What is a nonlinear element. Nonlinear elements. Nonlinear electric chains

If a addiction U.(I.) or I.(U. linene and his resistance r constantly ( R. \u003d S. onst. ) , then such element Call linear (LE) and electrical chain consisting only from linear elements - linear electrical chain .

Wah linear element symmetric And it is a direct, passing through the origin of the coordinates (Fig. 16, curve 1). Thus, the Ohm law is performed in linear electrical circuits.

If a addiction U.(I.) or I.(U.) any electrical circuit element not linear and its resistance depends on the current in it or voltage at its conclusions ( R. ≠ S. onst. ) , then such element Call not linear (NE) , and electrical circuit with at least one nonlinear element - nonlinear electrical chain .

Wah nonlinear elements nonmemolinene, and sometimes can be asymmetrical, for example, in semiconductor devices (Fig. 16, curves 2, 3, 4). Thus, in nonlinear electrical circuits, the dependence between the current and voltage does not obey Ohm's law.

Fig. 16. Linear and nonlinear elements:

curve 1. - LE (resistor); curve 2. - NE (incandescent lamps with metal thread); curve 3. - NE (incandescent lamps with coal thread;

curve 4. - Wah NE ( semiconductor diode.)

Example linear element is resistor.

Examples nonlinear elements serve: Incandescent lamps, thermistors, semiconductor diodes, transistors, gas-discharge lamps, etc.Symbol Na is shown in Fig. 17.

For example, with an increase in the current flowing through the metal thread of incandescent of the electrical lamp, its heating increases, and therefore, its resistance increases. Thus, the resistance of the incandescent lamp is non-permanently.

Consider the following example. Tables with resistivity values \u200b\u200bof elements at different current and voltage values \u200b\u200bare given. Which table corresponds to a linear, what nonlinear element?

Table 3.

R., Oh.

Table 4.

R., Oh.

Answer the question, what of the charts is the law of Oma? What element does this schedule match?

1 2 3 4

And what can be said about schedules 1.2 and 4? What elements characterize these graphics?

The nonlinear element at any point of the WAH is characterized by a static resistance, which is equal to the ratio of the voltage to the current corresponding to this point (Fig. 18). For example, for point but :

.

In addition to static resistance, the nonlinear element is characterized by differential resistance, under which the attitude of an infinitely small or very small increment of the voltage ΔU to the corresponding increment Δi is understood (Fig. 18). For example, for point but Wah can be recorded

where β - the angle of tilt the tangent spent through the point but .

These formulas constitute the basis of the analytical method of calculating the simplest nonlinear chains.

Consider examples. If the static resistance of the nonlinear element at a voltage U 1 \u003d 20 V is 5 ohms, then the current strength I 1 will be ...

Static resistance of the nonlinear element at a current 2 A will be ...

Conclusion on the third issue: the linear and nonlinear elements of the electrical circuit differ. In nonlinear elements, the Ohm law is not performed. Nonlinear elements are characterized in every point of the Wah static and differentiated resistance. Nonlinear elements include all semiconductor devices, gas-discharge lamps and incandescent lamps.

Question number 4. Graphic method for calculating nonlinear

electrical chains (15 min.)

To calculate nonlinear electrical circuits, graphic and analytical calculation methods are applied. The graphic method is simpler and it we will consider in more detail.

Let the source of EMS. E. with internal resistance r. 0 Has two successively connected nonlinear elements or resistance Ns1 and Ns2. . Known E. , r. 0 , Wah. 1 NS1 and Wah. 2 Ns2. It is required to determine the current in the chain I. n.

First, we build a linear element r. 0 . This is a straight line passing through the origin of the coordinates. The voltage U falling on the contour resistance is determined by the expression

To build addiction U. = f. ( I. ) , it is necessary to fold graphically 0, 1 and 2 , summing up ordinates corresponding to one abscissa, then another, etc. We get a curve 3 representing the battle of the entire chain. I use this flush, we find a current in the chain I. n. Resizing voltage U. = E. . Then, using the found current value, via 0, 1 and 2 We find the desired stress U. 0 , U. 1 , U. 2 (Fig. 19).

Let the source of EMS. E. with internal resistance r. 0 nourishes two parallel connected nonlinear elements or resistance Ns1 and Ns2. Who are known. Required to determine the current in the branches of the chain I. 1 and I. 2 , voltage drops on the internal resistance of the source and on nonlinear elements.

Build Wah. I. n. = f. ( U. aB ) . For this we fold graphically 1 and 2 , summing the abscissa corresponding to one ordinate, then another ordinate, etc. We are building the entire chain (curve 0,1,2 ). For this we fold graphically 0 and 1,2 , Summing up the orders corresponding to certain abscissions.

