Common Base Transistor
Common Collector Transistor
Common emitter transistor
Bipolar Transistor Switching Circuits
A signal source is connected between the base and the emitter of the transistor connected according to the scheme with a common emitter, and the load is connected to the collector. The poles of the same signs of the power sources are connected to the emitter of the transistor. The input current of the cascade is the base current of the transistor, and the output current is the collector current. This is shown in Figure 20, for example, the inclusion of a bipolar p-n-p transistor in the electrical circuit.
Figure 20 - Circuit with a common emitter transistor p-n-p
In practice, they cost one power source, not two. The direction of current flow at the terminals of the transistor is given in the figure. Turning on the n-p-n transistor is exactly the same as turning on the p-n-p transistor, but in this case you will have to change the polarity of both power supplies.
Figure 21 - Circuit with a common emitter transistor n-p-n
The gain of the cascade is equal to the ratio of the collector current to the base current and can usually reach from tens to several hundreds. A transistor included in a circuit with a common emitter can theoretically give the maximum signal gain in power, relative to other options for turning on the transistor. The input resistance of the cascade under consideration, equal to the ratio of the base-emitter voltage to the base current, ranges from hundreds to thousands of ohms. This is less than that of a cascade with a transistor connected according to a common collector circuit. The output signal of the cascade with a common emitter has a phase shift of 180 ° relative to the input signal. Temperature fluctuations have a significant impact on the operation mode of the transistor, which is turned on according to a common emitter circuit, and therefore special temperature stabilization circuits should be used. Due to the fact that the collector junction resistance of the transistor in the considered cascade is higher than in the cascade with a common base, more time is required for the recombination of charge carriers, and, therefore, the cascade with a common emitter has the worst frequency property.
A load is connected to the emitter of the transistor, connected according to the scheme with a common collector, and an input signal is supplied to the base. The input current of the cascade is the base current of the transistor, and the output current is the emitter current. This is shown in Figure 22, which shows the connection circuit of a bipolar p-n-p transistor.
Figure 22 - Circuit with a common collector transistor p-n-p
The output signal is removed from the load resistor connected in series with the output of the emitter. The input of the cascade has a high resistance, usually from tenths of a megaohm to several megaohms due to the fact that the collector junction of the transistor is locked. And the output resistance of the cascade is, on the contrary, small, which allows the use of such cascades to match the previous cascade with the load. A cascade with a transistor connected in accordance with a common collector circuit does not amplify the voltage, but amplifies the current (usually 10 ... 100 times). The phase of the input voltage of the signal supplied to the cascade coincides with the phase of the output voltage, i.e. its inversion is absent. It is because of the conservation of the phase of the input and output signal that the cascade with a common collector has another name - emitter follower. The temperature and frequency properties of the emitter follower are worse than those of the cascade in which the transistor is connected according to a circuit with a common base.
Figure 23 - Circuit with a common base transistor p-n-p
In the cascade, assembled according to the scheme with a common base, the input signal voltage is supplied between the emitter and the base of the transistor, and the output voltage is removed from the collector-base terminals. The inclusion of the transistor p-n-p structure according to the scheme with a common base is shown in Figure 23.
In this case, the emitter junction of the component is open and its conductivity is high. The input impedance of the cascade is small and usually ranges from units to hundreds of ohms, which is attributed to the disadvantage of the described inclusion of the transistor. In addition, for the functioning of the cascade with a transistor connected according to the scheme with a common base, two separate power sources are required, and the current gain of the cascade is less than unity. The gain of the voltage cascade often reaches from tens to several hundred times.
The advantages include the ability to operate the cascade at a significantly higher frequency compared to the other two options for turning on the transistor, and the weak effect on the operation of the cascade of temperature fluctuations. That is why cascades with transistors connected according to the scheme with a common base are often used to amplify high-frequency signals.
