Integrating devices. Devices integrated on modern motherboards

Previous analog signal processing devices had frequency-independent feedback circuits, i.e. b=const and does not depend on frequency. The integrating and differentiating amplifiers, unlike previous devices, have frequency-dependent feedback circuits. To do this, the OS circuit includes a capacitance, the resistance of which depends on the frequency.

The integrating amplifier is built on the basis of an inverting amplifier, replacing the feedback circuit R2 on WITH, rice. 20.7.

Rice. 20.7. Functional diagram of the integrating device

Due to the second assumption we have

I input +i c =0,

The left pin is grounded, so the output voltage is equal to the voltage across the capacitor.

(20.5)

If a constant voltage surge is applied to the input, then

, the output voltage increases linearly with time. The “-“ sign indicates that the slope is negative.

When applying rectangular pulses to the input, you can obtain a parallel voltage. If the input signal is an alternating voltage according to the cosine law, i.e. U in =U in cosωt, That .

The amplitude-frequency response of the integrating device on a double logarithmic scale must strictly correspond to a 1st order low-pass filter with a roll-off equal to 6 dB per octave or 20 dB per decade.

The gain of the integrating amplifier can easily be obtained from the gain of the inverting amplifier by replacing R2 on X s,

. (20.6)

From expression (20.6) it is clear that with increasing frequency the K(ω). As already noted, unlike previous devices, b depends on frequency and is complex. At high frequencies b=1 and the phase shift of the feedback circuit is zero, as with frequency-independent. The accuracy of integration depends on the choice of integration constant t=RC and on the parameters of the op-amp. To increase accuracy, it is advisable to use adjusted op-amps with small I input.

Integrator, integrator, computing device for determining integral , for example, like where X And at- input variables. Input variables can be mechanical movement, pressure, electric current (voltage), number of pulses, temperature, etc. I. at. used as an independent computing device when solving mathematical problems using integration methods; can serve as an element of an automatic control system (integrating link); be part of a computer; used to simulate a physical process, etc. For example, hydraulic I. at. used to study unsteady processes of heat transfer, filtration, and diffusion. The variables under study are reflected by the liquid levels in the vessels communicating through the so-called resistance tubes. If the taps in the tubes are opened, the initial liquid levels will be redistributed in accordance with the specified conditions. Finding the values of the output quantity is reduced in this case to measuring the liquid levels in the vessels. The main element of electronic I. at. continuous action (analog) is an electric capacitor, the voltage on which is proportional to the integral of the current flowing through the capacitor in the feedback circuit operational amplifier . Such I. at. usually included in analog computers.

Digital I.u. are included in digital differential analyzers, as well as some specialized computing devices, for example interpolators . Integrating functions into digital I.U. is replaced by the operation of summing a finite number of consecutive values of this function (its increments), specified at discrete points. In this case, the input and output numerical information is represented in the form of electrical pulses, and integration is carried out by summing these pulses. By choosing the pulse price sufficiently small, it is possible to ensure the practically necessary accuracy when replacing the integral with a sum; accuracy of analogue I. limited.

Lit.: Feldbaum A. A., Computing devices in automatic systems, M., 1959; Digital analogues for automatic control systems, M.-L., 1960; Raymon F.A., Automation of information processing, trans. from French, M., 1961

M. M. Gelman.

Great Soviet Encyclopedia M.: "Soviet Encyclopedia", 1969-1978

Integrator

integrator, a computing device for determining the Integral, for example, of the form x and at- input variables. Input variables can be mechanical movement, pressure, electric current (voltage), number of pulses, temperature, etc. I. at. used as an independent computing device when solving mathematical problems using integration methods; can serve as an element of an automatic control system (integrating link); be part of a computer; used to simulate a physical process, etc. For example, hydraulic I. at. used to study unsteady processes of heat transfer, filtration, and diffusion. The variables under study are reflected by the liquid levels in the vessels communicating through the so-called resistance tubes. If the taps in the tubes are opened, the initial liquid levels will be redistributed in accordance with the specified conditions. Finding the values of the output quantity is reduced in this case to measuring the liquid levels in the vessels. The main element of electronic I. at. continuous action (analog) is an electrical capacitor, the voltage across which is proportional to the integral of the current flowing through the capacitor in the feedback circuit of the operational amplifier (See Operational amplifier). Such I. at. usually included in analog computers.