I use this flush, we find a current in the chain I. n. Tension U. = E. .

I use Wah. 1,2 , Determine the voltage U. aB Found current I. n. , and internal voltage drop U. 0 corresponding to this current. Then, using Wah 1 and 2 We find the desired Toki. I. 1 , I. 2 appropriate voltage U. aB (Fig. 20).

Consider the following examples.

With a consecutive connection of nonlinear resists with the characteristics R 1 and R 2, if the characteristic of the equivalent resistance R e ...

will be lower than the characteristic R 1

it will take higher characteristics R 1

it will pass, corresponding to the characteristic R 1

will be lower than the characteristic R 2

With a consistent connection of linear and nonlinear resistances with characteristics A and B, the characteristic of the equivalent resistance ...

will be below the characteristics A

will be higher than the characteristics of

will pass, corresponding to the characteristic A

will be below the characteristics b

Conclusion on the fourth question: nonlinear DC electrical circuits make up the basis of electronic circuits. There are two methods for their calculation: analytical and graphic. The graphical method of calculation makes it easy to determine all the necessary parameters of the nonlinear chain.

Content. Nonlinear elements. Saturation of magnetic materials. Segroesoelectrics, varistors and posistors. Nonlinear resistors. Semiconductor diode and its flock. The concept of bipolar transistors and thyristors. Linear voltage stabilizer. The principle of action of a field transistor and a bipolar transistor with an insulated shutter (IGBT).

The values \u200b\u200bof the elements R, C, L were introduced as coefficients between the current and voltage (R), the charge and voltage (C), as well as the magnetic stream and current (L). Next, the generalized law of Oma was formulated from these relations.

When considering the simplest tasks, the assumption was made that these values \u200b\u200bdo not depend on the elements of electromagnetic energy flowing according to these elements. And we are greatly enjoyed with the so-called linear elements and even picked up the corresponding "linear" components.

However, there are no linear components in nature!

They may have approximately linear parameters only in a certain current and voltage interval. Any substance falling into the effect of electromagnetic fields, one way or another, changes its structure and, accordingly, its physical characteristics, namely the specific resistance, dielectric and magnetic permeability and even a geometric shape. Therefore, the parameters of the components made from these materials are changed, since R \u003d RL / S; C »ES / L; L »MS / L. If these changes are not essential, we are talking about the linearity of the elements and the corresponding components. Otherwise, it is necessary to take into account these changes and then should talk about nonlinear elements and components.

Hugo nonlinear elements in substitution schemes have the following form:

nonlinear resistor

magnetic Country Inductive Coil

nonlinear Condenser - Varicap

Nonlinear elements are quite widely used in electrical circuits in order to change the waveform, in other words, to excite or absorb certain harmonics, from which the signal is made.

From a mathematical point of view, in this case, the coefficients composed of R, C, L depend on unknown parameters (current and voltage), and energy equations drawn up by Kirchhoff's rules become nonlinear With all the consequences for calculations.

The most common methods of their solutions are:

- approximationwhen the known non-linear dependence of the value of the element from the current or voltage is approximated by the sections of linear functions and is obtained for each of them solutions of linear equations;

- graphic methodwhen equations decide graphically using

known nonlinear graphic dependencies of the element from the current or voltage;

- machine methodWhen a non-linear dependence of the element value from current or voltage is approximated by a model mathematical function and solve integro-differential nonlinear equations with numerical methods.

nonlinear inductance In electrical engineering use weber-ampere characteristicswhich are similar to hysteresis curves VN for ferromagnetic materials that love to apply physicists. If on Weber-ampere characteristic l \u003d dy / di, then on VN-curves m \u003d db / dh, but y \u003d nbs, a h "i / r. Sometimes use volt-second characteristic, T. K. Y \u003d òUDT.

In approximation, this characteristic is usually divided into parts: until saturation is a straight line with a slope. m \u003d.dB /dH, and after saturation when Vm This is a straight line with m \u003d 1.. Values \u200b\u200bof residual magnetization INr. and coercive power Ns. The area occupied by the hysteresis loop, i.e., active losses for magnetization. Therefore, in most cases, they can be taken into account in the chain of the resistive element and exclude from the approximation of Weber-ampere characteristics.

