Subject: Theory of automatic control

Topic: NON-LINEAR ELEMENTS

1. Classification of non-linear elements

Non-linear deposits z = f (x) can be classified according to different signs:

1. For the smoothness of the characteristics: smooth - even at any point of the characteristic it is similar dz / dx, i.e. the function is differentiated (Fig. 1a, b); piecewise-linear - a characteristic, in which case one can develop the first (Fig. 2) or another kind (Fig. 2b).

Mal. 3

For symmetry: paired-symmetrical - symmetrical along the axis of ordinates, i.e. Z (x) \u003d z (- x) (Fig. 4a); unpaired-symmetrical - symmetrical to the cob of coordinates, with which z (x) = - z (- x) (Fig. 4b); not symmetrical (Fig. 4c).

Mal. 4

2. Non-linear lances

Lantsyuga are called non-linear, to the warehouse of which one would like to enter one non-linear element. Non-linear elements are described non-linear characteristics, which do not have a strict analytical view, are determined experimentally and are given in tabular or graphs.

The non-linear elements can be divided into two - and multipolar. Stop three (different types of conductors and electronic triodies) and more (magnetic transformers, rich winding transformers, notebooks, pentodes and in.) Poles, for the help of such stinks, come to the electric stake. Characteristically osoblivіstyu bagatopolyusnih elementіv Je those scho in zagalnomu vipadku їh vlastivostі viznachayutsya sіmeystvom characteristics scho predstavlyayut zalezhnostі vihіdnih characteristics od vhіdnih zmіnnih i navpaki: vhіdnі characteristics buduyut for row fіksovanih value of one of vihіdnih parametrіv, vihіdnі - for row fіksovanih value of one of vhіdnih.

For another sign of classification, non-linear elements can be divided into inertia and non-inertia. Elements are called inertia, the characteristics of which lie in the change of change. For such elements, static characteristics that signify fallowness between change values, Vіdrіznyayutsya vіd dynamіchnyh charac- teristics , which establish vzaєmozv'yazok mizh mitt'vimi zmenennja zminnyh. Elements without inertia are called, the characteristics of which do not lie in the change of change. For such elements, static and dynamic characteristics are taken into account.

The concept of inertial and non-inertial elements is visible: an element can be seen as inertia-free in the allowable (to the fringed animal) frequency range, when it goes beyond the intermediary of such faults, it can move into the category of inertial ones.

Depending on the type of characteristics, non-linear elements with symmetrical and non-symmetrical characteristics are differentiated. A characteristic is called symmetrical, so as not to be deposited directly, they determine її quantities, so that the symmetry of the cob of the coordinate system can be achieved. For an asymmetric characteristic, the mind does not win, so the presence of line element symmetrical characteristics allow in a whole series of variations to analyze the scheme, zdіysnyuchi yogo in the boundaries of one quadrant.

According to the type of characteristic, you can also divide all non-linear elements into elements with unambiguous and ambiguous characteristics. An unambiguous characteristic is named, which has a single value of y and navpak for a skin value of x. In the case of an ambiguous characteristic, the values ​​of x can be two or more than the value of y or not. For non-linear resistors, the ambiguity of the characteristics of the sound is due to the presence of a falling plane, and for non-linear inductive and semi-conductive elements - with hysteresis.

Nareshti, all non-linear elements can be divided into ceramic and non-ceramic. At the sight of non-ceramic ceramic non-linear elements (sound three-and-bagatopole) sweep the keruyuchi channels, changing the voltage, strum, light flow and in. In these, they change their main characteristics: volt-ampere, weber-ampere or coulomb-volt.

Fallow in view of warehouse non-linear elements, they are called non-linear lances.

3. Strength coefficient of the non-linear element

Let's look at the non-linear element (Fig. 5). Let a harmonic signal with an amplitude - A 0 and a significant first harmonic of the output signal be given to the input of the non-linear element.

With this, for input and output signals, you can record the onset of sleep

(1)

de: - vector modulus; is the vector argument.

Let's take a look at the characteristics of the non-linear element - as it is called the complex transfer coefficient of the non-linear element. This characteristic can be measured in the complex plane as well as the complex transmission coefficient of the linear part. If so, the characteristic is to lie in the frequency of the signal and not to fall in the same amplitude. Characteristic - lie in the amplitude of the input signal and not lie in the frequency, since the non-linear element is inertialess. For single-valued characteristics, the iogo value is a real value, and for rich-valued - complex.

