Bipolar transistor

A bipolar transistor is an electronic device containing Semi-conducteur of the family of the Transistor S. Its principle of operation is based on 2 junctions PN, one on line and one in reverse. The Polarization of opposite junction PN by a weak electric current (sometimes called effect transistor ) will make it possible “to order” a current much more important. It is the principle of the amplification of current.

The discovery of the bipolar transistor made it possible to replace the electron tubes effectively in the years 1950 and thus to improve the miniaturization and the fiabilisation of the electronic assemblies.

Types and Symbols

The catalogs of transistors comprise a high number of models. One can classify the bipolar transistors according to various criteria:

the type: NPN or PNP. These two types are complementary, i.e. the direction of the currents and tensions for the PNP is the complement of those of the NPN. Transistors NPN having in general characteristics better than the PNP, they are used. The continuation of the article will thus discuss only the circuits using of transistors NPN.
power: the transistors for the amplification of small signals dissipate only a few tens or hundreds of milliwatts. The transistors average power support a few Watts; the transistors of power, used for example in the audio amplifiers of power or the stabilized power supplies can support, on the condition of being placed on a adequate Refroidisseur, more 100W.
frequency band: transistors for low frequencies (function correctly until a few MHz), averages (until a few tens of MHz), high (until some GHz), even higher (maximum frequencies of oscillation of several hundreds of GHz)

The figure opposite watch the symbol and indicates the name of the 3 electrodes of the transistors. One can thus distinguish 3 interesting potential differences: Vbe, Vbc and Vce; and 3 currents: current of Base Ib, transmitter, IE and of collecting, Ic. However, these 6 variables are not independent. Indeed, one can write:
$Vce = Vcb + Vbe$ and $Ie = Ic + Ib$

Certain manufacturers propose many networks of characteristics, but this tendency is in the process of disappearance. Moreover, it should be known that the parameters characteristic of the transistors change with the temperature, and strongly vary from one transistor to another, even when they carry the same number.

Principle of operation

We will take the case of a type NPN for which the tensions Vbe and Vce and the current entering at the base are positive.

In this type of transistor, the transmitter, connected to the first zone NR, is polarized with a tension lower than that of the base, connected to the P. zone the Diode transmitting/base is thus on line polarized, and of the current (injection of electrons) circulates between the transmitter and the base.

At first sight, the bipolar transistor seems to be a symmetrical device thus reversible, but in practice, to function correctly, dimensions and the doping of the three parts are very different and do not allow a symmetrical operation. The principle of the bipolar transistor rests indeed on its geometry and the difference in doping between its various areas: the transmitter is strongly doped and the extension of the base, doped P, is very weak. This has two effects:

the reverse current of majority carriers holes type in the substrate P is negligible compared to the injection of electrons come from the transmitter, the recombinations thus remain marginal;

a great number of electrons injected by the transmitter are found projected towards the junction base-collector, the electric field not having time to act on the electrons in transit in the base.

Under normal functioning, the junction base-collector is polarized in reverse, which means that the potential of the collector is quite higher than that of the base. The electrons, in ballistic trajectory, are thus projected against a polarized junction in reverse. However, the potential difference, and thus of energy levels, induced an important tunnel effect which allows the near total these electrons to cross the zone of space charge and to find itself “collected” in the collector (from where the name)…

Simple model

Roughly thus, all the current from the transmitter is found in the collector. This current is a non-linear function of the tension base-transmitter. Strictly speaking , the bipolar transistor thus forms also part of the devices with transconductance, which produce a current modulated by a tension. However, in the majority of the cases, the transistor operates in a mode of small signals, quasilinear, where one prefers to regard it as an amplifier of current because the collector current is then a simple multiple of the basic current. In short, a fort running of the collector can be controlled by a small basic current (the relationship between the two currents is about 100-1000). However, the collector current cannot exceed a certain value: one has a phenomenon of saturation. For large signals the approach in transconductance is more relevant.

Model of Ebers-Moll

The model of EBERS-MOLL results from the superposition of the modes Forward and Reverse.

It consists in modelling the transistor by a power source placed between the collector and the transmitter.

This power source comprises two components, ordered respectively by the junction BE and junction BC.

The behavior of the two junctions is simulated by diodes.

August 1st

Electric characteristics

The figure opposite watch pace of characteristic Ic/Vce. Two principal zones are distinguished:

zone of saturation, for Vce tensions < 1V; in this zone, Ic depend at the same time on Vce and Ib;
linear zone: the collector current is nearly independent of Vce, it depends only on Ib.