The mode of operation of inductance coils with linear characteristics is chosen within large values \u200b\u200bof M or L. In this area, such magnetic devices are operating as throtters for the accumulation of magnetic energy, transformers for transmitting power through the magnetic connection of coils, as well as electric motors. At the same time, the non-linearity effect of magnetic materials is widely used to create magnetic amplifiers, ferroresonance stabilizers and even magnetic key elements in which magnetic materials are used with the so-called rectangular magnetic characteristic, where M can reach the values \u200b\u200bof 50 or more. Currently, there are mainly 3 types of magnetic materials in induces of inductance: electrotechnical Steel, amorphous iron (metaglass) and ferriteswith very diverse hysteresis curves.

Nonlinear inductors were historically created first due to the availability and low cost of magnetic materials, as well as the simplicity of their manufacture. They differ, first of all, with their reliability, but have large scale characteristics, and in connection with this high inertia. Losses on the magnetization and active losses for heating windings also represent a serious problem, especially in power electrical engineering. Therefore, at present, the use of nonlinear inductors is limited.

To represent addiction nonlinear tank Used pendant-voltage Characteristics, since C \u003d DQ / DU.

They are similar to ferromagnetic webm-ampere characteristics, only here is present the dielectric constant E \u003d DD / DE, where D is an electrical induction or an electrical displacement.

The most interesting dielectric to create nonlinear capacitors are segnetoelectrics, such as Segnetov Salt (Potassium Sodium Wincit), Barium Titanate, Bismuth Titanate, etc. due to the domain structure of electric dipoles, they possess low voltages High dielectric constant with E "1000, which, with raising voltage, decreases, similarly to magnetic permeability in ferromagnets. Therefore, in foreign literature they got a name ferroelectrics. These materials are widely used to create such linear capacitive elements, such as ceramic capacitors with a high specific density of the electrical energy, where they work in the unsaturated area of \u200b\u200bthe coil-voltage characteristic. Nonlinearity is used to create capacitors with a variable capacity, varicondwho have narrow use.

In a variable field in ferroelectrics, a change in the direction of the electric moment of dipoles, which are linked to large domains placed in crystal structures. This leads to a change in the geometric sizes of the crystal, the so-called effect electrotric. In magnetic materials there is a similar effect magnetostrictionBut it is difficult to use it due to the presence of an external winding. In some groups of ferroelectric crystals, similar to electrical processing effects are observed. it direct piezoelectric The effect is the appearance of an electric field (polarization) in a crystal in its mechanical deformation, and back - Mechanical deformation when the electric field appears. These crystal materials are called piezoelectrics, And they received extremely large use. The direct effect is used to obtain high voltages, in primary mechanical force converters (for example, microphones, pickups in sound mechanical recording systems), etc. Reverse effect is used in sound and ultrasonic emitters, in ultra-positioning systems (positioner movement of the hard disk head), etc. Both effects are used when creating resonant quartz generators where the dimensions of the crystals are selected in such a way that mechanical oscillations are in resonance with electrical. With a very high quality frequency of such a system, the stability and accuracy of the generator frequency setting are ensured. Two such crystals having a sound bond can transmit electrical power without electroplating due to which they are called piezotransformers.

The domain structure of both electrical and magnetic dipoles is disintegrated at a certain temperature, called the Curie point. In this case, the phase transition occurs and the conductivity of the ferroelectric is significantly changing. On this basis act posistoryIn which, with additional doping of the material, you can install a specific point of Curie. After reaching this temperature, the rate of increase of resistance can reach 1 com / hail.

In essence, it nonlinear resistorwhich has an S-shaped or "key" volt-ampere characteristic (WA).

That is, this element can work as an electrical key controlled by the passing current or external temperature.

Posistors are widely used to protect against current overloads in telephone analog networks, as well as to reset the magnetic energy from coils when they are disconnected, smooth start of motors, etc. Quite interesting use they found as regulated fuel elements in fan heaters in which the element itself is located Vastly at a constant temperature, and the electric power consumed is automatically maintained equal to the heat output. That is, the fan speed can be controlled by thermal power of such a heating device.

In another type of doping of the ferroelectric, the effect of non-linear dependence of its conductivity from voltage can be achieved, i.e. it is actually nonlinear resistor, called varistor. This effect is due to a change in a certain voltage of the conductivity of thin layers of the substance surrounding domains. Therefore, they are characterized volt-ampere characteristicwhere the function U (i) can be represented by a polynomial fifth degree. Nonlinear resistors are conveniently characterized by a static resistance of RR \u003d U / I and the differential resistance of RD \u003d DU / DI. It can be seen that at the linear section Rst ~ Rd, on the nonlinear section Rst £ RD.

Their basic application is the protection of electrical circuits from hazardous overvoltage switting emissions. In a varistor, the energy of such an emission turns into active and heats its mass. Therefore, the varistors are distinguished by two main parameters - the voltage at which it occurs, and the energy that the element is capable of absorbing without disturbing its performance.