A phototransistor is a transistor that is sensitive to the light flux that irradiates it. Typically, a discrete phototransistor is similar in design to a discrete transistor, with the difference that in the sealed case of the phototransistor there is a window, for example, made of glass or transparent special plastic, through which radiation enters the base region of the phototransistor. The inclusion of the phototransistor in the electric circuit is such that the positive pole of the external power source is connected to the emitter, the load resistor is connected to the collector, which in turn is connected to the negative pole of the power source. When the base region is irradiated, charge carriers are generated. The highest concentration of the main charge carriers will be in the base, which will lead to the opening of the phototransistor, and minority charge carriers will migrate to the collector junction. Therefore, irradiation of the phototransistor leads to an increase in the current of its collector. The greater the illumination of the base area, the more significant the collector current of the phototransistor will become. Thus, the phototransistor can be controlled both as a conventional bipolar transistor, varying the base current, and as a photosensitive device. The important parameters of the phototransistor include dark current, lighting current, and integrated sensitivity. Dark current is the collector current in the absence of irradiation. Lighting current - collector current in the presence of radiation. Integral sensitivity is the ratio of the collector current strength of the connected phototransistor to the luminous flux.
Phototransistors are used in optocouplers, automation and remote control devices, in street lighting devices, etc.
The switching circuit of a bipolar transistor with a common emitter is shown in Figure 5.15:
The characteristics of the transistor in this mode will differ from those in the common-base mode. In a transistor connected according to a circuit with a common emitter, there is a gain not only in voltage, but also in current. The input parameters for the circuit with a common emitter will be the base current I b, and the collector voltage U k, and the output characteristics will be the collector current I k and the emitter voltage U e.
Earlier, when analyzing a bipolar transistor in a common base circuit, a relationship was obtained between the collector current and the emitter current in the following form:
In the scheme with a common emitter (in accordance with the first law of Kirchhoff).
after regrouping the factors we get:
(5.30)
Fig. 5.15. Common emitter transistor
The coefficient α / (1-α) in front of the factor I b shows how the collector current I k changes with a single change in the base current I b. It is called the current gain of a bipolar transistor in a common emitter circuit. Denote this coefficient by β.
(5.31)Since the value of the transmission coefficient α is close to unity (α\u003e 1). For values \u200b\u200bof the transmission coefficient α \u003d 0.98 ÷ 0.99, the gain will lie in the range β \u003d 50 ÷ 100.
Taking into account (5.31), as well as I к0 * \u003d I к0 / (1-α), expression (5.30) can be rewritten in the form:
(5.32)
where I k0 * \u003d (1 + β) I k0 is the thermal current of a single p-n junction, which is much higher than the collector thermal current I k0, and r k is defined as r k * \u003d r k / (1 + β).
Differentiating equation (5.32) with respect to the base current I b, we obtain β \u003d ΔI k / ΔI b. It follows that the gain β shows how many times the collector current I k changes with a change in the base current I b.
To characterize the quantity β as a function of the parameters of the bipolar transistor, recall that the emitter current transfer coefficient is defined as α \u003d γ · κ, where. Consequently, 
. For β, a value was obtained: β \u003d α / (1-α). Since W / L 
(5.33)
Figure 5.16a shows the current-voltage characteristics of a bipolar transistor connected according to a circuit with a common emitter with a base current as a parameter of the curves. Comparing these characteristics with similar characteristics for a bipolar transistor in a common base circuit, you can see that they are qualitatively similar.
Let us analyze why small changes in the base current I b cause significant changes in the collector current I k. The value of the coefficient β, significantly greater than unity, means that the transfer coefficient α is close to unity. In this case, the collector current is close to the emitter current, and the base current (recombination in physical nature) is significantly less than the collector and emitter current. With the coefficient α \u003d 0.99 out of 100 holes injected through the emitter junction, 99 are extracted through the collector junction, and only one recombines with the electrons in the base and contributes to the base current.