When the transistor works in this zone, it can be regarded as an amplifier of current: the output current, Ic is proportional to the current of entry, Ib. the Ic/Ib report/ratio, called profit while running of the transistor, is one of the fundamental characteristics of this one; it is generally noted by the Greek letter β. The β of the illustrated transistor is worth 100. It is important to hold account owing to the fact that, for a given transistor, β increases with the temperature. In addition, the β of transistors in the same way standard present a great dispersion. That obliges the manufacturers to indicate classes of profit. If one takes for example a very widespread transistor like the BC107, the profit while running varies from 110 to 460. The manufacturer then tests the transistors after manufacture and adds a letter after the number, to indicate the class of profit has, B, C…

The Ic/Vbe figure shows that, for a transistor working in the zone of saturation, the Vbe tension varies very little. In lower part of Vbe = 0,65V, the transistor does not lead. When this value is exceeded, called tension of threshold, the collector current increases exponentially. In practice, Vbe generally lies between 0,65V (for Ic of some my) and 1V (for the transistors of power traversed by one Ic important, EP. 1A)

In addition to the profit while running, one uses some other electric characteristics to qualify operation of a transistor:

its Frequency of transition $F_T$ , characteristic its speed of operation (produced accessible profit-band); the able the transistor is to reach a high transconductance for a low capacity, the more the frequency of transition is large; thanks to the technological advancements, one reaches $F_T$ thus nowadays several tens of gigahertz. The bipolar transistors are in that higher than the field-effect transistors.
its tension of Early $V_ {EA}$ , all the more large as the transistor behaves like an ideal source of current; resistance transmitter-collector corresponds to the ratio between the tension of Early and the collector current.
its Transconductance (profit tension-current), directly related to the collector current (at first approximation, it is worth $g_m=I_c/V_ {HT}$ where one with the thermal Tension $V_ {HT} =kT/e$ who is of 26mV to room temperature). Well-sure, each transistor being designed to function correctly in a certain beach of current, it is useless to amplify the current beyond a certain limit to increase the profit.

General principles of implementation

As the parameters of a transistor (and particularly the β) vary with the temperature and from one transistor to another, it is not possible to calculate the properties of the circuits (profit in tension…) with high degree of accuracy. The 4 basic principles given below make it possible to simplify calculations.

the currents collector and transmitter of a transistor can be regarded as equal, except in the event of thorough saturation.
So that a current Ic circulates in the transistor, it is necessary to provide him a basic current equal (for an operation in the linear zone) or superior (for an operation in the zone of saturation) to Ic/β.
When the transistor is conducting, the tension Vbe base-transmitter lies between 0,6 and 1V.
the tension collector-transmitter has little influence on the collector current as long as one works in the linear zone of the characteristics.

The following law is useful for the more elaborate assemblies.

For two transistors identical to same temperature, the same Vbe tension defines same running Ic.

Amplifying assemblies

See also: common Base, Collecting commun run, Transmitting commun run

Generally, one can distinguish two great types of operation of the transistors:

operation in the linear zone of the characteristics; it is used when it is a question of amplifying signals coming from a source or of another (microphone, antenna…) ;
operation in commutation: the transistor commutates between two states, the state blocked (càd. that Ic are null, it is the point B in the figure above) and the state saturated (weak Vce, it is the item A). The fast circuits avoid this state has, which corresponds to an excess of carriers in the base, because these carriers are long to evacuate, which lengthens the switching time of the state saturated towards the blocked state.

In the paragraphs which follow, we will discuss operation of the transistor like amplifier. Operation in commutation is discussed in end of the article.

Polarization

Polarization makes it possible to place the point of rest of the transistor (state of the transistor when any signal is not applied to him) at the desired place of its characteristic. The position of this point of rest will fix the tensions and currents noted quiescent $I_ {b_O}, I_ {c_O}, V_ {ce_0}$ and $V_ {be_0}$ as well as the class of the amplifier (has, B, AB or C).

Right-hand side of static head

The way simplest to polarize an assembly of the type “collecting commun run” is represented on the diagram opposite. The base of the transmitter is connected to the supply voltage Vcc via R1, the collector is connected has Vcc via R2. For reasons of simplifications, the assembly is not charged. The relations between resistances R1 and R2 and the various tensions are the following ones:

$R1 = \ frac {V_ {DC} - V_ {be_0}} {I_ {b_O}}$

and:

R2 = \ frac {V_ {DC} - V_ {ce_0}} {I_ {c_O}}

who can be rewritten in the following way:

R2 = \ frac {V_ {DC} - V_ {ce_0}} {\ beta I_ {b_O}}

This simple diagram suffers however from a great defect: calculated resistances strongly depend on the profit while running β of the transistor. Out, this profit while running changes from one transistor with other (and that even if the transistors have same the references) and strongly varies according to the temperature. With such an assembly, the point of polarization of the transistor is not control. More complex assemblies are thus preferred to him but whose point of polarization depends less on the profit while running β of the transistor.

