O.C. / R i – transmission coefficient of the i-th input signal at the inverting input. In a non-inverting adder circuit, the input voltages are applied to the non-inverting input, and all resistors except the feedback resistance R O.C. , make them the same. The voltage at the output of such an adder is determined by the relation:

5.4.3.5. Comparators

A comparator (from English Compare) is a device that compares the signal voltage at one of the inputs with the reference voltage at the other input. When used as an op-amp comparator, a positive or negative saturation voltage will be set at its output ± U us. Typically, in an op-amp, the saturation voltage and supply voltage are related by the relation: ± U us = ±0.9U Pete . Comparators are used in many devices and circuits, for example:

In a Schmitt trigger or circuit that converts an arbitrary waveform into a square wave or pulse signal;

In the zero detector - a circuit indicating the moment and direction of passage of the input signal through 0 V;

In a level detector - a circuit that indicates the moment the input voltage reaches a given reference voltage level,

In a triangular or rectangular waveform generator, etc.

A distinctive feature of comparators is the lack of environmental feedback, i.e. The voltage gain is determined by the intrinsic gain TO 0 OU.

In Fig. 5.13. shows a comparator circuit that is sensitive to input voltage (−). In this circuit, the input signal is supplied to the inverse input, and the non-inverse input is used to set the reference voltage U op. Since both inputs are involved in the comparator circuit, to analyze its operation and the behavior of the output voltage, one should use

introduce the third basic switching circuit - differential switching of the op-amp and relation (5.10).

In the case when U op = 0 , the comparator circuit works as a zero detector (Fig. 5.13.b). In the case when U VX positive (during the first half-cycle), U EXIT equals − U US, since the input potential (+) is less than the input potential (−) (see Fig. 5.13. b). During the second half period, when U VX negative, U EXIT will equals + U US, since the input potential (+) is greater than the input potential (−). Thus, U EXIT shows when U VX positive or negative with respect to the zero reference voltage.

When U op > 0 The comparator circuit works as a level detector (Fig. 5.13. c). On the interval M–N U EXIT equals − U US, since the input potential (+) is less than the input potential (−) ( U op < U VX). At U VX < U op (intervalN–K) U EXIT equals + U US .

If you swap the inputs for supplying the input voltage and generating the reference, you can get a comparator circuit that is sensitive to the voltage at the input (+).

In practice, in some cases the input voltage may fluctuate around the reference level. Such oscillations are more than likely due to the inevitable interference on the wires approaching the input terminals of the op-amp (noise voltage). In this case the voltage U EXIT will fluctuate from one saturation level to another, which may lead to false alarms, measurement devices or actuators. In order to prevent the output voltage from reacting to false crossings of the reference level, positive feedback (POF) is introduced into the comparators. Such comparators are called comparators with PIC or regenerative comparators, Schmitt triggers. PIC is carried out by applying a certain part of the output voltage to the non-inverse input U EXIT using a resistive divider R3 -R4 (Fig. 5.14). The voltage generated by the resistive divider will have different values ​​because it depends on the sign U EXIT. It called upper or lower threshold voltage and in comparators with PIC it is installed automatically:

. (5.12)

Positive feedback creates a trigger effect, speeding up shifting U EXIT from one state to another. As soon as

U EXIT begins to change, regenerative feedback arises, forcing U EXIT change even faster. At a time equal to zero (Fig. 5.14. a, b), U VX negative, so the output voltage is + U US and a threshold will be set at the non-inverse input U P.V.. At a moment in time t1 voltage U VX > + U US and the comparator switches to voltage output − U US. In this case, a threshold will be set at the non-inverse input U P.N. . The next switching of the comparator will occur at the moment t2 , When U VX will become more negative than the voltage − U US . If the threshold voltages exceed the noise amplitude, then the PIC will not allow false alarms at the output (Fig. 5.14. a, b). Voltage range − U US ≤ U ≤ + U US is called “Hysteresis” or “Dead Zone”.

Lecture 6. Generators of harmonic oscillations. Key operating mode of transistors. Rectangular pulse generators.