Let's take a look at the examples of complex transmission coefficients for the most characteristic non-linear elements -.

1. Non-linear element of the type "pidsilyuvach z obmezhennyam". Lanka characteristics are shown in fig. 6. Similar characteristics to water different type pіdsilyuvalnі і vikonavchі elements of automation (electronic, magnetic, pneumatic, hydraulic and іn.) in the field of great input signals.

If the amplitude of the input input is less than a, then it is more linear without inertia, with which the coefficient is stronger up to a constant value. The phase difference between the input and output is equal to zero, but the characteristic of the non-linear element is symmetrical. The world has an increase in amplitude - the coefficient of strength changes. Some methods of investigating non-linear systems have a characteristic of the reverse complex transfer coefficient of the non-linear element (-1 /). The characteristic is shown in fig. 6.

Since there is no phase sound between the harmonics of the input and output signal, the characteristic changes from the speech wave.

A non-linear element of the "insensitive zone" type. Lanka characteristics are shown in fig. 7. Similar characteristics of the volodyt of a different type of signaling in the region of small input signals.

Mal. 7

If the amplitude of the input signal is adjusted within the range of ± a, then the output signal is equal to zero in the other direction, the output signal is equal to non-zero, since the peaks of the input harmonics are called. There is no phase sound. With large amplitudes of the input signal, the strength coefficient may be permanently significant, i.e., the non-linearity does not rob the source signal on the output signal.

3. Non-linear element of the type "tripositional relay without hysteresis". Characteristics of the lanka are shown in Fig. 8. Tsya characteristic is powerful for relay systems with a return call.

Since the characteristic is unambiguous, there is no phase sound. As the amplitude of the input signal® ¥, then the output signal is converted into a sequence of pulses. With small and large amplitudes, the coefficient k is maly.

Mal. 8

4. Non-linear element type "relay characteristic". Lanka characteristics are shown in (Fig. 9).

of the non-linear element is pointed at fig. 10.

Models of non-linear elements. Models of non-linear elements can be implemented by way of inclusion in the lancet of the operational pilot (at the entrance or in Zvorotniy zv'azok) Nonlinear bipoles. Fallow in view of the characteristics of a two-terminal network and the method of connection, it is possible to implement a non-linear fallow (Fig. 11a, b, c).

Models of non-linear lines are widely used when modeling automatic control systems on EOM.

literature

1. Atabekov G.I., Timofiev A.B., Kupalyan S.D., Khukhrikov S.S. Theoretical foundations electrical engineering (TOE). Non-linear electric lances. Electromagnetic field. 5th ed. View: Doe, 2005. - 432s.

2. Besekersky V.A., Popov O.P. "Theory of automatic control systems". Profesiya, 2003 - 752p.

3. Gavrilov Neliniyni lansyuga in circuit modeling programs. View: SOLON-PRESS, 2002. - 368s.

4. Dorf R., Bishop R. Automation. Modern control systems. 2002 - 832s.

5. Collection of tasks on the theory of automatic regulation and curing / Edited by V. A. Besekersky. - M .: Nauka, 1978.

non-linear element

non-linear element name the element, the parameters of which lie as it flows through the new struma, or as the voltage applied to the new one. Typical non-linear elements are a diode and a transistor. Їх parameters іttotno change during injection working streams і voltage .

Previously, linear elements were looked at, the parameters of which should not lie in the stream, which flows and applied voltage. For example, in the working range of voltage and streams, such radio elements, like resistors and capacitors, are driven by linear elements. On fig. 3.1 induction of current-voltage characteristics (CVC) of non-linear (1) and linear (2) resistors. Only when small voltages are injected, non-linear elements can be replaced by linear elements. For example, the characteristics of diodes and transistors are linearized, thus adding voltage DU < 0,1 В.

It is significant that the number of linear and non-linear elements are victorious parametric elements, the parameters of which lie at the same time . Acts of power of parametric elements are close to the power of non-linear elements, so in practice the change of parameters is driven by the supply of additional signals to the parametric element, and the parameters of the parametric elements as a result appear to be fallow in terms of voltage or streams in lances.