To avoid this problem, one has recourse to the complete diagram indicated below. Resistances R1 and R2 form a Tension divider which fixes either the current bases but the tension between base and the zero. The relation between the currents and tension can be written as follows:

$I_ {c_O} = \ frac {\ beta (V_ {eq} - V_ {be_0})}{R_ {eq} + (\ beta +1) R_4}$

with:

R_ {eq} = \ frac {R_ 1 R _2} {R_1 + R_2}

and

V_ {eq} =V_ {DC} \ frac {R_2} {R_1 + R_2}

R_ {eq}

and small in front of

(\ beta +1) R_4

, the relation current/tension can be written:

I_ {c_O} = \ frac {(V_ {eq} - V_ {be_0})}{R_4}

The current of polarization is then independent of the profit while running β of the transistor and is stable according to the temperature. This approximation also returns has to choose R1 and R2 so that the current which them cross-piece is large in front of

I_ {b0}

. Thus, the tension applied to the base of the transistor depends little on the basic current

I_ {b0}

The line of static head is a straight line plotted in the figure which gives Ic according to Vce. It passes by the Ucc point on the x axis, and the point Ucc/(R3+R4) on the axis of the Y. For a supply voltage, a R3 load and a resistance of R4 transmitter given, this line of load indicates the point of operation.

Characteristics dynamics

The complete diagram of an amplifier has transmitting commun run is represented on the figure above. Compared with the diagram used during the calculation of the point of polarization, the diagram used comprises in more the condensers of connection C1 and C2, the capacity of C3 decoupling as well as a Rl load.

The condensers of connection “prevent” the tension and D.C. current to be propagated in all the assembly and to find themselves in entry and exit or to modify the polarization of the other assemblies present in the final circuit. The capacities of decoupling make it possible “to remove” certain components (here R4) of the assembly in a certain frequency band.

The value of the condensers of coupling C1 and C2 is selected so that those have a sufficiently low impedance in all the range of the frequencies of the signals to amplify:

compared to the resistance of entry of the stage for the C1 condenser;
compared to the resistance of load for the C2 condenser;

The selected value of C3 so that its impedance weak is compared has that of R4 in the desired frequency band.

The condensers C1, C2 and C3 had not been represented until now, because they have an infinite impedance with the continuous one. The Rl load was not, it also, presents because the C2 condenser prevented the D.C. current of with polarization crossing it and thus from influencing the static characteristics of the assembly.

In order to calculate the characteristics of the assembly in dynamic mode, there is recourse has a small model signals of the transistor. This model makes it possible to describe the behavior of the transistor around its point of polarization. The model used here is simplest possible. It models the transistor thanks to a R_be resistance and a power source whose intensity is proportional to the basic current. If one wishes a finer modeling of the transistor, it is necessary to use a more complex model (Ebers-Moll for example). R_be resistance models the slope of the right-hand side V_be (Ib) at the point of polarization and this calculates as follows:

$R_ {Be} = \ frac {V_t} {I_ {be_0}} = \ frac {K T} {Q I_ {be_0}}$

with: V_t the thermal tension, K the Boltzmann constant, Q the Elementary charge, and T the temperature of the transistor in Kelvin S. has V_t room temperature is worth 25 mV.

With this model, one obtains easily:

$V_s= \ frac {R_ 3 R _l} {R_3+R_l} I_C$

I_b= \ frac {V_ {E}} {R_ {Be}}

I_c= \ beta I_b

If one notes G the profit in tension of the stage and S, his Transconductance. one obtains:

$G= \ frac {V_s} {V_e} = \ frac {\ beta R_ 3 R _l} {R_ {Be} (R_3+R_l)}$

S= \ frac {I_c} {V_e} = \ frac {\ beta} {R_ {Be}}

The transconductanc can be defined as follows: it is the variation of the collector current due to a variation of the tension base-transmitter; it is expressed in A/V. It is primarily determined by the D.C. current of transmitter IE (fixed by the circuit of polarization).