6.1. Harmonic generators

Harmonic oscillation generators are devices that convert direct current energy into the energy of electromagnetic oscillations of a sinusoidal shape of the required frequency and power. According to the method of excitation, they are divided into generators with independent excitation and self-excitation (autogenerators).

The block diagram of the self-oscillator is shown in Fig. 6.1. It represents an amplifier surrounded by positive feedback. Here Ќ - complex value of the amplifier voltage gain, έ - complex value of the transmission coefficient of the four-port feedback network (FOS). Frequency-dependent links are used as FOS: LC circuits in high-frequency self-oscillators and RC circuits in low-frequency ones.

In an amplifier covered by feedback, the following relations hold true:

Ů in = έ Ů out, Ů out = Ќ Ů input, from where you can write the expression for the output signal:

Ů out = Ќ έ Ů out. (6.1)

Expression (6.1) is valid under the condition Ќ έ = 1. (6.2)

The fulfillment of condition (6.2) ensures undamped oscillations in the self-oscillator. Taking into account the modules of the gain and feedback transmission coefficient and their phase shifts, we can write:

│ Ќ │е jφ │ έ │е jψ =Kе jφ εе jψ =1. (6.3)

Equality (6.3) must be satisfied if two conditions are met:

φ + ψ = 2π n(n= 0, 1, 2, 3….) (6.4),

Condition (6.4) is called the “phase balance condition” and means that positive feedback (POF) operates in the system.

Condition (6.5) is called the “amplitude balance condition” and means that energy losses in the self-oscillator are replenished with energy from the power source through the PIC circuit.

Weak oscillations that appear for some reason at the input of the amplifier are amplified by “K” times and weakened by “ε” times by the feedback circuit. Getting back to the amplifier input in the same phase, but with a larger amplitude. Then the process is repeated until oscillations with a constant amplitude (Kε= 1) are established at the output.

6.2.1. RC harmonic oscillators

In Fig. Figure 6.2 shows diagrams of RC self-oscillators of harmonic oscillations.

RC self-oscillators contain an active element (OE amplifier) ​​and a three-link RC chain of a differentiating (see Fig. 6.2, a) or integrating (see Fig. 6.2, b) type, connected to the PIC amplifier circuit. In addition, parallel connected alternating current R1 and R2 form the third resistance of a three-link RC circuit of differentiating type: (R1R2) / (R1 =R2) =R

Three-link RC circuits have amplitude-frequency and phase-frequency characteristics (AFC and PFC), shown in Fig. 6.3. From the graphs of the frequency response and phase response it is clear that the inflection point (point A) of the characteristics corresponds to the frequency ω 0 and phase ψ = 180 0 for a differentiating type RC circuit and ψ = -180 0 for an integrating type RC circuit. Point A corresponds to the quasi-resonance of the RC circuit, and the quasi-resonance frequency ω 0 is called the quasi-resonant frequency of the frequency-selective RC circuit.

Each RC chain provides a phase shift equal to 60 0 . The total shift of the three-link RC chain is 180 0 . The differentiating chain shifts the phase of oscillations towards the lag, and the integrating chain towards the advance.

The amplifier with OE itself shifts the output signal by 180 0 and the three-link RC chain also by 180 0. Thus, a signal is supplied to the amplifier input in phase with an output signal due to PIC. This ensures the phase balance condition.

Basic calculation ratios:

a) for a generator with a differentiating type RC circuit:

b) for a generator with an integrating type RC circuit:

6.2.2. RC oscillators based on operational amplifiers

A). RC oscillators with phase rotation in the feedback circuit

In the RC generators shown in Fig. 6.4, a three-link phase-shifting RC circuit of a differentiating or integrating type is connected between the inverting input and the output of the op-amp. Resistor R, included in the OOS circuit (see Fig. 6.4, a), performs two functions: as an element of the RC circuit link and as an element in the OOS circuit to increase stability. A similar task is performed by capacitor C in the generator circuit in Fig. 6.4, b. At the quasi-resonance frequency ω 0, the three-element RC circuits shift the phase by ±π, and the inverting op-amp shifts the phase by π.