As in lances, krim of linear elements, there are non-linear resistors and (or) non-linear capacitors and (or) non-linear coils, then such lanciug called non-linear . Processes in such a quantity in a wild manner are described by non-linear differential equations. There are no deep analytical methods for solving these problems. As a rule, numbers are based on EOM for additional numerical methods. For example, for the help of numerical methods, non-linear lances are analyzed in circuit modeling programs.

Main things, be powerful non-linear lancet, Not obov'yazkovo vivchati, folded and folded non-linear differential alignment. The great power of a non-linear lance will be manifested in simple lances, which can be avenged by one non-linear resistor. Before speech, simple non-linear lancers are most often victorious in radio electronics. For their analysis, one of the analytical methods is used - trigonometric formula method .

According to the method of trigonometric formulas, the current-voltage characteristic of a non-linear resistor is approximated by a polynomial:

de coefficient buti(i = 0, 1, 2, …, n) Lie in the mind of the VAC.

Let the harmonic voltage be reported to the non-linear element. Substituting this voltage in formula (3.1), we take away the strum that flows through the non-linear element:

Vicorist in trigonometric formulas:

let's rewrite the viraz for the struma at the sight of the sum of constant folding and harmonics of the struma with multiple frequencies (in the view of the Fur'є series):

From the analysis of virase (3.2), the power of non-linear circuits is evident - to generate new frequencies in the spectrum of the output signal, which were not in the spectrum of the input signal. The number of the most important harmonic in the spectrum of the output signal determines the degree of the approximating polynomial.

Apparently, the sum of harmonics of different, ale multiple frequencies produces a periodic signal, the form of which is reminiscent of the form of a harmonic wave. Otzhe, in non-linear stakes in a general way waveform is generated . A harmonic signal can become inharmonious, a tricot signal can become trapezoidal, etc.

On fig. 3.2 shows the spectrum of the input (Fig. 3.2, but) I output (Fig. 3.2, b) Signals of a non-linear lance, described by a polynomial of the tertiary degree. Yak Bachimo, at the exit signal appeared on
standing up to compose, as well as a friend and third harmonica. It is significant that the creation of new harmonics, which the input signal did not have, does not violate the laws of causality and energy conservation.

New frequencies, constant storage and other harmonics, can be taken for an additional parametric element - an analog multiplier, supplying a new keying harmonic signal with a frequency exactly equal to the frequency of the input voltage applied to the element.

The power of non-linear lances to generate new harmonics and call-to-reap the shape of the signal is widely victorious in radio electronics when combined with different devices. Let's take a look at the actions of these outbuildings, most often used in practice.

non-linear pidsiluvach

non-linear pidsiluvach - tse pіdsilyuvach on the working transistor in the non-linear mode, scho can increase the coefficient brown dії(Figure 3.3).

The characteristic feature of the circuit is the presence of a constant voltage displacement on the base of the transistor. Therefore, the transistor, when the input signal is present, will be closed, and the second constant stream of the base, the collector and the emitter will be practically zero. The transistor will only vibrate when a positive voltage is applied that is large in terms of the amplitude of the input voltage (the amplitude is due to but more than 0.1 V). It is significant that in some non-linear podsiluvachs it is possible to vikorate the tension of the zsuva. At this moment, the voltage vibrates either in a flickering, or in a small wave.

The work of a non-linear substation is described using additional flow and voltage diagrams (Fig. 3.4). On fig. 3.4, but the transmission I–V characteristic of the transistor is shown. Dependence of the voltage on the base of the transistor is shown in fig. 3.4, in. This harmonic voltage was applied through a different capacitor from the input voltage to the cascade. Yak bachimo, only positive napіvkhvili vkhіdnoї naprugi vіdkrivayut transistor.

The deposit leads to the reservoir stream every hour (Fig. 3.4, b) Otriman based on the curves of Fig. 3.4, but i 3.4, in. The sequence of prompting is shown by arrows. Collector strum, flowing through the resistor R N(Div. Fig. 3.3), creating a change in voltage on the collector of the transistor (Fig. 3.4, G). It is significant that when the collector struma increases, the voltage on the collector changes, so the voltage drop on the resistor increases R N. This explains the effect of phase inversion of the signal, which is due to the OE stages.