Fig. 5.16. Current-voltage characteristics of the KT215V bipolar transistor, connected according to the scheme with a common emitter:
a) input characteristics; b) output characteristics
A doubling of the base current (two holes must recombine) will cause a twice as large injection through the emitter junction (200 holes should be injected) and, accordingly, extraction through the collector (198 holes are extracted). Thus, a small change in the base current, for example, from 5 to 10 μA, causes large changes in the collector current, respectively, from 500 μA to 1000 μA.
TRANSISTOR - a semiconductor device for amplifying, generating and converting electrical vibrations, made on the basis of single-crystal semiconductor ( Si - silicon, or Ge - Germany), containing at least three areas with different - electronic ( n) and hole ( p) - conductivity. Invented in 1948 by the Americans W. Shockley, W. Brattain, and J. Bardin. According to the physical structure and mechanism of current control, bipolar transistors (often referred to simply as transistors) and unipolar (often called field effect transistors) are distinguished. In the first, containing two or more electron – hole transitions, both electrons and holes serve as charge carriers, and secondly, either electrons or holes. The term "transistor" is often used to refer to portable broadcast receivers on semiconductor devices.
The current in the output circuit is controlled by changing the input voltage or current. A small change in the input values \u200b\u200bcan lead to a significantly larger change in the output voltage and current. This amplifying property of transistors is used in analog technology (analog TV, radio, communication, etc.).
In this article we will consider a bipolar transistor.
Bipolar transistor can be n-p-n and p-n-p conductivity. Without looking into the inside of the transistor, one can note the difference in conductivities only in the polarity of the connection in practical circuits of power sources, capacitors, diodes, which are part of these circuits. The figure on the right graphically depicts n-p-n and p-n-p transistors.
The transistor has three outputs. If we consider a transistor as a four-terminal, then it should have two input and two output terminals. Therefore, some of the conclusions should be common, both for the input and output circuits.
Transistor Switching Circuits
Common emitter transistor - designed to enhance the amplitude of the input signal by voltage and current. In this case, the input signal, amplified by a transistor, is inverted. In other words, the phase of the output signal rotates 180 degrees. This circuit is the main one for amplifying signals of different amplitudes and shapes. The input impedance of the transistor cascade with OE is from hundreds of ohms to units of kilo-ohms, and the output resistance is from units to tens of kilo-ohms.
Common Collector Transistor - designed to amplify the amplitude of the input current signal. Voltage amplification in such a circuit does not occur. More correctly, the voltage gain is even less than unity. The input signal is not inverted by the transistor.
The input resistance of the transistor cascade with OK can be from tens to hundreds of kilo-ohms, and the output within hundreds of ohms - units of kilo-ohms. Due to the fact that, as a rule, a load resistor is located in the emitter circuit, the circuit has a large input resistance. In addition, due to the amplification of the input current, it has a high load capacity. These common-collector circuit properties are used to match transistor stages — like a “buffer stage”. Since the input signal, not amplified in amplitude, is “repeated” at the output, the switching circuit of a transistor with a common collector is also called Emitter follower.
There is still Common Base Transistor. There is this inclusion scheme in theory, but in practice it is implemented very hard. Such a switching circuit is used in high-frequency technology. Its peculiarity is that it has a low input impedance, and it is difficult to coordinate such a cascade at the input. My experience in electronics is not small, but speaking about this circuit for turning on the transistor, I'm sorry, I don’t know anything! A couple of times I used it as a "foreign" scheme, but I did not understand it. I will explain: according to all physical laws, a transistor is controlled by its base, or rather, by the current flowing along the base-emitter path. Using the input terminal of the transistor - the base at the output - is not possible. In fact, the base of the transistor through the capacitor is "planted" at a high frequency on the case, but it is not used at the output. And galvanically, through a high-resistance resistor, the base is connected to the output of the cascade (bias is applied). But to submit the bias, in fact, you can from anywhere, even from an additional source. Anyway, a signal of any shape entering the base is quenched through the same capacitor. In order for such a cascade to work, the input output - the emitter, through the low-resistance resistor, is "planted" on the housing, hence the low input resistance. In general, the inclusion of a transistor with a common base is a topic for theorists and experimenters. In practice, it is extremely rare. For his practice in designing circuits, he never encountered the need to use a transistor switching circuit with a common base. This is explained by the properties of this switching circuit: the input resistance is from units to tens of Ohms, and the output resistance is from hundreds of kilograms to units of megaohm. Such specific parameters are a rare need.