The basic design ratios are the same as in transistor RC oscillators

B). RC oscillator without phase rotation in the feedback circuit

In this generator, shown in Fig. 6.5, a PIC was used at the input of the op-amp through the Wien bridge. The Wien bridge consists of serial and parallel RC links, which have the highest transmission coefficient at the quasi-resonant frequency ω 0 (see Fig. 6.5b). In this case, the phase shift is equal to 0 (see Fig. 6.5, c). To ensure balance

The phase output of the Wien bridge is connected to the non-inverting input of the op-amp. OOS elements R1, R2 increase the stability of the generator. Variable resistor R1 changes the depth of OOS.

Basic design relationships for this scheme:

f G = 1/ 2πRC;ε 0 = 1/3; C = 1/2πRf.

6.3. Key operating mode of the transistor

The circuit diagram of an electronic switch based on a bipolar transistor is shown in Fig. 6.6. A transistor switch based on a common emitter circuit in static mode has two stationary states. The transistor is locked and the operating point “B” is in the cutoff region -

region II, limited from above by the current-voltage characteristic corresponding to I b = - I k0. Both pn junctions are closed. There is no current in the transistor, the collector potential (U KE ots) is close to the value E k. The cutoff condition of the transistor is U VX = U BE ≤ 0.

The transistor is open and the operating point “A” is in the saturation region - region I, limited on the right by the line from which the static current-voltage characteristics emerge. Both p-n junctions of the transistor are open. The maximum current flows through the transistor - the collector saturation current I to us. The collector voltage is close to zero. Transistor saturation condition U VX = U BE > 0.U K E > 0.

To calculate tansistor switches, the current criterion of the saturation condition is often used:

I B ≥I K N /β =I B N, where I B N and I K N are the base current and the collector current at the saturation limit.

In saturation mode, the transistor can be considered as an equipotential point - a point with the same potential of all electrodes. In this case, the collector current in saturation mode can be defined as I K N ≈ E K /R K, base current I B N ≈I K N / β ≈ E K /βR K. Then, for a given value of the input voltage, the resistance in the base circuit is:

R B =U VX /I B N = (U VX βR K) / E K. (6.6)

6.4. Parameters of a single rectangular pulse and pulse sequence

Let's consider the main parameters of a single pulse. A real single rectangular voltage pulse generated by a key semiconductor device is shown in Fig. 6.7.

The pulse parameters are: amplitude U m, duration t and, determined at the level of 0.1 U m or at the level corresponding to half the amplitude (active duration), duration of the leading edge t f, duration of the cutoff t s (rear edge) and decay of the top of the pulse ∆U.

The parameters of the pulse sequence (Fig. 6.8) are: pulse amplitude U m, repetition period T, repetition frequency

f= 1 /T, pulse duration t and, pulse pause duration t p, duty cycle γ = t and /T and the reciprocal of the filled factor ia, called duty cycle q = 1/ γ =T/t and.

6.5. Rectangular pulse generators (multivibrators)

To generate a periodic sequence of rectangular voltage pulses with the required parameters, generators called multivibrators are used. Multivibrators belong to the class of pulse technology devices intended. As in any generating devices designed to generate pulses, in their circuit the key element (transistor, operational amplifier) ​​is covered by positive feedback using RC circuits that ensure the relaxation process. Relaxation devices operate in two modes: self-oscillating and standby. In standby mode, one output pulse or a packet of such pulses is generated for each input signal. In self-oscillating mode, generators form a continuous sequence of pulses. Such generators are used in digital technology as master oscillators and frequency dividers.

There are a wide variety of methods for constructing multivibrator circuits. The most widespread are multivibrator circuits based on operational amplifiers (op-amps). The possibility of creating a multivibrator using an op-amp is based on the use of an op-amp as a threshold element (comparator). The circuit of a symmetrical multivibrator using an op-amp (t И1 =t И2) is shown in Fig. 6.9. Let's consider the operation of the multivibrator, taking into account the time diagram of its operation (Fig. 6.10).