Nonlinear resistors All sorts of types occupy a large place in modern electrical engineering. Generally speaking, any conductor is nonlinear. If you pass the current through a conventional copper wire, then at first its resistance, as is known, will be changed as R0 (1 + αt). This dependence will be maintained while the wire is not melted and then the resistance will remain constant before evaporation of the material. And in this state, the wire becomes actually insulator.

The resistance of the conductor R is inversely proportional to the current density, so the resistance of the copper bare conductor is considered linear to the current density 10 A / mm2 . With the deterioration of the heat unit from the conductor, this value decreases. For example, in the winding of inductance coil, this value can be at 2 A / mm2. Since when data is exceeded, the current density values \u200b\u200boccurs increasing heat output, which leads to its melting, they are considered permissible current density values And used when choosing safe sections of the conductors.

In this principle work fusethe cross section of the conductor in which corresponds to the limit value of current passing through it. But if inserting the power of more than 1010 W / g in the wire, then evaporation, bypassing the stage of melting, will go on adiabat and the pressure wave of evaporated from the surface of the gas will create inside the material of the colossal density of the substance. In this case, it was possible to release gold atoms from their electronic shell and conduct thermonuclear reactions.

With a certain voltage sufficient to appear in the gas of a sufficient number of carriers electrical chargesIn the gas gap begins to pass the electric current. This phenomenon is called gas dischargeAnd the gas-discharge gap itself can be considered as non-linear resistance from the next Wah.

Gas discharge devices were very widespread in quality and indicators, welding machines and smelting units, electrical keys and plasma chemical reactors, etc.

In 1873, F. Gutry opened the effect of nonlinear conductivity in a vacuum lamp with a thermionic cathode. When the cathode was negative potential, its electrons created an electric current, and in the opposite polarity they were locked on the cathode and there were practically no carriers in the lamp. For a long time This effect was not in demand, while in 1904 the needs of radio engineering did not led to the creation of a thermionic (vacuum) diode. And since the electrical field is responsible in such a conduction device, the introduction of additional small potentials makes it possible to control the flux of electrons, that is electric shock. Thus, were created electric field controlled Nonlinear resistors (radiolm views), which replaced large, inertia and current-driven nonlinear magnetic systems. The main disadvantages of the radiolmp were an incandescent cathode that requires a separate power source and appropriate cooling, as well as quite large dimensions due to a vacuum flask.

Therefore, almost simultaneously with vacuum (thermo) diode was created solid diode based on p-n transition which is formed at the point of contact of two semiconductors with different type conductivity. but technological difficulties The production of pure semiconductor materials several detained the introduction of these elements with respect to radiolmpamps.

When contacting two areas with different type of conductivity, the charge carriers of them permanently penetrate (diffundated) into the next area where they are not the main carriers. At the same time, non-compatinated acceptors (negative charges) remain in the R-region, and in the N-region, non-compatible donors ( positive charges) that form spatial charge area(ORZ) with an electric field that prevents further diffusion of charge carriers. In zone p-n transitionthe equilibrium with the contact difference of potentials is created, which is for the silicon widely used in semiconductor devices "0.7 V.

When connecting an external electric field, this equilibrium is broken. With a direct displacement ("+" in the region of the R-type), the width of the OPZ decreases and the concentration of non-core carriers is exponentially increasing. They are compensated for the main carriers entering through contacts from the external circuit, which creates direct currentExponentially increasing as the direct displacement voltage increases.

With reverse displacement ("-" in the region of the R-type), the width of the OPZ increases and the concentration of non-core carriers is reduced. The main media in this zone do not come, and reverse current It is due only to the removal of non-core carriers from the OPZ and does not depend on the applied voltage. Direct and reverse currents may differ in 105 - 106 times, forming a significant nonlinearity of the Wah. For defined meaning Inverse voltage charge carriers with its free movement can gain energy sufficient to form new pairs of charges when they are collided with neutrals, which in turn gain energy and participate in the birth of new steam. The emerging avalante current sweeps all potential barriers on its path, turning the semiconductor into a regular conductor.

Hugo semiconductor diode.

Typical Form of the P-N Transition Vach (Diode)

Approximation of the "ideal" diode is the perfect electric key controlled by the polarity of the voltage. However, this parameters do not take into account such as:

1) Direct voltage drop When direct current flows, which is in many real devices 1 -1.5 V, and this leads to active losses p \u003d (1¸1,5) i, and, consequently, to heat the element and limit currents for a particular element. The solution of thermal challenges for cooling semiconductor devices, as well as their thermal stability, are one of the main problems when designing electrical devices. Inversely proportional dependence of the direct voltage drop from temperature limits the use of instruments with P-N transitions in parallel connections.