The bipolar transistor can operate in the key and linear (amplifier) \u200b\u200bmodes. The key mode is used in various control circuits, logic circuits, etc. In the key mode, the transistor can be in two operating states - open (saturated) and closed (locked) state. The linear (amplifying) mode is used in harmonic signal amplification circuits and requires maintaining the transistor in a "half" open, but not saturated state.
To study the operation of the transistor, we will consider the switching circuit of a transistor with a common emitter as the most important switching circuit.
The circuit is shown in the figure. On the diagram VT - actually the transistor. Resistors R b1 and R b2 - the bias circuit of the transistor, which is an ordinary voltage divider. It is this circuit that provides the bias of the transistor to the "operating point" in the mode of amplification of the harmonic signal without distortion. Resistor R to - load resistor of the transistor cascade, designed to supply an electric current to the collector of the electric current of the power source and its limitations in the "open" transistor mode. Resistor R e - the feedback resistor, in essence, increases the input resistance of the cascade, while reducing the gain of the input signal. Capacitors C perform the function of galvanic isolation from the influence of external circuits.
To make it easier for you to understand how a bipolar transistor works, we will draw an analogy with a conventional voltage divider (see figure below). For starters, a resistor R 2 make the voltage divider controlled (variable). By changing the resistance of this resistor, from zero to an "infinitely" large value, we can get the voltage from zero to the value supplied to its input at the output of such a divider. Now, imagine that a resistor R 1 the voltage divider is the collector resistor of the transistor stage, and the resistor R 2 a voltage divider is a collector-emitter transistor junction. At the same time, by applying a control action in the form of an electric current to the transistor base, we change the collector-emitter junction resistance, thereby changing the parameters of the voltage divider. The difference from a variable resistor is that the transistor is controlled by low current. This is exactly how a bipolar transistor works. The above is shown in the figure below: 
For the transistor to operate in signal amplification mode, without distorting the latter, it is necessary to ensure this same operating mode. They talk about the bias of the base of the transistor. Competent specialists amuse themselves with the rule: a transistor is controlled by current - this is an axiom. But the bias mode of the transistor is set by the base-emitter voltage, and not by the current - this is reality. And for someone who does not take into account the bias voltage, no amplifier will work. Therefore, in the calculations its value should be taken into account.
So, the operation of the bipolar transistor stage in the amplification mode occurs at a certain bias voltage at the base-emitter junction. For a silicon transistor, the bias voltage is in the range of 0.6 ... 0.7 volts, for a germanium transistor - 0.2 ... 0.3 volts. Knowing this concept, you can not only calculate transistor stages, but also check the health of any transistor amplifier stage. It is enough to measure the bias voltage of the base-emitter of the transistor with a multimeter with high internal resistance. If it does not correspond to 0.6 ... 0.7 volts for silicon, or 0.2 ... 0.3 volts for germanium, then look for a malfunction here - either the transistor is faulty, or the bias or decoupling circuits of this transistor cascade are faulty.
The above is shown on the graph - current-voltage characteristic (CVC). 
Most of the “specialists”, looking at the presented CVC, will say: What nonsense is drawn on the central chart? So the output characteristic of the transistor does not look! It is presented on the right chart! I’ll answer, everything is right there, but it started with electronic vacuum tubes. Previously, the voltage-current characteristic of the lamp was considered to be the voltage drop across the anode resistor. Now, they continue to measure on the collector resistor, and on the graph are attributed letters indicating the voltage drop across the transistor, which is deeply mistaken. On the left chart I b - U be The input characteristic of the transistor is presented. On the central chart I to - U ke The output current-voltage characteristic of the transistor is presented. And on the right chart I R - U R a current-voltage graph of a load resistor is presented R to, which is usually given as a current-voltage characteristic of the transistor itself.