The shape of the voltage on the collector of the transistor is strictly controlled by the shape of the harmonic input signal. In these curves of the signal form, the power of non-linear lances is manifested, they are connected to the vibrations in the stream of the transistor of additional harmonics. For a change, create a two-stroke scheme. The circuit has two transistors of various types, which are used in the heat of the moment. Why is it a transistor type p-r-p vіdkrivaєtsya when applying a positive napіvhvili naprug, then the other, r-p-r-transistor, turns on when a negative voltage is applied to the input voltage.

Basically the achievement of a non-linear spy - zbіlsheniy coefіtsієnt korisnoї ї ії (KKD). The improvement of the CCD is explained by the fact that for a part of the hour the transistor in the working non-linear substation is shut down and does not save energy from the life.

Non-linear subsilience vicorists are found in self-oscillators (for example, in impulse dzherels of life of the EOM), in subsidiaries of tension (for example, in pressure subsidiaries sonic frequency), in the capacity of pіdsilyuvachіv-medzhuvаchіv, in transmissions, etc.

frequency multiplier

frequency multiplier - the price of non-linear extension, the frequency at the output is a few times higher than the frequency of the input signal. The frequency multiplier has the power of non-linear elements - to generate harmonics with frequencies that are multiples of the frequency of the input signal.

The simplest frequency multiplier circuit will be based on the resonant booster circuit (Fig. 3.5). When a harmonic signal with a large amplitude is applied to the input cascade, harmonics with frequencies are blamed in the transistor collector stream, in total the number of times the frequency of the input signal is shifted. The resonant circuit (navantage of the cascade) is tuned to the frequency of one sound in
outgoing harmonics. At this frequency in the circuit, resonance is generated, and at the output cascade there is a harmonic voltage, the frequency of which in the whole number of times is greater than the frequency of the input signal. It is significant that the swag of the passage of the contour is due to be small, so that only one harmonica was seen.

Razrahunok output voltage of the frequency multiplier is carried out according to the formula:

de - complex opir parallel kolivalny contour, - amplitude n th harmonics of the transistor collector strum. With the exact tuning of the parallel circuit to the frequency, harmonics are seen to be taken away: so the reactive support of the inductance coil is compensated by the reactive support of the capacitor to the circuit.

The frequency multiplier can be doubled by victorious parametric lance (analogue multiplier) and giving a harmonic signal at the same time to the input of the multiplier. Frequency multipliers are widely used in computers to extract more clock frequencies when using a low-frequency setting of a quartz oscillator.

Non-linear elements, as it has already been pointed out, are all conductors and electronic accessories that can be processed with great input signals. on the low frequencies Equivalent circuits of these devices can be represented in terms of resistive non-linear elements, the features of which are determined by the current-voltage characteristics, i.e., by the streak deposits in the applied voltage hour . Therefore, resistive non-linear elements are also called inertia-free non-linear elements.

to finish off high frequencies the characteristics of the non-linear elements are influenced by the fallow frequency. Tsya zalezhnistnost umovolena:

the sumirnist hour, which is rubbed on the nose through the attachment and the process of recombination, with a period of pouring in and negokolivan. Yakshcho trivality of these processes composing a part of the period of coliving, the external strum will fit in phase with the input signal, i.e., the attachment will become inertial. Inertia

introduction of additional frequency-deposited reactivities into the equivalent circuit.

Static characteristics of electronic accessories (stinks are fast stream) Dosit again to characterize the device only in the range of quiet frequencies, de yogo can be made resistive, i.e., bezіnertsіynim. On fig. 2.1 induction of current-voltage characteristics of typical non-linear resistors and їх smart designation: Conductor (a) and tunnel (b) diodes, bipolar and field effect transistors, Dinistora The characteristics of vacuum tubes (diodes, triodes, tetrodes, pentodes) are similar to those shown in fig.

Characteristics are unambiguous and rich. In unambiguous skin values, the argument shows a single value of the function for given values ​​of the parameters (Fig. 2.1 a, c-e). In other cases, one value of the same value has a different value (Fig. 2.16, e). It is significant that the hysteresis characteristics are richly significant.

Non-linear elements are subdivided into ceramic and non-ceramic. Before the first ones, there are rich electrical accessories that can separate the input and output (transistors, grid electronic or ion accessories), the shards in them can control the output characteristic of the change in the input. Non-ceramic and two-electrode attachments (diodes).