2) Reverse Toki. which can be neglected only if they are few of the magnitude of less direct currents.

3) Tension avalanche breakwhich determines the limit of the functionality of the element during reverse voltage, to which you need to pay attention, especially when impulse work with inductive elements. However, the total thickness of the crystal limits the inverse voltages of the size of 1-2 kV. Further increase in the reverse voltage is possible only with the sequential assembly of elements with the equalization of feed currents.

4) Temporal characteristicsin particular recovery time (The transition time from conductive to the non-conductive state), which is actually the time of removal from the OPDs of non-core carriers and its expansion. And this parameter is determined by diffuse processes with characteristic durations of 10-5 s. When simulating the pulse characteristics, 2 capacitive elements are used in the diode substitution schemes: barrier Capacitywhich is determined by the size of the OPD and the volume charge (it is essential at inverse voltages), as well as diffuse capacitywhich is determined by the concentration of basic and non-core carriers (it is essential with direct voltage drop). The diffuse container determines the times of accumulation and resorption of a nonequilibrium charge in the ORZ and can reach a magnitude of several dozen nanofarad. Development technological processes In the manufacture of diodes made it possible to significantly affect pulse characteristics and reduce the recovery time to dozen nanoseconds in fast and ultra-best diodes.

Therefore, designed for the Spice program mathematical model The real semiconductor diode and its further modifications is a rather complicated mathematical expression that includes up to 30 constants installed by the user to simulate a particular element.

Work on the reduction of direct voltage drop led to the creation schottky diodesin which the P-N transition is replaced by the Schottki barrier formed by a semiconductor pair. This made it possible to reduce the size of the OPDs and reduce the direct voltage drop in approximately a direct drop, but at the same time the allowable reverse voltage was significantly reduced (< 250 В) и увеличились обратные токи. При этом улучшились импульсные характеристики, что позволило применять эти диоды при частотах до 100 кГц.

A sharp decrease dynamic resistance (Rd \u003d DU / DIT) When the inverse breakdown voltage allows you to use diodes as voltage stabilizers, like varistrars. But diodes, in contrast to the varistors, have lower dynamic resistance values. However, it should be borne in mind that in the stabilization mode in the P-N OPDs, the energy is highlighted equal to P \u003d Ul. pr × i. Therefore were created zener diodes and avalanche diodes with a reinforced heat resistance of the P-N transition and based on them stabilians.

When direct current passes in the OPD, recombination of charge carriers with photon radiation, the wavelength of which is determined by the semiconductor material. Variating the composition of this material and the design of the element, you can create lEDs with coherent ( laser diodes) and non-coherent radiation for a very wide spectral range, from ultraviolet to infrared light.

The development of semiconductor technologies led to the creation bipolar transistorwhich represents three layers of semiconductor material with different type of conductivity, N-P-n or P-N-P. These layers are called Collector-Emitter. Thus, 2 consecutive p-n of the transition turned out, but with multidirectional conductivity. To achieve the transistor effect, it is necessary that the conductivity of the emitter was greater than the conductivity of the base, and the base thickness was comparable to the width of the OPZ transition to the reverse conduction. For n-P-N works The transistor according to the scheme with a common base to the collector is connected to a positive pole of the source, to the issuer - negative, and the additional source opens the transition base-emitter. At the same time in thin basic layer The non-core carriers will begin to flow - electrons. Some of them, under the influence of the collector's positive potential, will pass through the closed transition of the base-collector, causing an increase in the current collector, as the reverse current through this transition. And the current collector can be a few hundred times the datch current ( transistor effect).

Thus, the bipolar transistor can be represented as non-linear resistance controlled by the base current.

Hugo bipolar transistors have the following form:

Bipolar Transistor Vach or Collector Current Dependency from Voltage UCE UC (IC) Collector for Transistor 2N2222 for Different Base Currents.

Thus, the collector current is determined by the base current, but this dependence at small basic currents is significantly nonlinear. This is the so-called active mode.

With large base currents, when a complete opening of the transition collector-base is achieved, the transistor goes into saturation with a minimum voltage drop collector-emitter equal to the dual contact potential difference "1,2¸1.4 V (two consecutive ones open P-N transition). We get saturated mode.

From here there are 2 possibilities for using transistors - in active mode, as amplifier, and in saturated mode - as electric key.

Consider as an example using the transistor in active mode - linear stabilizer Voltage.