Digital I.u. are part of digital differential analyzers, as well as some specialized computing devices, for example Interpolator. Integrating functions into digital I.U. is replaced by the operation of summing a finite number of consecutive values of this function (its increments), specified at discrete points. In this case, the input and output numerical information is represented in the form of electrical pulses, and integration is carried out by summing these pulses. By choosing the pulse price sufficiently small, it is possible to ensure the practically necessary accuracy when replacing the integral with a sum; accuracy of analogue I. limited.

M. M. Gelman.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

Integrated plant protection
Integrating factor

See what an “integrating device” is in other dictionaries:

INTEGRATOR- integrator, will calculate. a device for determining integrals of certain types. Used as a standalone. device or in will calculate. cars. According to the method of representing the quantities of I. at. divided into analog and digital. The most widely used... ...

Integrator- Integrating device, integrator... Brief explanatory dictionary of printing

Harmonic analyzer- a computing device for finding harmonic amplitudes of complex periodic functions (See Periodic function). They are used in dynamic studies of engine crank mechanisms, for preliminary assessment of the influence...

Phase shifting circuit- an electrical circuit at the output of which the phases (See Oscillation phase) of the oscillations of individual harmonic components of the spectrum of the signal propagating through it differ from the phases of the corresponding components at the input. In F. c. with concentrated... ... Great Soviet Encyclopedia

Integrator- the same as the Integrating device... Great Soviet Encyclopedia

Digital Differential Analyzer- a specialized digital integrating machine, the basis of which is made up of digital integrating devices (See Integrating device) (integrators) that perform integration over an independent variable specified in the form of increments ... Great Soviet Encyclopedia

HYDROINTEGRATOR- (from hydro... and lat. integro I replenish, restore) an integrating device, in which integration operations are modeled by the accumulation of liquid... Big Encyclopedic Polytechnic Dictionary

INTEGRATOR- (from Latin integro I replenish, restore) 1) mechanical. a device for determining integrals of certain types (for example, for calculating moments of inertia, areas of plane figures). See also Planimeter. 2) Same as integrating device... Big Encyclopedic Polytechnic Dictionary

Flow meters- A device that measures the flow rate of a substance passing through a given section of a pipeline per unit time is called a flow meter. If the device has an integrating device with a counter and serves to simultaneously measure the amount of a substance, then... ... Wikipedia

Flow meter- Flow meter is a device that measures the flow rate of a substance passing through a given section of a pipeline per unit of time. If the device has an integrating device with a counter and is used to simultaneously measure the amount of a substance, then its ... ... Wikipedia

Integrating devices, like differentiating devices, use the properties of a capacitor. The electric current flowing through a capacitor is proportional to the rate of change of voltage across it:

This description of the processes of differentiation and integration is valid under ideal conditions (the internal resistance of the voltage source tends to zero, the current source tends to infinity).

However, especially in passive circuits, this is not the case. Let us consider the passive integrating R.C.- chain (Fig. 2.7.1.).

Rice. 2.7.1. RC integrating circuit diagram

For such a circuit we can write:

i 1 (t)=i 2 (t)+i 3 (t)

(2.23.)

after conversion:

(2.24)

or else:

Where u 0 (t) is ideal integration, and the second term is the absolute error of integration.

At u in(t)=const=E, the ideal solution is determined by the expression

The general solution to equation (2.23.) has the form:

If = K y - circuit gain,

T is the time constant of the circuit.

then we can write:

U 0 (t) = K y

U U 0 = U in = DU U out (t) t

Fig.2.7.2. Integration error

Using the above method, it is easy to determine the operating time of the circuit, within the permissible error.