Let us assume that until time t1 the voltage between the inputs of the op-ampu D > 0. This determines the voltage at the outputu OUT =U − US and at its non-inverse inputu + = − γU − US, where γ =R3 /(R3 +R5) is the transfer coefficient positive feedback circuits. The presence of voltage −U HAC at the output determines the process of charging capacitor C2 through resistor R4 with the polarity indicated in Fig. 6.9 without parentheses. At time t1, the exponentially changing voltage at the inverse input of the op-amp (Fig. 6.10., c) reaches the voltage at the inverse input − γU − NAS. The voltage between the inputs of the op-amp becomes equal to zero, which causes a change in the polarity of the voltage at the output: u OUT = U + US (Fig. 6.10, a). The voltage at the non-inverse input u + changes sign and becomes equal to γU + US (Fig. 6.10, b), which corresponds to the voltage between the inputs of the op-amp u D< 0 иu ВЫХ =U + НАС. С момента времениt 1 начинается перезаряд конденсатора от уровня

− γ U − US.

The capacitor tends to recharge in a circuit with resistor R4 to the level U + US with the voltage polarity indicated in brackets (Fig. 6.9). At time t2, the voltage on the capacitor reaches the value γU + US. Voltage u D becomes zero. This causes the op-amp to switch to the opposite state (Fig. 6.10, a - c). Further processes in the circuit proceed similarly.

Pulse repetition period of a symmetrical multivibrator

Т = t И1 +t И2 = 2t И. (6.7)

Pulse repetition rate

f= 1 /T= 1 / 2t I. (6.8)

Time t And can be determined by the duration of the interval t I1 (Fig. 6.10, a), which characterizes the recharge of capacitor C2 in a circuit with resistor R4 and voltage U + US from the level − γU − US to γU + US (Fig. 6.10, c).

The recharging process is described by the well-known relationship:

Where
,
,
.

If in expression (6.10) we put
, you can determine the time t AND :

. (6.11)

Assuming that for the op-amp
, relations (6.11), (6.7) and (6.8) can be reduced to the form:

. (6.14)

Asymmetrical multivibratort И1 ≠t И2. To do this, it is necessary that the time constants of the multivibrator timing circuits be unequal across half-cycles. This is achieved by including in the feedback circuit, instead of resistor R4, two parallel branches consisting of a resistor and a diode (Fig. 6.11).

Diode VD2 is open when the polarity of the output voltage is positive, and diode VD1 is open when the polarity is negative. Therefore, in the first case τ 1 = С2R ״ 4, and in the second τ 2 = С2R ׳ 4. The pulse durations t И1 and t И2 of an asymmetrical multivibrator are calculated according to the relation (6.11), and the frequency according to the formula f = 1/T= 1/ (t И1 +t И2).

To determine the energy properties of pulse devices and the energy impact of the pulse on the load, the concept of the average pulse value over a period (the constant component of the pulse) is introduced. For a rectangular sequence of pulses with an active load, the average value of voltage and current over a period is determined by the relations:

,
.

The effective value of voltage and current for a period is determined by the relations:

,

6.6. Power transistor switchesMOSFETAndIGBT

Designed for switching high currents (MOSFET - tens of amperes, IGBT -

hundreds and thousands of amperes) at operating voltages of hundreds of volts. Used in various types of voltage converters (DC–DC, DC–AC), frequency converters for controlling electric drives, etc.

Operating principleMOSFET approximately the same as low-power insulated-gate field-effect transistors with induced conduction channel. In Fig. 6.12. shows the vertical structure of an n-channel MOSFET. This structure is performed by the double diffusion method, which consists of the following: on a n + - type substrate with an introduced epitaxial layer, the first diffusion is carried out (boron is a p-type impurity). Next, by diffusion of a donor impurity (phosphorus), a source with a high concentration of n + - type carriers is created. The drain contact is located at the bottom. This structure allows you to create a maximum contact area between the drain and source in order to reduce the resistance of the leads. The polysilicon gate electrode is isolated from the source metal by a layer

SiO2. The channel in a power transistor is formed on the surface of the p-regions below the gate oxide, with the p-regions connected to the source.