In this circuit, the transistor is included in the circuit with a common collector, i.e. the sources of the collector current and the base current are connected by a common point and the control current enters the database through the RV resistor. Since the transition base-emitter is open, it can be assumed that the voltage drop on it does not depend on the current and is an amount equal to the potential barrier UBe \u003d 0.6-0.7V. In the absence of stabitron DZ, the output voltage according to the UOUT ~ UIN RL / RV + RL voltage divider rule. Stabilitron DZ supports a constant voltage level based on Uz. But then uout \u003d Uz - UBE is a permanent value and does not depend on the input voltage and current current. For constant toke. Loads and, accordingly, a database current, any increase in the input voltage UIN will not change the collector current, as the dynamic transition resistance collector-base in the active transistor mode is close to ¥. At the same time, changing the load current will simply lead to a change in the base current and, accordingly, to changing the current collector.

The operation of the bipolar transistor in saturation mode requires large control currents, proportioned by magnitude and durability with switched currents. Therefore, it was proposed thyristorconsisting of 4 serial P-N-P-N layers.

When the control current is turned on, the first P-N transition opens (the base-emitter of the transistor Q1) and electrons from the emitter begin to penetrate through second P-N transition (base-collector of the transistor Q1) .. it opens third P-N Transition (Base-Emitter p-N-P transistora Q2) and, respectively, the second P-N transition (base-collector of the transistor Q2). This most ensures the flow of current in the first P-n transition and the control current is no longer needed. A deep link between all transitions ensures their saturation.

Thus, we managed to transfer the system to a short pulse of the control current to a saturated state with a voltage drop of about 2 V. To turn off the current in this structure, it is necessary to reduce it to 0, and this is sufficiently simply obtained with a harmonic signal. As a result, we received powerful semiconductor keys for alternating current networks, driven by short pulses at the beginning of each half-period.

Change the conductivity of the semiconductor structure can also be used to apply an electrical field to it, which will create additional media for current. These media will be at the same time basicand they do not need to diffuse anywhere. This circumstance gives two advantages compared to bipolar structures.

First, the periods of changes in conductivity decrease, and secondly, the control is carried out by a potential signal at a practically zero current, that is, the main current is almost independent of the control current. And one more advantage occurred due to the homogeneity of the semiconductor structure controlled by an electric field - this is a positive temperature coefficient of resistance, which made it possible to produce these structures with microelectronics tools in the form of individual microes (up to several million per square meters) and, if necessary, connect them in parallel.

Created on this principle transistors got a name field(in foreign literature Fet or Field Emission Transistor). Currently developed a large number of Diverse designs of such devices. Consider field-effect transistor with an isolated shutter in which the control electrode ( gate), separated from the semiconductor insulating layer, as a rule, aluminum oxide. This design was called TIR (metal-semiconductor metal) or MOP (metal-semiconductor metal). The space of the semiconductor, where additional carriers are formed under the influence of the electric field, called canal, entrance and exit to which, respectively, are called source and stock. Depending on the manufacturing technology, the channels may be induced (in N-material a p-conductivity is created or vice versa) or built-in (in N-material create space with p-conductivity or vice versa). The figure shows the typical horizontal design of the TIR transistor with induced and with a built-in r-channel.

Hugo TIR transistor

Here are the transfer characteristics of the BUZ11 transistor, namely the flow of the flow of the flow and voltage of the stock source from the voltage value on the gate. It can be seen that the opening of the transistor begins with a certain value of the URP and is quite quickly included in saturation.

Here is the static characteristic of the BUZ11 transistor, namely the dependence of the flow of flow from the voltage of the stock source. Tags marked Points of transition to saturation mode

Stability of field transistors to current overloads, high input resistance, which allows to significantly reduce control losses, high switching speed, positive temperature coefficient of resistance - all this allowed the instruments with field control not only to practically displace bipolar devices, but also to create a new direction in electrical engineering - intellectual power electronics,where control of energy flows almost any power is carried out with clock frequencies About tens of kilohertz, i.e. actually in real time.

However, at high currents, field transistors are inferior to bipolar transistors in the magnitude of direct losses. If in bipolar transistor Subject to saturation, the loss is determined by P \u003d IKUPR, where the UPR is practically independent of current and approximately equal to the height of the potential barrier on two open p-N transitions, then in the field transistors P \u003d Ic2 RPD, where RPD is mainly the resistance of a homogeneous channel.

The solution to this problem was found in combining field control with a bipolar transistor. Such a bipolar transistor with an isolated shutter is more famous under its IGBT trade name (Insulation Gate Bipolar Transistor).

Hugo for IGBT.