The disadvantages of an integrating RC circuit are primarily determined by:

1. Short integration time.

2. Too low output voltage for a given error.

3. The circuit can only operate on a high-resistance load.

Active integrating device uses an op-amp with deep negative feedback that performs mathematical integration operations. An active integrator is widely used in analog computing devices and information-measuring technology; its circuit is shown in Fig. 2.7.3:

Rice. 2.7.3. Active integrating device

Based on Kirchhoff's laws, we can write:

We solve the system of equations together, excluding

The resulting expression can be integrated and get:

result error

At K y tends to infinity, tends to 1, and tends to 0, then

. (2.26.)

The right term of expression (2.25.) is several times smaller than the right term of the expression of the passive chain (2.24). Consequently, expression (2.26) ensures that the integration operation is performed with an accuracy of K y times greater than passive R.C.-chain.

When performing integration, it is necessary to set the initial condition at t=0.

This is provided by the circuit shown in Figure 2.7.4. Before the input signal is supplied to the integrator using switch K, a predetermined voltage U 0 is supplied to capacitance C, which is formed by the circuit +/- E, R 2, C, R 3. After turning off this circuit, the initial voltage remains on the capacitor, from the level of which integration is carried out.

Rice. 2.7.4. Active integrating device with the ability to set the initial value

In practice, integrators with many inputs and simultaneous performance of integration and summation operations are often used. The output signal is determined by the formula:

Uout (t)= -

For a multi-input integrator using inverting and non-inverting inputs (Fig. 2.7.5.), the expression for U out has the form:

U out

Security questions

1. What examples of using modeling methods to solve practical problems do you know?

2. What is the system of analogies based on?

3. What methods of constructing analog computing devices do you know?

4. What types of errors characterize the accuracy of analog computing devices?

5. What is the purpose of the main differential devices used in analog technology?

6. How is the error of passive adding devices determined?

7. Conduct a comparative analysis of the errors of passive and active adding devices. What factors have the greatest influence on the accuracy of adding devices?

8. Derive a formula for determining the differentiation time of a passive differentiating circuit for a given relative error: at R = 1 Ohm, C = 0.1 μF, du = 2%.

9. What examples of the use of an active differentiating device do you know? Give the diagrams and their characteristics.

10. Using formulas that describe the operation of a passive integrating circuit, justify its disadvantages.

11. How to set the initial conditions at t = 0 for an active integrating device?

12. What are the main sources of error in a passive integrating circuit and an active integrating device?

In pulsed devices, the master generator often produces rectangular pulses of a certain duration and amplitude, which are intended to represent numbers and control elements of computing devices, information processing devices, etc. However, for the correct functioning of various elements, in the general case, pulses of a very specific shape other than rectangular are required , having a given duration and amplitude. As a result, there is a need to pre-convert the master oscillator pulses. The nature of the transformation may vary. Thus, it may be necessary to change the amplitude or polarity, duration of the master pulses, or delay them in time.

Conversions are mainly carried out using linear circuits - four-terminal networks, which can be passive and active. In the circuits under consideration, passive quadripoles do not contain power supplies; active ones use the energy of internal or external power supplies. With the help of linear circuits, transformations such as differentiation, integration, shortening of pulses, changes in amplitude and polarity, and delay of pulses in time are carried out. The operations of differentiation, integration and shortening of pulses are performed by differentiating, integrating and shortening circuits, respectively. Changing the amplitude and polarity of the pulse can be done using a pulse transformer, and delaying it in time using a delay line.

Integrating circuit. In Fig. 19.5 shows a diagram of the simplest circuit (passive two-terminal network), with which you can perform the operation of integrating the input electrical signal applied to terminals 1-1 | , if the output signal is removed from the 2-2" terminals.

Let's create a circuit equation for instantaneous values of currents and voltages according to Kirchhoff's second law:

It follows that the circuit current will change according to the law

If we choose the time constant is large enough, then the second term in the last equation can be neglected, then i(t) = uin (t)/R.