On the graph there is a linear portion used to linearly amplify the input signal, limited by points A and FROM. Midpoint - IN, is precisely the point at which it is necessary to contain a transistor operating in an amplifier mode. This point corresponds to a certain bias voltage, which is usually taken in calculations: 0.66 volts for a transistor of silicon, or 0.26 volts for a transistor of germanium.
According to the current-voltage characteristic of the transistor, we see the following: in the absence or at a low bias voltage at the base-emitter junction of the transistor, there is no base current and collector current. At this point, at the collector-emitter junction, the entire voltage of the power source drops. With a further increase in the bias voltage of the base-emitter of the transistor, the transistor begins to open, the base current appears and the collector current grows with it. Upon reaching the "work area" at a point FROM, the transistor enters the linear mode, which continues to the point A. In this case, the voltage drop at the collector-emitter junction decreases, and at the load resistor R toon the contrary increases. Point IN - the operating bias point of the transistor, - this is the point at which, at the junction of the collector - emitter of the transistor, as a rule, the voltage drop is set equal to exactly half the voltage of the power source. The frequency response from the point FROMto the point A called the displacement workspace. After point A , the base current and therefore the collector current increase sharply, the transistor fully opens - it enters saturation. At this point, the voltage due to the structure drops at the collector-emitter junction n-p-n transitions, which is approximately 0.2 ... 1 volt, depending on the type of transistor. All other voltage of the power source drops on the load resistance of the transistor - resistor R to., which also limits the further growth of collector current.
In the lower "additional" figures, we see how the voltage at the output of the transistor changes depending on the signal supplied to the input. The output voltage (voltage drop across the collector) of the transistor is out of phase (180 degrees) to the input signal.
Calculation of a transistor cascade with a common emitter (OE)
Before proceeding directly to the calculation of the transistor cascade, we pay attention to the following requirements and conditions:
The calculation of the transistor cascade is carried out, as a rule, from the end (i.e., from the output);
To calculate the transistor cascade, it is necessary to determine the voltage drop at the collector-emitter junction of the transistor in the idle mode (when there is no input signal). It is chosen so as to obtain the most undistorted signal. In a single-cycle circuit of a transistor cascade operating in "A" mode, this is usually half the value of the voltage of the power source;
Two currents run in the emitter circuit of the transistor - the collector current (along the collector-emitter path) and the base current (along the base-emitter path), but since the base current is quite small, it can be neglected and it can be assumed that the collector current is equal to the emitter current;
A transistor is an amplifying element, so it’s fair to say that its ability to amplify signals must be expressed by some value. The gain value is expressed by an indicator taken from the four-terminal theory - the base current gain in the switching circuit with a common emitter (OE) and it is denoted - h 21. Its value is given in the directories for specific types of transistors, moreover, usually in the directories there is a plug (for example: 50 - 200). For calculations, usually choose the minimum value (from the example, select the value - 50);
Collector ( R to) and emitter ( R e) resistances affect the input and output resistances of the transistor stage. We can assume that the input impedance of the cascade R I \u003d R e * h 21, and the output is R o \u003d R to. If the input impedance of the transistor stage is not important for you, then you can do without a resistor at all R e;
Resistor Ratings R to and R e limit the currents flowing through the transistor and the power dissipated on the transistor.
The order and example of the calculation of the transistor cascade with OE
Initial data:
Supply voltage U i.p.\u003d 12 V.
Choose a transistor, for example: KT315G transistor, for it:
P max\u003d 150 mW; I max\u003d 150 mA; h 21>50.
Accept R k \u003d 10 * R e
The voltage of the operating point of the transistor is adopted U be \u003d 0.66 V
Decision:
1. We determine the maximum static power that will be dissipated by the transistor at the moments of passage of the alternating signal through the operating point B of the static mode of the transistor. It should be a value that is 20 percent less (0.8 factor) of the maximum transistor power specified in the manual.