If you see a deak (straight), then the fallowness is called a return. So, the direct characteristics of the reversible

Attachments, which can be used for falling poles on the volt-ampere characteristics, de pokhіdnі or called attachments with a negative support. Depending on the fact that the shape of the characteristics of the attachment is guessed, two types of negative supports are distinguished: a support-type, the type of current-voltage characteristics of which is similar to that shown in Fig. 2.16; stinks are called negative supports, keratinized by tension, shards of tension itself unequivocally indicate the mode of their work; S-type support, volt-ampere characteristics of which are similar to fig. 2.1e; stinks are called negative supports, keratinized strums, so their regime is clearly defined as flowing through the attachment as a strum. Yakscho in fig. remember the coordinate axes, then the characteristic of which accessory will take a figurative form. Differential support for elements of both types - negative on plots and positive for their boundaries. Attachments such as tunnel diodes, Gunn diodes, lamps with the presence of a dynatron effect in them; accessories-type - devices ion (gastrons, neon lamps) and heaters (dinistry, thyristors, avalanche-transit diodes) accessories.

For the development of schemes with non-linear elements, graphic, analytical and machine methods are used. The advantage of graphic methods is the possibility of a final designation of streams and voltages in the circuit when given її parameters. However, the graphical solution does not allow the establishment of analytical deposits between changing parameters in the annex and the values ​​of iogo strums and voltage, the determination of the optimal values ​​of the parameters, etc. when analyzing folding schemes especially with high accuracy, analytical solutions appear either cumbersome or practically impractical. Then stop the machine methods of follow-up.

Significantly graphically (Fig. 2.2) strum, which flows through a resistive non-linear element, under the voltage

Vykoristovuvaniya for this method of projections field in the foot: on the graph we mark the values ​​\u200b\u200bof i in different moments and then, according to the current-voltage characteristics, it is known that the values ​​of the stream and the influence of their plane

To check the rest of Pobudov’s fallow, manually start the designated struma at the moment, depending on the maximum, minimum and average values ​​of the stress and only then know the intermediate value of the struma. When the harmonic signal (2.1) is injected, the strums appear as a periodic function and frequency of a slightly different form.

yakscho staleness U(I) or I(U linear i yoga opir R permanently ( R = h onst ) , then such element name linear (LE) , A electric lance, what is folded only with linear elements - linear electric lance .

VAC of the line element symmetrical i is a straight line that passes through the cob of coordinates (Fig. 16, curve 1). In this order, Ohm's law is victorious in linear electric lances.

yakscho staleness U(I) or I(U) Whether there is an element of an electric stake NOT linear, and yogo opir lie in the strum in a new one, or the tension on yogo visnovki ( R ≠ h onst ) , then such element name NOT linear (NOT) , And the electric lansyug when present I would like one non-linear element - non-linear electric lance .

CVC of non-linear elements indirectness, and sometimes they can be non-symmetrical, for example, for heating fittings (Fig. 16, curves 2, 3, 4). In this manner, in non-linear electric lances, the fallowness between the stream and the tension do not support Ohm's law.

Mal. 16. CVC of linear and non-linear elements:

curve 1- VAH LE (resistor); curve 2- VAH NE (lamp fired with a metal thread); curve 3- VAH NE (lamps of roasting with a hollow thread;

curve 4- VAC NOT (napіvprovіdnikovogo diode)

butt line element є resistor.

butts non-linear elements to serve: heating lamps, thermistors, conductive diodes, transistors, gas discharge lamps, etc. Smarter recognition NOT shown in fig. 17.

For example, with an increase in the struma, which flows through the metal threads of the heating of an electric lamp, the heating increases, and also, the growth of the opir. In this rank, opir lampi rozzharyuvannya is not fast.

Let's look at the attacking butt. The table with the values ​​of the support elements for different values ​​of the struma and the voltage is given. How does the table support a linear, how a non-linear element?

Table 3

Table 4

Give advice on nutrition, on which of the graphs of images is Ohm's law? To which element does this schedule apply?

1 2 3 4

What can you say about charts 1,2 and 4? What elements characterize these graphs?

The non-linear element at any point of the VAC is characterized by a static support, which supports the pressure to the struma, which supports this point (Fig. 18). For example, for a point but :

.

A non-linear element with a static support is characterized by a differential support, for which it is reasonable to assume an infinitely small or even a small increase in the voltage ΔU to a significant increase in ΔI (Fig. 18). For example, for a point but VAC can be written

de β - cut nakhily dotichny, drawn through a point but .