The voltage across the capacitor (at 2-2" terminals) will be equal to

(19.1)

From (19.1) it is clear that the circuit shown in Fig. 19.5, performs the operation of integrating the input voltage and multiplying it by a proportionality coefficient equal to the inverse value of the circuit time constant:

The timing diagram of the output voltage of the integrating circuit when a sequence of rectangular pulses is applied to the input is shown in Fig. 19.6.

Differentiation chain. Using a circuit, the diagram of which is shown in Fig. 19.7 (passive four-port network), you can perform the operation of differentiating the input electrical signal supplied to terminals 1-1", if the output signal is removed from terminals 2-2". Let's create a circuit equation for instantaneous values of current and voltage according to Kirchhoff's second law:

If the resistance R is small and the term i(t)R can be neglected, then the current in the circuit and the output voltage of the circuit taken from R,

(19.2)

Analyzing (19.2), we can see that with the help of the circuit under consideration, the operations of differentiating the input voltage and multiplying it by a proportionality coefficient equal to the time constant τ = RC are performed. The shape of the output voltage of the differentiating circuit when a series of rectangular pulses is applied to the input is shown in Fig. 19.8. In this case, theoretically, the output voltage should be alternating pulses of infinitely large amplitude and short (close to zero) duration.

However, due to the difference in the properties of the real and ideal differentiating circuits, as well as the finite steepness of the pulse front, the output receives pulses whose amplitude is less than the amplitude of the input signal, and their duration is determined as t and = (3 ÷ 4) τ = (3 ÷ 4) RC.

In general, the shape of the output voltage depends on the ratio of the input signal pulse duration t and the time constant of the differentiating circuit τ. At moment t 1, the input voltage is applied to resistor R, since the voltage across the capacitor cannot change abruptly. Then the voltage across the capacitor increases exponentially, and the voltage across the resistor R, i.e., the output voltage, decreases exponentially and becomes equal to zero at the moment t 2 when charging of the capacitor is complete. At small values of τ, the duration of the output voltage is short. When the voltage u BX (t) becomes zero, the capacitor begins to discharge through the resistor R. Thus, a pulse of reverse polarity is formed.

P
Active integrating and differentiating chains have the following disadvantages: both mathematical operations are implemented approximately, with known errors. It is necessary to introduce corrective elements, which, in turn, greatly reduce the amplitude of the output pulse, i.e., without intermediate amplification of the signals, n-fold differentiation and integration are practically impossible.

These disadvantages are not characteristic of active differentiating and integrating devices. One possible way to implement these devices is to use operational amplifiers (see Chapter 18).

Active differentiator. The diagram of such a device using an operational amplifier is shown in Fig. 19.9. Capacitor C is connected to input 1, and resistor R oc is connected to the feedback circuit. Since the input resistance is extremely high (R in -> ∞), the input current flows around the circuit along the path indicated by the dotted line. On the other hand, the voltage and input amplifier in this connection are very small, since K u -> ∞, therefore the potential of point B of the circuit is practically equal to zero. Therefore, the input current

(19.3)

The output current i(t) is at the same time the charging current of capacitor C: dq= Сdu BX (t), from where

(19.4)

Equating the left sides of equations (19.3) and (19.4), we can write - and out (t)/R oc = С du in (t)/dt, from where

(19.5)

Thus, the output voltage of the operational amplifier is the product of the time derivative of the input voltage multiplied by the time constant τ = R OS C.

A
active integrating device. The circuit of an integrating device based on an operational amplifier, shown in Fig. 19.10, differs from the differentiating device in Fig. 19.9 only in that capacitor C and resistor R oc (in Fig. 19.10 -R 1) have swapped places. As before, R input -> ∞ and voltage gain K u -> ∞. Consequently, in the device, capacitor C is charged with current i(t) =u BX (t)/R 1 . Since the voltage on the capacitor is almost equal to the output voltage (φ B = 0), and the operational amplifier changes the phase of the input signal at the output by an angle π, we have

(19.6)

Thus, the output voltage of an active integrating device is the product of a certain integral of the input voltage over time by a factor of 1/τ.