Power dissipated in the transistor

For an amplifying assembly in class has, the power dissipated in the transistor is worth:

$P = Vce.Ic + Vbe.Ib$

where Vce and Vbe are the continuous potential differences between the collector and the transmitter, the base and the transmitter, and Ic, Ib are respectively the transmitter and collector currents. This power does not vary when a signal is applied to the entry of the amplifier. As the profit while running (béta) of the transistor is generally very high (a few tens to a few hundreds), the second term is generally negligible.

Why calculate the power dissipated in the transistor? To evaluate the temperature of the junction it of the transistor, which cannot exceed approximately 150°C for a normal functioning of the amplifier.

The temperature of junction will be calculated using the thermal Loi of Ohm.

In our example, the power dissipated in the transistor is worth 4.2.10^-3 + 0,65.20.10^-6 = 8.0mW. The temperature of the junction, if the room temperature is of 25°C and the thermal resistance junction-environment of 500°C/W, is worth 25 + 500.5,3.10^-3 is 27,65°C.

The transistor in commutation

One calls operation in repeating spring an operating process of the transistor where the transistor either is blocked or traversed by a sufficiently important current so that it is saturated (càd. Vce reduced to less 1V). In the figure opposite, when the Int switch is opened, Ib is null, therefore Ic are null and Vc = Ucc (not B on the characteristics of the transistor). On the other hand, when one closes Int, a current (Ucc - Vbe)/RB circulates in the base. The transistor thus will try to absorb a collector current Ic equal to β.Ib. However, generally, the RL load is selected so that Ic are limited to a value lower than β.Ib, typically 10.Ib. The transistor is then saturated (not has on the characteristics).

Power dissipated in the transistor

The power dissipated in the transistor can be calculated by the formula:

$P = (Vce.Ic + Vbe.Ib) .RC$

Vce, Vbe, Ic, Ib were above defined, RC is the cyclic report/ratio, i.e. the fraction of the time during which the transistor is conducting. In an operation in commutation, the power dissipated in the transistor is much lower than that dissipated in the load. Indeed, when the transistor is blocked, Ic and Ib are null and thus P is worth 0; and when the led transistor, Ic can be high (until several amps for the transistors of power) but Vce is weak, it is the tension of saturation (0,2 with 1V). The power dissipated in the load is worth, it

$P = ((Ucc - Vce). Ic) .RC$

where Ucc is the supply voltage.

Applications

Operation in repeating spring is frequently used to control loads such as:

bulbs with incandescence; it is necessary to use bulbs whose nominal voltage is equal or slightly higher than Ucc (when a bulb is supplied by a tension lower than its nominal voltage, it lights less but its lifespan is increased);
Electroluminescent diode or LED; in this case, the diode is placed in series with RL, the latter being used to limit the current in the diode; the terminal voltage of a LED varies between 1,5 and 3,6V according to the current which traverses it and its color (which depends on material employed for its manufacture);
relay reels: the nominal voltage of the reel of the relay will be selected equal to Ucc; it is necessary to place in parallel on the reel a diode whose cathode is connected to Ucc; the diode will protect the transistor by avoiding the appearance of a important Surtension at the time when Ic are stopped.

Example

That is to say to control a bulb of 12W. We will choose a Ucc food of 12V, and a transistor able to carry the current of the bulb, that is to say 1A.

Basic resistance will be calculated to provide to the base a I/10 current, that is to say 100mA. Rb will thus be worth 12/100.10^-3 = 120Ω. The power dissipated in the transistor, when it leads, is worth 0,2.1 + 0,75.100.10^-3 is 265mW. We considered that Vce in saturation was worth 0,2V and Vbe in saturation 0,75V, they are typical values.

We note that here, contrary to the situation where the transistor is not saturated, the power related to the basic current is not negligible any more compared to the power related to the collector current. This is due to the fact that the tension collector-transmitter is very weak during saturation.

Note:: at the time of the lighting of the bulb, its filament is cold and present a resistance quite lower than its hot resistance; consequently, the current circulating in the bulb and thus in the transistor right after lighting is much higher than the 1A which circulates once the hot filament; it is thus necessary to choose a transistor able to accept this point of current to lighting.

See too

Internal bonds

Amplifying electronics
Effect Early
amplifying Assemblies:

For bipolar Transistor:

common Base;
Collecting commun run;
Transmitting commun run.

For Field-effect transistor:

common Drain;
common Grid;
common Source.

External bonds

Course on the bipolar transistor by Andre Bonnet
Course on the bipolar transistor by Jean-Jacques Rousseau
Course on linear bipolar transistor amplification by Laurent Lubrano
Course on the Bipolar transistor in commutation by Laurent Lubrano and C. CAR

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