These formulas form the basis of the analytical method of analysis of the simplest non-linear lines.

Let's take a look at it. As for the injection of a static opir of a non-linear element at a voltage of U 1 = 20 V, 5 Ohm, then the power of the stream I 1 warehouse ...

Static support of a non-linear element at strum 2 A warehouse ...

Visnovok on the third meal: separate the linear and non-linear elements of the electric stake. Non-linear elements do not have Ohm's law. Non-linear elements are characterized in the skin point of the CVC by a static and differential support. Non-linear elements can be addressed with heaters, gas discharge lamps and heating lamps.

Nutrition number 4. Graphical method for the analysis of non-linear

electric lancers (15th century)

For the design of non-linear electric lines, a graphical and analytical method of design is required. The graphic method is simple and easy and can be looked at more clearly.

Let dzherelo EPC E with internal support r 0 live two sequentially connected non-linear elements or a support HC1 і Hc2 . in the house E , r 0 , VAC 1 HC1 and VAC 2 Hc2. It is necessary to designate a strum in lancius I n

On the back, I will be the CVC of the linear element r 0 . Tse is straight, scho to pass through the cob of coordinates. The stress U, falling on the contour support, is determined by the

To encourage fallow U = f ( I ) , It is necessary to fold graphically VAC 0, 1 і 2 , Summative ordinates, one abscissa, then another, etc. take the curve 3 , What is the CVC of the whole lancer. Vicorist qiu CVC, we know the strum in the lance I n , What is the voltage U = E . Potim, vikoristovuyuuchi know the value of the struma, according to the CVC 0, 1 і 2 we know the voltage U 0 , U 1 , U 2 (Fig. 19).

Let dzherelo EPC E with internal support r 0 live two parallel connected non-linear elements or a support HC1 і Hc2 , VAC of any of them. It is necessary to mark the strum in the tails of the lanceug I 1 і I 2 , The voltage drop on the internal support of the dzherel and on the non-linear elements.

I will be VAC I n = f ( U ab ) . For which warehouse graphically CVC 1 і 2 , Summative abscissa, depending on one ordinate, then another ordinate, etc. We will be the VAC of the entire lance (curve 0,1,2 ). For which warehouse graphically CVC 0 і 1,2 , Podsumovuyuchi ordinates, scho vіdpovіdat sing abscissa.

Vicorist qiu CVC, we know the strum in the lance I n , Vіdpovіdny pruzі U = E .

vicorist VAC 1,2 , Vyznajmo the voltage U ab , Vіdpovіdne to the known current I n , I internal voltage drop U 0 , Vіdpovіdne tsomu current. Potim, vikoristovuyuchi CVC 1 і 2 we know shukani strumi I 1 , I 2 , Vidpovidnі napruzі U ab (Fig. 20).

Let's take a look at the steps.

With the subsequent connection of non-linear supports with the characteristics R 1 and R 2, which is the characteristic of the equivalent support R E ...

go below characteristics R 1

pass the characteristics R 1

pass, showing the characteristics of R 1

go below characteristics R 2

With the subsequent connection of a linear and non-linear support with characteristics a and b, the characteristic of an equivalent support ...

go below characteristics

pass the characteristics

pass, showing the characteristics of a

go below characteristics b

Visnovok on the fourth meal: non-linear electric lances of the post-strumu form the basis of electronic lances. I use two methods of analysis: analytical and graphic. The graphical method of analysis allows you to simply assign all the necessary parameters of a non-linear lance.

Lantsyuga are called non-linear, to the warehouse of which one would like to enter one non-linear element.

Non-linear elements are called, the parameters of which lie in the value of i (or) directly connected with these elements of the change (voltage, struma, magnetic flux, charge, temperature, light flux and in.). Non-linear elements are described by non-linear characteristics, which do not have a strict analytical view, are determined experimentally and are set in tables or graphs.

Non-linear elements can be divided into two- і rich polarity. Stop three (different types of conductors and electronic triodies) and more (magnetic transformers, rich winding transformers, notebooks, pentodes and in.) Poles, for the help of such stinks, come to the electric stake. Characteristically osoblivіstyu bagatopolyusnih elementіv Je those scho in zagalnomu vipadku їh vlastivostі viznachayutsya sіmeystvom characteristics scho predstavlyayut zalezhnostі vihіdnih characteristics od vhіdnih zmіnnih i navpaki: vhіdnі characteristics buduyut for row fіksovanih value of one of vihіdnih parametrіv, vihіdnі - for row fіksovanih value of one of vhіdnih.