The lightly doped n-type region (often called the drift region) allows the device to withstand high voltage when it is turned off.

Since the MOSFET is a transistor that operates on majority charge carriers, excess carriers do not accumulate in it, which determine the dynamics of the bipolar transistor. The dynamics are determined only by the gate oxide layer, as well as by two capacitances: the input gate-source SG and the output drain-source SSI.

Modern converter devices require the transistor to be turned on and off at a high frequency - hundreds of kHz and even a few MHz. The resistance between the gate and source of a MOSFET is tens of megaohms, but it is shunted by the input capacitance CZ, which significantly affects the design of the transistor control circuit. At a high switching speed of the transistor, the capacitance C ZI heavily loads its control circuit. MOSFET has a characteristic called the forward transfer characteristic (Fig. 6.13).

The drain current is zero up to a voltage called threshold (U pore), and then increases with increasing voltage (U zi). Manufacturers define Upore as the voltage at which the drain current reaches a certain value, for example 1 mA. To achieve drain current I from 1, it is necessary to charge the capacitance to voltage U zi1. That is, the charging time of the input capacitance, and therefore the turn-on time of the transistor, will be determined by the current generated by the control circuit.

Let's calculate the required current from the control circuit when switching MOSFETs. Let C SI = 4 nF, U SI 1 = 12 V, and the charging time of the input capacitance should be 40 ns.

From the known relation for capacity

i c =C(du c /dt)

let's define: I z =C zi U zi 1 /t on = 4 ·10 -9 ·12 / 40 ·10 -9 = 1.2A.

Thus, in order to switch the MOSFET in a given time, the control logic must provide significant current. In modern technology, specialized controllers (drivers) are used to control powerful MOSFETs, which can directly supply voltage to the gate with an amplitude of the order of 12-15 V and a pulse current of 1.5-3 A, providing a large charging current for the input capacitance.

IGBT(IsolatedGateBipolarTransistor) – bipolar transistor with an insulated gate. Find use in many high voltage and high ampere applications: drives, inverters, devices uninterruptible power supply etc. The vertical structure of IGBT is shown in Fig. 6.14, a. In an insulated gate bipolar transistor, a powerful pnp bipolar transistor and a control MOSFET are connected in one crystal according to a composite circuit. The basis of the structure is heavily doped p-type silicon. A MOSFET is connected between the base and collector of the bipolar transistor (BT). In fact, in the IGBT structure, two BTs can be distinguished: VT2 - with the structure p + -n - - p - and VT1 - with the structuren + - p - -n - (Fig. 6.15). The operation of these transistors is controlled by the MOSFET. For the diagram in Fig. 6.15. the following relations are valid:

i k 2 =β 2 i e2 ;i k 1 =β 1 i e1 ;i e =i k 1 +i k 2 +i c .

That is, the drain current of the field-effect transistor i c =i e (1 – β 1 – β 2) or through the slope S = ∂I c / ∂U zi

IGBT power section current:

i k ≈i e = (SU ​​GE) / (1 – β 1 – β 2) =S EKV U GE, where S EKV =S/ (1 – β 1 – β 2) is the equivalent slope of the IGBT. At β 1 + β 2 = 1S, the IGBT ECV significantly exceeds the slope of the SMOSFET.

The speed of IGBT is significantly lower than the speed of MOSFET (tens of kilohertz). The turn-on time of the IGBT is approximately the same as that of the BT (approximately 80 ns), but the turn-off time is much longer. This is determined by the fact that the IGBT does not have the ability to speed up the turn-off process by creating a negative base current (its base circuit includes a MOSFET, which closes much faster). On

Figure 6.16. shows the process of turning off the IGBT with an active-inductive load. At the beginning, the collector current decreases quickly and then slowly reaches zero. The initial stage corresponds to the portion of the device current that flows through the MOSFET. The trailing tail part (current tail) is actually the BT current when the base is broken