As can be seen, here to the vertical design of the field transistor was added as a substrate P + - layer and between the emitter E and the collector K was formed a bipolar P-N-P transistor. Under the influence of positive potential on the gate g, the conductive channel occurs in the R-area, which opens the transition J1. In this case, the injection of the low-level N is the layer begins the injection of non-core carriers, the J2 layer is opened and the current is started between the collector and the emitter, which is supported by the carriers in the p-layer, which hold the P-N transition J1 in the open state. The voltage drop on JGBT is determined by the voltage drop on the open P-N transitions J1 and J2, as well as in the usual bipolar transistor. JGBT shutdown times are determined by the time of dissolving non-core media from these transitions. That is, the device is turned on as a field transistor, and turns off as bipolar, as can be seen on the example of switching the GA100T560U_IR instrument.

This structure can be represented as a combination of a field control transistor and a bipolar main transistor.

The temperature dependence of the voltage drop on JGBT is determined by the negative coefficient at the j2 transition and the positive coefficient on the channel of the p-layer, as well as the N-layer. As a result, developers managed to make the prevailing positive temperature coefficient, which opened the road to parallel connecting these semiconductor structures and made it possible to create instruments into almost unlimited currents.

Assembly on IGBT for switching

voltage up to 3300 V and currents

Classification of nonlinear elements

Nonlinear electric chains

Section II. Nonlinear chains

Nonlinear chains are chains in which there are at least one nonlinear element, a nonlinear element is an element for which the current and voltage connection is set by a nonlinear equation.

IN nonlinear chains The principle of imposition is not fulfilled, and therefore there are no general methods for calculating. This causes the need to develop special methods for calculating for each type of nonlinear items and their mode.

Nonlinear items classified:

1) in physical nature: conduction, semiconductor, dielectric, electronic, ion, etc.;

2) the nature divide on resistive, capacitive and inductive;

Wah KVH Wah.

3) by type of characteristics All elements are divided

On symmetrical and asymmetrical. Symmetric - these are those whose characteristic is symmetric relative to the origin. For non-symmetrical elements, the positive direction of voltage or current is chosen forever and forever and for them in reference books is given. Only such a direction can be used when solving problems using these WAs.

On unambiguous and ambiguous. Ambiguous when one current or voltage value on the WH corresponds to several points;

4) inertial and non-indication elements.Inertial elements are called such elements in which nonlinearity is due to the heating of the body during current passage. T. K. Temperature cannot change arbitrarily quickly, then when passing by such an element alternating current With a sufficiently high frequency and unchanged valid, the temperature of the element remains almost constant during the entire period of current change. Therefore, for instantaneous values, the element turns out to be linear and is characterized by a constant value of R (I, U). If the current current value is changed, the temperature will change and the result is another resistance, i.e., for existing values, the element will become non-linear.

5) controlled and unmanaged elements. Above we talked about unmanaged elements. The controlled elements include elements with three or more conclusions, in which, changing current or voltage in one output, can be changed by other conclusions.

Depending on the specific task It is convenient to use certain parameters of the elements and the total number is large, but most often used static and differential parameters. For a resistive bipolar element, this will be static and differential resistance.

At a specified point of Wah

At a given working point Wah

1. Give a small voltage increment. Find over the Wah caused by this increment, the increment of the current and take their attitude. The disadvantage of this method is that it is necessary to reduce the accuracy of the calculation Du and DIBut it's hard to work with the schedule.

2. To the specified point of the curve, tangent and then according to the geometric determination of the derivative, receive

Where increments are taken on this tangent and may be great.

If the mode of operation of the nonlinear element is known, its static resistance is known at this point, as well as voltage and current, so it can be replaced with one of the 3 methods.

If it is known that during the operation of the circuit, the current and voltage change within the "more or less straight line of the WAH", then this area is described by the linear equation and put it in compliance with such an equivalent circuit.

Linearize this section of the equation of type U \u003d A + IBThe coefficients of the equation are fulfilled.

For i.\u003d 0 I. U \u003d u 0 \u003d a,

L11 Nonlinear chains

Topics of SRSP

Preparation for measurements, care for devices. [L1], p.135-140.

Main literature

1. M.S. Sternzat and A.A.Sapozhnikov, Meteorological devices, observations and their treatment, L, GMI, 1959

2.O.A. Gorodetsky, I.I.Gource, V.Vrin, meteorology, methods and technical means of observations, GMI, L, 1984

additional literature

1. Instructions by hydrometeorological stations and posts, Part 1, Almaty, 2002

2. A.V. Kapustin, N.P. Rostoruk, Technical means Hydrometeorological service, SP, 2005

3. N.P. Fateev, verification of meteorological devices, GMI, L, 1975

4. Guide for the verification of meteorological devices, GMI, L, 1967

The properties of the elements of the electrical circuit (resistance, inductance, capacity) are described by their static characteristics. The static characteristic of active resistance is its voltamper characteristic. For inductance, the static characteristic is a Weber-ampere characteristic: the dependence between the current I and the magnetic flux F. The static characteristic of the container is the relationship between the charge Q and the voltage U c. It is called a coat-voltage characteristic.