For another sign of classification, non-linear elements can be divided into inertiaі inertialess. Elements are called inertia, the characteristics of which lie in the change of change. For such elements static characteristics, which signify the fallowness between the fluctuating values ​​of the change, dynamic characteristics, scho establish vzaєmozv'yazok mizh mittevimi zmenennja zminnyh. Elements without inertia are called, the characteristics of which do not lie in the change of change. For such elements, static and dynamic characteristics are taken into account.

The concept of inertial and non-inertial elements is visible: an element can be seen as inertia-free in the allowable (to the fringed animal) frequency range, when it goes beyond the intermediary of such faults, it can move into the category of inertial ones.

In the fallow, in view of the characteristics, the non-linear elements of the symmetricalі asymmetrical characteristics. A characteristic is called symmetrical, so as not to lie in a straight line, they assign її quantities, so that the symmetry of the cob of the coordinate system is possible:. For an asymmetric characteristic, Umov does not win, so . The presence of a non-linear element with a symmetrical characteristic allows in a whole series of variations to analyze the circuit, which works within the boundaries of one quadrant.

According to the type of characteristic, you can also divide all non-linear elements into elements unequivocallyі ambiguous features. An unambiguous characteristic is named, which has a single value of y and navpak for a skin value of x. In the case of an ambiguous characteristic, the values ​​of x can be two or more than the value of y or not. For non-linear resistors, the ambiguity of the characteristics of the sound is due to the presence of a falling plane, for which, and for non-linear inductive and semi-synthetic elements - with hysteresis.

Nareshti, all non-linear elements can be divided into kerovaniі non-ceramic. At the sight of non-ceramic ceramic non-linear elements (sound three-and-bagatopole) sweep the keruyuchi channels, changing the voltage, strum, light flow and in. In these, they change their main characteristics: volt-ampere, weber-ampere or coulomb-volt.

Non-linear electric lances of post-strumu

The non-linear power of such lances indicates the presence of non-linear resistors in them.

In connection with the voltage of non-linear resistors, the direct proportionality between the voltage and the stream cannot be characterized by one parameter (one value). Spivvіdnoshnja mizh tsimi values ​​in zagalny fallow fall not only in vіd їх mittevikh meaning, Ale і vіd pokhіdnih i іntegraіv per hour.

Parameters of non-linear resistors

Zalezhno in the minds of the robotic non-linear resistor and the nature of the task, they separate the static, differential and dynamic support.

Since the non-linear element is inertia-free, then the vins are characterized by the first two of the overriding parameters.

static support increase the tension on the resistive element until it flows through the new struma. Zocrema for point 1 I–V characteristic in fig. one

.

pid differential support it is reasonable to consider an infinitely small increase in voltage to a similar increase in struma

.

Significantly, that the non-ceramic non-linear resistor has a constant, or you can take a negative value (plot 2-3 VAC in Fig. 1).

At the time of the inertial non-linear resistor, the understanding of the dynamic support is introduced

depends on the dynamic CVC. Fallow in the form of a change of change, for example, a struma, it may change not only the value, but also the sign.

Methods for rozrahunka of non-linear electric lances of a post-strum

The electric mill of the non-linear lances is described on the basis of the laws of Kirchhoff, which may have a wild character. With any trace of memory, scho for non-linear lancers, the principle of imposition is unacceptable. In connection with this method, the analysis method, developed for linear circuits on the basis of Kirchhoff's laws and the overlay principle, does not expand on non-linear lances in a casual manner.

There are no formal methods of rozrahunka of non-linear lancers. Vіdomi priyomi і ways to find different possibilities and areas of congestion. In a wild way, when analyzing a non-linear lance, the system of non-linear alignments can be overcome by offensive methods:

• graphic;
• analytical;
• graph-analytical;
• iterative.