Accept P ras.max \u003d 0,8 * P max\u003d 0.8 * 150 mW \u003d 120 mW
2. Determine the collector current in static mode (no signal):
I k0 \u003d P races max / U ke0 \u003d P races max / (U i.p. / 2) \u003d 120mW / (12V / 2) \u003d 20mA.
3.
Given that half of the supply voltage drops on the transistor in static mode (without signal), the second half of the supply voltage will drop on the resistors:
(R k + R e) \u003d (U i.p. / 2) / I k0 \u003d (12V / 2) / 20mA \u003d 6V / 20mA \u003d 300 Ohm.
Given the existing range of resistors, as well as the fact that we have chosen the ratio R k \u003d 10 * R e, we find the values \u200b\u200bof the resistors: R to \u003d 270 ohms; R e \u003d 27 ohms.
4. Find the voltage on the collector of the transistor without a signal. U k0 \u003d (U ke0 + I k0 * R e) \u003d (U i.p. - I k0 * R k) \u003d (12 V - 0.02 A * 270 Ohms) \u003d 6.6 V.
5. Determine the current base control transistor: I b \u003d I c / h 21 \u003d / h 21 \u003d / 50 \u003d 0.8 mA.
6. The total base current is determined by the bias voltage at the base, which is set by the voltage divider R b1,R b2. The current of the resistive base divider should be much more (5-10 times) the base control current I bso that the latter does not affect the bias voltage. We select the divider current 10 times greater than the base control current: R b1,R b2: I div. \u003d 10 * I b \u003d 10 * 0.8 mA \u003d 8.0 mA.
Then the impedance of the resistors R b1 + R b2 \u003d U / I div. \u003d 12 V / 0.008 A \u003d 1500 Ohms.
7. We find the voltage at the emitter in standby mode (no signal). When calculating the transistor cascade, it is necessary to take into account: the base-emitter voltage of the working transistor cannot exceed 0.7 volts! The voltage on the emitter in the mode without an input signal is approximately equal to: U e \u003d I k0 * R e \u003d 0.02 A * 27 Ohms \u003d 0.54 V,
where I k0 is the quiescent current of the transistor.
8. We determine the voltage at the base U b \u003d U e + U be\u003d 0.54 V + 0.66 V \u003d 1.2 V
From here, through the formula of the voltage divider we find: R b2 \u003d (R b1 + R b2) * U b / U, etc. \u003d 1500 Ohm * 1.2 V / 12V \u003d 150 Ohm
R b1 \u003d (R b1 + R b2) -R b2 \u003d 1500 Ohms - 150 Ohms \u003d 1350 Ohms \u003d 1.35 kOhms.
According to the resistor series, due to the fact that through the resistor R b1 base current also flows, we select the resistor in the direction of decrease: R b1\u003d 1.3 kOhm.
9. Separating capacitors are selected based on the desired amplitude-frequency characteristics (bandwidth) of the cascade. For the normal operation of transistor stages at frequencies up to 1000 Hz, it is necessary to choose capacitors with a nominal value of at least 5 μF.
At lower frequencies, the amplitude-frequency characteristic (AFC) of the cascade depends on the time of recharging of the separation capacitors through other elements of the cascade, including elements of neighboring cascades. The capacity should be such that the capacitors do not have time to recharge. The input impedance of the transistor stage is much greater than the output impedance. The frequency response of the cascade in the low frequency region is determined by the time constant t n \u003d R in * C inwhere R I \u003d R e * h 21, C in - separation input capacity of the cascade. C out transistor cascade it C in of the next cascade and it is calculated in the same way. Cascade low cutoff frequency (cutoff frequency cutoff frequency response) f n \u003d 1 / t n. For high-quality amplification, when designing a transistor stage, it is necessary to choose that the ratio 1 / t n \u003d 1 / (R in * C in)<
The calculation of the key mode of the transistor stage is carried out in exactly the same way as the earlier calculation of the amplifier stage. The only difference is that the key mode assumes two states of the transistor in the standby mode (without signal). It is either closed (but not shorted) or open (but not oversaturated). In this case, the working points of "rest" are outside the points A and C shown on the CVC. When the transistor must be closed on the circuit in a state without a signal, it is necessary to remove the resistor from the previously shown circuit of the cascade R b1. If it is required that the transistor in the idle state be open, it is necessary to increase the resistor in the cascade circuit R b2 10 times from the calculated value, and in some cases, it can be removed from the circuit.