The static characteristic of the element of the chain is expressed by some functional dependence Y \u003d F (x).

The function y can be considered as a response to the impact of x.

The static parameter of the chain element is called the relationship

Differential parameter is equal

The differential parameter is often called a steepness (S)

Since y \u003d px, then

Parameters of linear elements do not depend on the mode of operation ie From the magnitude of exposure x.

Therefore, the static characteristics of a linear (passive) element is a direct, passing through the origin of the coordinates (Fig. 9.1.), And the differential parameter is the direct, parallel axis X (Fig. 9.2.).

Fig. 9.1. Static characteristics of the linear element

Fig. 9.2. Differential parameter of the linear element

The values \u200b\u200bof the static and differential parameters of the linear element coincide, i.e.

where M y and M x is the scale of the x and y, at m y \u003d m x p \u003d p d \u003d TGA.

For the nonlinear item, it is characteristic that its parameters depend on the mode of operation, i.e. From the magnitude of exposure x.

Draw a static characteristic of some kind of AD. (Fig. 9.z).

Fig. 9.3. Static characteristic AD.

At any arbitrary point, the characteristic M, the static parameter is determined by the angle A - the inclination of the sequential, carried out from the origin of the coordinates to the point M (Fig. 9.3).

If m x \u003d m y, then p \u003d TGA.

The differential parameter (steepness) at the same point is proportional to the tangent of the angle B between the tangent to the curve at a given point and the axis x (Fig. 9.3).

Any chaotic system should have nonlinear elements or properties. In the linear system there can be no chaotic oscillations. In the linear system, periodic external influences are caused after the transition processes are attenuating the periodic response of the same period (Fig. 2.1). (Exceptions are parametric linear systems.) In mechanical systems, the following nonlinear components are possible:

1) nonlinear elastic elements;

Fig. 2.1. Scheme of possible signal transformations in linear and nonlinear systems.

2) nonlinear attenuation, similar to friction and slip;

3) dead move, gap or bilinear springs;

4) most hydrodynamic phenomena;

5) nonlinear boundary conditions.

Nonlinear elastic effects can be associated with either properties of substances or with geometric features. For example, the ratio of stresses in the sample of rubber and its deformation is non-linear. However, although the ratio of stresses and deformations of steel is usually linearly up to the yield strength, strong bends, plates or shells can be non-linearly connected to the attached forces and moments. Similar effects associated with strong displacements or turns, in mechanics are usually called geometric nonlinearities.

Nonlinear properties of electromagnetic systems are due to the following factors:

1) nonlinear resistances, tanks or inductive elements;

2) hysteresis in ferromagnetic materials;

3) nonlinear active elements like vacuum lamps, transistors and diodes;

4) effects characteristic of moving media, such as electromotive force, where V is the speed, and B is a magnetic field;

5) electromagnetic forces, for example, where j - current, or, where M is a dipole magnetic moment.

Examples of nonlinear devices are such conventional electrical circuits such as diodes and transistors.

Fig. 2.2. Nonlinear problems with several equilibrium positions: A - a longitudinal bending of a thin elastic rod under the action of axial load on the end; 6 - longitudinal bending of an elastic rod with nonlinear magnetic mass forces.

Magnetic materials such as iron, nickel or ferrite are characterized by nonlinear material ratios between the magnetization field and the magnetic flux density. Via operating amplifiers and diodes some experimenters can be collected negative resistance with bilinear volt-ampere characteristic (see ch. 4).

Not in any system, it is easy to identify nonlinearity, firstly, because we are often accustomed to argue in the language of linear systems, and secondly, because the main components of the system can be linear and non-linearity is a thin effect. For example, individual fastening farm elements can be linearly elastic, but they are assembled so that there are gaps and there is nonlinear friction. Thus, nonlinearity can be hidden under boundary conditions.

In an example with a curved rod, non-linear elements are released without difficulty (Fig. 2.2). In any mechanical device, which has more than one position of static equilibrium, there is a gap, a dead stroke or non-linear rigidity. In the case of a rod extended by the load at the end (Fig. 2.2, a), the culprit is the geometric nonlinearity of rigidity. In the rod, bending magnetic forces (Fig. 2.2, b), the source of chaotic behavior of the system are nonlinear magnetic forces.