Graphic methods of rozrahunka

When vikoristanny tsikh methods zavdannya vyrishuetsya path graphic pobudov on the square. With this, the characteristics of all the lances of the lancer should be written in the function of one slanderous argument. Zavdyaki tsomu the system of equalization is reduced to one non-linear equalization with one unknown. Formally, during the rozrahunka, the lancers are separated with the last, parallel and zmishanim half-shells.

a) Lantsyugi with the last z'ednannyam resistive elements.

In the case of a sequential connection of non-linear resistors, a strum is accepted as a wild argument, which flows through the sequentially connected elements. Rozrahunok held in such a sequence. After setting the I–V characteristic of okremi resistors in the system of Cartesian coordinates, the resulting accumulation will be . Then, on the axis of the stress, a point is added, which is in the reverse scale of the given value of the stress at the entrance of the lancet, so that the perpendicular is added to the peretina from the fallow. From the point of the cross line of the perpendicular to the curve, it descends orthogonal to the entire stream - the point of crossing the fluted stream in the lane is removed, according to the known value of any of the alternate fallows, the stresses on the okrem are determined resistive elements.

Zastosuvannya zaschennoї tehniki іlustruyut graphіchnі pobudovi in ​​fig. 2b 2, a.

A graphical solution for the last non-linear lance with two resistive elements can be carried out by another method - by the method of retining. In this case, one of the non-linear resistors, for example, with the CVC in Fig. 2, a, is taken into account by the internal support of the dzherel s EPC E, and the other one - by the voltage. Todі on the basis of spivvіdnoshennia point a (div. fig. 3) the crossover of the curves i determines the robotic lancer mode. The curve will be a way to see the abscissa VAC s EPC E for different values ​​of the struma.

Vikoristannya given method most rationally with the last connection of linear and non-linear resistors. In this case, the linear resistor is taken for the internal support of the dzherel, and the linear CVC of the rest will be at two points.

b) Lanziugs with parallel connections of resistive elements.

When connecting non-linear resistors in parallel, a voltage is applied in parallel to the connected elements in the capacity of a wild argument. Rozrahunok held in such a sequence. After setting the I–V characteristic of okremi resistors in the system of Cartesian coordinates, the resulting accumulation will be . Potіm on osі strumіv vіdkladaєtsya point vіdpovіdna in obranomu masshtabі zadanіy velichinі Strum dzherela on vhodі lantsyuga (at nayavnostі on vhodі lantsyuga dzherela naprugi zavdannya virіshuєtsya vіdrazu Shlyakhov vіdnovlennya perpendicular of points vіdpovіdnoї Target napruzі dzherela to peretinu of CVC) of yakoї vіdnovlyuєtsya perpendicular to the peretina with fallow land. From the point of the crossbar of the perpendicular to the curve, it drops orthogonal to the entire voltage - the point of the voltage is removed on the non-linear resistors, according to the known value of some of the fallows, streams in the bushes with the same resistive elements are indicated.

The choice of this technique is illustrated graphically in fig. 4b 4, a.

c) Lances with a series-parallel (zmishanim) connection of resistive elements.

1. The examination of such lancets is carried out in the following sequence:

Pochatkov's circuit is connected to the lance with the last connection of resistors, for which there will be a resultant CVC in parallel with the connected elements, as shown in paragraph b).

2. To carry out the analysis of the otrimanoi circuit with the last connection of resistive elements (div. Paragraph a), on the basis of which then the streams are shown at the output parallel pins.

Two node method

For lancers who want to eliminate two knots or get to such ones, you can use the two knots method. With the help of a graphical method of implementation, the method of wine polygaє in the attack:

There will be graphs of strum fallows in all i-th veins in the function of the main value - the stress between nodes m and n, for which the skin from the ventral curves is shifted along the axis of the stress parallel to itself, galusi, and then mirror-like the perpendicular, inspired at this point.

It appears that in some point the first Kirchhoff law is graphically implemented . Vіdpovіdnі danіy dоchtsі strumi є vіrіshennyam zavdannya.

The method of two nodes can be implemented in another version, which is considered as a lesser number of graphic prompts.

Like a butt, we can look at the lance in fig. 5. For it, we can see the voltages on the resistive elements in the function:

;

(1)

.

(3)

We gave a strum, which flows through one of the resistors, for example, from the other gypsum, and rozrakhovuєmo, and then according to the selections (1) and (3) it is known and і according to fallows і - vіdpovіdnі їm і і etc. The results are calculated in Table. 1, in the remaining column, which is the sum of the strums