The calculation of the transistor cascade is over.
The switching circuit of a bipolar transistor with a common emitter is shown in Figure 5.15:
The characteristics of the transistor in this mode will differ from those in the common-base mode. In a transistor connected according to a circuit with a common emitter, there is a gain not only in voltage, but also in current. The input parameters for the circuit with a common emitter will be the base current I b, and the collector voltage U k, and the output characteristics will be the collector current I k and the emitter voltage U e.
Previously, when analyzing a bipolar transistor in a common base circuit, a relationship was obtained between the collector current and the emitter current in the following form:
In the scheme with a common emitter (in accordance with the first law of Kirchhoff).
after regrouping the factors we get: (5.30)
Fig. 5.15. Common emitter transistor
The coefficient α / (1-α) in front of the factor I b shows how the collector current I k changes with a single change in the base current I b. It is called the current gain of a bipolar transistor in a common emitter circuit. Denote this coefficient by β.
Since the transmission coefficient α is close to unity (α< 1), то из уравнения (5.31) следует, что коэффициент усиления β будет существенно больше единицы (β >\u003e 1). For values \u200b\u200bof the transmission coefficient α \u003d 0.98 ÷ 0.99, the gain will lie in the range β \u003d 50 ÷ 100.
Taking into account (5.31), as well as I к0 * \u003d I к0 / (1-α), expression (5.30) can be rewritten in the form:
(5.32)
where I k0 * \u003d (1 + β) I k0 is the thermal current of a single p-n junction, which is much higher than the collector thermal current I k0, and r k is defined as r k * \u003d r k / (1 + β).
Differentiating equation (5.32) with respect to the base current I b, we obtain β \u003d ΔI k / ΔI b. It follows that the gain β shows how many times the collector current I k changes with a change in the base current I b.
To characterize the quantity β as a function of the parameters of the bipolar transistor, recall that the emitter current transfer coefficient is defined as α \u003d γ · κ, where. Consequently, . For β, a value was obtained: β \u003d α / (1-α). Since W / L<< 1, а γ ≈ 1, получаем:
(5.33)
Figure 5.16a shows the current-voltage characteristics of a bipolar transistor connected according to a circuit with a common emitter with a base current as a parameter of the curves. Comparing these characteristics with similar characteristics for a bipolar transistor in a common base circuit, you can see that they are qualitatively similar.
Let us analyze why small changes in the base current I b cause significant changes in the collector current I k. The value of the coefficient β, significantly greater than unity, means that the transfer coefficient α is close to unity. In this case, the collector current is close to the emitter current, and the base current (recombination in physical nature) is significantly less than the collector and emitter current. With the coefficient α \u003d 0.99 out of 100 holes injected through the emitter junction, 99 are extracted through the collector junction, and only one recombines with the electrons in the base and contributes to the base current.
Fig. 5.16. Current-voltage characteristics of the KT215V bipolar transistor included in the circuit with a common emitter: a) input characteristics; b) output characteristics
A doubling of the base current (two holes must recombine) will cause a twice as large injection through the emitter junction (200 holes should be injected) and, accordingly, extraction through the collector (198 holes are extracted). Thus, a small change in the base current, for example, from 5 to 10 μA, causes large changes in the collector current, respectively, from 500 μA to 1000 μA.